Spatial and temporal variation of coda Q[-1] in California

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Content SPA TIA L A N D T E M P O R A L V A R IA T IO N OF C O D A Q-1 IN C A L IF O R N IA by Jenn-Y ih P eng A D issertation P resen ted to the FA C U LT Y OF T H E G R A D U A T E SC H O O L U N IV E R S IT Y OF S O U T H E R N C A L IF O R N IA In Partial Fulfillment o f the R equirem ents for the D egree D O C T O R OF P H IL O S O P H Y (G eological Sciences) D ecem b er 1989 UMI Number: DP28586 All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. Published by ProQuest LLC (2014). Copyright in the Dissertation held by the Author. UMI Dissertation Publishing UMI DP28586 Microform Edition © ProQuest LLC. All rights reserved. This work is protected against unauthorized copying under Title 17, United States Code ProQuest LLC. 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, Ml 48106- 1346 UNIVERSITY OF SOUTHERN CAUFORNIA THE GRADUATE SCHOOL UNIVERSITY PARK LOS ANGELES, CAUFORNIA 90089 This dissertation, written by under the direction of Dissertation Committee, and approved by all its members, has been presented to and accepted by The Graduate School, in partial fulfillm ent of re quirements for the degree of Ph.D. Ge, D O CTO R OF PHILOSOPHY Dean of Graduate Studies D a te .... DISSERTATION COMMITTEE Chairperson A C K N O W L E D G E M E N T S I gratefully acknowledge my advisor, Professor Keiiti Aki, for his con stant patience and insightful guidence throughout the past four years. His strong support to this study and enormous assistance in the w riting of this dissertation is greatly appreciated. His enthusiastic and endless interest on coda waves for the past 2 decades inspired me to undertake this study. I learned from him not only scientifical knowledge but also continuing insis tency in seeking the tru th of nature. I also appreciate his giving me an opportunity to become one of his students four years ago when I had a very difficult time at USC. To him, I give my sincere gratitude and wholehearted respect. Also gratefully acknowledged are the members of my dissertation com m ittee, Professor Charles G. Sammis, Professor Vincent W. Lee and P ro fessor Steve P. Lund for their constructive comments to this work. Special thanks are due to Mr. John Faulkner for the m em orable ex perience th at we shared for the past 6 years at USC and his kindness in providing the com puter program s. I also thank Dr. W. H. K. Lee at USGS, Menlo Park, for his help in retrieving and processing the d a ta recorded from central California, and Professor Hiroo Kanam ori and Dr. Lucy Jones for their kind help in providing the d ata from CIT-USGS seismic network. I also thank Professor Anshu Jin for her helpful suggestion and criti cism on my work. Particularly, I thank Dr. Syhhong Chang, Mr. Rafael Benites for their cheerful friendship. My deepest thanks go to my parents and my wife, Jessie Wu, for their love and understanding during the past several years. To them , my thanks can not be described ju st by words. This work was supported by N ational Science Foundation under grant EAR-8720856. T A B L E O F C O N T E N T S A C K N O W L E D G E M E N T S ...............................................................................ii A B S T R A C T ........................................................................................................ x xiv C H A P T E R 1 IN T R O D U C T IO N ................................................................. 1 Scope and Objective ...............................................................1 Previous Work .......................................................................... o Framework and O verview .......................................................9 C H A P T E R 2 M O N T E -C A R L O S IM U L A T IO N OF C O D A F O R M A T IO N B Y D ISC R E T E S C A T T E R E R S ...............................13 Introduction .............................................................................13 Basic Formulas ....................................................................... 13 Controlling Factors of Coda Envelope Decay ..............22 Physical Mechanism for the Variability of Individual Coda Q~1 M easurements ................................................... 30 Vertical and Lateral Extent of Zone Containing S c a tte re rs .............................................................................. 39 Discussion and Conclusions ............................................... 50 C H A P T E R 3 SPA TIA L V A R IA T IO N OF C O D A Q~l ..............52 Introduction .............................................................................52 D a t a ........................................................................................53 M ethod of D ata A n a ly sis.................................................54 Estim ating the Spatial A uto-Correlation Function .. 64 Significance Test for the Auto-Correlation Function .66 Discussion on Spatial D istribution of Coda Q~1 .... 88 C H A P T E R 4 A T E M P O R A L V A R IA T IO N OF C O D A Q~l 1 71 iv Introduction ...........................................................................171 Reality of Temporal Change in Coda Q~l ...................172 Temporal Change in Coda Q~l in Southern California During 1982-1987 .......................................... 187 Spatial P attern of Coda Change Before and After January 1, 1986 ................................. 219 Temporal Change in Coda Q~l and b-Value Associated W ith Recent Three M oderate-Sized Earthquake in Southern California ............................... 244 C H A P T E R 5 P H Y S IC A L M E C H A N IS M F O R T E M P O R A L V A R IA T IO N IN C O D A Q ' 1 ..................................................................... 255 Fractal Model ....................................................................... 256 Dilatancy-Diffusion Model ............................................... 258 Creep M o d e l.......................................................................... 259 C H A P T E R 6 C O N C L U S IO N S .................................................................264 B IB L IO G R A P H Y .............................................................................................268 A P P E N D IX ..........................................................................................................274 LIST OF F IG U R E S Figure Page 2.1. Geom etry of source, receiver and scatterers...............................................15 2.2. Configuration of radiation patterns for SV and SH waves....................17 2.3. Distances and angle associated with the case of single scattering. . 19 2.4. Distances and angles associated with the case of double scattering. 21 2.5. Plot of log P n versus tim e w ith N=100 for single, double and triple scattering................................................................................................................24 2.6. Plot of log Pn versus tim e with N=100 for the single and double scat tering....................................................................................................................... 26 2.7. Plot of log Pn versus tim e w ith N=250 for the single and double scat tering....................................................................................................................... 27 2.8. Plot of log P n versus tim e with N=450 for the single and double scat tering....................................................................................................................... 28 2.9. Plot of log P n versus tim e with N=600 for the single and double scat tering....................................................................................................................... 29 2.10. Histograms of coda (1/Q )xl000 at 1.5 Hz with tim e window 20-45 sec for the case of N =200........................................................................................ 32 2.11. Histograms of coda (1/Q )xl000 at 1.5 Hz with tim e window 20-45 sec for the case of N =600........................................................................................ 33 2.12. D istribution of observed individual 1/Q in the Long Valley caldera of the Round Valley, California, earthquake of Nov. 23, 1984................. 37 2.13. D istribution of synthetic individual 1/Q obtained from the num erical experim ent for the case of N =200................................................................. 38 VI 2.14. Plot of In P n vs. tim e for the case of vertical extent of zone containing scatterers equals to 10 km ................................................................................40 2.15. Plot of In P n vs. tim e for the case of vertical extent of zone containing scatterers equals to 50 km ................................................................................41 2.16. Plot of In P n vs. time for the case of vertical extent of zone containing scatterers equals to 100 km ............................................................................. 42 2.17. Fault zone w ith a finite thickness for the case of lateral extent of zone containing scatterers.......................................................................................... 45 2.18. Plot of In P n vs. tim e for lateral extent of zone containing scatterers equals to 10 km ....................................................................................................46 2.19. Plot of In P n vs. tim e for lateral extent of zone containing scatterers equals to 60 km ....................................................................................................47 2.20. Plot of In P n vs. tim e for lateral extent of zone containing scatterers equals to 150 km ................................................................................................. 48 3.1. M idpoints distribution with tim e window 15-30 sec at 1.5 Hz in south ern California........................................................................................................58 3.2. M idpoints distribution w ith tim e window 20-45 sec at 1.5 Hz in south ern California........................................................................................................59 3.3. M idpoints distribution w ith tim e window 30-60 sec at 1.5 Hz in south ern California........................................................................................................60 3.4. M idpoints distribution with time window 20-45 sec at 1.5 Hz in central California................................................................................................................61 3.5. M idpoints distribution with time window 30-60 sec at 1.5 Hz in central California................................................................................................................62 3.6. M idpoints distribution w ith time window 50-100 sec at 1.5 Hz in central California............................................................................................................... 63 3.7. Spatial autocorrelation functions for tim e window 15-30 sec in southern California................................................................................................................67 3.8. Spatial autocorrelation functions for tim e window 20-45 sec in southern California................................................................................................................68 3.9. Spatial autocorrelation functions for tim e window 30-60 sec in southern California............................................................................................................... 69 3.10. Spatial autocorrelation functions for tim e window 15-30 sec for the synthetic Gaussian random set of coda 1/Q in southern California. 70 3.11. Spatial autocorrelation functions for tim e window 20-45 sec for the synthetic Gaussian random set of coda 1/Q in southern California. 71 3.12. Spatial autocorrelation functions for tim e window 30-60 sec for the synthetic Gaussian random set of coda 1/Q in southern California. 72 3.13. Spatial autocorrelation functions for tim e window 20-45 sec in central California................................................................................................................73 3.14. Spatial autocorrelation functions for tim e window 30-60 sec in central California................................................................................................................74 3.15. Spatial autocorrelation functions for tim e window 20-45 sec for the synthetic Gaussian random set of coda 1/Q in central California. .75 3.16. Spatial autocorrelation functions for tim e window 30-60 sec for the synthetic Gaussian random set of coda 1/Q in central California. . 76 3.17. Spatial autocorrelation functions for three tim e windows at 1.5 Hz in southern California............................................................................................. 78 3.18. Spatial autocorrelation functions for three tim e windows at 3 Hz in southern California............................................................................................. 79 3.19. Spatial autocorrelation functions for three tim e windows at 6 Hz in southern California............................................................................................. 80 3.20. Spatial autocorrelation functions for three tim e windows at 12 Hz in southern California............................................................................................. 81 3.21. Spatial autocorrelation functions for different frequencies w ith tim e window 15-30 sec in southern California.....................................................83 3.22. Spatial autocorrelation functions for different frequencies w ith tim e window 20-45 sec in southern California.....................................................84 3.23. Spatial autocorrelation functions for different frequencies w ith tim e window 30-60 sec in southern California..................................................... 85 3.24. Spatial autocorrelation functions for tim e window 20-45 sec in central California................................................................................................................86 3.25. Spatial autocorrelation functions for time window 30-60 sec in central California................................................................................................................87 3.26-a-l. M ap of coda 1/Q shown in shade with time window 15-30 sec at 1.5 Hz in southern California................................................................................ 90 3.26-a-2. M ap of coda 1/Q shown in shade with tim e window 15-30 sec at 3.0 Hz in southern California................................................................................ 91 3.26-a-3. M ap of coda 1/Q shown in shade w ith tim e window 15-30 sec at 6.0 Hz in southern California................................................................................ 92 3.26-a-4. M ap of coda 1/Q shown in shade w ith tim e window 15-30 sec at 12.0 Hz in southern California................................................................................ 93 3.26-a-5. Map of coda 1/Q shown in shade w ith tim e window 15-30 sec at 24.0 Hz in southern California................................................................................ 94 IX 3.26-b-l. 3.26-b-2. 3.26-b-3. 3.26-b-4. 3.26-b-5. 3.26-c-l. 3.26-C-2. 3.26-C-3. 3.26-C-4. 3.26-C-5. 3.26-d-l. 3.26-d-2. 3.26-d-3. Map of coda 1/Q shown in numerical values of the m ean with tim e window 15-30 sec at 1.5 Hz..............................................................................95 M ap of coda 1/Q shown in numerical values of the m ean w ith time window 15-30 sec at 3 Hz................................................................................. 96 M ap of coda 1/Q shown in numerical values of the m ean w ith tim e window 15-30 sec at 6 Hz................................................................................. 97 M ap of coda 1/Q shown in numerical values of the mean w ith tim e window 15-30 sec at 12 Hz...............................................................................98 Map of coda 1/Q shown in numerical values of the m ean with time window 15-30 sec at 24 Hz...............................................................................99 M ap of the standard error of the m ean in coda 1/Q w ith tim e window 15-30 sec at 1.5 H z...................................................................... M ap of the standard error of the m ean in coda 1/Q w ith ti 15-30 sec at 3 Hz........................................................................ M ap of the standard error of the mean in coda 1/Q w ith ti 15-30 sec at 6 H z........................................................................ M ap of the standard error of the mean in coda 1/Q w ith ti 15-30 sec at 12 H z....................................................................... M ap of the standard error of the mean in coda 1/Q w ith ti 15-30 sec at 24 Hz...................................................................... M ap of num ber of m idpoints used for calculating the m ean values with time window 15-30 sec at 1.5 Hz..................................................................105 Map of num ber of m idpoints used for calculating the m ean values with time window 15-30 sec at 3 Hz.....................................................................106 Map of num ber of m idpoints used for calculating the m ean values with tim e window 15-30 sec at 6 Hz..................................................................... 107 . . . . 100 me window . . . . 101 me window . . . . 102 me window .... 103 me window .... 104 3.26-d-4. M ap of num ber of m idpoints used for calculating the m ean values with tim e window 15-30 sec at 12 Hz...................................................................108 3.26-d-5. M ap of num ber of m idpoints used for calculating the m ean values with tim e window 15-30 sec at 24 Hz...................................................................109 3.27-a-l. M ap of coda 1/Q shown in shade w ith tim e window 20-45 sec at 1.5 Hz......................................................................................................................... 110 3.27-a-2. M ap of coda 1/Q shown in shade with tim e window 20-45 sec at 3.0 Hz..................................................................................................................I l l 3.27-a-3. M ap of coda 1/Q shown in shade with tim e window 20-45 sec at 6.0 Hz..................................................................................................................112 3.27-a-4. M ap of coda 1/Q shown in shade with tim e window 20-45 sec at 12.0 Hz..................................................................................................................113 3.27-a-5. Map of coda 1/Q shown in shade w ith tim e window 20-45 sec at 24.0 Hz..................................................................................................................114 3.27-b-l. M ap of coda 1/Q shown in numerical values of the m ean with tim e window 20-45 sec at 1.5 H z............................................................................115 3.27-b-2. M ap of coda 1/Q shown in numerical values of the m ean w ith tim e window 20-45 sec at 3 Hz............................................................................... 116 3.27-b-3. M ap of coda 1/Q shown in numerical values of the m ean with tim e window 20-45 sec at 6 Hz............................................................................... 117 3.27-b-4. M ap of coda 1/Q shown in numerical values of the m ean with tim e window 20-45 sec at 12 Hz.............................................................................118 3.27-b-5. M ap of coda 1/Q shown in numerical values of the m ean with tim e window 20-45 sec at 24 Hz.............................................................................119 3.27-c-l. 3.27-C-2. 3.27-C-3. 3.27-C-4. 3.27-C-5. 3.27-d-l. 3.27-d-2. 3.27-d-3. 3.27-d-4. 3.27-d-5. 3.28-a-l. 3.28-a-2. 3.28-a-3. M ap of the standard error of the m ean in coda 1/Q w ith tim e window 20-45 sec at 1.5 Hz............................................................................................ 120 M ap of the standard error of the m ean in coda 1/Q with tim e window 20-45 sec at 3 Hz............................................................................................... 121 M ap of the standard error of the m ean in coda 1/Q with tim e window 20-45 sec at 6 Hz................................................................................................122 M ap of the standard error of the m ean in coda 1/Q w ith tim e window 20-45 sec at 12 Hz............................................................................................. 123 M ap of the standard error of the m ean in coda 1/Q w ith tim e window 20-45 sec at 24 Hz............................................................................................. 124 M ap of num ber of m idpoints used for calculating the m ean values w ith tim e window 20-45 sec at 1.5 Hz.................................................................. 125 M ap of num ber of m idpoints used for calculating the m ean values with tim e window 20-45 sec at 3 Hz..................................................................... 126 M ap of num ber of m idpoints used for calculating the m ean values w ith time window 20-45 sec at 6 H z..................................................................... 127 M ap of num ber of m idpoints used for calculating the m ean values w ith time window 20-45 sec at 12 H z................................................................... 128 M ap of num ber of m idpoints used for calculating the m ean values with time window 20-45 sec at 24 Hz................................................................... 129 M ap of coda 1/Q shown in shade w ith tim e window 30-60 sec at 1.5 Hz............................................................................................................................ 130 M ap of coda 1/Q shown in shade w ith tim e window 30-60 sec at 3 Hz. 131 M ap of coda 1/Q shown in shade w ith tim e window 30-60 sec at 6 Hz. 3.28-a-4. 3.28-a-5. 3.28-b-l. 3.28-b-2. 3.28-b-3. 3.28-b-4. 3.28-b-5. 3.28-c-l. 3.28-C-2. 3.28-C-3. 3.28-C-4. 3.28-C-5. 132 M ap of coda 1/Q shown in shade w ith time window 30-60 sec at 12 Hz............................................................................................................................ 133 M ap of coda 1/Q shown in shade w ith time window 30-60 sec at 24 Hz............................................................................................................................134 M ap of coda 1/Q shown in num erical values of the m ean w ith tim e window 30-60 sec at 1.5 H z............................................................................135 M ap of coda 1/Q shown in numerical values of the m ean with time window 30-60 sec at 3 Hz............................................................................... 136 M ap of coda 1/Q shown in num erical values of the m ean with time window 30-60 sec at 6 Hz............................................................................... 137 M ap of coda 1/Q shown in numerical values of the m ean w ith tim e window 30-60 sec at 12 Hz............................................................................. 138 M ap of coda 1/Q shown in numerical values of the m ean w ith tim e window 30-60 sec at 24 Hz............................................................................. 139 M ap of the standard error of the m ean in coda 1/Q w ith tim e window 30-60 sec at 1.5 H z............................................................................................ 140 M ap of the standard error of the m ean in coda 1/Q w ith tim e window 30-60 sec at 3 Hz................................................................................................141 M ap of the standard error of the m ean in coda 1/Q w ith tim e window 30-60 sec at 6 Hz................................................................................................142 M ap of the standard error of the m ean in coda 1/Q w ith tim e window 30-60 sec at 12 Hz............................................................................................. 143 M ap of the standard error of the m ean in coda 1/Q w ith tim e window 30-60 sec at 24 Hz............................................................................................. 144 xiii 3.28-d-l. M ap of num ber of m idpoints used for calculating the m ean values with tim e window 30-60 sec at 1.5 Hz..................................................................145 3.28-d-2. M ap of num ber of m idpoints used for calculating the m ean values w ith tim e window 30-60 sec at 3 Hz..................................................................... 146 3.28-d-3. M ap of num ber of m idpoints used for calculating the m ean values w ith tim e window 30-60 sec at 6 Hz..................................................................... 147 3.28-d-4. M ap of num ber of m idpoints used for calculating the m ean values w ith time window 30-60 sec at 12 Hz...................................................................148 3.28-d-5. M ap of num ber of m idpoints used for calculating the m ean values with tim e window 30-60 sec at 24 Hz...................................................................149 3.29-a-l. M ap of coda 1/Q shown in shade w ith tim e window 50-100 sec at 1.5 Hz............................................................................................................................ 150 3.29-a-2. M ap of coda 1/Q shown in shade w ith tim e window 50-100 sec at 3 H z............................................................................................................................151 3.29-a-3. M ap of coda 1/Q shown in shade w ith time window 50-100 sec at 6 H z............................................................................................................................152 3.29-a-4. M ap of coda 1/Q shown in shade w ith tim e window 50-100 sec at 12 Hz............................................................................................................................ 153 3.29-a-5. M ap of coda 1/Q shown in shade with tim e window 50-100 sec at 24 H z............................................................................................................................ 154 3.29-b-l. M ap of coda 1/Q shown in numerical values of the m ean with tim e window 50-100 sec at 1.5 Hz..........................................................................155 3.29-b-2. M ap of coda 1/Q shown in numerical values of the m ean with tim e window 50-100 sec at 3 Hz............................................................................. 156 3.29-b-3. M ap of coda 1/Q shown in num erical values of the m ean w ith tim e window 50-100 sec at 6 Hz............................................................................. 157 3.29-b-4. 3.29-b-5. 3.29-c-l. 3.29-C-2. 3.29-C-3. 3.29-C-4. 3.29-C-5. 3.29-d-l. 3.29-d-2. 3.29-d-3. 3.29-d-4. 3.29-d-5. M ap of coda 1/Q shown in num erical values of the m ean with tim e window 50-100 sec at 12 H z...........................................................................158 M ap of coda 1/Q shown in num erical values of the m ean w ith tim e window 50-100 sec at 24 H z...........................................................................159 M ap of the standard error of the m ean in coda 1/Q with tim e window 50-100 sec at 1.5 Hz..........................................................................................160 M ap of the standard error of the m ean in coda 1/Q with tim e window 50-100 sec at 3 Hz............................................................................................. 161 M ap of the standard error of the m ean in coda 1/Q with tim e window 50-100 sec at 6 Hz............................................................................................. 162 M ap of the standard error of the m ean in coda 1/Q w ith tim e window 50-100 sec at 12 Hz........................................................................................... 163 M ap of the standard error of the m ean in coda 1/Q with tim e window 50-100 sec at 24 Hz........................................................................................... 164 M ap of num ber of m idpoints used for calculating the m ean values with tim e window 50-100 sec at 1.5 Hz................................................................165 Map of num ber of m idpoints used for calculating the m ean values w ith tim e window 50-100 sec at 3 Hz................................................................... 166 M ap of num ber of m idpoints used for calculating the m ean values w ith tim e window 50-100 sec at 6 Hz................................................................... 167 M ap of num ber of m idpoints used for calculating the m ean values with tim e window 50-100 sec at 12 Hz.................................................................168 M ap of num ber of m idpoints used for calculating the m ean values w ith tim e window 50-100 sec at 24 Hz.................................................................169 xv 3.30. P-wave velocity anom aly for 0-40 km obtained by Raikes (1980). 170 4.1. Tem poral variation of coda 1/Q obtained by Jin and Aki (1989) using the riverside record for the past 55-year period since 1933.............. 174 4.2. Tem poral variation of coda 1/Q w ith tim e window 15-30 sec at 1.5 Hz for entire southern California........................................................................ 175 4.3. Tem poral variation of coda 1/Q with tim e window 15-30 sec at 3 Hz for entire southern C alifornia........................................................................ 176 4.4. Tem poral variation of coda 1/Q with tim e window 15-30 sec at 6 Hz for entire southern C alifornia........................................................................ 177 4.5. Tem poral variation of coda 1/Q w ith tim e window 15-30 sec at 12 Hz for entire southern California........................................................................ 178 4.6. Tem poral variation of coda 1/Q with time window 15-30 sec at 24 Hz for entire southern California.........................................................................179 4.7. Tem poral variation of coda 1/Q w ith time window 20-45 sec at 1.5 Hz for entire southern California........................................................................ 180 4.8. Tem poral variation of coda 1/Q with tim e window 20-45 sec at 3 Hz for entire southern California........................................................................ 181 4.9. Tem poral variation of coda 1/Q with tim e window 20-45 sec at 6 Hz for entire southern California.........................................................................182 4.10. Tem poral variation of coda 1/Q w ith time window 20-45 sec at 12 Hz for entire southern California.........................................................................183 4.11. Tem poral variation of coda 1/Q w ith time window 20-45 sec at 24 Hz for entire southern C alifornia........................................................................ 184 4.12. Regionalization m ap of eight subareas in southern California 189 4.13. Tem poral variation of coda 1/Q for time window 15-30 sec at 1.5 Hz in subarea 1..........................................................................................................190 4.14. Tem poral variation of coda 1/Q for tim e window 15-30 sec at 3 Hz in subarea 1...............................................................................................................191 4.15. Tem poral variation of coda 1/Q for tim e window 15-30 sec at 6 Hz in subarea 1...............................................................................................................192 4.16. Tem poral variation of coda 1/Q for tim e window 15-30 sec at 12 Hz in subarea 1...............................................................................................................193 4.17. Tem poral variation of coda 1/Q for tim e window 15-30 sec at 24 Hz in subarea 1...............................................................................................................194 4.18. Tem poral variation of coda 1/Q for tim e window 20-45 sec at 1.5 Hz in subarea 1......................................................................................................... 195 4.19. Tem poral variation of coda 1/Q for tim e window 20-45 sec at 3 Hz in subarea 1...............................................................................................................196 4.20. Tem poral variation of coda 1/Q for tim e window 20-45 sec at 6 Hz in subarea 1...............................................................................................................197 4.21. Tem poral variation of coda 1/Q for tim e window 20-45 sec at 12 Hz in subarea 1...............................................................................................................198 4.22. Tem poral variation of coda 1/Q for tim e window 20-45 sec at 24 Hz in subarea 1...............................................................................................................199 4.23. Tem poral variation of coda 1/Q for tim e window 30-60 sec at 1.5 Hz in subarea 1......................................................................................................... 200 4.24. Tem poral variation of coda 1/Q for tim e window 30-60 sec at 3 Hz in subarea 1...............................................................................................................201 4.25. Tem poral variation of coda 1/Q for tim e window 30-60 sec at 6 Hz in subarea 1...............................................................................................................202 x v ii 4.26. Tem poral variation of coda 1/Q for tim e window 30-60 sec at 12 Hz in subarea 1.............................................................................................................. 203 4.27. Tem poral variation of coda 1/Q for tim e window 30-60 sec at 24 Hz in subarea 1.................................................................................................................62 4.28. Tem poral var204 4.28 Tem poral variation of coda 1/Q for tim e window 20-45 sec at 3 Hz in subarea 2.............................................................................................................. 205 4.29. Tem poral variation of coda 1/Q for tim e window 20-45 sec at 3 Hz in subarea 3.............................................................................................................. 206 4.30. Tem poral variation of coda 1/Q for tim e window 20-45 sec at 3 Hz in subarea 4 .............................................................................................................. 207 4.31. Tem poral variation of coda 1/Q for tim e window 20-45 sec at 3 Hz in subarea 5...............................................................................................................208 4.32. Tem poral variation of coda 1/Q for tim e window 20-45 sec at 3 Hz in subarea 6.............................................................................................................. 209 4.33. Tem poral variation of coda 1/Q for tim e window 20-45 sec at 3 Hz in subarea 7...............................................................................................................210 4.34. Tem poral variation of coda 1/Q for tim e window 20-45 sec at 3 Hz in subarea 8...............................................................................................................211 4.35. Tem poral variation of coda 1/Q for time window 20-45 sec at 12 Hz in subarea 2...............................................................................................................212 4.36. Tem poral variation of coda 1/Q for tim e window 20-45 sec at 12 Hz in subarea 3.............................................................................................................. 213 4.37. Tem poral variation of coda 1/Q for tim e window 20-45 sec at 12 Hz in subarea 4...............................................................................................................214 xviii 4.38. Tem poral variation of coda 1/Q for tim e window 20-45 sec at 12 Hz in subarea 5...............................................................................................................215 4.39. Tem poral variation of coda 1/Q for tim e window 20-45 sec at 12 Hz in subarea 6...............................................................................................................216 4.40. Tem poral variation of coda 1/Q for tim e window 20-45 sec at 12 Hz in subaxea 7...............................................................................................................217 4.41. Tem poral variation of coda 1/Q for time window 20-45 sec at 12 Hz in subarea 8...............................................................................................................218 4.42. Sign of difference in showing the two values in the m ean of coda 1/Q before and after Jan. 1, 1986 w ith the tim e window 15-30 sec at 1.5 Hz............................................................................................................................ 220 4.43. Sign of difference in showing the two values in the m ean of coda 1/Q before and after Jan. 1, 1986 with tim e window 15-30 sec at 3 Hz. 221 4.44. Sign of difference in showing the two values in the m ean of coda 1/Q before and after Jan. 1, 1986 with tim e window 15-30 sec at 6 Hz. 222 4.45. Sign of difference in showing the two values in the m ean of coda 1/Q before and after Jan. 1, 1986 with the tim e window 15-30 sec at 12.0 Hz............................................................................................................................ 223 4.46. Sign of difference in showing the two values in the m ean of coda 1/Q before and after Jan. 1, 1986 with the tim e window 15-30 sec at 24.0 Hz............................................................................................................................ 224 4.47. Sign of difference in showing the two values in the m ean of coda 1/Q before and after Jan. 1, 1986 w ith the tim e window 20-45 sec at 1.5 Hz............................................................................................................................ 225 4.48. Sign of difference in showing the two values in the m ean of coda 1/Q before and after Jan. 1, 1986 w ith tim e window 20-45 sec at 3 Hz. 226 4.49. Sign of difference in showing the two values in the m ean of coda 1/Q before and after Jan. 1, 1986 w ith tim e window 20-45 sec at 6 Hz. 227 4.50. Sign of difference in showing the two values in the m ean of coda 1/Q before and after Jan. 1, 1986 w ith the tim e window 20-45 sec at 12.0 Hz............................................................................................................................ 228 4.51. Sign of difference in showing the two values in the m ean of coda 1/Q before and after Jan. 1, 1986 w ith the tim e window 20-45 sec at 24.0 Hz............................................................................................................................ 229 4.52. M ogi’s donut-like p attern for tim e window 15-30 sec...........................231 4.53. M ogi’s donut-like p attern for tim e window 20-45 sec...........................232 4.54. Num ber of m idpoints used for com puting the difference in the m ean of coda 1/Q for tim e window 15-30 sec at 1.5 Hz.......................................234 4.55. Num ber of m idpoints used for com puting the difference in the m ean of coda 1/Q for tim e window 15-30 sec at 3 H z.......................................... 235 4.56. Num ber of m idpoints used for com puting the difference in the m ean of coda 1/Q for tim e window 15-30 sec at 6 H z.......................................... 236 4.57. Num ber of m idpoints used for com puting the difference in the m ean of coda 1/Q for tim e window 15-30 sec at 12 H z........................................ 237 4.58. N um ber of m idpoints used for com puting the difference in the m ean of coda 1/Q for tim e window 15-30 sec at 24 H z........................................ 238 4.59. N um ber of m idpoints used for com puting the difference in the m ean of coda 1/Q for tim e window 20-45 sec at 1.5 Hz.......................................239 4.60. Num ber of m idpoints used for com puting the difference in the m ean of coda 1/Q for tim e window 20-45 sec at 3 H z.......................................... 240 xx 4.61. Num ber of m idpoints used for com puting the difference in the m ean of coda 1 /Q for tim e window 20-45 sec at 6 H z.......................................... 241 4.62. N um ber of m idpoints used for com puting the difference in the m ean of coda 1/Q for tim e window 20-45 sec at 12 H z........................................242 4.63. N um ber of m idpoints used for com puting the difference in the m ean of coda 1/Q for tim e window 20-45 sec at 24 H z........................................243 4.64. Regions I, II,IF and III used for the tem poral change of coda 1/Q with the occurrence of the three recent occurred m oderate-sized earthquake. 245 4.65. Tem poral variation of coda 1/Q w ith the occurrence of W hittier- Narrows earthquake of Oct. 1, 1987 for tim e window 20-45 sec at 1.5 Hz.....................................................................................................................247 4.66. V ariation of b-value with the occurrence of W hit tier-N arrow s earth quake of Oct. 1, 1987 in region 1................................................................. 248 4.67. Tem poral variation of coda 1/Q w ith the occurrence of N orth Palm Springs earthquake of July 8, 1986 for tim e window 15-30 sec at 1.5 Hz in region II.................................................................................................... 249 4.68. Tem poral variation of coda 1/Q w ith the occurrence of N orth Palm Springs earthquake of July 8, 1986 for tim e window 15-30 sec at 1.5 Hz in region IF ................................................................................................... 250 4.69. V ariation of b-value with the occurrence of N orth Palm Springs earth quake of July 8, 1986 in region IF ...............................................................251 4.70. Tem poral variation of coda 1/Q with the occurrence of Superstition Hills earthquake of Nov. 24, 1987 for the tim e window 30-60 sec at 1.5 H z............................................................................................................................ 252 xxi 4.71. V ariation of b-value w ith the occurrence of Superstition Hills earth quake of Nov. 24, 1987 in region III...........................................................253 X X ll LIST OF TABLES TA BLE Page 2.1. Variability range in coda (1/Q )xl000. for the case of N =200 and N =600.................................................................................................................... 34 2.2. Standard error of individual m easurem ent of (1/Q )x l0 0 0 . for the cases of N=200 and N =600......................................................................................... 36 2.3 Slopes of single and double scattering for various thickness of vertical extent of zone containing scatterers.............................................................. 43 2.4 Slopes of single and double scattering for various thickness of lateral extent of zone containing scatterers.............................................................. 49 4.1a M ean of coda 1/Q before and after Jan. 1, 1986 and its percentage difference in the m ean for tim e windows 15-30 sec and 20-45 sec. 185 4.1b M ean of coda 1/Q before and after Jan. 1, 1986 and its percentage difference in the m ean for tim e windows 30-60 sec................................186 xxiii A B S T R A C T It is well known th at the decay rate of seismic coda power of local earthquakes is a geophysical param eter whose spatial variation strongly correlates w ith the seismicity level. Numerous reports have been published indicating th at the coda decay rate also shows tem poral variation in rela tion to the occurrence of a m ajor earthquake. T he present thesis represents a system atic investigation for delineating the spatial and tem poral behav ior of coda decay rate expressed as ’ ’coda Q -1 ” for central and southern California, taking advantage of a large am ount of existing digital d ata from the regional network operated by the U.S.G.S. and C.I.T.. In order to assess the reliability of coda Q -1 m easurem ent, we shall first apply a M onte-Carlo sim ulation to sim ulate the seismic coda form a tion in arandom m edium characterized by random ly distributed discrete scatterers to estim ate the variability of individual coda Q -1 m easure m ent. The advantage of this M onte-Carlo experim ent is easy to include effects of m ultiple sacttering, variation in the source m echanism and a non- uniform distribution of scatterers. The synthetic coda envelope thus ob tained was in excellent agreem ent with the theoretical prediction by Gao et al. (1983) for single, double and triple scattering. By using a statistically uniform ly distributed scatterers over a region of lithosphere w ith dim en sion 300x300x100 km 3 in length, w idth and depth, we found the num ber of scatterers needed to satisfactorily approxim ate the random ly heteroge neous continuous m edium for coda decay curve to be about 100 for our case. We found th at the observed coda Q~l variance and its dependence xxiv on the lapse time window as well as on frequency can be explained by a finite num ber of effective scatterers. We showed, for exam ple, th at the ob served variability of coda Q~l in the case of R ound Valley earthquake of Nov. 23, 1984 can be explained by the effective num ber of scatterers being about 200. We also found th a t the coda decay envelope is significantly affected by the thickness ranging from 10 to 100 km of vertical extent of zone containing scatterers. However, for the case of a finite lateral extent of fault zone ranging from 10 to 150 km containing scatterers, the coda decay is less sensitive to the thickness of zone as com pared to the case for the finite vertical extent of zone containing scatterers. We then determ ined coda Q ~l for about 1000 local earthquakes with m agnitudes 2.0<M <3.5 recorded at approxim ately 200 stations in central and southern California. In order to investigate the spatial behavior of coda Q - 1 , each m easured coda Q~l for a particular source and receiver was assigned to the 0.2° x 0.2° block which contains the m idpoint between the source and receiver. Calculating the spatial auto-correlation function of coda Q - 1 , we found th a t the coherence distance is dependent on the choice of tim e window for coda Q ~l m easurem ent. Longer and later tim e windows show a longer coherence distance as expected from the single-scattering theory. We also found spatial periodicity both in central and southern California ( wave length A = 180km for the form er and A = 230km for the latter). From m aps of coda Q - 1 , we found th at the high coda Q~l is concentrated continuously along the m ain San A ndreas fault in central California , but, the high coda Q~l zone is spread as patches in southern California. Also, the low Q region roughly coincides w ith the region of low xxv crustal P velocity as obtained by Raikes (1980) in southern California. W ith regard to the tem poral variation, we first established the physical reality of coda Q~l change by elim inating sources of fictitious tem poral change in coda Q ~l which have been proposed in the literature. Coda Q ~l reached a m inim um around 1985 and has risen sharply since 1986 for all subareas of southern California, tim e windows and frequencies. This sim ultaneous change of coda Q -1 over all of southern California is unlikely to be due to the creep wave propogation along the plane boundary of north Am erican continental plate and Pacific sea plate as hypothesized by Savage (1971). By com paring average values of coda Q~l before and after Jan. 1, 1986 for all 0.2° xO.2° blocks, we found a M ogi’s donut-like p attern in which the region of increase in coda Q~l was surrounded by a zone in which coda Q~l decreased at more than one frequency band. The tem poral change of coda Q~l and b-value in relation to the occurrence of three recent m oderate-sized earthquakes in southern California shows a positive correlation in agreem ent with the result obtained by Jin and Aki (1989) from the Riverside record for the 55-year period since 1933. O ur new observations on the tem poral variation of coda Q~l are in a good agreem ent w ith the creep model discussed by Jin and Aki (1989), in which aseismic creep fracture over cracks w ith a characteristic size de term ines the coda Q ~C Thus, the creep m odel expresses our preferred physical m echanism causing the observed tem poral coda Q~l change. xxvi C H A P T E R I IN T R O D U C T IO N This chapter includes descriptions of the problem s, statem ents of ob jectives, a review of related literature and chapter organization for all the works conducted in this thesis. S C O P E A N D O B J E C T IV E In the beginning of instrum ental seismology when they first succeeded recording the m otion of the E arth due to an earthquake in early 1880’s, seismologists were very much puzzled by the presence of oscillations lasting for a long time. They set aside, however, the m ain part of the seism ogram for m any years, and concentrated on the observation and analysis of the tim es of the first arrivals of P- and S- waves. The result was the successful classical seismology, exemplified by the Jeffreys-Bullen travel tim e table of 1940, which brought out the internal structure of the earth as a function of distance from the center of the earth. Then, the m axim um am plitude of a seism ogram was used to estim ate the size of an earthquake by separating the source and the p ath effects empirically, and led to the m onum ental work of G utenberg-R ichter on the seismicity of the E a rth based on the instrum entally determ ined m agnitude of an earthquake. The wave theoretical approach in earthquake seismology, however, had to wait until early 1960’s when the world-wide standardized seism ograph was established and digital com puters becam e available. T he first successful quantitative analysis of to tal wave-form was applied to long-period surface 1 waves, for which a simple laterally homogeneous earth model is an adequate first approxim ation. W ith the deploym ent of high-density seism ograph n et works, it was soon realized th at the analysis of short-period waves requires a three-dim ensionally heterogeneous earth model. The determ inistic three-dim ensional modelling of short-period seismic waves is not an easy task even w ith a current super com puter. An alterna tive way to study them is the stochastic modelling. It was shown by Aki (1969) th a t the p art of a seismogram m ost appropriate for the stochastic modeling is the coda part th at puzzled the founders of instrum ental seis mology. This is because the coda can be considered as the superposition of small contributions from num erous scatterers distributed m ore or less uni formly throughtout the lithosphere. This simple stochastic m odelling was able to explain many extraordinary properties of coda waves such as their independence on the locations of earthquake sources and receiver sites, as well as the characteristics of wave p ath connecting the source and receiver. In particular, the rate of coda am plitude decay is independent of the in dividual source or receiver locations and represents an average property of the region containing the source and receiver. T he coda decay rate was m easured by a param eter called coda Q~1, and there have been num erous studies of the regional varaiation of coda Q~l since the poineering work by Aki and Chouet (1975), R autian and K halturin (1978) and T sujiura (1978). It was soon found th a t the coda Q -1 varies greatly from place to place and strongly correlates w ith degree of seismicity. For instance, the tectonically active regions such as California and Jap an exhibit higher coda Q ~l values th an those of seismically stable ones such as C anadian shield 2 and eastern U.S. (Singh and H errm ann, 1983). As reviewed by Herraiz and Espinosa (1987), the difference in coda Q~l m easured in m any regions of the earth shows the greatest divergence at frequency around 1 Hz, and tends to converge tow ard higher frequencies. The range of fluctuation originating from different geographic distribution in coda Q~l at 1 Hz is more th an one order of m agnitude between active and stable areas. As pointed out by Jin and Aki (1989), the stable C anadian shield and the active southw estern Jap an share the same crustal P-wave velocity structure, bu t they have significantly different values of coda Q ~ l . The higher sensitivity of coda Q~l to the tectonic activity than seismic velocity may be explained by the stan d ard linear solid model of Zener (1948) which predicts th at the peak absolute value of Q~l is com parable to the fractional difference in velocity between the relaxed and unrelaxed state. Jin and Aki (1989) suggests th at the coda Q~l may be roughly proportional to the crack density of the lithosphere. The most intriguing aspect of the coda Q ~l th at invites researcher’s atten tio n is its tem poral variation. It was first observed by Chouet (1979) for the earthquakes in the Stone Canyon area, California. It was shown th at the change could not be attrib u ted to tem poral changes in epicenters, focal depths and m agnitudes of earthquakes used for the Q m easurem ents, instrum ental change or rainfall. Numerous reports on the tem poral change in coda Q~l associated w ith an earthquake occurrence have been published since Jin (1981) and Gusev and Lemzikov (1985). Some papers describe its precursory change, and others dem onstrate the difference in coda Q~l before and after a m ajor earthquake. 3 One of the m ain objectives of the present thesis is to establish the physical reality of the coda Q~1 change in time. There are two alternative ways to accom plish this objective. One is to use a controlled seismic source and repeat m easurem ents w ith the same source and receiver over a certain tim e period. This can elim inate the effect of change in seismic source, but it is expensive and we m ust be very lucky to choose the right tim e and place where the mesurable change occurs. In the present thesis, we choose to use n atu ral seismic sources, nam ely small earthquakes, for which d a ta are available from the regional seismic network in California operated over m any years. This will increase the chance of finding the tim e and place where the change in coda Q _1 may be occurring. We need, however, to gain the necessary accurracy in coda Q~l by averaging over m any m easurem ents for b o th ways. In order to gain the accuracy in coda Q _1 by averaging over m any m ea surem ents, it is essential to have a good knowledge and understanding of variation in coda Q -1 among individual m easurem ents. We shall m ake ob servational and theoretical studies of the variation in coda Q~1 am ong indi vidual m easurem ents. Our theoretical study will rely on a M onte-Carlo ex perim ent using a model of the lithosphere containing random ly distributed scatterers. We shall first exam ine the validity of the single-scattering m odel used for defining the coda Q~l by evaluating the contribution of m utiple- scattering. We then study the variance of individual coda Q _1 m easure m ents w ith special focus on its dependence on the selected tim e window and frequency band. Results from the M onte-Carlo experim ents are com pared w ith observations in order to understand the cause of variation am ong in 4 dividual coda Q~l m easurem ents. The understanding will give us the basis for attain in g the desired accurracy in coda Q~l by averaging over m any m easurem ent s. W ith this preparation, we shall proceed to describe the d ata, m ethod of analysis, and the result for coda Q ~1 in California since digital recording was applied to the regional network (about 1981). We shall first concen tra te on the spatial behavior of coda Q - 1 , and estim ate its spatial auto correlation function for various frequency band and time-window selected for the coda Q~l m easurem ent. We shall find th at the observed depen dence of spatial auto-correlation function on the selected time-window is consistent w ith our basic assum ption of coda composed of S to S single-back- scattered waves. T he spatial distribution of coda Q~l is then constructed by assigning the m easured coda Q~l at the m idpoint of the source and reciever. N ext, we shall divide California into subareas, and com pare the tem poral change in coda Q~l am ong different areas. We are particularly inter ested in the possible m igration of coda Q~l change along the plate bound ary, because Jin and Aki (1989) suggested th a t coda Q~l m ay be reflecting activities of creep fracture in the ductile p art of the lithosphere. T he m igra tion of creep waves along the plate boundary was first proposed by Savage (1971), but none of the claims m ade since then of observing them have been convincing. O ur special atten tio n will be given to the spatial behaviour of the rem arkable tem poral increase in coda Q~l which started in 1985-1986 throughout southern California. We found a rem arkable M ogi’s donut p a t tern for time-windows 15-30 sec and 20-45 sec in southern California for 5 the observed difference in the m ean of coda Q~l before and after Jan., 1986. We shall also discuss the characteristic change in coda Q~l and b- value which m ay be related to the occurrences of the N orth Palm Springs, W hit tier-N arrow s and Superstition Hill earthquakes. Finally, we shall discuss the physical mechanisms th at may be respon sible for the observed tem poral varaiation in coda Q~l . We shall consider the problem from three distinct viewpoints based on the fractal model, the dilatancy-diffusion m odel and the creep model. P R E V IO U S W O R K This section cites the relevant literature and describes the evolution of theory and practice on the seismic coda. Aki (1969) pointed out th at the later portion of seismograms shows the sim ilar am plitudes and spectra contents irrespective of epicentral dis tances using aftershocks of Parkfield earthquake of June 28, 1966. This sim ilarity of coda excitation for different stations w ithin a local network enabled him to form the backscattering m odel of seismic coda. T sujiura (1978) also show'ed th at the coda and S waves have sim ilar site effects at M t. D odaira in Jap an over a wide frequency range (1-25 Hz). The site effect for coda observed by T sujiura is about the m edian of site effect for S waves, but significantly different from th a t for P waves. Furtherm ore, excellent agreem ents were obtained am ong Q~l of coda, Q ~ 1 of S and Q~l of Lg estim ated by various m ethods (Aki, 1980; 1981; Aki and Chouet, 1975; T sujiura, 197S; Akam atsu, 1980; Roecker, 1982; Rovelli, 1982; Pulli, 1983; N uttli, 1973; Street, 1976; Bollinger, 1979; N uttli and H erm ann, 1981; 6 Singh and Herm ann, 1983; Campillo 1986). These findings support the S to S single backscattering m odel proposed by Aki in 1980 , which is used extensively in m easuring coda Q ~l by m any researchers around the world. The contribution of m ultiple scattering to coda has been studied by several researchers (Kopnichev,1977; Gao et a/., 1983a; 1983b; Wu, 1985; Frankel and Clayton, 1986; Frankel and W ennerberg, 1987). B ut the sepa ration of intrinsic Q~l and scattering Q ~l introduces a severe nonunique ness in sim ultaneously determ ining these param eters from the data. For this reason, we still use the form ula based on the single-scattering model. We now use it, however, by strictly defining the tim e window for which the Q~l is determ ined, and m ake several m easurem ents for different choices of tim e window to distinguish the possible effect of m ultiple scattering. In addition to the system atic geographic variation of coda Q ~l at 1 Hz correlating w ith the tectonic activity as m entioned in the preceding section, coda Q ~l shows a frequency dependence th a t also varies system atically place to place. T he frequency dependence is ususally expressed as Q = Q ofm for frequencies higher than about 1 Hz [ / is frequency and Qq is the value of Q at 1 Hz]. According to Singh and H errm ann (1983), m is 0.1 in the central U.S., 0.6 in California and in general shows a larger value for tectonically active regions. Even w ithin a small area, m shows a significant variation. For exam ple, we found th at m = 0.6 for Coyote Lake, 0.8 to 0.9 for Parkfield, 0.9 to 1.0 for Coalinga and 1.2 for Long Valley. According to W u and Aki (1985), if the atten u atio n is due to scattering, the 1-D power spectrum of inhom ogeneity of the form W (K )= C k-m_1 where k is the wave num ber, can account for the power law of frequency dependence of Q. In 7 other words, the area w ith greater m may be characterized by heterogeneity richer in longer wavelengths. Recently, additional support of the spatial coda Q~l correlation with seismicity was found by Jin and Aki (1988) by taking advantage of the old record of historical earthquakes available in China, they showed th a t high Q regions are devoid of great earthquakes (M >7) and low Q regions are full of them . They found th a t the critical Q value above which area is aseismic is about 300. Based on above observations, they concluded th a t the spatial coda Q~l correlates directly w ith the fracture of lithosphere related to the current tectonic activity. One of the m ost exciting aspects of coda Q~l study is its possible use as an earthquake precursor. The tem poral change in coda Q ~l was first reported by Chouet (1979) using local earthquakes at Stone Canyon, California. He showed convincingly th a t the tem poral change is real and not due to an artifact of d ata processing. There were, however, no m ajor earthquakes w ith which he could associate the change in coda Q - 1 . Since then, tem poral change of coda Q~l associated w ith m ajor earthquakes have been reported by many researchers (Jin, 1981; W ilson et al., 1983; Rhea, 1984; W yss, 1985; Gusev and Lemzikov, 1985; Novelo-Casanova et al., 1985; Tsukuda, 1985; Sato, 1986; Jin and Aki, 1986; Peng et al., 1987; Su and Aki, 1989). In m ost of the above reported cases, coda Q~l was anom alously high for a period preceding to the occurrence of the m ain shock. In few cases, however, the change was opposite and coda Q~l becam e higher in the aftershock area after the occurrence of the m ain shock. In several cases, the Q ~l from coda waves and Q ~l from P- waves show the opposite pattern. 8 Still, in other cases, the coda Q -1 changes w ithout an obvious relation to a m ajor earthquake. Thus, the p attern of coda Q -1 change in tim e dom ain is much m ore com plicated than the observed spatial coda Q~l variation which shows a rem arkably simple correlation w ith the current seismicity. Significant correlation between the tem poral change in b-value and th a t in coda Q ~l has been observed for several cases, b u t puzzlingly the correlation is positive in some cases (T sukuda, 1988, Jin and Aki, 1989) but negative in other cases (Jin and Aki, 1986; Robinson, 1987; Aki, 1985). Jin and Aki (1989) used a creep model to explain b o th the positive and negative correlations of coda Q~l and b-value. Since the variation of coda Q~l in short tim e span m ay be attrib u ted to the state of aseismic fracture which m ay have some effect on seismic fracture. T he effect depends on the scale length of creep. Thus as proposed by Jin and Aki (1989), the different sense of correlation is dependent upon w hether the characteristic size of creep fracture is in the lower or upper p art of the m agnitude range from which b-value is estim ated. Sato (1988a) pointed out th a t the tem poral changes in coda Q~l can be fictitiously introduced if any system atic change is involved in (1) focal m echanism of earthquakes, (2) focal depths, epicenters and m agnitudes, (3) selected lapse tim e window and (4) selected stations used in the analysis of coda Q m easurem ents. In order to establish the reality of tem poral variation in coda Q - 1 , it is necessary to exclude above possible fictitious effects. 9 F R A M E W O R K A N D O V E R V IE W This section describes the stru ctu re of this thesis, which consists of four chapters. In chapter 2, we develop a num erical m odel for studying the coda for m ation by backscattered seismic shear waves travelling through a m edium characterized by random ly distributed discrete scatterers. First, we for m ulate our M onte-Carlo sim ulation procedure. Secondly, we discuss the various controlling factors in form ing the coda envelope such as (a): the num ber of scatterers in a given region ,(b): the geom etry of double couple point source and (c): the effect of m ultiple scattering. At this stage, the m ost com m only used single scatteing m odel as initially proposed by Aki and Chouet(1975) is validated. Thirdly, we use the observed coda Q~Y from M am m oth Lakes , California, ( see the A ppendix) and the synthetic coda Q ~ 1 generated from a specific num ber of scatterers in the considered m edium to discuss the physical reason for the long-puzzled large variance in coda Q~l am ong individual m easurem ents. This study also helps to un derstand the time-window and frequency dependence of variance of coda Q ~l m easurem ents. Finally, the effect of depth and thickness of the zone containing scatterers will be considered in relation to the slope change of synthetic coda envelope. In chapter 3, the spatial variation of coda Q~l is studied. We pro cessed about 1,000 local earthquakes, in the range of m agnitude from 2.0 to 3.5 recorded either by CA LN ET in central California or USGS-CIT n et work in southern California. Based on the coda Q~l m easurem ents, the 10 spatial Q~l m aps using 0 .2° x 0.2° grid are constructed for three lapse tim e windows and five frequency bands. From the observed spatial autocor relation functions for different tim e windows, it is found th a t the critical distance at which the correlation becomes insignificant is roughly equal to the travel distance for back-scattered S waves to arrive near the end of the tim e window. This is consistent w ith our S to S back-scattering m odel of coda waves. We observed a positive peak in auto-correlation for the dis tance about 230 km independent of tim e window and frequency in southern California and a sim ilar peak at around 180 km in central California. In order to elim inate the possibility of fictitious spatial coherence due to d ata processing, G aussian random num bers were used to replace the observed coda Q -1 and test the significance of the observed peak for b o th central and southern California. The spatial distribution of low Q region from CA LN ET d a ta is concentrated along the m ain San A ndreas fault in cen tral California, however, th a t from USGS-CIT d a ta in southern California shows low Q regions spread as patches. The low Q region in southern Cali fornia roughly coincides w ith the low crustal velocity region as determ ined by Raikes (1980) using the teleseismic P-delay data. In chapter 4, we focus on the tem poral variation in coda Q ~ l . In order to establish the reality of tem poral change of coda Q~1, we system atically divide the studied area from south to n o rth into subareas of rectangular shape. We found th a t the coda Q~l showed a very characteristic change during the past several years in southern California. Change is very sim ilar to th a t observed by Jin and Aki (1989) using records at a single station, Riverside. Coda Q~l showed a m inim um in about 1985, and then increased 11 sharply after 1985-1986. This p a ttern appear to show up for all frequencies, tim e-windows and subareas into which southern California is divided. This sim ultaneous change is difficult to a ttrib u te to any of the various fictious effects considered by Sato (1988a). T he change m ust be real and m ust have occurred sim ultaneously over the entire southern California region. By com paring average values of coda Q -1 before and after Jan. 1986, for all 0.2° x0.2° blocks, we found a M ogi’s donut-like p a tte rn in which the increase in coda Q _1 occurred in a region surrounded by th e zone in which the coda Q~l decreased at m ore th an one frequency band. The tem poral change of coda Q~l and b-value associated w ith three recent occurred m oderate sized earthquakes in southern California shows the positive correlation in agreem ent w ith the result of Jin and Aki (1989) obtained from the Riverside record for the past 55-year period since 1933. In chapter 5, we discuss the physical m echanism for causing the tem poral change in coda Q. T he tem poral change requires a more sophisticated m odel to explain the change pattern. We exam ine the existing models and arrive at our preferred m odel to explain the observed tem poral coda Q~1 change and its relation to seismicity. In chapter 6 , we sum m arize m ajor conclusions from the preceding four chapters and propose several research directions by th e use of the coda m ethod. In the appendix, we include one paper which is entitled ”Tem poral Change in C oda Q A ssociated W ith the R ound Valley, California, E a rth quake of November 23, 1984” published in April issue of 1987 in Journal of Geophysical Research. 1 2 C H A P T E R II M O N T E -C A R L O S IM U L A T IO N O F C O D A F O R M A T IO N B Y D IS C R E T E S C A T T E R E R S I N T R O D U C T IO N In this chapter, we shall discuss the properties of seismic coda form ed in a given region containing random ly d istributed discrete scatterers. F irst, we shall describe the basic form ulas used in our num erical sim ulation exper im ent. Then, we shall investigate various factors affecting th e coda decay envelope such as the contribution of m ultiple scattering, the num ber of scat terers per unit volume, the source m echanism and statistically non-uniform random distribution of scatterers. The physical m echanism determ ining the variance of coda Q -1 among individual m easurem ents is sought from a com parision of observed coda Q~l at M am m oth Lakes, California, and synthetic coda Q~l generated by our num erical experim ents. We found th at by an adequate choice of the num ber of scatterers per unit volume, the observed large variance of coda Q~l can be well explained. We shall then study w hether the scatterers are concentrated in the shallow p art of the crust or m ore or less uniform ly distributed throughout the lithosphere, and finally study how the change in the lateral extent and thickness of the zone containing scatterers affects the coda decay rate. B A S IC F O R M U L A S Consider a volume of the lithosphere w ith thickness 100 km and area 13 300x300 k m 2 as shown in figure 2.1. T he recording station located on the surface is designated by A and a seismic source (earthquake) located 10 km below the station by X. D iscrete scatterers are designated by O - In this configuration, a seismic source will em it the prim ary wave propogat- ing outw ard through the region, and a scatterer sends the scattered waves to the statio n when hit by the prim ary wave. The single scattering case is simple and considers the scattered waves which encountered only one scatterer. T he m ultiple scattering cases consider the scattered waves which encountered two or more scatterers before reaching the station. The effect of the free surface can be sim ulated by p u ttin g image scat terers at distances above the surface equal to the depth to real scatterers. T he net effect is essentially doubling the scattered energy arrivals. T he procedure for perform ing the above sim ulation is described below. F irst, we need to specify the locations of the discrete scatterers. We use a random num ber generator which generates r/i uniform ly distributed from 0 to 1 ,and put X t = Li x 773 i_ 2 (2.1a) Yi = L w x 773,-1 (2.16) Z t = L h x 773 , (2 .1c) where ( , Yi, Z, ) is coordinate of scatterer location, i = 1 ,2 ,3 ........, and the length, w idth and thickness of the volume of lithosphere are designated as T/, L w, Lh respectively. 14 : Earthquake : Station : Scatterer Figure 2.1 Geometry of source, receiver and scatterers . 300 km X A O 15 N ext, we use the form ulas in C hapter 4, p. 115, of Aki and Richards (1980) to find th e far-field displacem ent due to a given earthquake source. (22> < 2 3 > where, y is rigidity, A is fault plane area, p is density, /3 is shear wave velocity, U is tim e-derivative of displacem ent, r is travelling distance, and, T sv and JrSH are the radiation p attern s for SV and SH waves. Typically, these radiation p attern s can be expressed in term s of angles < /> 3y 6, A, i^ and < j> shown in figure 2.2. T he angles of take-off (i$) and azim uth (< /> ) are determ ined by the direction of ray p ath from the source to scatterer, and the angles of strike (<^a), dip (8) and rake (A) are determ ined for a given source m echanism . In order to relate the param eters of random ly hetrerogeneous m edium such as the scattering coefficient g(@) w ith the distribution of discrete scat terers, we shall consider the prim ary waves incident upon a heterogeneous region of volume V. The squared am plitude of backseatterered waves can then be given by (see Aki (1981)) I A |2 _ I A |2V g W , |Al1 ~ |Ao1 T r f i ? {2A) where A\ is am plitude of backscattered waves, A0 is incident prim ary shear waves, R is travelling distance from source to heterogeneous region, V is volume of heterogeneous region, g(0) is directional scattering coefficient. In the single scattering case, the squared am plitude of backscattered waves can be expressed as: 1 6 North North East < Departing ray Figure 2.2 Configuration of radiation patterns for SV and SH waves. 17 3 _ Vxg(g) A,2Mg 1 4 ir R | ( 4 ^ /? a )2R 2 ( ’ A * = ( / s v ) 2 + ( / s h ) 2 (2 .6 ) and, R i -(- R 2 ti = p (2-7) where is the tim e of arrival of the single back-scattered wavelet m ea sured from the origin tim e of the earthquake. M q is the seismic m om ent.The distances and angles associated w ith a single scattering are defined as shown in figure 2.3. For the isotropic scattering case, the directional scattering coefficient equals to the reciprocal of m ean free path . Considering a heterogeneous region bounded by two spherical surfaces w ith radius r and r + A r centered at the source-receiver coincident point (Aki and Chouet, 1975), the corre sponding coda power spectral density P(yj\t) can be w ritten as: (2-8 ) i where the sum is taken over the total num ber of back-scattered wavelets arriving in the tim e interval between t (= ^ ) and t -f At(= ^ ) , and, (j)i{lj) is the Fourier transform of individual wavelet. In our M onte-Carlo experim ent for a random m edium characterized by random ly distributed discrete scatterers, the contribution of single scattering corresponding to P(u>\t) in eq. (2.8) is obtained by: P " = ( 5^ ) S 4 ? 1291 18 V . 1 Figure 2.3 Distances and angle associated with the case of single scattering. 19 where th e sum is taken over the to tal num ber of back-scattered rays arriving in th e tim e interval betw een tn and tn+\ (in o ther words tn < ti < £„+i). For the double scattering case, the squared am plitude A 2 can be de fined as: 2 g(fer)Va g(tfia)Vi A 2M2 K Z _ * O V - " _____--S — u / 9 101 2 47rRgr 47rR^2 (47rp/ d3)2R f A nd the contribution of double scattering to P(uj\t) is obtained by P n = y ^ y ^ A 2 / ( t n+ i — t n ) ( 2 . 1 1 ) i j where the sum over i and j is m ade over all double back-scattered rays arriving at the station in the tim e interval betw een tn and £„+i (in other words tn < t2 < £„+1), and ta = R l + R^2 + Rzr (2.12) T he distances and angles associated w ith a double scattering are defined as shown in figure 2.4. As for the triple scattering case, similarly, th e squared am plitude A3 can be given by: ,2 g(g3r)V3 g(g23)V2g(fll2)Vl A?Mg 3 47rR |r 47rRg3 47rR22 (47rp/?3)2R 2 R l + R 12 + R 23 + R*3r zoi/l \ t3 = -------------- ^-------------- (2.14) P n — y ^ y ^ y ^ A 3 / ( t n + i — t n ) ( 2 . 1 5 ) i j k where the sum is taken over the to tal num ber of triple back-scattered rays arriving in the tim e interval betw een tn and t n+1 (in other words tn < 13 < tn+l )• 20 V2 ^ 2 V ! Figure 2.4 Distances and angles associated with the case of double scattering. 2 1 In this num erical experim ent,for simplicity, we assum e isotropic scat tering in all cases. In other words, g(6) in eqs. (2.5), (2.10) and (2.13) is assum ed to be a constant. By definition, it is given by the reciprocal of m ean free p a th (/), and can be w ritten as / is defined as 9(0) = g = l~l = na (2.16) where n is the density of scatterers (N /V ), N is the to tal num ber of scat terers and V is the volume of the region , and a is the cross section of a scatterer. We plot Pn in eqs. (2.9), (2.11) and (2.15) as functions of £n , and determ ine the slope of the envelope for single, double and triple scattering, respectively. This m ethod is sim ilar to C houet (1976), but uses the M onte- Carlo approach to save com puter tim e. We shall use this m ethod to study various controlling factors of the coda decay envelope as described in the next section. C O N T R O L L IN G F A C T O R S O F C O D A E N V E L O P E D E C A Y As shown in figure 2.1, we place the seismic source at the center of the region containing the scatterers at a depth of 10 km, and the station on the surface im m ediately above th e source. We then generate locations of N scatterers (N is varied from 100 to 600) by the procedure of random num ber generation described earlier. We then calculate Pn over 60 different realizations of random num bers in this m edium and obtain the sum of Pn for a given interval tn and tn+1 according to equations (2.9), (2.11) and 2 2 (2.15) for single, double and triple scattering cases respectively. We plot Pn as a function of tn. Since the horizontal length of our region is 300 km, the coda envelope up to the lapse tim e of 100 sec is free from th e artifact of the boundary. /? is assum ed to be 3.0 km /sec. Figure 2.5 shows one of the synthetic coda com puted by th e above procedure for the case of N equals to 100. T he decay curves for single, dou ble and triple scattering are denoted by solid-line, dash-line and dot-line respectively. The dash-dot-line represents the sum of all the energy con trib u ted from single, double and triple scattering processes. T he required com puter tim e is, of course, the longest for the triple scattering, and in creases sharply w ith N. For instance, for the VAX 11/750, the practical lim it for N is about 100 for the triple scattering. However, if we neglect the triple scattering, the lim it for N can be easily increased to 1000. It was found th a t the synthesized coda power shows t ~2 decay depen dence for the single scattering, t~ l dependence for the double scattering an d t° dependence for the triple scattering. This dependence on tim e agrees w ith the theoretical prediction by Gao et al., (1983) for the case of uniform random ness for single, double and triple scattering. T he d ep artu re of our result from the theoretical prediction at the early lapse tim e is probably due to the scarcity of sam pled scatterers. We define the m ean free tim e as the m ean free p a th divided by the velocity of shear waves. In this case, the m ean free p a th is 100 km and th e m ean free tim e is 34 sec. From th e com parision betw een th e single scattering curve and the sum curve, it is clear th a t the energy due to single scattering dom inates before the m ean free tim e , after which th e contribu- 2 3 lo g Pn I u > I 00 I 100 10 Time Figure 2.5 Plot of log Pn vs. time with N=100 for single, double and triple scattering. tion of m ultiple scattering becomes significant. B ut, rem arkably, we found th a t the decay curve for the sum case is also linear w ith the slope of about -1.5. This agrees w ith the diffusion m odel of A ki-Chouet (1975, eq. (13)) and Frankel-W ennerberg (1987) in which the coda power decay follows the tim e dependence of t -3 / 2. A lthough the diffusion theory is applicable to lunar seism ogram s, it had been shown by D ainty and Toksoz (1981) th at the diffusion m odel is not appropriate for the terrestrial coda. Likewise, the excellent agreem ent between coda Q and Q of S waves found by Aki(1980) for Jap an supported the single scattering model. M ore recently, M ayeda et al. (1989) using the Radiative Transfer Theory of W u (1985) found th at the m ean free p a th in southern California ia as short as 15-18 km, and yet the coda Q ~l agrees w ith the scattering Q~l plus absorbing Q~l estim ated by the R adiative Transfer Theory, supporting the single-scattering model. A pparently, the single-scattering m odel seems to work where it should not. Sato (1988b) recognized this and proposed a m odel of fractally d istributed scatterers. Recently, an ultrasonic experim ent was conducted by Koji M atsunam i of K yoto U niversity in Jap an to test the m odels of coda waves. His ex perim ents used a duralum in plate w ith random ly distrib u ted small holes. T he em itter is used to generate an im pulsive source norm al to the edge of plate. T he seism ograms were then recorded by the receiver which was located 4 cm away from the source. T he experim ent showed an excellent agreem ent w ith G ao’s theoretical results. Since our results are in agree m ent w ith Gao et al., (1983), M atsunam i’s results support our com puter sim ulation on coda decay. Then, our M onte-C arlo experim ent provides an 25 10 100 time in seconds Figure 2.6 Plot of log Pn vs. time with N=100 for single and double scattering. log Pn to -4 10 100 time in seconds Figure 2.7 Plot of log Pn vs. time with N=250 for single and double scattering. log Pn I I in I I I o o I to 0 0 10 100 time in seco n d s Figure 2.8 Plot of log Pn vs. time with N=450 for single and double scattering. log Pn CO GO 100 10 time in seco n d s Figure 2.9 Plot of log Pn vs. time with N=600 for single and double scattering. effective and inexpensive way to study various characteristics of coda de cay and its variation, in spite of the outstanding puzzle about diffusion vs. single-scattering. A random ly heterogeneous m edium w ith a given scattering coefficient g (the reciprocal of m ean free p ath) m ay be approxim ated by our m odel of discrete scatterers, if we choose the volume represented by a single scatterer (e.g. V\ in eq. (2.5)) to be equal to Vo/N, where N is the to tal num ber of scatterers in the region w ith volume V0. Since the validity of approxim ation depends on N, we com pared the results for N =100, 250, 450 and 600. All cases correspond to the same m ean free p ath of 250 km. For these cases, the contribution from triple scattering is very weak w ithin our observed lapse tim e window, and only single and double scattering is considered. We found th a t the synthetic coda shape is very stable irrespective of the choice of N when N ranges from 100 to 600 as shown in figures 2.6-2.9. T he com puter tim e for this case is roughly proportional to T V 2, and this stability of coda shape allows us to economize the com puter tim e by choosing sm aller N. P H Y S IC A L M E C H A N IS M F O R T H E V A R IA B IL IT Y O F I N D IV ID U A L C O D A Q-1 M E A S U R E M E N T S For m any years, it has been recognized th a t the observed coda Q~l m easured for individual earthquakes show a large variation in a given area. T he range of variation m easured by the variance shows a strong dependence on the lapse tim e window as well as the frequency band used for coda analysis. For instance, in the case of the M am m oth Lakes, California (see A ppendix), the individual coda Q~l m easurem ent showed system atically 30 larger variance for shorter tim e window, and sm aller variance for higher frequency band. In order to explain the above dependence of the variance on the lapse tim e and frequency band. We conducted the following num erical experim ents. We shall assum e th a t th e variability of individual coda Q ~l m easure m ents is caused by random fluctuation in th e contribution from scatterers to a given tim e window of coda. We shall th en sim ulate the actual d eter m ination of individual coda Q~l value by (1) generating the coda envelope for one realization of random scatterer locations, (2) fitting the form ula to the envelope which is given by [lnPntl] = K - ^ (2.16) where K is a constant and uj is the centered frequency band, Pn and tn are obtained through the steps described in previous section, and (3) de term ining the value of coda Q ~l or Q~l by the least squares m ethod. We repeat th e above procedure for m any realization of random scatterer loca tions to find the variability of individual coda Q ~l m easurem ent. Using the above procedure, we studied the dependence of the variability of coda Q ~l m easurem ents on the to tal num ber N of scatterers. Figures 2.10 and 2.11 show the histogram s of coda Q~l x 103 at 1.5 Hz determ ined for the tim e window 20 to 45 sec for the cases of N — 200 and 600 respectively. T he synthetic coda Q~l are d istributed over b o th positive and negative values, because the m edium m odel has no atten u atio n . Here, we are interested in the variability of coda Q~l . We found from figures 2.10 and 2.11 th a t the range of coda Q -1 xlOOO variation decreases from about 40 to 25 when N is 31 § o f sam ples CO to o in o o C O o CM 2 0 -4 5 Sec Ns=200, 1.5 Hz -40 -20 0 20 40 60 (l/Qc)M000 Figure 2.10 Histogram of coda (1/Q)xl000 at 1.5 Hz with time window 20-45 sec for the case of N=200. 2 0 -4 5 Sec (1.5 Hz) CO CO o CO O T 0) o a w = * * s O O -20 40 0 20 (1/Qc)*1000 Figure 2.11 fiistogram of coda (1/Q)xl000 at 1.5 Hz with time window 20-45 sec for the case of N=600. 60 N-200 1 m e H z ^ '“ s < £ e c ) 2 0 - 4 5 3 0 - 6 0 5 0 - 1 0 0 i 5 4 0 16 4 .5 3 0 2 0 8 2 .3 6 0 10 4 1.2 12 0 5 2 0 .6 2 4 0 3 1 0 .3 N - 6 0 0 tim e H z ^ ^ s i ,§ e c ) 2 0 - 4 5 3 0 - 6 0 5 0 - 1 0 0 l 5 2 5 8 2 .5 3 0 13 4 1.3 6 0 7 2 0 .7 12 0 4 1 0 .4 2 4 0 2 0 .5 0 .2 T ab le 2 .1 Variability range in coda (1/Q)xl000 for the cases of N— 200 and N— 600. 34 increased from 200 to 600. The range of coda Q~l m easured by the variance at various frequencies for various choice of tim e windows are shown in table 2.1. It is also found th a t the difference in range of coda Q~~l xlOOO betw een N =200 and N =600 decreases w ith the increase of lapse tim e. O ur sim ula tion of coda form ation is based on the packet of energy tran sp o rted by a ray, and the sim ulated envelope is independent of frequency. In this case the m easured Q - 1 , by definition, becomes inversely proportional to frequency. Likewise, the sim ulated range of coda Q~~l is also inversely proportional to the frequency. As shown later, this is approxim ately in agreem ent w ith the observed frequency dependence of range of coda Q~l variation. In order to estim ate the statistical characteristics of the coda Q~l variation, we com pute its standard deviation for different to tal num ber of scatterers, lapse tim e window and frequency. Table 2.2 shows the stan d ard error of individual m easurem ent, for N =200 and N =600. From this table, we find th a t the stan d ard error also shows the same dependence on N as the range of variation. A longer tim e window in coda Q~~l m easurem ent will sam ple a larger p art of lithosphere. A larger sam ple volume m eans a g reater num ber of scatterers involved, and therefore results in the increased stability in resul ta n t coda Q -1 estim ates. Thus, we found in our num erical experim ents a strong tren d for variability decrease in coda Q~l m easurem ents w ith the increasing lapse tim e. Let us now com pare th e results of num erical experim ents w ith the ob servation from the M am m oth Lakes area to find if indeed we can explain the observation w ith our m odel for any reasonable choice of N. Figure 2.12 35 N -200 20-45 (see) 30-60 (sec) 50-100 (sec) S.D. SD. SD. 1.5 5.11 2.61 0.75 3 2.57 1.31 0.37 6 1.26 0.67 0.19 12.0 0.64 0.33 0.09 24.0 0.32 0.17 0.05 N=600 20-45 (sec) 30-60 (sec) 50-100 (sec) S.D. SJ>. S.D. 1.5 3.93 1.34 0.43 3 1.97 067 0.21 6 0.98 0.33 0.11 12.0 0.49 0.17 0.05 24.0 0.25 0.08 0.03 Tabic 2.2 Stanard error of individual measurement of (1/Q)xl000 for the cases of N=200 and N=600. 36 T T (i/<Wiooo < I /0 ) M O O O T T ' (1/9)-1000 I li- M W - i -------- 1 -------- 1 » — i--------- --------- r - # I I* i It 3 (I/O)* 1000 Figure 2.14 Distribution of observed individual 1/Q in the Long Valley cadera of the Round Valley, California, earthquake of Nov. 23,1984. No. o f Samples 20-45 sec. (Ns*200,3 Hz) -20 -12.5 -7 .5 -2 5 (1/Qc)*1000 30-60 sec. (Ns=200,1.5 Hz) (2 2 0 3 - 1 1 (1/Qc)*1000 3 0 -6 0 sec. ( N s = 2 0 0 ,3 H z) 30-60 sec. (N s=200,12 Hz) w 20 (1/Qc)*1000 -2.25 -1.75 -1 .2 5 -0 .7 6 -0.25 0.2 5 0.7 5 1 25 1 75 2 25 (l/Q c )* l« M Figure 2.15 Distribution of synthetic individual 1/Q obtained from the numerical experiment, for the case of N=200. co 00 shows the distribution of observed individual coda Q~l in the Long Val ley caldera, separating aftershocks (shaded area) and foreshocks (unshaded area) of the R ound Valley, California, earthquake of Novem ber 23, 1984. O bserved variability of coda Q -1 for the foreshocks and its dependence on frequency and tim e window are very sim ilar to the result of our num eri cal experim ent for N =200 as shown in figure 2.13. We interpret this value of N as the effective num ber of strong scatterers contributing to the m ain p art of coda energy. The observed narrow er range of variability and lower Q -1 values for aftershocks m ay m ean th a t larger cracks were closed after the m ainshock and scatterers contributing to coda have become weaker b u t effectively m ore num erous. V E R T IC A L A N D L A T E R A L E X T E N T O F Z O N E C O N T A IN I N G S C A T T E R E R S In the preceding sections, we considered discrete scatteres distrib u ted m ore or less uniform ly in a given region w ith uniform thickness. In this section, we shall study the coda envelope for the zone containing scatterers w ith various vertical and horizontal extents. T he purpose of inspecting the effect of the vertical extent of a zone containing scatterers is to address the question w hether the scatterers contributing to the coda form ation are confined to the shallow p art of the lithosphere, or, d istrib u ted down to the u p p er m antle. For the effect of lateral extent of zone containing scatterers, it is our goal to sim ulate coda envelope form ation in an area w ith a narrow zone of strong scatterers as m ight be anticipated in the zone of San A ndreas fault in California. We shall be particularly interested in 3 9 I n Pn tingle double sum 100 Time o Figure 2.14 Plot of In Pn vs. time for the case of vertical extent of zone containing scatterers equals to 10 km. I n Pn -5 10 tingle double sum 15 20 100 Time Figure 2.15 Plot of In Pn vs. time for the case of vertical extent of zone containing scatterers equals to 50 km. I n Pn single double sum 100 Time to Figure 2.16 Plot of In Pn vs. time for the case of vertical extent of zone containing scatterers equals to 1001cm . Zone of Scatterers (Km) Ms M <j 10 2.98 2.60 20 3.04 2.51 30 2.95 2.34 40 2.82 2.21 50 2.68 2.00 60 2.56 1.67 70 2.40 1.44 80 2.24 1.20 90 2.13 0.98 100 1.97 0.90 * Ms Slope for single scattering * Md Slope for double scattering Table 3 Slopes of single and double scattering for various thickness of vertical exetnt of zone containg scatterers. 43 the different m anner in which the single scattering and double scattering are affected by these factors. Figure 2.14 is the coda decay shape when the zone containing scatterers is restricted in the upperm ost 10 km. In this case, we find th a t th e decay ra te is sim ilar between the single and double scattering, w ith th e slope of the curve logP (t) vs. log t being -2.98 for the form er and -2.60 for the latter. B oth single and double scattering curves decay faster th an those for the case of uniform ly d istrib u ted scatterers. As we increase th e zone containing scatterers to 50 km, the decay rate will becom e sm oother, b u t, the slopes are still less th an or equivalent to -2.0 as shown in figure 2.15 and table 2.3. In figure 2.16, the slope for single scattering case approaches -2.0 as the zone containing scatterers extends to 100 km and th a t for double scattering becom es close to -1.0. Table 2.3 sum m arizes the results for single and double scatterin g for various thickness. It is clear th a t the thinner the zone, the decay is stronger for b o th single and double scattering. This is opposite to our sim ple intuition th a t we expect weaker decay for th in n er zone because th e scattered waves are m ore confined in a plane, becom ing like surface waves. Com paring the zone of z=10 km (figure 2.14) and th a t of z=100 km (figure 2.16), we find an interesting result th a t the relative contribution of single-scattering is greater for the case of th in n er zone. This result is sim ilar to S ato ’s result (1988b) th a t the coda decay becom es stronger and the single scattering dom inates over longer tim e interval in a m edium w ith fractal distribution of scatterers w ith sm aller fractal dim ension D, because the sm aller D m eans m ore clustered scatterers. Finally, we w ant to study the effect of the lateral extent of a fault zone 4 4 Figure 2.17 Fault zone with a finite thickness for the case of lateral extent of zone containg scatterers. 45 I n Pn -10 single double sum -15 -20 100 Time Figure 2.18 Plot of In Pn vs. time for the case of lateral extent of zone containing scatterers equals to 10 km. I n Pn -10 tingle double sum -15 -20 100 Time Figure 2.19 Plot of In Pn vs. time for the case of lateral extent of zone containing scatterers equals to 60 km. 4^ I n Pn single double sum 100 Time 4^ 00 Figure 2.20 Plot of In Pn vs. time for the case of lateral extent of zone containing scatterers equals to 150 km. Range of Fault Zone (Km) Ms Md 10 2.00 0.30 20 2.00 0.67 30 2.00 0.84 40 2.11 0.95 50 2.10 0.89 60 2.00 0.88 70 2.00 0.81 80 2.00 0.80 90 1.99 0.80 100 2.00 0.77 n o 1.95 0.69 150 2.12 0.75 * 80% scatterers along the fault zone * 20% scatterers outside the fault zone Table 4 Slopes o f single and double scattering for various thickness of lateral exetnt of zone containg scatterers. 49 w ith d ep th of 100 km containing scatterers on the coda decay. We consider a fault zone w ith a finite thickness as shown in figure 2.17. Let 80% of the scatterers d istrib u te inside the fault zone, while the rem aining scatterers are d istrib u ted evenly random distrib u tio n on b o th sides separated by the fault zone. As we increase the thickness of fault zone from 10 km to 150 km , unlike the case of changing the d ep th , th e slope for single scattering is very stable when the thickness is varied from 10 to 150 km as shown in figures 2.18 ( A d=10 km ), 2.19 ( A d = 6 0 km ) and 2.20 ( A d= 150 km ). B ut we found significant difference on the slope of double scattering am ong above th ree cases. Table 2.4 lists all the slopes for different fault zone cases. Interestingly, we found th a t the coda decay slope is less sensitive to lateral extent th a n th a t to vertical extent of the zone containing scatterers. We see, however, again th a t the single-scattering dom inates double scattering over a long tim e interval when the scatterers are confined in a narrow er zone. DISCUSSIO N AN D CONCLUSIONS We conclude this chapter by sum m arizing several conclusions obtained above. A practical and inexpensive num erical sim ulation m ethod was devel oped to synthesize coda envelope decay. We used this approach successfully to in terp ret the characteristics of observed coda envelope decay and the variability of individual coda Q~l m easurem ents. We found th a t 1. The synthetic coda decay shape shows excellent agreem ent w ith the theoretical prediction by G ao et al., (1983) for the case of uniform 50 random ness for single, double and triple scattering. 2. The slope for the coda envelope decay on the log power vs. log tim e plot for the sum case is also linear w ith the slope of -1.5 as contrast to the slope of -2 for single backscattering model. 3. We tested the validity of using a finite num ber N of discrete scat terers to approxim ate a heterogeneous m edium for 100<N <600, and found th a t N =100 is satisfactory. 4. The physical m echanism causing large variation am ong individual coda Q _1 m easurem ents was studied. The range of coda Q~l variation and the stan d ard error decrease w ith the increase of lapse tim e, num ber of scatterers and frequency. 5. T he observed absolute value of the variance in coda Q ~x for the foreshocks of R ound Valley earthquake, California, of Nov. 23, 1984 and its dependence on tim e-w indow and frequency are well explained in term s of the num ber of effective scatterers contributing to the of coda energy equals to 200 w ithin the 300x300x100 k m 3 volume of lithosphere. 6. The coda decay envelope is significantly affected by the thickness of vertical extent of zone containing scatterers. We found th a t the thinner the zone, the decay is stronger for b o th single and double scattering and th e relative contribution of single scattering is greater. 7. For the case of finite lateral extent of zone containg scatterers, the coda decay envelope is less sensitive to the w idth of the zone th a n it is to th e d epth studied in 6 above. 51 C H A PTER III SPATIAL VARIATION OF CODA Q"1 IN TRO DUCTIO N In chapter 1, we discussed earlier works on the sp atial and tem poral correlation betw een coda Q ~l and seismicity. Seismicity, nam ely th e spatial and tem poral behavior of earthquake occurrence, is a com plex phenom enon p artly because earthquake occurrences are essentially discontinuous b o th in space and tim e. For exam ple, it is im possible to find any p artial differential equation th a t m ay govern the seismicity. On the other hand, we believe th a t coda Q~l is a stru ctu ral p aram eter of lithosphere representing some degree of m echanical im perfections averaged over a certain volum e sam pled by coda waves. If so, coda Q~l should be continuous in space and tim e, and should be easier to u n d erstan d th an seismicity. T his is the reason why we are interested in th e spatial and tem poral behavior of coda Q - 1 . Since coda Q~l appears to be related to seismicity, we are hoping th a t the b e tte r understanding of coda Q ~l will lead to the b e tte r u nderstanding of seismicity. In this chapter, we investigate the spatial behavior of coda Q ~l in Cal ifornia. F irst, we shall describe the digital d a ta to be processed for coda Q -1 m easurem ents . T hen, we shall explain the m ethod for determ ining coda Q -1 values. T he Q ~l m ap is constructed by assigning the m easured individual Q~l value at the m idpoint betw een source and receiver, and aver aging them over the m idpoints falling in each block w ith sides 0 .2° latitu d e by 0 .2° longitude into which a p a rt of C alifornia is divided. T he Q~l m aps 5 2 vided. T he Q ~l m aps are constructed for three lapse tim e windows and five frequencies. From th e spatial distribution of coda Q ~l m easurem ents, we obtain the spatial auto-correlation functions. We shall th en stu d y the dependence of observed spatial auto-correlation functions on th e tim e win dow and frequency. T he significance of observed sp atial coherence is tested by p u ttin g a G aussian random series in place of th e observed coda Q~l values. Finally, we shall study the correlation of coda Q ~l distribution w ith geological and seismic features of the region. DATA T here are two distinct d a ta sets used for our analysis. One was recorded by C A LN E T in central California operated by U.S.G.S. at M enlo Park. T he o th er was recorded by U SG S-CIT seismic netw ork which cov ers southern California. A bout 1000 local earthquakes w ith th e m agnitude range from 2.0 to 3.5 were processed through the CU SP (Caltech-U SG S Seismic Processing) digital d a ta recording system . This m agnitude range was selected for well-recorded coda p art of seism ogram s, and for avoiding th e problem of satu ratio n (clipping in seism ogram ) and background noise contam ination. For those d a ta from C A LN ET in central California, the collected earth quakes are m ostly n ear the San A ndreas fault w ith concentration around the Parkfield-C oalinga area. In addition, seventy earthquakes in the Long Valley area were included in this d a ta set. All these earthquakes occurred in th e tim e period from 1978 to 1984. E arthquakes collected from U SG S-CIT seismic netw ork in southern 5 3 California occurred in the tim e period from 1982 to 1987. T hey are m ore broadly d istrib u ted th an those in central California, b u t still concentrated to several areas such as K ern River, Owens Valley and San Jacin to fault zone. O ur d a ta include foreshocks and aftershocks of the N orth Palm Springs earthquake of July 8 , 1986, w ith m agnitude 5.6, and the W hittier- N arrow s earthquake of O ctober 1, 1987 w ith m agnitude 5.9, and foreshocks of the S uperstition Hills earthquakes of m agnitude 6.2 and 6.6 which oc curred on Novem ber 24, 1987. These case histories offered excellent targets for studying th e reality of precursory change in coda Q~l which we shall address in the next chapter. All seism ogram s used in the analysis of coda Q ~ 1 m easurem ents were visually exam ined to insure th a t they are free from problem s such as glitches due to m alfunction in recording device, satu ratio n , overlapping dual events, noise disturbance, poor-quality recording and too early term ination. We used only coda waves arriving after twice the S arrival tim e at each statio n following th e rule introduced by R au tian and K halturin (1978). METHOD OF DATA ANALYSIS T he observed coda am plitude decay rate, as first recognized by Aki(1969) in the records of aftershocks of the Parkfield, California, e a rth quake of 1966, is largely independent of hypocentral distance, and the char acteristics of p articu lar p a th joining the earthquake source and record ing statio n . T he above observation has been explained by considering coda waves as the superposition of back-scattered waves from num er ous sm all-scale heterogeneities random ly d istributed throughout the litho 54 sphere. Thus, in a statistical sense, the observed coda decay slope or coda Q ~l can be tre ated as an stru ctu ral p aram eter of lithosphere averaged over th e region through which the back-scattered waves are propagated. In m ost coda studies, the form ula based on th e single scatterin g (first Born) approxim ation derived by Aki and C houet (1975) has been adopted as th e basic equation in estim ating coda Q ~ l . In this form ula, the time- dependent coda power spectrum P(uj\t) at frequency u and lapse tim e around t (m easured from th e origin tim e) is expressed as th e com bination of source, site and p a th effects. T he form ula is given by P{w\t) = C(w)t-aeirr (3.1) w here C(u;) is independent of t and is determ ined by the earth q u ak e source, scatterin g and recording site effects at frequency w, a is a constant th a t depends on the geom etric spreading factor (a = 2 for body waves, a = 1 for surface waves assum ing hom ogeneous and unbounded u n p ertu rb ed m edia). Q c l is th e Q~l representing apparent atten u atio n of prim ary and scattered waves due to loss by intrinsic absorption and scattering. T he m ultiple scattering effect on coda waves has been considered by several researchers (Kopnichev,1977; Gao et a/.,1983a;1983b; Frankel and W ennerberg, 1987), and we also presented th e results of our study on vari ous effects of m ultiple scattering using th e num erical experim ent in chapter 2. T he form ula including the m ultiple scattering effect m ust contain scat tering Q~l and intrinsic Q -1 separately. This makes it practically very difficult to uniquely determ ine b o th Q ’s by using th e m ultiple scattering model. On the other hand, observations have shown widely and consis 55 tently th a t equation (3.1) explains the observed coda decay very well, and the coda Q ~ 1 determ ined by the use of equation (3.1) agrees quite well w ith Q ~l of S waves and Lg waves determ ined independently (Aki (1980); W u (1984); and Cam pillo et a/., (1985)). For this reason, we shall continue to use eq. (3.1) to determ ine coda Q - 1 , b u t carefully specifying the tim e window for which the coda Q~l is evaluated in order to assess the effect of m ultiple scattering case by case. By taking th e n atu ral logarithm of b o th sides of eq. (3.1), we obtain ln[P{u\t)t2} = lnC{uj) - (3.2) ^ C Because C(u>) is independent of tim e, lnC(uj) can be considered as a constant in determ ining the coda Q ~x for a given u, and we can obtain Q ~ 1 from th e slope of ln[P(u;\t)t2] against t. The coda pow er spectrum P(uj\t) is estim ated by th e m oving window technique of discrete Fourier transform (w ith tim e length 5.12 sec and m ov ing the window by 2.56 sec). The background noise spectrum was estim ated by taking th e interval w ith the same length as the D F T window preceding the P wave first arrival. T he noise power spectrum is su b stracted from each m easured coda power spectrum . T he discrete Fourier transform is calculated for th e tim e window startin g from the lapse tim e twice the S a r rival tim e and ending w here the estim ated signal power spectrum becom e com parable to the noise power spectrum . We then averaged the squared D F T over each octave frequency band centered at 1.5, 3, 6 , 12 and 24 Hz, and applied the linear regression analysis using equation (3 .3) to o btain Q~l . For a specified coda tim e window, only 56 the d a ta w ithin the specified tim e window were used to perform the linear regression. To assure reliable results from th e regression, those d a ta which h ad regression correlation coefficients less th a n 80% were excluded. T he obtained coda Q~l for a p articu lar source and receiver is assigned to th e m idpoint of the epicenter and station. This is because th e m idpoint is th e surface projection of the center of ellipsoidal region sam pled by coda waves arriving at any given lapse tim e. Figures 3.1 through 3.6 show exam ples of m idpoints distribution for three different windows for b o th southern and central C alifornia (15-30 sec, 20-45 sec and 30-60 sec for southern Cal ifornia, and 20-45 sec, 20-45 sec and 30-60 sec for central C alifornia) at frequency 1.5 Hz. We now construct m aps of coda Q ~l for different tim e windows and frequencies by grouping the coda Q ~l values assigned to m idpoints located in a given 0 .2° xO.2° block and calculating the m ean of these coda Q ~x values. M aps of m ean coda Q -1 for b o th central and southern California were th en constructed and shown in figures 3.26 through 3.29. T he choice of tim e window is different betw een two regions. T he tim e windows for central California are 20-45 sec, 30-60 sec and 50-100 sec, and the tim e windows for southern C alifornia are 15-30 sec, 20-45 sec and 30-60 sec. We showed two versions of geographic representation of m ean Q ~l values . In one of them , we classified the m ean value into four intervals each containing a q u arter of m easurem ents and in the other, we showed the num erical values of the m ean. T he form er version is labeled w ith ”a ” like figure 3.26-a, and the la tte r w ith ”b ” like figure 3.26-b. T he frequency bands centered at 1.5, 3, 6 , 12 and 24 Hz were designated by 1, 2 , 3, 4 and 5, respectively, at the end of 57 Latitude (N ) 153015/m id 118 Longitude ( W ) Figure 3.1 Midpoint s distribution with time window 15-30 sec at 1.5 Hz in southern California. 58 Latitude (N ) 2 0 4 615/m id c * - co CD CO e • % • •• *«> • • a ^ __ CO CO CO 120 118 116 122 Longitude ( W ) Figure 3.2 Midpoint s distribution with time window 20-45 sec at 1.5 Hz in southern California. 59 Latitude (N) 306015/m id CO .} V CO 120 122 118 Longitude ( W ) 116 Figure 3.3 Midpoint s distribution with time window 30-60 sec at 1.5 Hz in southern California. 60 Latitude (N) 2 0 4 515/m id o CO C T . 122 124 120 11 . Longitude ( W ) 116 114 Figure 3.4 Midpoint s distribution with time window 20-45 sec at 1.5 Hz in central California. 61 Latitude (N ) 3 0 6 015/m id o • • • C O _ _ C O • • CO 118 122 120 Longitude ( W ) 116 124 Figure 3.5 Midpoint s distribution with time window 30-60 sec at 1.5 Hz in central California. 6 2 Latitude (N ) 5010015/m id o CO CO *; 118 122 120 Longitude ( W ) 124 Figure 3.6 Midpoint s distribution with time window 50-100 sec at 1.5 Hz in central California. 63 block as X{. We then select a radius rn by rn = n x 20km (3 .3 ) and draw circles w ith radius r n centered at th e center of th e ith block. N ext, we calculate the m ean of individual coda Q _1 assigned to m idpoints located in the ring betw een the two circles w ith radii r n and r n+1, and designate it as yt( r n). We th en calculate the correlation coefficient 7 for a fixed r n by the following stan d a rd form ula (see p. 484 in th e N um erical Recipes by Press et al., (1986)), 7 (rn) = ^ ■ - ^ ■ ( ; n ) - F ( r n ) ) (3 .4 ) w here, M is the to tal num ber of 0.2° by 0.2° blocks containing num ber of m idpoints g reater th an three, ~ x is the m ean of x[s, yt( r n ) is th e m ean of y[s and 1 M * = 1 E 1 ' (3-5 ) 1=1 1 M y{rn) = (3-6) 1 = 1 We call 7 ( r n ) the spatial autocorrelation of coda Q ~ l , and plot it as a function of rn as shown, for exam ple, in figure 3.7 for the range of rn from 0 to 300 km. T he range of 7 lies betw een 1 to -1 as the perfect positive correlation changes to perfect negative correlation. T he value of 7 is zero w hen the variables Xi and yi(rn) is com pletely uncorrelated. 64 the figure identification like figure 3.26-a-l, figure 3.26-a-2, figure 3.26-a-3, figure 3.26-a-4 and figure 3.26-a-5. T he stan d ard error of the m ean value is shown in figures labeled w ith ” c” . For exam ple, the stan d a rd errors of the m ean values shown in figure 3.26-b-l are shown in figure 3.26-c-l. W hen a given block contains only one m id-point, the corresponding stan d ard error m aps shows a vacant block. As another m easure of the reliability of m ean, we also show the num ber of m idpoints used for calculating th e m ean in figures labeled w ith ”d ” . For exam ple, the num ber of m idpoints used for calculating th e m ean values shown in figure 3.26-b-l are shown in figure 3.26-d-l. E S T IM A T IN G T H E S P A T IA L A U T O -C O R R E L A T IO N F U N C T I O N In order to un d erstan d the spatial behavior of coda Q _1, it is essential to know how sm oothly it varies in space. Since the sm oothness of spatial variation can be expressed by the spatial auto-correlation function, we shall try to estim ate it by the following procedure. In order to estim ate the spatial auto-correlation function, we need to calculate the correlation betw een coda Q ~l values assigned at two m id points sep arated by a distance r. We m ay preaverage the coda Q~l over nearby m idpoints to stabilize th e variables before taking the correlation. If we choose, however, the extent of averaging too large, we shall lose spatial resolution in th e resultant auto-correlation function. A fter several trials, we decided to adopt the following steps. F irst, we designate the m ean value of coda Q ~l at the ith 0.2° by 0.2° 65 S IG N IF IC A N C E T E S T F O R T H E A T U O C O R R E L A T IO N F U N C T I O N A utocorrelation functions calculated by the procedure described above using th e coda Q ~l m easured from the southern C alifornia U SG S-CIT n e t work d a ta axe shown in figures 3.7, 3.8 and 3.9 for tim e windows 15-30 sec, 20-45 sec, and 30-60 sec respectively. In order to test th e significance of these auto-correlation functions, we shall first com pare them w ith th e case in which each of the coda Q ~1 values used for calculating them are replaced by a random num ber taken from a G aussian ensemble. We apply the sam e procedure used for calculating real coda Q~1 auto-correlation functions to the identical set of m idpoints at which the random num ber is now assigned. We rep eat this for m any different sets of random num bers and show the results in figures 3.10, 3.11 and 3.12 for tim e windows 15-30, 20-45 and 30-60 sec, respectively. T he relatively large range of fluctuation for tim e window 15-30 sec as com pared to the window 30-60 sec is due to the fewer m idpoints for th e form er as can be seen from the com parision of figures 3.1 w ith 3.3. C om paring the autocorrelation function for the coda Q ~ l values w ith th a t for the random num ber d ata, we find th a t some of th e features of the autocorrelation function of coda Q~l are unlikely due to random coinci dence. A utocorrelation functions calculated by using the coda Q ~ l m easured from central California C A LN E T netw ork d a ta are shown in figures 3.13 and 3.14 for tim e windows 20-45 sec and 30-60 sec. We also show the au- 66 4 M n t* —— (Xa) M « M < m Figure 3.7 Spatial autocorrelation functions for time window 15-30 sec in southern California. m 05 00 D Ik U m * (X b ) PM m m O B h ) Figure 3.8 Spatial autocorrelation functions for time window 20-45 sec in southern California. " \ ifr I DtoUwe Q ta) W Figure 3.9 Spatial autocorrelation functions for time window 30-60 sec in southern California. — J o Vmb Figure 3.10 Spatial autocorrelation functions for time window 15-30 sec for the synthetic Gaussian random set of coda 1/Q in southern California. 400 400 Figure 3.11 Spatial autocorrelation functions for time window 20-45 sec for the synthetic Gaussian random set of coda 1/Q in southern California. 0*) Figure 3.12 Spatial autocorrelation functions for time window 30-60 sec for the synthetic Gaussian random set of coda 1/Q in southern California. PtotM ww £ * * 0 Figure 3.13 Spatial autocorrelation functions for time window 20-45 sec in central California. / s D>«U»n» ( t a ) M n m O N Figure 3.14 Spatial autocorrelation functions for time window 30-60 sec in central California. 4 M O ta ) O ta ) Figure 3.15 Spatial autocorrelation functions for time window 20-45sec for the synthetic Gaussian random set of coda 1/Q in central California. Figure 3.16 Spatial autocorrelation functions for time window 30-60sec for the synthetic Gaussian random set of coda 1/Q in central California. tocorrelation functions obtained from th e synthetic coda Q~l values gener ated by different sets of G aussian random series to test th e significance of these au tocorrelation functions in figures 3.15 and 3.16 for b o th tim e win dows. T he relatively large range of fluctuation for the central C alifornia as com pared to th a t for the southern C alifornia is because m idpoints for the form er are d istrib u ted narrow ly along the San A ndreas fault while those for th e la tte r are m ore broadly d istrib u ted (see th e coda Q ~l m aps in figure 3.27-a-l). C om paring the autocorrelation functions of m easured coda Q -1 values w ith those of random num ber d ata, we find, sim ilarly to the southern C al ifornia, th a t some of the features of autocorrelation functions are n o t due to ran d o m coincidence. — C oda Tim e-W indow A nd Coherence D istance — T he m ost convincing non-random feature is the dependence of the au to co rrelatio n function on the choice of tim e window. As clearly shown in figures 3.17 through 3.20, where autocorrelation functions for three tim e windows in southern C alifornia are p lo tted together, th e longer and later tim e window corresponds to the slower decay in the correlation w ith th e distance separation for all frequency bands. If we define the distance at which th e correlation first comes close to zero as th e ” coherence distance” , th en the coherence distance is 110 to 160 km (depending on frequency) for tim e window 30-60 sec, and 30 to 60 km for tim e window 15-30 sec. T he in term ed iate tim e window 20 to 45 sec shows the interm ediate coherence distance of 70 to 110 km. T he average coherence distance is 135, 90 and 45 km for the three tim e windows closing at lapse tim e 60, 45 and 30 sec, 77 Correlation Coefficient 1.5 Hz iT 3 o 1 5 -3 0 S O 2 0 -4 5 S - * 3 0 -6 0 S d — 400 D i s t a n c e ( K m ) Figure 3.17 Spatial autocorrelation functions for three time windows at 1.5 Hz in southern California. 78 Correlation Coefficient 3 Hz o v * > 15-30 S O v 4 0 0 D i s t a n c e (Km) Figure 3.18 Spatial autocorrelation functions for three time windows at 3 Hz in southern California. 79 Correlation Coefficient 6 Hz m d 15-30 S O ^ \ 400 D i s t a n c e ( K m ) Figure 3.19 Spatial autocorrelation functions for three time windows at 6 Hz in southern California. 80 Correlation Coefficient 12 Hz o 2 0 -4 5 S < / > 1 5 -3 0 S 3 0 -6 0 S 400 D i s t a n c e ( K m ) Figure 3.20 Spatial autocorrelation functions for three time windows at 12 Hz in southern California. 81 respectively. T he above finding offers a strong support to our basic assum ption th a t coda waves are com posed of S to S single back-scattering waves, because th e distance traveled by S waves w ith a typical crustal shear velocity of 3.5 km /sec in half th e lapse tim e 60, 45 and 30 sec are 105, 79 and 53 km , which are close to th e corresponding observed coherence distance, namely, 135, 90 and 45 km respectively. — S patial Periodicity — A nother featu re of the autocorrelation function for southern C alifornia which appears to stan d th e significance test is th e positive peak at about th e distance separation of 230 km as shown m ost clearly for th e 20-45 sec window (see figures 3.21 through 3.23 w here au to co rrelatio n curves axe grouped according to tim e windows), suggesting spatial periodicity w ith w avelength of 230 km . T his periodicity consistently shows up for all tim e- windows and frequencies and is also supported by th e observed negative peak at ab o u t a half of 230 km shown b o th for the tim e-w indow 20-45 and 15-30 sec. T he absence of negative peak for tim e-w indow 30-60 sec can be explained by the larger region (w ith the coherence distance m ore th a n 100 km ) averaged by coda waves arriving in this window. Similarly, for those autocorrelation functions from central California, we also observe a persistent positive peak at ab o u t th e distance separation of 180 km as shown in figures 3.24 and 3.25. T his observed peak shows up for all frequencies for tim e windows 20-45 sec and 30-60 sec w ith higher am plitudes th a n for the southern California. T hus, th e sp atial periodic ity in central C alifornia is som ew hat shorter and ap p aren tly stronger th a n 82 Correlation Coefficient 15— 30 Sec d 400 D i s t a n c e ( K m ) Figure 3.21 Spatial autocorrelation functions for different frequencies with time window 15-30 sec in southern California. 83 Correlation Coefficient 20— 45 Sec 400 D i s t a n c e ( K m ) Figure 3.22 Spatial autocorrelation functions for different frequencies with time window 20-45 sec in southern California. 84 Correlation Coefficient 3 0 —6 0 S e c lO o 3 Hz O to 400 D i s t a n c e ( K m ) Figure 3.23 Spatial autocorrelation functions for different frequencies with time window 30-60 sec in southern California. 85 Correlation Coefficient 2 0 -4 5 Sec 400 D i s t a n c e ( K m ) Figure 3.24 Spatial autocorrelation functions for time window 20-45 sec in central California. 86 Correlation Coefficient 3 0 -6 0 Sec — - * \ 400 D i s t a n c e ( K m ) Figure 3.25 Spatial autocorrelation functions for time window 30-60 sec in central California. 87 th a t in southern California. T his difference in w ave-length and stren g th of periodicity m ay be explained to be due to th e difference in th e spatial d istrib u tio n of m idpoints betw een central and sou th ern California, if the periodicity is prim arily along the fault zone. In th a t case, th e w ave-length will be th e shortest in the direction along the fault zone, and the correla tion distance averaged over m ore diffusely d istrib u ted m idpoints will show ap p aren tly longer w ave-length w ith weaker am plitude. D IS C U S S IO N O N S P A T IA L D I S T R I B U T I O N O F C O D A Q "1 As m entioned earlier, figure 3.26-a-l through figure 3.29-d-5 show m aps of th e coda Q ~l m ean value in two different versions to g eth er w ith the sta n d ard error of the m ean and the num ber of m id-points used for calculating th e m ean for four tim e windows and five frequency bands. T he tim e win dows selected for the central C alifornia are 20-45, 30-60 and 50-100 sec, and those selected for southern C alifornia are 15-30, 20-45 and 30-60 sec. T hus, we are able to show the m ean coda Q~x for b o th regions in a single m ap for th e tim e windows, 20-45 and 30-60 sec. T he m ean coda Q~l d istrib u tio n shows some variations am ong differ ent frequency bands and different tim e windows, bu t there are some features which show up consistently. F irst, we find th a t while th e low Q zone is well defined narrow ly along th e m ain San A ndreas fault in the central California, it is spread as patches in the southern California. For exam ple, the segm ent of th e m ain San A n dreas fault betw een C ajon Pass and San Gorgonio M ountain shows higher Q value th an the o ther segm ent of th e m ain San A ndreas fault. We find 88 th a t th e Big P ine and the G arlock fault intersecting th e San A ndreas fault n ear th e big bend have as low Q as th e latte r, while th e San Jacin to and th e Elsinore fault subparallel to the San A ndreas fault show higher Q th a n th e la tte r in th e south of San Gorgonio M ountain. T he Los Angeles basin, especially around th e epicentral area of th e W hittier-N arrow s earthquake of 1987, is an o th er area showing consistently low Q. It is interesting to note the sim ilarity betw een our Q m ap for the sou th ern C alifornia and the m ap of P-velocity in th e top layer (0 to 40 km d ep th ) of a tom ographic m odel obtain ed by Raikes (1980) using telesism ic P tim e d a ta as shown in figure 3.30. In a very rough m anner, th e low Q region ap p ears to correlate w ith the low velocity region. Finally, we note th a t the periodicity of coda Q~l variation recognized earlier by th e correlation analysis is not obvious by a visual inspection. We still believe, however, th a t the periodicity is significant and not due to the artifact of d a ta analysis because of our test using th e random num ber d ata. T he observed w avelength around 200 km m ay have some bearing on the m echanical p ro p erty of th e lithosphere. 89 Latitude (N) 1 5 -3 0 Sec (1.5 Hz) 2 7 8 .3 ^Q > 103.9 1 103.9^Q > 81 .7 ■ 81.7^Q> 68.4 I 6 8 .4 * Q * 3 5 .4 I o CD CD CD 118 124 122 120 Longitude (W) Figure 3.26-a-l Map of coda 1/Q shown in shade with time window 15-30 sec at 1.5 Hz. 9 0 Latitude (N) 1 5 -3 0 Sec (3Hz) 1015.7£Q> 307.7 1 207.72Q> 170.4 1 170.4SQ> 145.4 I 145.42Q2 58.9 I o CO CO co 124 118 122 120 L ongitude (W ) Figure 3.26-a-2 Map of coda 1/Q shown in shade with time window 15-30 sec at 3 Hz. 91 Latitude (N) 1 5 -3 0 Sec (6Hz) Longitude (W) Figure 3.26-a-3 Map of coda 1/Q shown in shade with time window 15-30 6 Hz. 114 sec at 92 Latitude (N) 1 5 -3 0 Sec (12Hz) C \2 1426.7^Q > 719.7 | 719.7^Q > 585.8 B 585.8^Q> 507.5 I 507.5SQS 275.5 I c CD C O 124 122 120 L ongitude (W) Figure 3.26-a-4 Map of coda 1/Q shown in shade with time window 15-30 sec at 12 Hz. 93 Latitude (N) 1 5 -3 0 Sec (24Hz) 2326. lgQ> 1289.51 1289.5£Q>1071.3 1 1071.3§Q> 900.1 I 900.12Q> 326.1 I CD C D C\2 CO 118 124 120 Longitude (W ) 122 Figure 3.26-a-5 Map of coda 1/Q shown in shade with time window 15-30 sec at 24 Hz. 94 Latitude (N) 1 5 -3 0 Sec (1.5 Hz) o CO CO CO 124 122 120 Longitude (W ) Figure 3.26-b-l Map of coda 1/Q shown in numerical values of the mean with time window 15-30 sec at 1.5 Hz. Latitude (N) 1 5 -3 0 Sec (3 Hz) o CO CO C O CO CO 118 124 122 120 Longitude (W) Figure 3.26-b-2 Map of coda 1/Q shown in numerical values of the mean with time window 15-30 sec at 3 Hz. 96 Latitude (N) 1 5 -3 0 Sec (6 Hz) C \2 O CO CO 118 124 120 L ongitude (W ) 122 Figure 3.26-b-3 Map of coda 1/Q shown in numerical values of the mean with time window 15-30 sec at 6 Hz. Latitude (N) 1 5 -3 0 Sec (12 Hz) o CO CO CO CO 124 118 114 122 120 Longitude (W ) Figure 3.26-b-4 Map of coda 1/Q shown in numerical values of the mean with time window 15-30 sec at 12 Hz. 98 Latitude (N) 1 5 -3 0 Sec (24 Hz) o C O C O C O C O C O 124 120 Longitude (W) 116 Figure 3.26-b-5 Map of coda 1/Q shown in numerical values of the mean with time window 15-30 sec at 24 Hz. Latitude (N) 1 5 -3 0 Sec (1.5 Hz) o C O C O C O C O 124 122 120 L ongitude (W) Figure 3.26-c-l Map of the standard error of the mean in coda 1/Q with time window 15-30 sec at 1.5 Hz. 100 Latitude (N) 1 5 -3 0 Sec (3 Hz) CV2 o C O C O C O C O C O C V 2 118 124 120 L ongitude (W ) 122 Figure 3 . 2 6 - C - 2 Map of the standard error of the mean in coda 1/Q with time window 15-30 sec at 3 Hz. 101 Latitude (N) 1 5 -3 0 Sec (6 Hz) o CO C O C O 124 122 120 Longitude (W) 118 116 Figure 3.26-C-3 Map of the standard error of the mean in coda 1/Q with time window 15-30 sec at 6 Hz. Latitude (N) 1 5 -3 0 Sec (12 Hz) o C O 00 CO 00 CO C\2 CO 124 122 118 120 L ongitude (W) Figure 3 . 2 6 - C - 4 Map of the standard error of the mean in coda 1/Q with time window 15-30 sec at 12 Hz. 1 0 3 Latitude (N) 1 5 -3 0 Sec (24 Hz) C \2 CO CO CD CO C O C\2 C O 118 124 120 Longitude (W ) 122 Figure 3 . 2 6 - C - 5 Map of the standard error of the mean in coda 1/Q with time window 15-30 sec at 24 Hz. Latitude (N) 1 5 -3 0 Sec (1.5 Hz) O C O C O C \2 C O 124 118 120 L ongitude (W ) 122 Figure 3.26-d-l Map of the number of midpoints used for calculating the mean alues with time window 15-30 sec at 1.5 Hz. Latitude (N) 1 5 -3 0 Sec (3 Hz) o C O C O C O C O C O 118 120 L ongitude (W ) 122 124 Figure 3.26-d-2 Map of the number of midpoints used for calculating the mean alues with time window 15-30 sec at 3 Hz. Latitude (N) 1 5 -3 0 Sec (6 Hz) CM O C O C\2 CO 118 116 124 122 L ongitude (W) Figure 3.26-d-3 Map of the number of midpoints used for calculating the mean values with time window 15-30 sec at 6 Hz. Latitude (N) 1 5 -3 0 Sec (12 Hz) CN2 O __ C O co 118 116 120 L ongitude (W) 124 122 Figure 3.26-d-4 Map of the number of midpoints used for calculating the mean values with time window 15-30 sec at 12 Hz Latitude (N) 15— 30 Sec (24 Hz) C \2 O _ CO CO C O CO CO C\2 CO 118 116 124 122 120 Longitude (W) Figure 3.26-d-5 Map of the number of midpoints used for calculating the mean values with time window 15-30 sec at 24 Hz. 1 0 9 Latitude (N) 2 0 -4 5 Sec (1.5 Hz) 241.0^Q > 122.2 = 122.2^Q > 104.8 104.8^Q> 85.5 1 85.5SQS 32.2 I 124 122 120 118 Longitude (W ) 114 Figure 3.27a-1 Map of coda 1/Q shown in shade with time window 20-45 sec at 1.5 Hz. 110 Latitude (N) 2 0 -4 5 Sec (3Hz) 552.2^Q > 248.1 I 248.1 ^Q> 207.0 207.0^Q> 161.8 I 161.82Q2 75.2 I 124 122 120 118 L ongitude (W) Figure 3.27-a-2 Map of coda 1/Q shown in shade with time window 20-45 sec at 3 Hz. I l l Latitude (N) 2 0 -4 5 Sec (6Hz) L ongitude (W) Figure 3.27-a-3 Map of coda 1/Q shown in shade with time window 20-45 sec at 6 Hz. 112 Latitude (N) 2 0 -4 5 Sec (12Hz) 1997.8^Q > 783.0 I 783.0^Q > 655.3 I 655.3^Q> 534.3 I 534.32Q2 129.9 I 124 122 120 118 L ongitude (W) 116 Figure 3.27-a-4 Map of coda 1/Q shown in shade with time window 20-45 sec at 12 Hz. 113 Latitude (N) 2 0 -4 5 Sec (24Hz) 5230.1 *^Q> 1432.3H 1432.3 ^Q> 1227.5 1227.5^Q > 1038.8 I 1038.8£Q> 450.6 I 122 120 118 Longitude (W) Figure 3.27-a-5 Map of coda 1/Q shown in shade with time window 20-45 sec at 24 Hz. 114 11 Latitude (N) 2 0 -4 5 Sec (1.5 Hz) o cn 124 122 120 Longitude (W) 118 114 116 Figure 3.27-b-l Map of coda 1/Q shown in numerical values of the mean with time window 20-45 sec at 1.5 Hz. Latitude (N) 2 0 -4 5 Sec (3 Hz) o CO CO C D 00 CO C\2 CO 124 122 120 L ongitude (W) Figure 3.27-b-2 Map of coda 1/Q shown in numerical values of the mean with time window 20-45 sec at 3 Hz. 116 Latitude (N) 2 0 — 45 Sec (6 Hz) C \2 o C O CO CO CO a. I CO C\2 CO 118 120 L ongitude (W ) 124 122 Figure 3.27-b-3 Map of coda 1/Q shown in numerical values of the mean with time window 20-45 sec at 6 Hz. 117 Latitude (N) 2 0 -4 5 Sec (12 Hz) C \2 O C O C O C D C O 120 Longitude (W) 118 124 122 Figure 3.27-b-4 Map of coda 1/Q shown in numerical values of the mean with time window 20-45 sec at 12 Hz. 118 Latitude (N) 2 0 -4 5 Sec (24 Hz) C\2 '■ 't O C O C O C O CO CO C \2 CO 116 118 120 L ongitude (W ) 122 124 Figure 3.27-b-5 Map of coda 1/Q shown in numerical values of the mean with time window 20-45 sec at 24 Hz. 119 Latitude (N) 2 0 -4 5 Sec (1.5 Hz) C \2 O CC CO CO CO CO 116 118 120 122 124 L ongitude (¥) Figure 3.27c-1 Map of the standard error of the mean in coda 1/Q with time window 20-45 sec at 1.5 Hz. 120 Latitude (N) 2 0 -4 5 Sec (3 Hz) o C O C\2 CO 118 116 120 L ongitude (W) 122 124 Figure 3 . 2 7 - C - 2 Map of the standard error of the mean in coda 1/Q with time window 20-45 sec at 3 Hz. Latitude (N) 2 0 -4 5 Sec (0 Hz) o C O C O CO C O C O 120 118 116 124 122 L ongitude (W) Figure 3 . 2 7 - C - 3 Map of the standard error of the mean in coda 1/Q with time window 20-45 sec at 6 Hz. 122 Latitude (N) 2 0 -4 5 Sec (12 Hz) o C O CO C\2 CO 116 114 118 120 L ongitude (W ) 122 124 Figure 3 . 2 7 - C - 4 Map of the standard error of the mean in coda 1/Q with time window 20-45 sec at 12 Hz. 1 2 3 Latitude (N) 2 0 -4 5 Sec (24 Hz) o C O C O CO CO CO C\2 CO 116 118 120 L ongitude (W) 122 124 Figure 3 . 2 7 - C - 5 Map of the standard error of the mean in coda 1/Q with time window 20-45 sec at 24 Hz. Latitude (N) 2 0 -4 5 Sac (1.5 Hz) o C O CO CO 118 116 120 L ongitude (W) 124 Figure 3.27-d-l Map of the number of midpoints used for calculating the mean values with time window 20-45 sec at 1.5 Hz. Latitude (N) 2 0 -4 5 Sec (3 Hz) C \2 O CO CO CO CO CO 118 116 120 L ongitude (W) 122 124 Figure 3.27-d-2 Map of the number of midpoints used for calculating the mean values with time window 20-45 sec at 3 Hz. Latitude (N) 2 0 -4 5 See (6 Hz) o CO CO.' C O CO ^ __ CO CO 116 118 122 124 L ongitude (W) Figure 3.27-d-3 Map of the number of midpoints used for calculating the mean values with time window 15-30 sec at 6 Hz. Latitude (N) 2 0 -4 5 Sec (12 Hz) C\2 " 'f O __ CO CO CO C V 2 CO 118 116 124 122 120 L ongitude (W) 114 Figure 3.27-d-4 Map of the number of midpoints used for calculating the mean values with time window 20-45 sec at 12 Hz Latitude (N) 2 0 -4 5 Sec (24 Hz) o CO CO ■ m a CO C\2 CO 118 116 124 122 Longitude (W) Figure 3.27-d-5 Map of the number of midpoints used for calculating the mean values with time window 20-45 sec at 24 Hz. Latitude (N) 3 0 -6 0 Sec (1.5 Hz) o CO C O C D C O CO C\2 CO 345.2^Q > 136.5 | 136.5^Q > 114.9 114.9^Q > 96.9 I 96.9*Q* 39.6 I - • h 1 2 4 1 2 2 120 118 L ongitude (W) 1 1 6 Figure 3.28-a-l Map of coda 1/Q shown in shade with time window 30-60 sec at 1.5 Hz. 13Q Latitude (N) 3 0 -6 0 Sec (3Hz) o C O C O C O C O CO 815.0^Q> 279.8 I 279.8^Q> 243.2 1 243.2^Q> 200.4 I 2 0 0 .4 2 Q 2 4 8 .5 I 1 2 4 1 2 2 1 1 6 1 120 118 Longitude (W ) Figure 3.28-a-2 Map of coda 1/Q shown in shade with time window 30-60 sec at 3 Hz. 131 Latitude (N) 3 0 -6 0 Sec (6Hz) CV2 928.5^Q > 491.2 1 491.2^Q > 417.7 I 417.7^Q > 344.8 I 344.8SQS 108.7 I o CO CO C D ^ __ CO C\2 CO 118 124 122 120 Longitude (W) 116 Figure 3.28-a-3 Map of coda 1/Q shown in shade with time window 30-60 sec at 6 Hz. 132 Latitude (N) 3 0 -6 0 Sec (12Hz) o C O C O CO CO' C O 3 3 1 5 .6^Q > 869.2 1 869.2^Q > 737.7 7 37.7^Q > 619.3 I 619.32Q2 196.1 I 1 2 4 1 2 2 1 1 6 1 1 4 120 118 L ongitude (W) Figure 3.28-a-4 Map of coda 1/Q shown in shade with time window 30-60 sec at 12 Hz. 133 Latitude (N) 3 0 -6 0 Sec (24Hz) 10000.0 ^ Q > 1 6 6 6 .7 1 1666.7^Q > 1414.2 I 1414.2^Q > 1232.7 I 1232.7£Q> 328.9 I 124 122 120 118 Longitude (W) 116 Figure 3.28-a-5 Map of coda 1/Q shown in shade with time window 30-60 sec at 24 Hz. 134 Latitude (N) 3 0 -6 0 Sec (1.5 Hz) o C O CO o o. 114 118 116 120 L ongitude (W) 124 122 Figure 3.28-b-l Map of coda 1/Q shown in numerical values of the mean with time window 30-60 sec at 1.5 Hz. Latitude (N) 3 0 -6 0 Sec (3 Hz) C \2 O CO CO CO CO 120 L ongitude (W) 118 116 122 124 Figure 3.28-b-2 Map of coda 1/Q shown in numerical values of the mean with time window 30-60 sec at 3 Hz. Latitude (N) 3 0 -0 0 Sec (0 Hz) o CO CO CO CO C\2 CO 124 122 120 L ongitude (W) 118 Figure 3.28-b-3 Map of coda 1/Q shown in numerical values of the mean with time window 30-60 sec at 6 Hz. Latitude (N) 3 0 -6 0 Sec (12 Hz) o C O C O C O CO 118 120 L ongitude (W) 114 122 124 Figure 3.28-b-4 Map of coda 1/Q shown in numerical values of the mean with time window 30-60 sec at 12 Hz. Latitude (N) 3 0 -6 0 Sec (24 Hz) o 0 0 C O C O CO C O C\2 C O 120 L ongitude (¥) 118 116 122 124 Figure 3.28-b-5 Map of coda 1/Q shown in numerical values of the mean with time window 30-60 sec at 24 Hz. Latitude (N) 3 0 -6 0 Sec (1.5 Hz) o CD CO CO C\2 CO 116 124 122 120 L ongitude (W) 118 Figure 3.28-c-l Map of the standard error of the mean in coda 1/Q with time window 30-60 sec at 1.5 Hz. Latitude (N) 3 0 -0 0 Sec (3 Hz) o CO CO CO C O C V 2 C O 122 120 L ongitude (W) 118 116 124 Figure 3 . 2 8 - C - 2 Map of the standard error of the mean in coda 1/Q with time window 30-60 sec at 3 Hz. Latitude (N) 3 0 -6 0 Sec (6 Hz) o CO CO CO CO CO C O CO 116 118 120 122 124 L ongitude (W) Figure 3 . 2 8 - C - 3 Map of the standard error of the mean in coda 1/Q with time window 30-60 sec at 6 Hz. 142 Latitude (N) 3 0 -0 0 Sec (12 Hz) o C O CO CO 116 118 120 L ongitude (W) 122 124 Figure 3 . 2 8 - C - 4 Map of the standard error of the mean in coda 1/Q with time window 30-60 sec at 12 Hz. Latitude (N) 3 0 -6 0 Sec (24 Hz) C \2 O CO CO CO CO CO Cv2 CO 118 116 120 122 124 Longitude (W) Figure 3 . 2 8 - C - 5 Map of the standard error of the mean in coda 1/Q with time window 30-60 sec at 24 Hz. 144 Latitude (N) 3 0 -6 0 Sec (1.5 Hz) o CO CO CO CO CO 120 Longitude (W) 118 124 122 116 114 Figure 3.28-d-l Map of the number of midpoints used for calculating the mean values with time window 30-60 sec at 1.5 Hz. 145 Latitude (N) 3 0 -6 0 Sec (3 Hz) C \2 O C O 120 L ongitude (W) 118 116 122 124 Figure 3.28-d-2 Map of the number of midpoints used for calculating the mean values with time window 30-60 sec at 3 Hz. Latitude (N) 3 0 -6 0 Sec (6 Hz) o CO CO C O C O 118 116 120 Longitude (W) 124 122 Figure 3.28-d-3 Map of the number of midpoints used for calculating the mean values with time window 30-60 sec at 6 Hz. Latitude (N) 3 0 -6 0 Sec (12 Hz) o 116 114 118 120 L ongitude (If) 122 124 Figure 3.28-d-4 Map of the number of midpoints used for calculating the mean values with time window 30-60 sec at 12 Hz Latitude (N) 3 0 -6 0 Sec (24 Hz) C \2 O C O C O C O C O 116 118 120 Longitude (W ) 122 124 Figure 3.28-d-5 Map of the number of midpoints used for calculating the mean values with time window 30-60 sec at 24 Hz. Latitude (N) 5 0 -1 0 0 Sec (1.5 Hz) 124 122 120 118 Longitude (W) 116 Figure 3.29-a-l Map of coda 1/Q shown in shade with time window 50-100 sec at 1.5 Hz. 150 Latitude (N) 5 0 -1 0 0 Sec (3Hz) 124 122 116 114 120 118 L ongitude (W) Figure 3.29-a-2 Map of coda 1/Q shown in shade with time window 50-100 sec at 3 Hz. 151 Latitude (N) 5 0 -1 0 0 Sec (6Hz) o ’' f CO CO CO CO CO C\2 C O 1666.7^Q > 577.8 1 577.8^Q > 396.0 3 396.0^Q > 338.5 ■ 338.5^Q^ 157.5 I 124 122 +- 116 1 120 118 L ongitude (If) Figure 3.29-a-3 Map of coda 1/Q shown in shade with time window 50-100 sec at 6 Hz. 152 Latitude (N) 5 0 -1 0 0 Sec (12Hz) 5 0 0 0 .0 ^Q > 1069.5 I 1 0 6 9 .5£Q > 8 0 0 .0 1 8 0 0 .0 S Q > 6 7 8 .4 I 878.42Q2 263.3 I w-l 1 --------- 1 --------- 1 ---------1 ---------1 --------- 1 ---------1 ---------1 --------- 1 --------- h— 124 122 120 118 116 L ongitude (W) Figure 3.29-a-4 Map of coda 1/Q shown in shade with time window 50-100 12 Hz. 114 sec at 153 Latitude (N) 5 0 -1 0 0 Sec (24Hz) o CO CO CO C O CO C\2 CO 1 0 0 0 0 .0 ^ Q > 3 3 3 3 .3 g 3 3 3 3 .3 ^Q > 2 0 0 0 .0 I 2000.0^Q> 1428.6 I 1 4 2 8 .6 £ Q > 3 6 3 .6 I > 124 122 120 118 L ongitude (W) 116 4 Figure 3.29-a-5 Map of coda 1/Q shown in shade with time window 50-100 sec at 24 Hz. 154 Latitude (N) 5 0 -1 0 0 Sec (1.5 Hz) o C O C O C O C O C O 118 116 122 120 L ongitude (W) 114 124 Figure 3.29-b-l Map of coda 1/Q shown in numerical values of the mean with time window 50-100 sec at 1.5 Hz. Latitude (N) 5 0 -1 0 0 Sec (3 Hz) o CO CO CO CO CO C\2 CO 120 L ongitude (W ) 118 124 116 122 Figure 3.29-b-2 Map of coda 1/Q shown in numerical values of the mean with time window 50-100 sec at 3 Hz. Latitude (N) 5 0 -1 0 0 Sec (6 Hz) o CO CO C O C O CO C v2 C O 120 Longitude (W) 118 116 124 122 Figure 3.29-b-3 Map of coda 1/Q shown in numerical values of the mean with time window 50-100 sec at 6 Hz. Latitude (N) 5 0 -1 0 0 Sec (12 Hz) o CO CO CD CO CO C\2 CO 120 118 116 122 124 L ongitude (W ) Figure 3.29-b-4 Map of coda 1/Q shown in numerical values of the mean with time window 50-100 sec at 12 Hz. 158 Latitude (N) 5 0 -1 0 0 Sec (24 Hz) C \2 O 116 118 120 Longitude (W) 122 124 Figure 3.29-b-5 Map of coda 1/Q shown in numerical values of the mean with time window 50-100 sec at 24 Hz. Latitude (N) 5 0 -1 0 0 Sec (1.5 Hz) o CO CO CO CO 116 118 120 L ongitude (W) 122 124 Figure 3.29-c-l Map of the standard error of the mean in coda 1/Q with time window 50-100 sec at 1.5 Hz. Latitude (N) 5 0 -1 0 0 Sec (3 Hz) o CO CO C D CO CO 122 120 L ongitude (W) 118 116 124 Figure 3 . 2 9 - C - 2 Map of the standard error of the mean in coda 1/Q with time window 50-100 sec at 3 Hz. Latitude (N) 5 0 -1 0 0 Sec (0 Hz) Cv2 O CO CO C O C O CO C\2 CO 118 120 L ongitude (W) 116 124 122 Figure 3 . 2 9 - C - 3 Map of the standard error of the mean in coda 1/Q with time window 50-100 sec at 6 Hz. Latitude (N) 5 0 -1 0 0 Sec (12 Hz) o C O CO 120 118 116 124 122 L o n g itu d e (W) Figure 3 . 2 9 - C - 4 Map of the standard error of the mean in coda 1/Q with time window 50-100 sec at 12 Hz. 1 6 3 Latitude (N) 5 0 -1 0 0 Sec (24 Hz) o CO CO C O CO C O 118 116 120 Longitude (If) 122 124 Figure 3 . 2 9 - C - 5 Map of the standard error of the mean in coda 1/Q with time window 50-100 sec at 24 Hz. Latitude (N) 5 0 -1 0 0 Sec (1.5 Hz) o C O __ CO CO CO 114 118 116 122 124 Longitude (W ) Figure 3.29-d-l Map of the number of midpoints used for calculating the mean values with time window 50-100 sec at 1.5 Hz. Latitude (N) 5 0 -1 0 0 Sec (3 Hz) C \2 O CO CO CD CO CO 120 Longitude (W ) 118 124 116 122 Figure 3.29-d-2 Map of the number of midpoints used for calculating the mean values with time window 50-100 sec at 3 Hz. Latitude (N) 5 0 -1 0 0 Sec (6 Hz) C \2 O C O CO C O CO C O 114 116 118 120 Longitude (W) 122 124 Figure 3.29-d-3 Map of the number of midpoints used for calculating the mean values with time window 50-100 sec at 6 Hz. 167 Latitude (N) 5 0 -1 0 0 Sec (12 Hz) C \2 O CO CO CO 118 122 120 L ongitude (W) 124 Figure 3.29d-4 Map of the number of midpoints used for calculating the mean values with time window 50-100 sec at 12 Hz Latitude (N) 5 0 -1 0 0 Sec (24 Hz) C \2 O CO C O C D CO ^ __ CO 118 116 120 122 124 Longitude (W) Figure 3.29-d-5 Map of the number of midpoints used for calculating the mean values with time window 50-100 sec at 24 Hz. 169 SAN L 0 3 # • AN 6E I.E5 L ^-^SASIN N Layer 1 0 -4 0 km 2 0 0 k m Veloci ty :hange S lo w U -2 p e r c e n t F a s t Figure 30 P-wave velocity anomaly for 0-40 km obtained by Raikes (1980). 170 C H A P T E R IV T E M P O R A L V A R IA T IO N O F C O D A Q ~l I N T R O D U C T IO N In this chapter, we shall study one of the m ost intriguing aspects of coda waves, namely, the tem poral variation of coda Q ~l . A lthough the tem poral change of coda Q ~x in relation to the occurrence of m ajor earth quakes has been rep o rted by m any authors for m any seismic regions, the physical reality of the precursory change of coda Q~l has not yet been widely accepted by th e seismological com m unity. As sum m arized in an extensive review by Sato (1988a), there are several factors in th e m ethod for calculating coda Q~l th a t m ay generate fictitious tem poral change in coda Q~l . O ne of the m ain purpose of this chapter is to present m ore convincing evidence for the physical reality of coda Q~l change by paying a tten tio n to these sources of fictitious tem poral change. F ortunately, a very sharp and strong increase in coda Q ~l occurred thro u g h o u t th e southern California in 1986 offers an excellent d a ta set for our purpose. We shall study the sp atial p a tte rn of the 1986 change and find th a t the increase in coda Q~l occurs in several distinct areas, each surrounded by a zone in which coda Q ~l decreased for m ore th an one frequency bands during the same period, in a m anner rem inscent of M ogi’s donut m odel (1985) in which an area of precursory quiescence is surrounded by a zone of increased seismicity. T he area of increased coda Q _1 includes the Coachella segment of the San A ndreas fau lt, the Los Angeles basin, and the southern end of 171 the Sierra N evada fault. We then stu d y the possible m igration of th e coda Q~x increase due to the creep wave propagation hypothesized by Savage (1971), and concludes th a t the 1986 coda Q ~x increase occurred sim ultane ously throughout southern California w ithin the scatte r of d ata. Finally, we shall restrict our atten tio n to the epicentral areas of three recent m oderate sized earthquakes in southern California, namely, th e N orth Palm Springs (1986), W hit tier-N arrow s (1987), and S uperstition Hills (1987) earthquake, and exam ine th e p a tte rn of tem poral variation in coda Q ~l in relation to the occurrence of the m ainshock. We also exam ine the tem poral behaviour of b-value, and find th a t coda Q~l and b-value show precursory change sim ilar to typical p atte rn s reported by other authors. T he observed pos itive correlation betw een coda Q~l and b-value is also in agreem ent w ith the result of Jin and Aki (1989) obtained for the southern California for the 55-year period from 1933 to 1987. R E A L I T Y O F T E M P O R A L C H A N G E I N C O D A Q ~l As m entioned in chapter 1, the sources of fictitious tem poral change in coda Q ~l a ttrib u te d by critics are ( 1) change in epicenter locations of earthquakes used for coda Q~1 m easurem ents, (2 ) change in focal depths of earthquakes used for coda Q~l m easurem ents, (3) change in th e tim e window of coda waves used for estim ating coda Q - 1 , (4) change in the in strum ent characteristics and procedures for d a ta collection and analysis, (5) change in com bination of stations, and (6 ) change in the focal m echanism of earthquakes used for the coda Q~l m easurem ents. Recently, Jin and Aki (1989) addressed these factors in their discussion 172 of coda Q ~l change obtained from the Riverside records of the Benioff short-period seism ographs for the 55-year period from 1933 to 1987. They observed a large system atic change in coda Q ~l as shown in figure 4.1, which cannot be due to the factor (5). T he effects of factors (1) and (2) are also conclusively elim inated as possible causes of observed tem poral change by Jin and Aki(1989). We can now elim inate factors (3), (4) and (6 ) using our own results. As shown in figure 4.1, the coda Q ~ l m easured by Jin and Aki (1989) shows a sharp rise after a weak m inim um in 1985. T his rem arkable p a tte rn is also consistently observed in our results for the whole southern Califor nia. Figure 4.2 through 4.11 show the m ean of 30 coda Q~l m easurem ents p lotted at th e m idpoint of origin tim es of earthquakes used for the m easure m ents for all statio n s and earthquakes in southern California used in the present study, for 5 frequency bands and 2 tim e windows. We find th a t, ir respective of frequency bands and tim e windows, th e sam e p a ttern , namely, the recent increase in coda Q ~l after a m inim um in 1985, as observed by Jin and Aki(1989) from a single statio n record appears consistently in all these figures. To be m ore q u an titativ e, we also list the m ean of coda Q ~l calculated separately for earthquakes which occurred before and after Jan u ary 1, 1986 in tables la and lb for three tim e windows and five frequency bands. For tim e windows 15-30 sec and 20-45 sec, the change is about 20% irrespective of frequency. T he change for the tim e window 30-60 sec appears to be sm aller proabably due to excessive spatial averaging. Since the instrum ent, d a ta collection processing and analysis are en- 173 1 d ? II J I I I I I L J I L J I I I I I I I I L J I I L 1937 1945 1953 1961 Y E A R 1969 1977 1985 Figure 4.1 Temporal variation of coda 1/Q obtained by Jin and Aki (1989) using the Riverside record for the past 55-year period since 1933. - * ■ 3 4 ^ 4 .0 8 . 0 12.0 1/ 0*1000 ( i / Q ) n o o o (15-30 Sec) 1.5 Hz c v i 83 84 87 YEAR h -1 Figure 4.2 Temporal variation of coda 1/Q with time window 15-30 sec at 1.5 Hz S for entire southern California. (1/Q )*1000 ( 1 5 - 3 0 Sec) 3 Hz o__ 85 84 88 83 82 YEAR Figure 4.3 Temporal variation of coda 1/Q with time window 15-30 sec at 3 Hz for entire southern California. (1/Q )*1000 ( 1 5 - 3 0 Sec) 6 Hz 82 83 84 85 86 87 88 YEAR Figure 4.4 Temporal variation of coda 1/Q with time window 15-30 sec at 6 Hz for entire southern California. (1/Q )*1000 ( 1 5 - 3 0 Sec) 12 Hz oo-- 84 05 86 87 88 YEAR Figure 4.5 Temporal variation of coda 1/Q with time window 15-30 sec at 12 Hz oo for entire southern California. (1/Q )*1000 ( 1 5 - 3 0 Sec) 24 Hz t H 82 84 85 86 87 88 YEAR t - 1 o Figure 4.6 Temporal variation of coda 1/Q with time window 15-30 sec at 24 Hz for entire southern California. (1/Q )*1000 ( 2 0 - 4 5 Sec) 1.5 Hz CM___ o __ co — 82 84 85 86 87 88 YEAR Figure 4.7 Temporal variation of coda 1/Q with time window 20-45 sec at 1.5 Hz for entire southern California. (1 /Q )* 1 0 0 0 ( 2 0 - 4 5 Sec) 3 Hz H 1 ------ 1 ------ 1 ------ 1 ------ 1 ------1 ------ 1 ------ 1 ------1 ------1 ------1 ------ 1 ------ 1 ------ 1 ------ 1 ------1 ------ 1 ------1 -------1 — -t----- 1 ------ 1 ------ 1 -------1 ------» — 4-— h < D — T *-- C O — 0 0 YEAR Figure 4.8 Temporal variation of coda 1 A3 witii time window 20-45 sec at 3 Hz for entire southern California. (1/Q )*1000 ( 2 0 - 4 5 Sec) 0 Hz oo— C M — 85 86 88 YEAR Figure 4.9 Temporal variation of coda 1/Q with time window 20-45 sec at 6 Hz for entire southern California. (1/Q )*1000 ( 2 0 - 4 5 Sec) 12 Hz C V i — 85 86 87 88 YEAR Figure 4.10 Temporal variation of coda 1/Q with time window 20-45 sec at 12 Hz for entire southern California. ( 1/Q)* 1000 ( 2 0 - 4 5 Sec) 24 Hz C V 2 no C D o o 83 84 86 88 YEAR Figure 4.11 Temporal variation of coda 1/Q with time window 20-45 sec at 24 Hz for entire southern California. 15-30 sec >86 <86 % difference 1.5 13.62 11.58 18 % 3 6.48 5.63 15 % 6 3.28 2.74 20 % 12 1.87 1.60 17 % 24 1.05 0.83 27 % 20-45sec >86 <86 % difference 1.5 10.27 8.89 16 % 3 5.0 430 16 % 6 2.66 231 15 % 12 1.55 135 15 % 24 0.89 0.74 20 % Table 4.1a Mean of coda 1/Q before and after Jan. 1, 1986 and its percentage difference in the mean for time windows 15-30 sec and 20-45 sec. 185 30-60 sec >86 <86 % difference 1.5 9.0 7.65 18 % 3 4.25 3.74 14 % 6 2.27 2.13 7 % 12 1.39 1.24 12 % 24 0.81 0.66 23 % Table 4.1b Mean of coda 1/Q before and after Jan. 1, 1986 and its percentage difference in the mean for time window 30-60 sec. 186 tirely different betw een our result and th a t of Jin and Aki (1989), we can conclusively elim inate th e factor (4) as causing the observed change. Since we strictly enforced the fixed tim e window in our coda analysis, we can also conclusively elim inate th e factor (3). T he effect of change in source m echanism (factor (6 )) is th e m ost dif ficult one to elim inate when the result is based on a single statio n d ata, because of the possible tem poral change in seismic rad iatio n to a p artic u lar direction to the statio n from th e source. O ur d ata, on th e o th er hand, come from m any stations and sources d istrib u ted throughout the southern California, and involve a great num ber of radiation directions. T hus, the effect of change in source m echanism is expected to be averaged o u t in our result. If not, the effect will be very m uch different from th a t on the result o btained from a single statio n d a ta set. T hen, the sam e p a tte rn of coda Q ~l change obtained from the two studies should m ean th a t the observed change is not due to the change in source m echanism of earthquakes used for th e coda Q~l m easurem ents. Thus, we conclude th a t the tem poral change in coda Q - 1 , at least the one observed in southern California in recent years cannot be due to the artifact of d a ta processing, bu t due to the change in physical properties of the e ra th ’s interior affecting the form ation of coda waves. T E M P O R A L C H A N G E IN C O D A Q 1 IN S O U T H E R N C A L I F O R N IA D U R I N G 1982-1987 Now th a t the reality of tem poral change in coda Q _1 is well estab lished, we shall investigate how the p a tte rn of change varied from place to 187 place in southern California. For this purpose, we divide southern Califor nia into eight subareas of equal size w ith dim ension of 1.25° in longitude x 1° in latitu d e as shown in figure 4.12. We group individual coda Q~l m easurem ents for m idpoints lying in each of these subareas. We th en com p u te the m ean of first 30 consecutive coda Q -1 values and plot it at the m edian of origin tim es of earthquakes used for the m easurem ents. T he m ean is taken then for the next 30 consecutive m easurem ents w ith 15 over lapping w ith the preceding m ean, and so on. Figure 4.13 through figure 4.27, for exam ple, show the plot of m ean coda Q ~l as a function of tim e for 3 tim e windows and 5 frequency bands for the subarea 1. A lthough we see considerable flunctuation from one frequency to an o th er as well as from one tim e window to another, the m inim um in coda Q ~1 around 1985, and the increase afterw ards are com m on features to all of them . T he flunc tu atio n shown for subarea 1 is representative of all o th er subareas. W ith this flunctuation in m ind, we shall now com pare the result am ong different subareas. For this purpose, we chose the tim e window of 20-45 sec, because th e available d ata are significantly less for the tim e window 15-30 sec, and th e spatial averaging becom e too severe for the tim e window 30-60 sec. We show the result for two frequencies 3 Hz and 12 Hz to represent the low and high frequency bands. Figure 4.28 through figure 4.34 show the tem poral change in coda Q~1 for the tim e window 20-45 sec and frequency 3 Hz for subareas 2 through 8 . Figure 4.35 through figure 4.41 show the sam e for frequency 12 Hz. C om paring these figures, we conclude th a t although we see consistently a m inim um in coda Q ~l around 1985 followed by an increase tow ard 1987, 188 L a titu d e (N ) r- co CD co u o co CO CO CO C\2 C O . 120 122 Longitude (W ) Figure 4.12 Regionalization map of eight subareas in southern California. 189 (1/Q)* 1000 H h (15-30 Sec) 1.5 Hz 1 4 ----1 ----1 ----1 ----1 ----1 ----1 ----1 ----1 ----1 ----1 ----1 ----1 ----1 ----1 ----1 ----1 ----1 ----H C O C M . co-- 82 H 1 h H 1 ----1 ----H H 1 ----1 ----h 83 84 85 Y E A R 86 H 1 ----1 ----h H H 87 CO o Figure 4.13 Temporal variation of coda 1/Q for time window 15-30 sec at 1.5 Hz in subarea 1. H 1 ---- 88 (1/Q)*1000 (15-30 Sec) 3 Hz 1 CO co i n — H 1 ---- 1 ----- 1 ---- 1 ---- 1 ---- 1 ----- 1 ---- 1 ---- 1 ---- 1 ----- 1 ---- 1 ---- 1 ---- 1 ---- 1 ---- 1 ---- 1 ---- 1 ---- 1 ---- 1 ---- h - t 1 ------1 ------1 ------1 ----- 1 ------1 ------1 ------1 ------1 ------1 ------1 ----- 1 ------1 ----- 1 ----- 1 ----- 1 ------1 ----- 1 --------- 1 ---1 ------1 ----- 1 ------ 1 ----- h 82 83 84 85 86 87 YEAR Figure 4.14 Temporal variation of coda 1/Q for time window 15-30 sec at 3 Hz in subarea 1. H 1 ---- 88 ( i/Q ) n o o o (15-30 Sec) 6 Hz 1 C D to xt- IO 0 0 (O c v i' C M — H 1 h H 1 ------ 1 ------ 1 ------ 1 ------ 1 ------ 1 ------ 1 ------ 1 ------ 1 ------ 1 ------ 1 ------ 1 ------ h ? ♦ ----♦ ----* ----* ----j ----1 --- 1 — I ---- 1 ----1 ----1 ----1 ----1 ----1 ----1 --- H 1 1 1 1 ----1 ----1 ----1 ---- 1 ----1 ----1 ----r 02 83 84 85 86 87 Y E A R Figure 4.15 Temporal variation of coda 1/Q for time window 15-30 sec at 6 Hz in subarea 1. (1/Q)* 1000 (15-30 Sec) 12 Hz 1 < o W YEAR Figure 4.16 Temporal variation of coda 1/Q for time window 15-30 sec at 12 Hz in subarea 1. (1/Q)* 1000 (15-30 Sec) 24 Hz 1 -* I * ------ 1 ------ 1 ------ 1 ------1 ------ 1 ------ 1 ------1 ------ 1 ------ 1 ------ 1 ------ 1 ------1 ------ 1 ------ 1 ------ 1 ------ 1 ------1 ------ 1 ------ 1 ------ 1 ------ 1 ------1 ------ 1 ------ H < U GO o ' C O o 82 H 1 ----1 ----1 ---- 1 ----1 ----1 ----1 ---- 1 ----1 ----1 ----1 ---- 1 ----1 ----1 ----1 ---- 1 ----1 ----1 ----1 ----1 ----f - 83 84 85 Y E A R 86 87 CO 4 ^ Figure 4.17 Temporal variation of coda 1/Q for time window 15-30 sec at 24 Hz in subarea 1. H h ^ 1 --- 88 ( 1/Q )*1000 (20-45 Sec) 1.5 Hz 1 lO — 85 86 83 87 82 Y E A R Figure 4.18 Temporal variation of coda 1/Q for time window 20-45 sec at 1.5 Hz in subarea 1. (1/Q)*1000 (20-45 Sec) 3 Hz 1 C D — 83 02 85 84 86 87 88 C D 0 5 Y E A R Figure 4.19 Temporal variation of coda 1/Q for time window 20-45 sec at 3 Hz in subarea 1. ( 1/Q )*1000 2 .5 3 3.5 (20-45 Sec) 6 Hz 1 ^ — i— i — i — |— i— I — i— i — |— i — i — i — i — |— i— i— i — i— |— i— i— i — i— |— i — h w- in ■ H 1 ------1 ------1 ------1 -------1 ---- 1 ----- 1 ----- 1 ------1 -----1 ------ 1 ----- 1 ------1 ----- 1 ----- 1 ----- 1 ----- 1 ----- 1 -------- 1 -- 1 ------1 ----- 1 ------1 ---------1 -- 1 ------H 82 83 84 85 86 87 C D -j YEAR Figure 4.20 Temporal variation of coda 1/Q for time window 20-45 sec at 6 Hz in subarea 1 . ■ \ — i— 88 ( 1 /Q )* 1 0 0 0 (20-45 Sec) 12 Hz 1 H 1 ------1 ------1 ------ 1 ------ 1 ------ 1 ------1 ------ 1 ------1 ------ 1 ------ 1 ------ 1 ------ 1- H 1 ----1 ----1 ---- 1 ----1 ----h 0 2 — L O CO 0 0 85 Y E A R Figure 4.21 Temporal variation of coda 1/Q for time window 20-45 sec at 12 Hz in subarea 1. (20-45 Sec) 24 Hz 1 v H 00 o co o 86 84 82 86 Y EA H Figure 4.22 Temporal variation of coda 1/Q for time window 20-45 sec at 24 Hz in subarea 1. (1/Q)*1000 (30-60 Sec) 1.5 Hz 1 H 1 ----1 ----1 ---- 1 ----1 ----h H 1 ---- 1 ----1 ----h CV 2 co co— —I 1 1 1 1 h — H 1 1 1 1 1 1 1 ( 1 1 H 82 83 84 85 — 1 — i — i — i — i — — i — i — i — H 86 87 88 t o o o YEAR Figure 4.23 Temporal variation of coda 1/Q for time window 30-60 sec at 1.5 Hz in subarea 1. (i/Q)nooo (30-60 Sec) 3 Hz 1 83 04 82 t o © Y E A R Figure 4.24 Temporal variation of coda 1/Q for time window 30-60 sec at 3 Hz in subarea 1. (30-60 Sec) 6 Hz 1 co— C V 2 — 63 84 86 87 g YEAR Figure 4.25 Temporal variation of coda 1/Q for time window 30-60 sec at 6 Hz in subarea 1 . (i / q)*iooo (30-60 Sec) 12 Hz 1 83 82 84 Y E A R Figure 4.26 Temporal variation of coda 1/Q for time window 30-60 sec at 12 Hz in subarea 1. ( l/Q )*1000 0.6 0.8 (30-60 Sec) 24 Hz 1 H 1 ------ 1 ------ 1 ------ 1 ------ t ------ 1 ------ 1 ------ 1 ------ 1 ------ 1 ------ 1 ------ 1 ------ 1 ------ 1 ------ 1 ------ 1 ------ 1 ------ 1 ------ 1 ------ 1 ------ 1 ------ 1 ------ 1 ------ 1 ------ 1 ------ 1 ------ 1 ------ f t o O H 1 ------1 ------1 ------ 1 ------1 ------1 ----- 1 ------ 1 ------1 ----- 1 ------1 ------ 1 ------1 ----- 1 ------1 ------ 1 ------1 ----- 1 ------1 ------ 1 ----- 1 ------1 ----- h 62 63 84 65 Y E A R 66 67 88 Figure 4.27 Temporal variation of coda 1/Q for time window 30-60 sec at 24 Hz in subarea 1. ( l/Q ) * 1 0 0 0 H 1 ---- 1 ----1 ----h (20-45 Sec) 3 Hz 2 H 1 ----1 ----1 ----1 ----1 ----1 ----1 - H 1 ----1 ---- 1 ----1 ----1 ----1 - C D - T*-- to o C m YEAR Figure 4.28 Temporal variation of coda 1/Q for time window 20-45 sec at 3 Hz in subarea 2. ( 1/Q )»1000 <0 - - lO — co-- 0 2 to o OS (2 0 -4 5 Sec) 3 Hz 3 H 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ----1 1 1 1 1 1 ( 1 1 - * -------- ‘ ----'----1 ----* ----1 ----* ----i ----1 ----1 ----1 ----1 ----1 ----1 ----1 ----1 ----1 ----1 ----1 ----1 ----1 ----1 ----1 ----1 ----1 ----1 ----1 ---- 03 04 85 YEAR 86 87 8 8 Figure 4.29 Temporal variation of coda 1/Q for time window 20-45 sec at 3 Hz in subarea 3. ( 1 /Q )* 1 0 0 0 (20-45 Sec) 3 Hz 4 to o C D lO * H h - i 1 ----1 ----1 ----1 ----1 ----1 --- 1 ----1 ----1 ----1 ----h H 1 h - I 1 ----- 1 ----- 1 ----- 1 ----- 1 ----- 1 ----- 1 ----- 1 ----- 1 ----- 1 ----- 1 ----- 1 ----- 1 ----- 1 ----- 1 ----- 1 ----- 1 ----- 1 ------ 1 ----- 1 ----- 1 ----- 1 ------ h 02 83 84 85 86 87 YEAR Figure 4.30 Temporal variation of coda 1/Q for time window 20-45 sec at 3 Hz in subarea 4. (i/Q)nooo (20-45 Sec) 3 Hz 5 H 1 ----1 ----1 ---- 1 ----1 ----1 ----1 ---- 1 ----1 ----1 ----1 ---- 1 ----1 --- 1 - H 1 ----1 ---- 1 ----1 ----1 ----1 - C O — t o o 00 Y E A R Figure 4.31 Temporal variation of coda 1/Q for time window 20-45 sec at 3 Hz in subarea 5. (1/Q )*1000 (20-45 Sec) 3 Hz 6 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 • 1 • --- r— C D — lO— -H 1 ----1 ----1 ----1 — 82 63 - i 1 ----- 1 ----- 1 -----1 -----1 -----1 -----H 84 85 Y E A R H 1 ----1 ----H 86 H 1 ---- 1 ----1 ----H 87 t o o CO Figure 4.32 Temporal variation of coda 1/Q for time window 20-45 sec at 3 Hz in subarea 6. (1/Q)*1000 (20-45 Sec) 3 Hz 7 H 1 ---- 1 ----1 ----1 ----1 ---- 1 ----1 ----1 ----h H 1 ---- H H 1 h C D - lO — 00 - - I 1 ------ 1 ------ 1 ------ 1 ------ 1 ------ 1 ------ 1 ------ 1 - - - - - - 1 ------ 1 - ----- 1 -- - - - - 1 -- - - - - 1 -- - - - - 1 ------ 1 -- - - - - 1 ------ 1 - - - - - - 1 -- - - - - 1 - - - - - - 1 ------ 1 - - - - - - 1 - - - - - - 1 - - - - - - - 1 - - - - - - i- - - - - - 1 - - - - - - ( - 82 83 84 85 86 07 88 Y E A R Figure 4.33 Temporal variation of coda 1/Q for time window 20-45 sec at 3 Hz ° in subarea 7. to (i/Q )nooo (20-45 Sec) 3 Hz 8 04 Y E A R Figure 4.34 Temporal variation of coda 1/Q for time window 20-45 sec at 3 Hz in subarea 8. ( 1/Q )*1000 (20-45 Sec) 12 Hz 2 02 03 04 Y E A R Figure 4.35 Temporal variation of coda 1/Q for time window 20-45 sec at 12 Hz in subarea 2. (1/Q )*1000 (20-45 Sec) 12 Hz 3 H 1 ------ 1 ------1 ------- 1 ------ 1 ------ 1 ------ 1 ------- 1 ------ 1 ------1 ------ 1 ------- 1 ------1 ------ 1 ------ h H 1 ------ 1 - C \2 — in t o t — 1 CO 82 H 1 - - - - - 1 ------i - - - - - ------ 1 ------1 ------ 1 ------1 - ----- 1 ------1 - - - - - 1 ------1 ------ 1 - - - - - 1 - - - - - 1 - - - - - 1 ------ 1 ------1 ------ 1 ------1 ------ 1 - - - - - 1 - - - - - 1 - 83 84 85 Y E A R 86 87 Figure 4.36 Temporal variation of coda 1/Q for time window 20-45 sec at 12 Hz in subarea 3. (20-45 Sec) 12 Hz 4 83 85 88 Y E A R Figure 4,37 Temporal variation of coda 1/Q for time window 20-45 sec at 12 Hz in subarea 4. (i/Q)nooo (20-45 Sec) 12 Hz 5 1 ------ 1 ------ 1 ------ 1 ------ 1 ------ 1 ------ 1 ------ 1 ------ 1 ------ 1 ------ 1 ------ 1 ------- 1 ------ 1 ------ 1 ------1 ------ 1 ------ 1 ------1 ------ 1 ------- 1 ------ 1 ------ 1 ------ h C V I- t o Y E A R Figure 4.38 Temporal variation of coda 1/Q for time window 20-45 sec at 12 Hz in subarea 5. ( i / q)* iooo (20-45 Sec) 12 Hz 6 H 1 ------ 1 ------- 1 ------ 1 ------ 1 ------1 ------ 1 ------ 1 ------1 ------ 1 ------ 1 ------1 ------ 1 ------1 ------- 1 ------ 1 ------ 1 ------1 ------- 1 ------ 1 ------ h C M — ID 82 83 84 85 YEAR 86 87 88 to i-* o Figure 4.39 Temporal variation of coda 1/Q for time window 20-45 sec at 12 Hz in subarea 6. (1/Q)* 1000 (20-45 Sec) 12 Hz 7 85 86 83 84 82 Y E A R Figure 4.40 Temporal variation of coda 1/Q for time window 20-45 sec at 12 Hz in subarea 7. (1/Q)*1000 C \2 ■ (20-45 Sec) 12 Hz 8 H ------ 1 ------ 1 ------ 1 ------ h H 1 ------- 1 ------1 ------1 ------1 ------ 1 ------1 ------1 ------1 ------ 1 ------ 1 ------h I H 1 H H I 1 ----- 1 -----1 -----1 -----h 82 83 84 85 86 t o h -1 0 0 YEAR Figure 4.41 Temporal variation of coda 1/Q for time window 20-45 sec at 12 Hz in subarea 8. th e flunctuation am ong subareas is considerable and we cannot find any system atic change which m ay be a ttrib u te d , say, to a steady m igartion along th e plane boundary as proposed by Savage (1971) for creep in the ductile paxt of p late boundary. In view of flunctuations am ong different tim e- windows and frequencies (figure 4.13 thro u g h 4.27) and am ong different subareas, we can only conclude th a t the tem poral change in coda Q ~x was sim ultaneous throughout southern C alifornia w ithin th e scatter of our observations. S P A T IA L P A T T E R N O F C O D A Q ~l C H A N G E B E F O R E A N D A F T E R J A N U A R Y 1 , 1986 In figure 4.13 through 4.41 showing the tem poral variations in coda Q ~l for different tim e-w indows, frequencies and subareas, we noticed th a t th e increase after 1985 is not clear in certain cases. T here is the possibility th a t th e am ount of increase or even its sense varies from place to place. To be m ore q u an titativ e, we com pared m ean coda Q ~l values for each 0.2° xO.2° m esh introduced in chapter 3 separately calculated for th e e a rth quakes which occurred before and after Jan u ary 1, 1986. Figures 4.42 through 4.51 show the sign of difference betw een th e two values (solid cir cles for increase in the m ean coda Q -1 and open circles for the decrease in th e m ean coda Q ~l after Jan u ary 1, 1986) for two tim e windows and five frequency bands. T he result for tim e window 30 to 60 sec is not shown be cause of less clear p a tte rn th a n the o th er windows due probably to excessive spatial averaging. For b o th tim e windows, 15-30 and 20-45 sec, the coda Q ~ 1 increased 2 1 9 Latitude (N) 153015/<86> C O C O CO in C O C O 116 120 122 Longitude (W) Figure 4.42 Sign of difference in showing the two values in the mean of coda 1/Q before and after Jan. 1, 1986 with time window 15-30 sec at 1.5 Hz. 2 2 0 Latitude (N) 15303/<86> CO ZD CO o o CO CO CO Longitude (W) Figure 4.43 Sign of difference in showing the two values in the mean of coda 1/Q before and after Jan. 1, 1986 with time window 15-30 sec at 3 Hz. 2 2 1 Latitude (N) 15306/<86> CO CO CO Longitude (W) Figure 4.44 Sign of difference in showing the two values in the mean of coda 1/Q before and after Jan. 1, 1986 with time window 15-30 sec at 6 Hz. 2 2 2 Latitude (N) 1 5 3 0 1 2 /<86> CO CO CO C O ' C\? C O 120 116 Longitude (W) Figure 4.45 Sign of difference in showing the two values in the mean of coda 1/Q before and after Jan. 1, 1986 with time window 15-30 sec at 12 Hz. 223 Latitude (N) 153024/<86> co CD CO U O C O CO 120 LongiHide (W) Figure 4.46 Sign of difference in showing the two values in the mean of coda 1/Q before and after Jan. 1, 1986 with time window 15-30 sec at 24 Hz. 224 Latitude (N) 2 0 4 5 1 5 /<86> co C D CO CO CO CO 20 116 LonL'ii ude (W) Figure 4.47 Sign of difference in showing the two values in the mean of coda 1/Q before and after Jan. 1, 1986 with time window 20-45 sec at 1.5 Hz. 225 Latitude (N) 20453/< 86> co C O CO C O CO 120 116 Longitude (W) Figure 4.48 Sign of difference in showing the two values in the mean of coda 1/Q before and after Jan. 1, 1986 with time window 20-45 sec at 3 Hz. 2 2 6 Latitude (N) 2 0 4 5 6 /<86> L O CO CO o o o o CO CO cv C O . 120 122 Longitude (W) Figure 4.49 Sign of difference in showing the two values in the mean of coda 1/Q before and after Jan. 1, 1986 with time window 20-45 sec at 6 Hz. 227 Latitude (N) 2 0 4 5 1 2 /<86> C O CO L O C O Tf__ CO CO CO cv 120 Lonsitudf* (W) Figure 4.50 Sign of difference in showing the two values in the mean of coda 1/Q before and after Jan. 1, 1986 with time window 20-45 sec at 12 Hz. 228 Latitude (N) 2 0 4 5 2 4 /<86> co C D C O C O CO 20 116 Longii ude (W) Figure 4.51 Sign of difference in showing the two values in the mean of coda 1/Q before and after Jan. 1, 1986 with time window 20-45 sec at 24 Hz. 229 for 75% of th e m eshes, and decreased for 25% of them . T he d istrib u tio n of increased and decreased meshes shows a ra th e r system atic p atte rn . In order to show th e p a tte rn m ore concisely, we classified meshes into two groups for each tim e window. In one of them , the coda Q ~l decreased for m ore th a n one frequency bands. In the o ther, the coda Q -1 decreased at m ost for one frequency band. Figures 4.52 and 4.53 show these two groups of m eshes for the tim e window 15-30 and 20-45 sec respectively (solid circles for th e coda Q~l decrease at m ost for one frequency band and open circles for the coda Q~l decrease for m ore th a n one frequency bands). T he 20-45 sec tim e window result gives a broader geographic coverage b u t w ith stro n g er sp atial sm oothing th a n the 15-30 sec tim e window. B oth figures, however, show essentially the sam e p a tte rn . T he stronger increase in coda Q ~ 1 occurred in several distinct regions, each surrounded by a zone in which coda Q ~l decreased for m ore th a n one frequency bands. This is rem inscent of M ogi’s (K anam ori,1981; M ogi,1985) donut m odel in which an area of precursory quiescence is surrounded by a zone of increased seismicity. Peng et al. (1987, in th e appendix) also discussed this type of m odel in explaining the tem poral-spatial change in coda Q~l associated w ith the R ound Valley earthquake of 1984. T he area of increased coda Q ~l includes th e Coachella valley segm ent of the San A ndreas fault for which the highest probability of occurrence of m ajo r earthquakes has been assigned am ong all m ajo r fault segm ents in California. It also includes the Los Angeles basin (figure 4.53 shows a zone of increased coda Q~l roughly coinciding th e N ew port-Inglew ood fau lt) and th e sou th ern end of th e Sierra N evada fault. 2 3 0 Latitude (N) 15— 30 Sec C D CO C O 120 '122 116 118 L o n g itu d e (W) Figure 4.52 Mogi's donut-lipke pattern for time window 15-30 sec. 231 Latitude (N) 2 0 -4 5 Sec co C O . 120 116 L o n g itu d e (W) Figure 4.53 Mogi’s donut-lipke pattern for time window 20-45 sec. 232 In order to m ake sure if th e M ogi’s donut-like p a tte rn is not due to th e artifact insufficient num ber of m idpoints near the peripheral m eshes, we show th e num ber of m idpoints used for com puting the difference in m ean Q ~l values before and after Jan ., 1986, for two tim e-w indow s and five frequency bands in figures 4.54 th ro u g h 4.63. C om paring them w ith figures 4.52 and 4.53 for tim e windows 15-30 sec and 20-45 sec respectively, we find th a t some m eshes showing th e decrease in Q~x contain sufficient num ber of m idpoints. Thus, the M ogi’s donut-like p a tte rn m ay be real at least in p art. If we consider the area w ith increased coda Q ~l is in p rep aratio n for a m ajo r earthquake in the m anner sim ilar to the M ogi’s donut m odel, the N orth P alm Springs earthquake of 1986, the W hit tier-N arrow s earthquake of 1987, and the S uperstition Hills earthquake of 1987 m ay belong to ac tive zones surrounding the area of a m ajor earth q u ak e p rep aratio n . On the o th er h and, in th e case of the R ound Valley earth q u ak e of 1984, the anom a lous increase in coda Q ~l occurred in the Long Valley caldera outside th e epicentral area of the m ainshock. In o ther words, those three already oc curred m oderate-sized earthquakes m ight be responsible for the observed change in coda Q ~ l . Yet an o th er possibility is th a t the observed coda Q ~ l which we now believe has physical reality m ay have no relation w ith the occurrence of m ajo r earthquakes. Obviously, we need m any m ore m easurem ents of coda Q -1 and case histories in relatio n to the occurrence of m ajo r earthquakes to establish th e coda Q ~l as a reliable earthquake precursor. For this purpose, in the 233 Latitude (N) 1 5 3 0 1 5 co C O CO CO C\2 C O , 116 122 120 L o n g itu d e (W) Figure 4.54 Number of midpoints used for computing the difference in the mean of coda 1/Q for time window 15-30 sec at 1.5 Hz. 234 Latitude (N) 15303 CO CD CO CO CO CO 116 122 120 L o n g itu d e (W) Figure 4.55 Number of midpoints used for computing the difference in the mean of coda 1/Q for time window 15-30 sec at 3 Hz. 235 Latitude (N) 15306 00 in CO CO CO CO C\2 CO 122 120 116 L o n g itu d e (W) Figure 4.56 Number of midpoints used for computing the difference in the mean of oda 1/Q for time window 15-30 sec at 6 Hz. 236 Latitude (N) 153012 co uo co oo 0 0 00 118 L o n g itu d e (W) 120 116 122 Figure 4.57 Number of midpoints used for computing the difference in the mean of coda 1/Q for time window 15-30 sec at 12 Hz. 2 3 7 Latitude (N) 153024 CD___ CO CO C O C O 120 116 122 L o n g itu d e (W) Figure 4.58 Number of midpoints used for computing the difference in the mean of coda 1/Q for time window 15-30 sec at 24 Hz. 238 Latitude (N) 2 0 4 5 1 5 CO C O C O C O 118 L o n g itu d e (W) 116 122 120 Figure 4.59 Number of midpoints used for computing the difference in the mean of coda 1/Q for time window 20-45 sec at 1.5 Hz. 2 3 9 Latitude (N) 20453 CO 1 St 1 C O C O C\2 CO 116 118 120 122 L o n g itu d e (W) Figure 4.60 Number of midpoints used for computing the difference in the mean of coda 1/Q for time window 20-45 sec at 3 Hz. 240 Latitude (N) 2 0 4 5 6 co in co CO C\2 CO. 118 122 120 L o n g itu d e (W) Figure 4.61 Number of midpoints used for computing the difference in the mean of coda 1/Q for time window 20-45 sec at 6 Hz. 2 4 1 Latitude (N) 2 0 4 5 1 2 co CO m co CO C\2 CO, 116 118 122 120 L o n g itu d e (W) Figure 4.62 Number of midpoints used for computing the difference in the mean of coda 1/Q for time window 20-45 sec at 12 Hz. 242 Latitude (N) 2 0 4 5 2 4 co C O CO m co co co co C\2 CO, 116 120 122 L o n g itu d e (W) Figure 4.63 Number of midpoints used for computing the difference in the mean of coda 1/Q for time window 20-45 sec at 24 Hz. 243 rem ainder of this chapter, we shall give a special atte n tio n to th e tem poral variation of coda Q~1 in the vincinities of the th ree m oderate-sized earthqaukes occurred recently in southern California. T E M P O R A L C H A N G E IN C O D A Q ~l A N D b -V A L U E A S S O C IA T E D W I T H R E C E N T T H R E E M O D E R A T E -S IZ E D E A R T H Q U A K E S I N S O U T H E R N C A L IF O R N IA T he three m oderate-sized earthquakes, of which we like to present the case history of coda Q ~l precursor, are the N orth P alm Springs e a rth quake of July 8,1986 (M = 5.6), the W hit tier-N arrow s earth q u ak e of O ct. 1, 1987 (M = 5.9) and the the S uperstition Hills earthquakes of Nov. 24, 1987 (M = 6.2 and 6 .6 ). Figure 4.64 shows the three separate rectan g u lar regions centered at the epicenters of above three erathquakes. T hey are m arked as re gion I(LA B ), II(N P ) and III(S S JC ) for the W hit tier-N arrow s, N orth Palm Springs and S uperstition Hills earthquake, respectively. For region II, we also consider a sm aller region IF of size of 0.4° x 0.4°. T h e tem poral varia tion of coda Q ~ l for each of these regions is calculated in the sam e m anner as was done earlier for subareas 1 through 8 . As a m a tte r of fact, region I is alm ost identical to subarea 4, and region III to sub area 1. Nevertheless, we shall show, for convenience, coda Q ~l at 1.5 Hz for region I in figure 4.65 for the tim e window 20-45 sec, for region II and II’ in figure 4.67 and 4.68, respectively, for th e tim e w'indow 15-30 sec, and for the region III in figure 4.70 for the tim e window 30-60 sec. T he choice of earlier window for region II and I I ’ is because of som ew hat localized n atu re of the anom aly 244 L a t i t u d e ( N ) CO CO • o in CO CO CO CO 122 120 116 Longitude ( W ) Figure 4.64 Regions I, II, 1 1 ' and HI used for the temporal change of coda 1/Q with the occurrence of three recently occurred moderate-sized earthquake. 2 4 5 associated w ith the N orth P alm Springs earthquake (Su and Aki, 1989), and the choice of later tim e window for region III is to increase th e am ount of available d ata. In all cases, we find a peak in coda Q ~ 1 ab o u t one year before th e occur rence of m ainshock, and th e m ainshock occurrs w hen coda Q - 1 is decreas ing. T his behavior is th e m ost typical one rep o rted by o th er researchers as discussed earlier. A ccording to Im oto (1988) and S m ith (1986), a sim ilar p a tte rn has been rep o rted for the tem poral change of b-value before several earthquakes in Jap an , New Zealand and California. We, therefore, decided to com pute the b-value for our cases. A continuous catalog of earthquakes in sou th ern C alifornia obtained from CIT-U SG S seismic netw ork which starts from 1982 was used to select the earthquakes for calculation of b-value. Using this catalog, we chose earthquakes located w ithin regions I,II’ and III.. We th en calculate the b-value by the use of U tsu-A ki form ula given by = J o g e M - Mo w here e is the exponential co nstant, M is the average m agnitude of all e a rth quakes w ith m agnitudes above threshold m agnitude M q. In our case, M is the average m ag n itu d e over 70 consecutive earthquakes and the threshold m agnitude M 0 is chosen as 2.0. The calculated b value is p lo tted at the m edian of origin tim e of earthqukaes used for the calculation. T he resu ltan t b-value vs. tim e plots are shown in figure 4.66 for region I, figure 4.69 for region II’ and figure 4.71 in region III. T he neighbouring p oints in these figures share the sam e 35 earthquakes. A lthough the p a tte rn s of tem poral 246 0001.(b/i) (20— 45 Sec) 1.5 Hz L A B H 1 ---- 1 ----h- | < ---- 1 ---- 1 ---- 1 ---- |---- 1 ---- I ---- 1 ---- 1 ---- 1 ---- 1 ---- 1 ---- 1 ---- 1 ---- 1 ---- 1 ---- 1 ---- 1 ---- 1 ---- 1 ---- 1 ---- 1 ---- 1 ---- 1 - CM__ O __ 00— L 82 H — i— i— i— — I — i— i— i— — i— i— i— i— — i— y ■ ■ t < — — i— » — i— i- 83 8 5 Y E A R 88 H 1 H to Figure 4.65 Temporal variation of coda 1/Q with the occurrence of Whittier- Narrows earthquake of Oct. 1,1987 for time window 20-45 sec at 1.5 Hz. L A B (70) C M — 83 84 82 YEAR to Figure 4.66 Variation of b-value with the occurrence of Whittier-Namows o o earthquake of Oct. 1,1987 in region I. ( 1/Q)* 1000 (15-30 Sec) 1.5 Hz NP (larger box) to co Y E A R Figure 4.67 Temporal variation of coda 1/Q with the occurrence of North Palm Springs earthquake of July 8,1986 for time window 15-30 sec at 1.5 Hz in region II. (i/Q)nooo ( 1 5 - 3 0 Sec) 1.5 Hz NP - i — i — i — i — |— i — i — i — i — |— i — i — i — i — |— i — i — i — i — |— i — i — t— i — [ 00 < o _ _ CM__ to C f x o C O H 1 -------- 1 -------- 1 -------- 1 --------- 1 -------- 1 -------- 1 -------- 1 ------------- 1 ----1 -------- 1 -------- 1 -------------- 1 ----1 ------- H-------- 1 --------- 1 -------- 1 --------♦--------1 -------- 1 -------- 1 ------- 82 83 84 85 86 87 YEAR Figure 4.68 Temporal variation of coda 1/Q with the occurrence of North Palm Springs earthquake of July 8,1986 for time window 15-30 sec at 1.5 Hz in region II'. NP(70) I jo 06 84 85 82 Y E A R Figure 4.69 Variation of b-value with the occurrence of North Palm Springs t-1 earthquake of July 8, 1986 in region IT . (1/Q)*1000 (30-60 Sec) 1.6 Hi SSJC o__ C 0 - - 84 Y E A R Figure 4.70 Temporal variation of coda 1/Q with the occurrence of Superstition Hills earthquake of Nov. 24, 1987 for time window 30-60 sec at 1.5 Hz. 2.5 SSJC(70) CM - - 83 82 86 87 88 YEAR Figure 4.71 Variation of b-value with the occurrence of Superstition Hills earthquake of Nov. 24,1987 in region III. change are not exactly th e sam e betw een the coda Q ~ l and b-value, it is cleax th a t th e general tre n d is sim ilar to each other. T he correlation is def initely positive in agreem ent w ith the result of Jin and Aki (1989) obtained from th e Riverside record for th e 55-year period since 1933. In ch ap ter 5, we shall address the physical m echanism for tem poral v ariation in coda £?_1, an d show th a t the creep m odel proposed by Jin and Aki (1989) for explaining th e observed correlation betw een coda Q ~x and b-value is supported by our new observations given in this chapter. 254 C H A P T E R V P H Y S IC A L M E C H A N IS M F O R T E M P O R A L V A R IA T IO N IN C O D A Q~l I N T R O D U C T I O N As m entioned earlier th e coda Q ~l depends on frequency in the form ( \ m y-j , for f > f 0 = 1 Hz, and Qq 1 shows a strong positive correlation w ith seism icity in th e sp atial dom ain. Seismi- cally active regions such as Ja p a n and C alifornia always show higher Qq 1 and m as com pared to stable regions such as the C an ad ian shield an d th e eastern U nited S tates. T he positive correlation betw een Qq 1 an d seism icity was a ttrib u te d by Jin and Aki (1989) to the well know n relatio n betw een seismic atten u atio n and th e crack density (e.g. O ’Connell and B udiansky (1974)). Thus, th e m ore severe th e lithosphere is fractu red , th e higher Qq 1 becom es. However, for th e case of coda Q~l variation in tim e, the rela tion of coda Q ~ 1 w ith seism icity is not so sim ple as th a t in th e case of coda Q ~ l change in space. For exam ple, the anom alously high coda Q ~l is som etim es observed during the period of seismic quiescence, and in m any cases, th e aftershocks usually show low coda Q ~l in spite of th eir high rate of occurrence. F urtherm ore, the tem poral variation of coda Q ~l and th a t of b-value shows positive correlation in some cases such as sou th ern Cali fornia discussed in C h ap ter 4, b u t show negative correlation in o th er cases (N ovelo-Casanova, 1985; Jin and Aki, 1986). In order to explain above com plex tem poral behavior of coda Q ~l change, Jin and Aki (1989) exam ined its physical m echanism from the following three view points, nam ely th e fractal m odel, the dilatancy-diffusion m odel and the creep m odel. They 255 concluded th a t the creep m odel explained all th eir significant observations. Here, we shall describe their m odels and discuss if new results o btained in this thesis are consistent w ith their conclusion or not. F R A C T A L M O D E L T he fractal n a tu re of 3-D inhom ogeneities in th e lithosphere as evi denced from seism ic waves scattering was first stu d ied by W u (1985). He introduced th e concept of bandlim ited fractal random m edium (B LFR M ) to characterize the observed power law frequency dependence of th e ap p arent a tte n u a tio n assum ing th a t th e a tten u a tio n is due to scatterin g by the B L FR M . W u showed th a t the fractal dim ension D of inhom ogeneity is related to the power m by D — 3 — m /2 . T hus, a stable region has larger fractal dim ension D corresponding to sm aller m as com pared to the seism ically active region. A nother fractal view point was taken by Sato (1988a) who considered th a t the scatterers are d istrib u ted fractally w ith a fractal dim ension D. As sum ing th a t th e num ber of scatteres in a sphere of radius R is proportional to R d , he found th a t the power of tim e t in th e coda power decay repre senting th e geom etrical spreading factor becom es equal to [(D — 2)k — 3] for th e k — th order scattering. In other words, th e stronger decay in coda waves pow er occurs for sm aller fractal dim ension. T hen, the seism ically active region w ith stronger coda decay will have sm aller fractal dim ension. T he above relation betw een D and coda decay predicted by S ato ’s th e ory is a ttra c tiv e because it m ay offer a link betw een th e coda Q ~l precursor (often showing peak in Q ~x before th e earth q u ak e as discussed in C hap 256 te r 4) and various precursors obtained from th e catalogue of earthquakes such as quiescence, sw arm s, b u rsts and o ther seism icity precursors (see e.g. G abrielov et al. (1986)). T hese seism icity precursors m ay be considered as m anifestation of intensified clustering and localization of fractures. P re cursory clustering of fractu res is also supported by th e observed general increase in th e variance of coda Q -1 m easurem ents as p ointed out by Sato (1988b). T he intensified clustering would correspond to decrease in fractal dim ension. T hen, the positive correlation betw een b-value and coda Q ~x corre sponds to the negative correlation betw een b and D, while th e negative correlation betw een b-value and coda Q -1 to th e positive correlation be tw een b and D. T he positive correlation betw een b and D was proposed by Aki (1981) from a h y pothetical process of generating sm all events from large ones, and has been sup p o rted by T urcotte (1986), K ing (1984) and others. On the o th er hand, H irata (1988) found a negative correlation be tw een observed b-value and fractal dim ension D estim ated from the spatial d istrib u tio n of epicenters in Jap an . It m ay be th a t there are two distinct seismic regim es; coda Q ~x corre lates negatively w ith b and b correlates positively w ith D in one of them , an d th e senses of correlation are reversed in th e other. As Jin and Aki (1989) pointed out, however, S ato ’s (1988a) theory m ay not be applicable to the coda Q ~x studied by them , because th e observed Q ~x is clearly re lated to th e exponential law p a rt and not to th e pow er law p a rt (ao of th eir p ap er) of the decay. In fact, th e observed power ao did not show any correlation w ith b-value contradicting the prediction by S ato ’s theory. F ur therm ore, it is difficult to explain from this view point w hy th e observed 257 coda Q 1 and b ten d to decrease im m ediately before m ainshocks, which would im ply declustering or anti-localization. O ur new results given in C h ap ter 4 reinforce the above argum ents against th e fractal m odel. O ur coda Q ~l clearly expresses the exponential p art of th e coda decay, and bo th coda Q ~l and b-value showed decrease im m ediately before all three earthquakes we investigated. DILATANCY-DIFFUSIO N MODEL In a review on m echanism of precursory seismic quiescence, Scholz (1988) argued persuasively for dilantancy hardening coupled w ith the K aiser effect to be the cause of quiescence. Let us try to in terp rete the correlation betw een coda Q ~ 1 and b-value by dilatancy-diffusion m odel. A key elem ent of th e dilatancy-diffusion m odel (N ur, 1972; Scholz et al, 1973; A nderson and W hitecom b, 1975) is , of course, dilatancy or open ing of cracks th a t will reduce the pore pressure and increase the frictional stren g th of fau lt. O pening of cracks would cause g reater scatterin g and a tte n u a tio n for seismic waves, and coda Q ~l would increase. Increase in frictional stren g th would cause quiescence. T his w ould explain th e observed change in coda Q ~ 1 and seism icity before th e M isasa earth q u ak e discussed earlier (T su k u d a, 1987). This, however, contradicts equally convincing ev idences of R obinson (1987) who found th a t low coda Q ~l coincides w ith a low ra te of seismicity. Since th e stress concentration is greater for larger cracks under the sam e applied stress, we m ay expect th a t dilatan cy could occur preferentially for larger cracks, and larger events becom e relatively quiet as com pared to 258 th e sm aller events, m aking b-value greater. T his would explain observed cases of positive correlation betw een coda Q ~1 and b-value, b u t not cases of negative correlation. M ore fundam entally, dilatancy-diffusion is a recurring process in e a rth quake cycles. T he tem poral variation of coda Q ~l and b-value for southern C alifornia during th e p ast 55 years observed by Jin and Aki (1989) do not seem to belong to such a sim ple category. It appears th a t they change som etim es in close relation w ith the occurrence of m ajo r earthquakes b u t no t always so. Some of the observed change in coda Q ~ 1 and b-value m ay belong to the category of ” tectonic precursors” ra th e r th a n th e category of ’’physical precursors” as discussed by Ishibashi (1988). T h e tectonic precursors are controlled m ainly by local tectonic settin g and have no di rect physical im plication in th e ru p tu re generating process for a p articu lar earth q u ak e fault. T he sim ultaneous increase in coda Q ~ 1 th ro u g h o u t the southern Cal ifornia after 1986 rep o rted in C h ap ter 4 indeed appears to be p a rt of the regional tectonic origin ra th e r th a n related directly to some specific fault segm ents. O ur new results thus reinforce Jin and A ki’s argum ents against th e dilatancy-diffusion m odel to explain the tem poral variation in coda Q - 1- C R E E P M O D E L A nother m echanism of seismic quiescence considered by Scholz (1988) is slip weakening (e.g. S tu a rt, 1979), in which stable slip prior to an e a rth quake causes a reduction in stress. W yss and H ab erm an n (1988) prefer 259 this m echanism to dilatancy hardening, because (1) th e la tte r is difficult to reconcile w ith th e observation th a t th e im m ediate hypocentral volum e shows no quiescence tendency and (2) at least for th e K alap an a earthquake of 1975, geodetic observations supported the reduced stress during th e qui escence period. T he slip-weakening m echanism has been d em o n strated using num erical experim ents by Cao and Aki (1985) to cause quiescence if a suitable critical w eakening displacem ent is chosen for th e m odel. T hey fu rth er suggested th a t quiescence should occur only for earthquakes w ith m agnitudes greater th a n a threshold m agnitude determ ined by the critical w eakening displace m ent. In fact, th e precursory peak in b-value observed by Sm ith (1986) and Im oto (1988) is consistent w ith this suggestion if b-value is determ ined for m agnitude range above and containing the thresh o ld m agnitude. If in creased stable sliding increases crack density and consequently coda Q - 1 , we shall have a period of seismic quiescence in which b o th coda Q ~ 1 and b-value increase. T his corresponds to the case of th e M isasa earth q u ak e discussed earlier. In fact, according to Im oto (1988), the quiescence ap peared for M >1.75, while in the sam e period earthquakes w ith 1.5< M < 1.75 showed steady increase w ith tim e sim ilar to exam ples discussed in Cao and Aki (1987). As m entioned earlier, in the case of T angshan earth q u ak e of 1976 the anom alously high coda Q~l period was coincident w ith th e low b-value period, co n trary to th e case of M isasa earthquake. A closer look at the original d a ta (Li et al, 1978) reveals th a t th e erathquakes w ith M >4.0 occurred at higher ra te and those w ith M <4.0 at lower ra te during this period th a n th e preceding norm al period. 260 Since coda Q~l often shows a m inim um during th e aftershocks, it is clear th a t the coda Q ~l does not represent the current seism icity in a short tim e span. Therefore, we should not relate th e high coda Q ~x during th e anom alous period for T angshan earth q u ak e directly to th e increase of seism icity for M >4.0. R ath er, we speculate th a t th e stable sliding or aseim ic creep is responsible for th e increase of coda Q ~ l . T he b-value m ay be reflecting seismic events which are related to aseimic creep. T he correlation betw een crrep and seism icity is intriguing as exem pli fied by creep on the San A ndreas fault. Creep on the San A ndreas fault has been studied since 1956 (Steinbrugge, 1960), an d the latest sum m ary of th e slip rate along th e fau lt from San Ju a n B a u tista to C holam e was given by B urford (1988). Since the creeping section of San A ndreas fault does not generate large earthquakes, it is clear th a t the correlation betw een seism icity and creep is negative for large m agnitude, say M > 7. B u rfo rd ’s sum m ary reveals a negative correlation also in a very small scale; th e seis m icity is relatively low in the central section where the slip ra te is highest. O n th e o th er hand, it is also tru e th a t th e seism icity of sm all earthquakes in general is m uch greater in the creeping section th a n in th e blocked sec tion of the San A ndreas fault. T hus, depending on th e sp atial scale and earth q u ak e m agnitude, th e correlation betw een creep and seism icity can be positive and negative. T he positive correlation betw een creep and seism icity m ay be a t trib u te d to the stress concentration caused by creep due to th e finite size of creeping crack. In fact, A ndrew s (1978) concluded from a consideration of energetics, th a t the observed statio n ary occurrence of a large num ber of sm all earthquakes requires eith er a generation of short wave length self 2 6 1 stress by a large earth q u ak e (which was used as th e basis for relating b-value w ith fractal dim ensions by Aki (1981)) or an occurrence of creep varying in am plitude of all length scales. Thus, the variation of coda Q ~l in short tim e span m ay be a ttrib u te d to the sta te of aseism ic fractu re which m ay have some effct caused by slip- weakening m echanism on seismic fracture. T he effect depends on the scale length of creep.T he seism icity m ay be depressed otherw ise, causing ap p aren t change in b-value, as well as quiescence. T hus, Jin and Aki (1989) assum ed th a t aseism ic activities tend to increase th e crack density and coda Q ~l in a seismic region. If the creep occurs w ith a certain predom inant crack size, the spatial stress concentration m ay enhance seism icity only for earthquakes w ith the com parable size. If this characteristic m agnitude M c is in the lower p art of the m agnitude range for which b-value is estim ated, the enhanced seism icity will show the increase in b. O n th e o th er hand, if M c is in th e u p p er p art of the m agnitude range, it will decrease b. T hen we can explain b o th positive and negative correlation betw een b-value and coda Q~l . For exam ple, th e difference betw een M isasa earth q u ak e and the Tang- shan earth q u ak e can be explained if th e creep scale length is sm all (corre sponding to 1 .5 < M C 1.75) for th e form er and large (correspond to 4< A fc< 5) for the latter. T he positive correlation found for so u th ern C alifornia m ay be explained if M c is in the lower p art of th e range of 3 < M < 6 . Jin and Aki (1989) fu rth er suggested th a t th e critical m agnitude M c m ay cause a d ep artu re of the frequency-m om ent relation from a sim ple self-sim ilar power-law relation and pointed out A ki’s (1987) finding of a kink in th e frequency-m agnitude relation for earthquakes recorded near the 2 6 2 N ew port Inglewood fault at m agnitude a little less th a n 3. T his critical m agnitude M c is also consistent w ith th e positive corre lation betw een coda Q~x and b-value for three southern C alifornia e a rth quakes rep o rted in C h ap ter 4, because these b-values were evaluated for th e m ag n itu d e range above 2. T hus, our new results support th e creep m odel proposed by the Jin and Aki (1989) to explain th e tem p o ral variation in coda Q ~x an d b-value. If th e creep m odel is correct, we can. m ake an interesting inference ab o u t the sp atial-tem poral behavior of creep in southern C alifornia from the observed sim ultaneous change in coda Q~l in C h ap ter 4. A pparently, creep does not propagate along th e Pacific-N orth A m erica p late b o u n d ary from south to n o rth w ith th e speed of on th e order of m ag n itu d e 10 k m /y r as suggested by Savage (1971). W ith in th e sca tte r of our m easurem ents, we could not recognize any clear m igration of creep ( coda Q ~x change) eith er south to n o rth or n o rth to south. T he change was sim ultaneous or th e m igration was faster th an a hundred kilom eters per year. From this observation, we feel th a t creep in th e lithosphere m ay not be narrow ly confined to th e San A ndreas fault b u t m ay be d istrib u ted broadly and diffusely along th e plate boundary. 2 6 3 C H A PT ER VI CONCLUSIONS In this chapter, we sum m arize m ajor conclusions from previous four chapters and recom m end fu rth er research directions by the use of coda m ethod. In ch ap ter 2, we developed an inexpensive an d effective num erical sim ulation approach to synthesize the coda envelope. T his m eth o d can easily incorporate effects of m ultiple sacttering, variation in th e source m echanism an d non-uniform d istrib u tio n of scatterers. T he sy n th etic coda envelope thus o btained showed excellent agreem ent w ith the theoretical prediction by G ao et al. (1983) for single, double and triple scattering. Using sta tis tically uniform ly d istrib u ted scatterers, we found the num ber of scatterers needed to satisfactorily approxim ate the random heterogeneous continuous m edium for coda decay curve to be about 100 for our case. O ur m ain sub ject of stu d y in this ch ap ter was th e physical m echanism for long-puzzled large variance of coda Q -1 m easurem ents in a given area. We were able to explain the observed coda Q ~l variance and its dependence on th e lapse tim e window as well as on frequency by a finite num ber of effective sc atte r ers. For exam ple, in the case of foreshocks of the R ound Valley earth q u ak e of Nov. 23, 1984, the observed variability of coda Q ~l was explained well by the effective num ber of scatterers being ab o u t 200. We also found th a t th e coda decay envelope is significantly affected by the thickness of vertical extent of zone containing scatterers. However, for the case of finite lateral extent of zone containing scatterers, the coda decay is less sensitive to the thickness of zone as com pared to the case for th e finite vertical extent of 264 zone containing scatterers. In ch ap ter 3, we used the form ula based on th e single scatterin g (first B orn) approxim ation derived by Aki and C houet (1976) to m easure the coda Q ~x from local earthquakes w ith m agnitudes 2 .0 < M < 3 .5 in Califor nia. T h e m easured coda Q ~l for a p articu lar source and receiver was then assigned to each 0 .2° x 0 .2° block in which the m idpoint betw een th e source and receiver lies. C alculating the spatial auto-correlation function of coda Q _1, we found th a t the coherence distance is dependent on the choice of tim e window for coda Q -1 m easurem ent; the longer and later tim e window shows slower decay in the correlation w ith distance as expected from the single-scattering theory. We also found spatial periodicity b o th in central C alifornia and in southern California. T he periodicity was of shorter wave length for th e form er (A = 180km) as com pared to th e la tte r (A = 230km). From m aps of coda Q - 1 , we found th a t the high coda Q ~l is concentrated continuously along th e m ain San A ndreas fault in central California. T he high coda Q ~l zone, however, is spread as patches in southern Califor nia including th e Big P ine and G arlock fault, and th e epicentral area of W hittier-N arrow s earthquake of O ct. 1, 1987. Also, it is shown th a t the low Q region roughly coincides w ith the low velocity region in the crust as o btained by Raikes (1980) in southern C alifornia using telesiesm ic P-delay d ata. In ch ap ter 4, we first elim inated all the sources of fictitious tem poral change in coda Q -1 considered by Sato (1988a) to establish th e physical reality of its tem poral change. We th en divided the stu d y area into eight subareas, and found th a t the coda Q~1 h ad its m inim um around 1985 and show sh arp increase startin g from 1986 for all subareas, tim e windows and 26 5 frequencies. T his sim ultaneous change of coda Q -1 th ro u g h o u t southern C alifornia is difficult to a ttrib u te to th e creep wave propagation along the plane b o u n d ary as hypothesized by Savage (1971). By com paring average values of coda Q ~l before and after Jan . 1, 1986 for all 0 .2° xO.2° blocks, we found a p a tte rn like M ogi’s donut in which th e increase in coda Q ~l occurred in a region surrounded by the zone in which coda Q ~ 1 decreased at m ore th a n one frequency bands. T he area of increased coda Q ~ 1 includes the C oachella segm ent of the San A ndreas fault, th e Los Angeles basin centered aro u n d the N ew port-Inglew ood fault and the southern end of the S ierra N evada fault. T he tem poral change of coda Q~l an d b-value in relation to the occurrence of recent th ree m oderate-sized earthquakes in southern California reveal approxim ately the sam e tre n d in w hich b o th increase to peak values before the earthquake, an d decrease from th e peak value w hen the earthquake occurs. In ch ap ter 5, we described three m odels, th e fractal m odel, dilatancy- diffusion m odel and creep m odel, as discussed by Jin and Aki (1989) in explaining the physical m echanism s of th e tem poral variation of coda Q -1 and exam ined if they can explain our new results or not. T he fractal and dilatancy-diffusion m odels are not considered as favorable m odels to explain th e com plex behavior of observed tem poral coda Q -1 change and its related seismicity. T he creep m odel involving a predom inant scale length of crack size, on th e o th er hand, can explain observed correlation betw een coda Q ~l and b-value. T hus, the creep m odel expresses our preferred physical m echanism causing the observed tem poral coda Q ~l change. In the present thesis, we believe th a t th e physical reality of tem poral change in coda Q ~x is established, we found a very rem arkable increase in 2 6 6 coda Q ~l startin g in 1985-86 apparently sim ultaneously th ro u g h o u t so u th ern California. For three m oderate-sized earthquakes occurred in 1986 and 1987, we found characteristic local change in coda Q ~l as well as in b-value associated w ith each of them . We also found a system atic sp atial p a tte rn for the change before and after Jan . 1, 1986, which suggests th e Mogi donut-like p a tte rn for several regions of southern C alifornia. An obvious question we ask is how th e current value of coda Q~x is d istrib u ted in southern C alifornia and how it is changing in tim e. This thesis covers only up to th e end of 1987, and already th e d a ta for th e one and half years period have been accum ulated. Did th e increase in coda Q ~l reach a peak value and sta rt decreasing at any place? A nother obvious question is w hat happened to central C alifornia when coda Q -1 increased sharply in southern California. T he coda wave d a ta available from the central C alifornia netw ork have not been analyzed since 1984. T he investigation of tem poral change in coda Q ~l in central C al ifornia m ay give a m ore definitive answ er to the question if creep wave propagating along th e p late boundary exists or not. A b e tte r und erstan d in g of w hat coda Q _1 really m eans is also im por ta n t. We need to define m ore precisely the lateral and vertical extent of volum e sam pled by coda waves. We need to find w hat fractio n scatterin g and absorption co n trib u te to coda Q~x. We need to know w hat are scat terers and absorbers con trib u tin g coda wave form ation. To answ er these question, we need b o th experim ental and theoretical studies. T he prob lem is fundam ental to th e und erstan d in g of stru ctu re an d processes in the lithosphere, and also im p o rtan t for the safety of hum an society against earthquake hazard. 267 B I B I O G R A P H Y A kam atsu, J., 1980, A tten u atio n p ro p erty of coda p a rts of seismic waves from local earthquake, Bull. Disa. Prev. Res. Int., K yoto U niv., 30, 1-16. Aki, K ., 1969, A nalysis of the seismic coda of local earthquakes as scattered waves, J. Geophy. Res., 74, 615-631. Aki, K., and C houet, B., 1975 O rigin of C oda Waves: Source, atten u atio n and scatterin g effects, J. Geophy. Res., 80, 3322-3342. Aki, K., 1980, A tten u atio n of shear waves in th e lithosphere for frequencies 0.05 to 25 Hz, Phys. E a rth P lanet. Interiors, 2 1 , 50-60. Aki, K., and P. R ichards, 1980, Q u an titativ e Seismology, Theory and M eth ods: W . H. Freem an, San Francisco, Calif. Aki, K., 1981, A probablistic synthesis of precursory phenom ena, in E a rth quake P rediction- An International Review, M. Ew ing Series, 4, AGU, ed. by D. W . Sim pson and P. G. Richards. Aki, K., 1981, A tten u atio n and scatterin g of short-period seismic waves in th e lithosphere, in Identification of Seismic Sources-E arthquakes or U n derground Explosions, E.S. Husebye and S. M ykkelveit, editors, D. Reidel P ublishing Co., D ordrecht, T he N etherlands, 515-541. Aki, K., 1987, M agnitude-frequency relation for sm all earthquakes: A clue to th e origin of fmax of large earthquakes, J. Geophy. Res., 92, 1349-1355. A nderson, D., and W hitecom b, J. H., 1973, T im e-dependent seismology, J. Geophy. Res., 80, 1497-1503. A ndrew s, D. J., 1978, Coupling of energy betw een tectonic processes and erathquakes, J. Geophy. Res., 83, 2259-2264. Bollinger, G. A., 1979, A ttenuation of th e Lg phase and the determ in atio n of 7 7 1 5 in th e sou th ern U nited S tates, Bull. Seism. Soc. Am ., 69, 45-63. B urford, R. 0 ., 1988, R etard atio n s in fault creep rates before local m od erate earthquakes along the San A ndreas fault svstem , central California, P A G E O P H , 126, 499-530. Cao, T ., and Aki, K., 1985, Seism icity sim ulation w ith a m ass-spring m odel and a displacem ent hardening-softening friction law, PA G E O P H , 1 2 2 , 10- 24. 2 6 8 C houet, B., 1976, Source, scatterin g and atten u atio n effects on high fre quency seismic waves, P h.D . Thesis, M assachusetts In stitu te of Technology, C am bridge, M assachusetts. C houet, B., 1979, Tem poral variation in the atten u atio n of earthquake coda near Stone Canyon, C alifornia, Geophy. Res. L ett., 6 , 143-146. D ainty, A. M ., and Toksoz, M. N., 1981, Seismic codas on th e E a rth and th e M oon: a com parision, Phys. E a rth P lanet. Interiors, 26, 256-266. Frankel, A., and C layton, R. W ., 1986, F inite difference sim ulation of seis mic scattering: im plications for the propogation of short-period seismic waves in the crust and m odels of crustal heterogeneity, J. Geophy. Res., 91, 6465-6489. Frankel, A., and W ennerberg, L., 1987, Energy-flux m odel of seismic coda: S eparation of scattering and intrinsic atten u atio n , Bull. Seismo. Soc. Am ., 77, 1223-1251. G ao, L. S.,Lee, C., Biswas, N. N., and Aki, K., 1983a, C om parision of th e effects betw een single and m ultiple scattering on coda waves for local earthquakes, Bull. Seism. Soc. A m ., 73, 377-389. G ao, L. S., Biswas, N. N., Lee, L. C., and Aki, K., 1983b, Effects of m ul tiple scatterin g on coda waves in three-dim ensional m edium , P u re Appl. G eophys., 1 2 1 , 3-15. G abrielov, A. M., D m itrieva, O. E., Kelis-Borok, V. I., Kosobokov, V. G., K uznestov, I. V., Levshina, T. A., M irzoev, K. M., M olchan, G. M ., Kh, I. M., N egm atullaev, Pisarenko, V. F ., Prozoroff, A. G., R ien h art, W ., R otvain, I. M ., Shebalin, P. N., Shnirm an, M. G., Yu, S., Shreider, 1986, A lgorithm s of long-term earthquake prediction, T he Regional C enter of Seismology for South A m erica, Lim a, Peru. G usev, A. A., and Lemzikov, V. K., 1985, P ro p erties of scattered elastic waves in the lithosphere of K am chatka: P aram eters and tem poral varia tions, Tectonophysics, 1 1 2 , 137-153. H aberm ann, R. E., 1988, P recursory seismic quiescence: P ast, present and fu tu re, PA G E O PH , 126, 279-318. H erraiz, M ., and Espinosa, A. F ., 1987, C oda waves: a review, P A G E O P H , 125, 499-578. H irata, N., 1988 personal com m unication. Im oto, M., 1988, personal com m unication. 2 6 9 Ishibashi, K., 1988, Tw o categories of earth q u ak e precursors, physical and tectonic, and th eir roles in interm ediate-term earth q u ak e prediction, PA G E O PH , 126, 687-700. Jin, A., 1981, D u ratio n of coda waves and th e back-scattering coefficient, p ap er presented at th e Sym posium on Seismology in C hina, S tate Seismo. B ur., Shanghai, C hina. Jin, A., and Aki, K ., 1986, Tem poral change in coda Q before th e T angshan earthquake of 1976 and the Haicheng earth q u ak e of 1975, J. Geophy. Res., 91, 665-673. Jin, A., and Aki, K., 1988, Spatial and tem poral correlation betw een coda Q ~x and seism icity in C hina, Bull. Seism. Soc. Am ., 78, 741-769. Jin, A., and Aki, K., 1989, Spatial and tem poral correlation betw een coda Q ~l and seism icity and its physical m echanism , J. Geophy. Res., in press. King, G. C. P., 1984, T he accom odation of large strain in th e upper litho sphere of th e E a rth an d other Solids by Self-Sim ilar fault System s: th e geom etrical origin of b-value, PA G E O PH , 1 2 1 , 761-815. K opinchev, Y. F., 1977, T he role of m ultiple scatterin g in th e form ation of a seim sm ogram ’s tail (English T ran.), Izv. Akad. N auk SSSR, Fiz. Zemli, 13, 394-398. Li, Q., ei a l , 1978, T im e and Space Scanning of the b-value- A m ethod for m onitoring th e developem ent of catastrophic earthquakes, A cta G eophysica Sinica, 2 1 , 101-105 (in Chinese). M ayeda, K., Su, F ., and Aki, K., 1989 Seismic albedo from th e hypocentral distance dependence of to tal seismic energy in sou th ern California, E astern Section, Seismo. Soc. Am ., 60, 20 Mogi, K., 1985, E arthquake prediction, pp. 1-355, A cadem ic Press, O r lando, Florida. N ovelo-Casanova, D. A., Berg, E., Hsu, V., and Helsley, C. E., 1985, Tim e- space variation seismic S-wave coda atten u atio n (Q - 1 ) and m agnitude dis trib u tio n (b-values) for the P etalan earthquake, Geophy. Res. L ett., 1 2 , 789-792. N uttli, O .W ., 1973, Seismic wave atten u atio n and m agnitude relations for eastern N orth A m erica, J. Geophy. Res., 78, 876-885. N ur, A., 1972, D ilatancy, pore fluids, and prem onitory variations of j* - travel tim es, Bull. Seismo. Soc. Am., 62, 1217-1222. 270 O ’Connell, R. J., and Budiansky, B., Seismic velocities in dry and sa tu ra te d cracked solids, J. Geophy. Res., T9, 5412-5416. Peng, J. Y., Aki, K., Lee, W . H. K., C houet, B., Johnson, P., M arks, S., N ew berry, J.T ., Ryall, A. S., S tew art, S., and T ottingham , D. M., 1987, T em poral change in coda Q associated w ith th e R ound Valley , California, earthquake of N ovem ber 23, 1984, J. Geophy. Res., 92, 3507-3526. Press, W . H., B. P. Flannery, S. A. Teukolsky, and W . T. V etterling, 1986, N um erical Recipes, T he A rt of Scientific Com puting: C am bridge Univ. Press, Cam bridge. Pulli, J. J., 1984, A tten u atio n of coda waves in New England, Bull. Seism. Soc. Am ., 74, 1149-1166. Raikes, S. A., 1980, Regional variations in the up p er m antle stru c tu re be n eath southern California, Geophys. J. R. astr. Soc., 63, 187-216. R au tian , T. G., K halturin, V. I., M artinov, V. G., and M olnar, P., 1978, P relim inary analysis of the sp ectra content of P and S waves from local earthquakes in the G arm , T adjikistan region, Bull. Seism. Soc. Am ., 6 8 , 949-971. R hea, S., 1984, Q determ ined from local earthquakes in th e S outh C arolina coastal plain, Bull. Seism. Soc. Am ., 74, 2257-2268. Robinson, R., 1987, Tem poral varaiation in coda d u ratio n of local e a rth quakes in the W ellington region, New Zeland, PA G E O PH , 125, 579-596. Roecker, S. W ., Tucker, B., King, J., and H atzfeld, D., 1982, E stim ates of Q in central A sia as a function of frequency and d ep th using th e coda of locally recorded earthquakes, Bull. Seism. Soc. Am ., 72, 129-149. Rovelli, A., 1982, O n the frqequency dependence of Q in Friuli from short- period digital records, Bull. Seism. Soc. Am., 72, 2369-2372. Sato, H., 1984, A ttenuation and envelope form ation of three-com ponent seism ogram s of sm all local earthquakes in random ly inhom ogeneous lith o sphere, J. Geophy. Res., 89, 1221-1241. Sato, H., 1986, Tem poral change in a tten u a tio n intensity before and after eastern Y am anashi earthquake of 1983, in central Jap an , J. Geophy. Res., 91, 2049-2061. Sato, H., 1988a, T em poral change in scatterin g and a tten u a tio n associated w ith the earthquake occurrence— a review of recent studies on coda waves, P A G E O PH , 126, 465-498. 271 Sato, H., 1988b, Is the single scattering m odel invalid for the coda excitation at long lapse tim e?, PA G E O PH , 128, 43-47. Savage, J., 1971, A theory of creep waves p ropogation along a transform fault, J. Geophy. Res., 76, 1954-1966. Scholz, C. H., 1988, M echanism s of Quiescence, P A G E O PH , 126, 701-718. Singh, S. K., and H errm ann, R. B., 1983, R egionalization of crustal coda Q in th e continental U nited States, J. Geophy. Res., 8 8 , 527-538. Steinbrugge, K. V., Zacher, E. G., Tocher, D., W h itten , C. A., and Clair, C. N., 1960, Creep on the San A ndreas fault, Bull. Seismo. Soc. Am., 50, 389-415. S treet, R. L.,1976, Scaling n o rtheastern U nites S taes/so u th eastem C ana dian earthquakes by th eir L g waves, Bull. Seism. Soc. A m ., 6 6 , 1525-1537. S tu a rt, W . D., 1979, Starin-softening prior to tw o-dim ensional strike-slip faulting, J. Geophy. Res., 84, 1063-1070. Su, F., and Aki, K., 1989, Spatial and tem poral variation in coda Q ~l associated w ith th e N orth Palm Springs earthquake of 1986, in press, PA G E O PH . T sujiura, M., 1978, S pectral analysis of th e coda waves from local e a rth quakes, Bull. E arth q u ak e Res. Inst., Tokyo U niv., 53, 1-48. T sukuda, T ., 1985, C oda Q before and after a m edium -scale earthquake, p ap er presented at the 23rrf G eneral Assem bly of IA S P E I, Tokyo. T urcotte, D. L., 1986, Fractals and fragam entation, J. Geophy. Res., 91, 1921-1926. W ilson, M., W yss, M., and K oyanagi, R., 1983, T em poral atten u atio n change in the Koae fault system , southern Hawaii [abs], EOS T ransactions AGU, 64, 761. W u, R. S., 1984, Seismic wave scattering and the sm all scale inhom o geneities in th e lithosphere, Ph. D. Thesis , M assachusetts In stitu te of Technology, C am bridge, M assachusetts. W u, R. S., 1985a, M ultiple scattering and energy tran sfer of seismic waves, separation of scatterin g effect from intrinsic atte n u a tio n , I., theoretical m odelling, Geophy. J. R. astr. Soc., 82, 57-80. Wu, R. S., 1985b, F ractal dim ensions of fault surfaces and th e inhom ogene ity spectrum of the lithosphere revealed from seismic wave scattering, to 272 be published in Proceedings of the In tern atio n al Sym posium on M ultiple S catterin g in R andom M edia and R andom Rough Surfaces, Ju ly 29- Aug. 2, 1985, P ennsylvania S tate University. W u, R. S., and Aki, K., 1985, S cattering characteristics of elastic waves by an elastic heterogeneity, Geophysics, 50, 582-595. W yss, M ., 1985, Precursory phenom enoa before large earthquake, E arth q . P red ict. Res., 3, 519-543. W yss, M ., and H aberrm ann, R. E., P recursory seismic quiescence, PA- G E O P H , 126, 319-332. Zener, C., 1948, E lasticity of m etals, U niversity of Chicago Press, Chicago, 1 1 1 . 273 A P P E N D I X We include the JG R p aper entitled ”T em poral C hange in C oda Q A ssociated W ith th e R ound Valley, California, E arth q u ak e of Novem ber 23, 1984” . In this p aper, we present observed coda Q _1 variation associ ated w ith th e R ound Valley earthquake of 1984, California an d suggest the Mogi donut m odel to reconcile conflicting results on coda Q ~ 1 precursor published in previous studies. 274 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 9 2 , NO. 85, PAGES 3 5 0 7 -3 5 2 6 , APRIL 10, 1987 TEMPORAL CHANGE IN CODA Q ASSOCIATED WITH THE ROUND VALLEY, CALIFORNIA, EARTHQUAKE OF NOVEMBER 23, 1984 J . Y. P e n g ,1 K. A k l , 1 B. C h o u e t ,2 P. J o h n s o n ,2 W. H. K. L e e ,2 S. M arks,2 J . T. N ew b e rry ,3 A. S, R y e l i , 1 * S. V. S t e w a r t ,2 and D. M. T o c tln g h e a 2 A b s t r a c t . Seven thousand selsm ogram s of s m a ll e a r th q u a k e s In th e Mammoth L a k es-B ish o p a rea were u sed t o measure v a lu e s of Q from th e d eca y o f the ear th q u a k e cod a. These m easurem ents were compared b etw een e v e n t s th a t o cc u r red b e f o r e and a f t e r the Round V a lle y earth q u ak e (M - 5 .7 ) . W e found th a t in r e g io n s near the main shock e p i c e n t e r , m easurem ents o f coda Q-1 f o r ea r th q u a k e s t h e t o cc u r r e d a f t e r the m ain shock were h ig h e r than f o r t h o s e e a r th q u a k e s t h a t o cc u r r e d p r io r to the main s h o c k . The o p p o s i t e b eh a v io r was found fo r r e g io n e f a r t h e r away from th e main sh o c k , n am ely, low er coda Q~1 a f t e r th e main shock than b e f o r e . M easurem ents of code Q~1 in th e Long V a lle y c a l d e r a , o u t s i d e of the im m ediate s o u r c e r e g io n of the e a r th q u a k e , were h ig h e r than in su r ro u n d in g a re a s b e f o r e th e main srtock, but th e d i f f e r e n c e d is a p p e a r e d a f t e r the c c u r r e n c e o f the main s h o c k . T h is i n d i c a t e s th a t :he tem p oral v a r i a t i o n in coda Q~1 i s com parable to i t s s p a t i a l v a r i a t i o n . The doughnut model ( s e i s m i c i t y q u ie s c e n c e surrou nd ed by a zone of a c t i v i t y ) w hich was Invoked f o r e x p l a i n i n g th e p r e c u r s o r y s e i s m i c i t y p a t te r n ap pears to be s i m i l a r w it h the ob se rv ed coda Q“ 1 v a r i a t i o n a s s o c i a t e d w it h the Round V a lle y e a r th q u a k e . The o b se rv ed s p e t i a l v a r i a t i o n s in coda Q~3 a l s o h e lp to r e c o n c i l e c o n f l i c t i n g r e s u l t s p u b lis h e d in p r e v io u s s t u d i e s of th e coda Q~1 p r e c u r s o r . I n t r o d u c tio n Many r e s e a r c h e r s have shown in v a r io u s are a s of th e w orld th a t th e coda decay r a t e of l o c a l e a r th q u a k e s , f i r s t d ls c u s e e d by Aki [ 1 9 6 9 ] , i s a s t a b l e p aram eter w hich i s i n s e n s i t i v e to s o u r c e and r e c e i v e r l o c a t i o n s w it h in an a re a and r e f l e c t s th e a v e r a g e p r o p e r ty of th e a r e a c o n t a in in g th e s o u r c e s and r e c e i v e r s . The i n t e r p r e t a t i o n of th e coda d e c a y r a t e in terms o f ap paren t a t t e n u a t i o n o f b e c k - s c a t t e r i n g S waves has been l a r g e l y s u c c e s s f u l [K o p n lch ev, 1977; T s u j i u r a , 1978; A ki, 1980b; R oecker e t a l . , 1982; S a to , 1977, 1 9 8 4 ]. The Q"1 o f S waves thue I n f e r r e d from th e coda d ecay r a te i s c a l l e d "code Q“ l . ” R e c e n t ly , tem p o ra l ch en gee of code Q- 1 have been r e p o r te d b e f o r e and a f t e r la r g e e a r th q u a k e s . Among t h e s e r e p o r ts er e ( 1 ) a 30Z i n c r e a s e in coda Q_ l b e fo r a th e 1975 K aweli (M «7.2) e a r th q u a k e [Wyss, 1 9 8 5 ], ( 2 ) a 20Z i n c r e e s e in code Q~l b e f o r e 3 la r g e e a r th q u a k e s (M «8.0) in th e Kuri1-Kam chatka l Depertm ent of G e o lo g ic a l S c i e n c e s , U n i v e r s i t y of S outh ern C a l i f o r n i a , Los A n g e le s . 2U .S . G e o lo g ic a l S u rv ey , Menlo Park, C a l i f o r n i a 3S ie r r a G e o p h y s ic s , I n c . , S e a t t l e , W ashin gton . '•Canter fo r S e is m ic S t u d i e s , A r li n g t o n , V lr g l n - l e . C o p yr igh t 1987 by th e American G e o p h y s ic a l U nion. Paper number 6B6034. 0 1 4 8 - 0 2 2 7 /8 7 /0 0 6 B - 6 0 3 4 S 0 5 .0 0 a rea [Gusev and Lemxikov, 1 9 8 5 ], ( 3 ) a 30Z I n c r e a s e in the v e l u e o f coda Q ~ 1 m easured e t 6Hz b e fo r e the P e t a t l e n ee rth q u ek a (M -7 .6 ) in Mexico (N o v elo -C esa n o v e e t a l . , 1 9 8 5 ], (4 ) an om alou sly h ig h coda Q ~ 1 b e f o r e th e e a s t e r n Yamaneshi ear th q u a k a (M -6 .0 ) o f 1983 in c e n t r e l Japan (S a to , 1 9 8 6 ], (5 ) a 300Z in c r e e s e in code Q_ l in the 3 y e e r s b e f o r a the Tangshen e e rth q u ek e (M -7.8 ) of 1976 and a com parable change f o r the Haicheng e a r th q u ak e (M“ 7 .3 ) o f 1975 in China (J in and A ki, 1 9 8 6 ], ( 6 ) a 10-20Z d e c r e e e e in coda Q _ l d urin g the 2 -3 year p e r io d b e f o r e th e M lsasa earth q u ake (M -6 .2 ) o f O c to b e r, 1983 in T o t t o r l , Japan [Tsukuda, 1 9 8 5 ]. O ther e v ld e n c a s u g g e s t i n g the tem p oral changes in code Q~1 have a l s o been re p o r te d [C hou et, 1979; J i n , 1981; W ilson e t a l . , 1983; Rhee, 1 9 8 4 ], There i s a p o s s i b i l i t y ch at the code Q_ l ch an ges w it h o u t an o b v io u s r e l a t i o n to an major e a r th q u e k e . W e p rob ab ly cen n o t r e j e c t t h i s h y p o t h e s le f o r our c a s e . In moet o f th e above r e p o r te d c a s e s , code Q_ l wae a n o m a lou sly h ig h f o r a p e r io d p r e c e d in g th e o c c u r r e n c e o f th e main s h o c k . In some c a s e s [ e . g . , Tsukuda, 1 9 8 5 ], how ever, th e change wes o p p o s i t e and coda Q ~ 1 became h ig h e r in th e e f t e r s h o c k a rea a f t e r che o c c u r r e n c e o f th e main sh o c k . The sample r e g io n s f o r che c a s e of J in and Akl [1 9 8 6 ] and o c h e r s are p rob a b ly such la r g e r chan che a fc e r s h o c k zone b eca u se s c a c i o n s f o r che c a s e o f J in and Aki [ 1986] are siore d ls c a n c ( - 1 0 0 km) from Che e p ic e n c e r chan in che c a s e o f Tsukuda [1 9 8 5 ] , in w hich cwo nearby s e i s m i c s c a c i o n s are about 10 km from Che e p ic e n c e r o f Che main s h o c k . Boch of Chese a p p a r e n c ly i n c o n s is c e n c p a c c e r n s may be e x p la i n e d i f coda Q ~ 1 in c r e a s e s w ic h in che a f c e r s h o c k zone buc d e c r e a s e s o u c s id e of ic when che main shock o c c u r s . In t h i s p a p er, we p resen c e v id e n c e chat su p p o rcs che above siodel u s in g daca □ b ca in ed in Che Mammoch L a k es-B ish o p a rea b e fo r e and a f c e r che Round V a lle y earch qu ak e (M -5 .7 ) o f November 23, 1984. □aca V e r c i c a l cosiponenc seism ogram a of 70 m icro ea rch q u ak es ( 1 .5 < M 'l < 3 .0 ) c o n s i s c i n g of 60 fo r e a h o c k s and 10 a f c e r s h o c k s o f che Round V a lle y , C a l i f o r n i a , ea r th q u ak e o f November 23, 1984, each re cord ed d i g i c a l l y ac 100 s a m p l e s /s ac a s u b sec of approxiaiaC ely 100 s c a c i o n s , were p r o c e s s e d chrou gh Che CUSP ( C a l i f o r n i a I n s tiC u c e o f T ech n olog y ( C a l t e c h ) - U .S . G e o lo g ic a l Survey (USGS) S eism ic P r o c e s s i n g ) syscem [Johnson and ScewarC, 1986]. Here we u se che words " fo r e s h o c k s" and " a f t e r s h o c k s " to mean ea r th q u a k e s th a t o ccurred r e s p e c t i v e l y b e fo r e and a f t e r th e Round V a lle y e a r th q u a k e , n o tin g ch a t th e y may not be c a u s a l l y r e l a t e d . A d e s c r i p t i o n of the daca p r o c e s s in g em ployed to e v a l u a t e th e coda Q~1 from t h i s d e t e b a s e i s g iv e n by Lee e t a l . [ 1 9 8 6 ] . The e p ic e n c e r o f che main shock wae ac 118.6*W and 37.5*N (F ig u r a 1 ) . S in c e O ctob er 1978, four 3507 275 3508 Peng e t a l . : T em p oral Changee In Coda Q R e g i o n a l i r a t i o n a l Mnp f o r F,ong V olley Art-fi Long Valley caldere ‘n ° j r a * - 3 IV a - 4 - - H (S. of Bishop) 119.1 119 118 9 118 8 118.7 1188 118.5 Longitude F i g . 1. A map show ing s e i s m i c s t a t i o n s and the e a r th q u a k e e p i c e n t e r s . T r i a n g l e s , r e c o r d in g s t a t i o n s o p e r a te d by th e U .S . G e o lo g ic a l Survey and by th e U n i v e r s it y o f Nevada; s o l i d c i r c l e s , fo r e s h o c k ; open c i r c l e s , a f t e r s h o c k s ; s t a r , th e Round V a lle y ear th q u a k e (M -5 .7 ) o f November 23, 1984. A lso shown a r e s i x r e g io n s used in t h i s s tu d y . R egion s I , I I , I I I , and IV are d e p ic t e d by dashed l i n e s . Region S i s bounded by th e s o l i d l i n e c o n t a in in g most o f r e g io n I I I and p a r ts o f r e g io n s I I and IV. Region T i n c l u d e s r e g io n s I I , I I I , and most o f r e g io n IV and i s r e p r e s e n t e d by th e d o t t e d l i n e . R egio n I i s th e Long V a lle y c a l d e r a , and r e g io n IV i s che n orth o f B ishop a r e a . Ospth vs. Time Round Valley Earthquake of Nov. 23.1984 JL. 1 2 1 9 8 6 Month F i g . 2a. The d i s t r i b u t i o n o f f o c a l d ep th s fo r f o r e s h o c k s and a f t e r s h o c k s . S o lid c i r c l e s r e p r e s e n t f o r e s h o c k s , w h ile open c i r c l e s r e p r e s e n t a f t e r s h o c k s . The arrow i n d i c a t e s che clme o f th e main shock w hich o cc u r r e d on November 23, 1984, w ith m agnitude 5 . 7 . 276 Peng e t a l . : T em poral Change* In Coda Q 3509 MaCalluda vs. T V Round Valley e a rth q u a k e (11-5.7) P ig . 2b. The d i s t r i b u t i o n of m agnitude v e r s u s t i n e f o r f o r e s h o c k s ( s o l i d c i r c l e s ) and a f t e r s h o c k s (op en c i r c l e s ) . ea r th q u a k e s w ith m agnitude ~ 6 and s e v e r a l earth q u ak e swarms w ith th o u sa n d s o f s m a lle r e v e n t s have occ u r red in th e Mammoth Lakes a re a [ J u lia n and S ip k in , 1 9 8 5 ). Our d i g i t a l d a t a , h ow ever, were c o l l e c t e d from A p r il 1984, when th e USGS o n - l i n e d a ta a c q u i s i t i o n sy ste m s s t a r t e d f u l l o p e r a t i o n , to January 1985. The g e n e r a l d i s t r i b u t i o n of e p i c e n t e r s i s s i m i l a r fo r f o r e s h o c k s and a f t e r s h o c k s ( F ig u r e 1 ) . The p a t t e r n s o f ea rth q u ake o c c u r r e n c e s do not show any o b v io u s ly s y s t e m a t i c change f o r th e p e r io d c o v e r in g our d ata s e t . Any change in coda Q “ , t h e r e f o r e , i s not l i k e l y a r e s u l t o f a change in s p a t i a l co v e r a g e by the coda waves due to a change in e a r th q u a k e l o c a t i o n s . W e a l s o found th a t the d i s t r i b u t i o n of f o c a l d ep th s ( 0 —15 km) d id not show any s y s t e m a t i c d i f f e r e n c e betw een f o r e s h o c k s and a f t e r s h o c k s ( F ig u r e 2 a ). M oreover, t h e r e i s not any s i g n i f i c a n t change in m agnitude e i t h e r b e f o r e or a f t e r th e main shock (F ig u r e 2 b ). Table L shows t h a t th ere i s not any s i g n i f i c a n t change e i t h e r in f o c a l d ep th s or m agn itu des b e f o r e and a f t e r th e main shock when the same s t a t i s t i c a l c^ *c a s u sed in t e s t i n g for ch a n ges in coda Q~ i s a p p l i e d . Method o f Data A n a l y s i s A ccord in g to R au tian and K h a lt u r in [ 1 9 7 8 ] , th e o b se rv ed coda d ecay r a t e becomes in d ep en d en t of h y p e r c e n t r a l d i s t a n c e f o r a l a p s e tim e (m easured from th e o r i g i n tim e ) more than t w ic e che t r a v e l tim e of d i r e c t S w av es. In th e p r e s e n t paper we have ch o sen two la p s e tim^ windows fo r che d e t e r m i n a ti o n s of coda Q“ , n am ely, 2 0-45 s and 30 -6 0 s , w hich rou gh ly co r r e s p o n d to che volume sam pled by che s i n g l e b a c k - s c a t t e r e d waves w it h in th e ra d iu s o f about 65 and 90 km from th e m idpoint o f s t a t i o n and e p i c e n t e r r e s p e c t i v e l y . W e did s c r e e n th e d a ta to in s u r e th a t cod a s waves a r r i v i n g e a r l i e r chan tw ic e Che S t r a v e l clme were e x c lu d e d . F o llo w in g Akl and Chouet ( 1 9 7 5 ] , th e coda power spectru m P ( u | t ) a v er a g ed o v er s fr e q u e n c y band c e n t e r e d at fr e q u e n c y < ■ > and cim« t (m easured from th e o r i g i n tim e ) i s e x p r e s s e d as U l C ’ P U j t ) - C (m )t“* e (1 ) where C(iu) r e p r e s e n t s Che coda s o u r ce f a c t o r ac che c e n t e r e d freq u en cy u, m i s a c o n s ta n t th a t depends on g e o m e t r ic a l s p r e a d in g (m*>2 f o r body w a v e s ), and Qc i s th e q u a l i t y f a c t o r Chat we w ish to determine. R e c e n t ly , F ran k el and C la y to n [1986] have q u e s t io n e d th e v a l i d i t y of th e s i n g l e - s c a t t e r i n g model which i s assumed fo r d e r i v i n g equation ;1). I f Che s i n g l e - s c a t t e r i n g model i s not applicable to Che cod a, the coda Q d e r iv e d by e q u a t io n (1) should not be eq u a l to che Q o f S w aves. O b s e r v a tio n s , how ever, have c o n s i s t e n t l y shown th a t both the coda Q and Q of S waves have very s i m i l a r frequency dependence and r e g i o n a l v a r i a t i o n for 1-25 Hz [Wu, 1984, Appendix A). R ecent work on Lg bv Oampillo e t a l . [1985] shows che fr e q u e n c y dependence TABLE 1. Means o f F o c a l Depths and Magnir .ies. Number o f E ven ts Used co C a lc u la t e Standard rrror o f th e Mean B efo r e and A f t e r che Main nhj.-n _______Fo reshock _______ _____ Af t e rs K <______ Mean Number SEM Mean Vuraoer ;EM o f i f _______________________ E ven ts____________________ Event_s________ F o c a l Depth 7 .2 3 59 0 . 39 6. 20 10 '.HI M agnitude 2 .3 8 59 0 . 0 5 2.5 7 10 i.IO D i f f e r e n c e betw een s h o r e s h o c k s and a f t e r s h o c k s is not s i g n i f i c a n t . SEM, sta n d a r d e r r o r of che mean. 277 3510 Peng e t a l . : T em poral Change* In Coda Q 2 0 - 4 5 3 e c f F o r « ito o c k J ) 2 0 - * 5 S«« 'A A .« r ib o c k s ) 119.9 L o n gitude 119.6 1 1 9 19.6 3 0 -9 0 S«c (ro rv ah o ck a) 3 0 - 9 0 3«c (A flarvbocks) 3 R J H*r —------ . - n ; s>* .V » . r* • ‘ f I • ' m * ’ \ : * 1 n r * L IS .8 L o n g ltu 4 « 'n 118.8 Longltud* F ig . 3. D i s t r i b u t i o n of m id p oin ta b etw een so u r ce* and r e c e iv e r * fo r d i f f e r e n t tim e w indow s. S o lid c i r c l e * , f o r e s h o c k s ; open c i r c l e s , a f t e r s h o c k s . Two s u b d i v i s i o n s of r e g io n I e n c l o s e d by the s o l i d l i n e s n o r th o f 37.6*N are d e f in e d fo r th e tim e windows 2 0 -4 5 s ( I ’ ) and 30 -6 0 s ( I " ) . Region I' i* at th e t i p o f th e arrow in F ig u r e s 3a and 3b, and r e g io n I” i s shown in F igu re* 3c and 3d. s i m i l a r to th e coda Q. In o t h e r w ords, o b s e r v a t io n s s u p p o rt th e s i n g l e - s c a t t e r i n g model f o r th e coda Q m easu rm en ts. Even i f th e m u lt ip le s c a t t e r i n g i s s i g n i f i c a n t , i t i s s t i l l c o n v e n ie n t t o u se e q u a tio n ( 1 ) as an e m p ir ic a l form u la b ecau se che s e p a r a t io n o f i n t r i n s i c Q“ 1 and s c a t t e r i n g Q-1 in che m u l t i p l e - s c a t t e r i n g c a s e I n tr o d u c e s a s e v e r e n o n u n iq u en ess in d e t e r m in in g t h e s e p a ra m eters from Che d a t a . The u se o f e q u a t io n (1 ) i s J u s t i f i e d e v e n f o r the m u l t i p l e - s c a t t e r i n g c a s e s as lo n g as th e tim e window i s s p e c i f i e d from w hich che coda i s s am p led . T aking che n a t u r a l lo g a r ith m o f both s i d e s o f e q u a t io n ( 1 ) g i v e s wt In P(u> | c) - In C(bi) - 2 In t ( 2 ) Qc B eca u se C(w) i s in d ep en d en t o f t im e , In C(<*) can be C reated as a c o n s t a n t in d e t e r m in in g coda Q~ * f o r a g iv e n u , and we have u c In P(u»|t) - In C(w) - 2 In c - -- (3) 1 c As in th e work by Lee e t a l . , [19861, we o b t a in e d coda Q- 1 th rou gh Che l i n e a r regression of e q u a t io n (3) fo r f i v e o c ta v e frequency bands c e n t e r e d sc 1.5, 3, 6, 12, and 24 Hz, respectively, by t a k in g a window s i z e o f 512 d a ta sam ples and moving th e window by 2.56 s and, at the same time, c o r r e c t i n g f o r che in stru m en t r e s p o n s e . The coda Q- * o b t a in e d f o r a p a r t i c u l a r source and r e c e i v e r i s a s s i g n e d to che m id p oin t of the s o u r c e and r e c e i v e r . We th en group the coda Q-1 d a ta a c c o r d in g t o th e l o c a t i o n o f Che midpoint 278 Peng et a l . : T em poral Changes In Coda Q 3511 TABLE 2a. Mean Coda Q ~l, Number of Samples Used to C a lc u la t e Mean and Standard Error of che Mean fo r F iv e Frequency Bands With th e Time Window 2 0-45 s in th e Long V a lle y C aldera (R egion I) F oreshock Af t e r s h o c k D if f e r e n c e In ( 1 / Q) Be tween Foreshocks and A f te r s h o c k s , Z Frequency Hz Number of ( 1 /Q ) x l0 0 0 Samples SEM ( 1 /Q )x l0 0 0 Number of Samples SEM 1.5 3* 6 12 24 11.31 167 6 .8 0 189 2 .3 5 137 0 .7 9 112 0 . 4 0 97 0 .2 8 0. 15 0 .0 9 0 .0 3 0 .0 2 9 .4 0 5 .7 4 1.9 8 0 .6 9 0. 33 5 8 9 8 6 1. 28 0 .4 3 0. 23 0. 10 0 .0 7 18 SEM, Standard e r r o r o f th e mean. ‘ S i g n i f i c a n t d i f f e r e n c e . TABLE 2b. Same as Table 2a fo r Time Window 3 0 -6 0 s ini Region I Foresho ck A ft e r s h o c k D if f e r e n c e in (1 /Q ) Between Foreshocka and A f t e r s h o c k s , Z Frequency Hz Number of ( 1 /Q ) x l0 0 0 Samplesi SEM ( 1 /Q ) x l0 0 0 Number o f Samples SEM 1.5 3* 6 12 24 11.59 99 6 .8 4 105 2 .2 8 81 0 .7 3 58 0 .3 6 50 0 .3 6 0. 18 0. 10 0 .0 4 0 .0 2 9 .4 0 5. 74 1.9 8 0 .6 9 0. 33 5 8 9 8 6 1.28 0 .4 3 0 .2 3 0 .1 0 0 .0 3 17.5 SEM, Standard ‘ S i g n i f i c a n t e r r o r o f the mean, d i f f e r e n c e . TABLE 2c. Same as Table 2a fo r Time Window 3 0-60 s in Region I F oresh ock Af t e r s h o c k D i f f e r e n c e in (1 /Q ) Between F oreshocks and A f t e r s h o c k s , Z Frequency Hz Number of ( 1 /Q ) x l0 0 0 Samples SEM ( I / Q ) x 1000 Numbe r o f Samples SEM 1.5 3* 6 12* 24 8 .9 4 180 4 .0 4 194 1.3 2 168 0 .7 1 171 0 .3 9 107 0 .2 4 0. 11 0 .0 4 0 .0 2 0 .0 2 7. 36 2.9 9 1. 36 0 .5 7 0. 36 19 19 15 18 11 0. 54 0 .2 2 0. 15 0. 04 0. 03 20 30 22 SEM, Standard e r r o r of th e mean. ‘ S i g n i f i c a n t d i f f e r e n c e . TABLE 2d. Same as Table 2a fo r Time Window 30-60 s in R egion I •• F oreshock A fte r s h o c k D if f e r e n c e in ( I/ Q) 3e tween F oreshocks and A f t e r s h o c k s , Z Frequency Hz Number of ( 1 /Q ) x l0 0 0 Samples SEM ( 1 /Q ) x l0 0 0 Number o f Samples SEM 1.5 3* 6 12* 24 8 .9 2 125 3 .8 0 126 1.31 107 0 . 7 0 110 0 .3 9 71 0 .2 9 0 .1 1 0 .0 4 0 .0 3 0 .0 2 7.36 2. 99 1.36 0. 57 0 .3 6 19 19 15 18 11 0. 54 0. 22 0. 15 0 .0 4 0 .0 3 19 24 20 SEM, Standard e r r o r of th e mean. ‘ S i g n i f i c a n t d i f f e r e n c e . 279 to 00 o O O fo g o O O O O O O O m U 1 0 0 o o o o f t f t O 7 0 co» 0 0*3 4 > N J O W o o o o o O O • — - - J U > L fl Q ^ O ' Ob Ob Q D O ' o o o o o TABLE 4b. Sam e as Table 2 a for Time Window 30-60 ■ in Region I I I SEM, Standard error of che mean ‘ S ig n if ic a n t d i f f e r e n c e . vj vj O' 'J U 1 o o o o o 0 . 0 o o *- O O K > U o n * n k n r • c f t f t 0 9 ^ S) O' w o o o o o O O O ► - K > O O N » O' O O O O O O ' € O B C T * O C O f t n f t a W n o ft < f t Peng e t a l . : T em po ral C hanges In Coda Q TABLE 6 a . Same as Table 2a fo r Time Window 2 0-45 s in Region S 15 13 Foreahock Af t e r s h o c k D if f e r e n c e in (1/Q ) Between Foreshocks and A f t e r s h o c k s , 2 Frequency Hz ( 1 / Q )x l0 0 0 Humber of Samples SEM ( 1 / Q )x l0 0 0 Number of Samples SEM 1.5 3* 6 12 24 8.8 6 4 .7 3 1.82 0 .7 9 0 .4 3 100 125 111 127 127 0 .2 7 0. 17 0 .0 7 0 .0 2 0 .0 2 11 .2 7 6 .0 2 2.2 2 0 .7 1 0 .5 2 28 21 20 23 27 1.23 0. 44 0 .2 0 0 .0 5 0 .0 5 24 SEM, Standard * S i g n l f i c a n t e r r o r o f th e d i f f e r e n c e . mean. TABLE 6b. Same as Table 2a fo r Time Window 30 -6 0 s in Region S Foreshock A fte r s h o c k D if f e r e n c e in (1/Q ) Between Foreahocka and A ft e r s h o c k s , Z Frequency Hz (1 /Q ) x l0 0 0 Number of Samples SEM ( 1 /Q ) x l0 0 0 Number o f Samples SEM 1.5 3 6* 12* 24 7 .6 0 3.32 1.29 0. 72 0 .4 3 142 184 163 219 165 0. 24 0. 13 0 .0 5 0 .0 3 0 .0 1 7 .3 2 3. 16 1.04 0.6 1 0 .4 2 37 32 24 38 44 0 .3 7 0. 19 0 .0 6 0. 03 0 .0 3 21 17 SEM, Standard * S l g n i f ic a n t e r r o r of the d i f f e r e n c e . mean. TABLE 7a. Same as Table 2a f o r Time Window 20-45 s in Region T Foreshock Af te r s h o c k D i f f e r e n c e In (1/Q ) Between F oresh ock s and A f t e r s h o c k s , Z Frequency Hz ( 1 /Q )x l0 0 0 Number of Samples SEM ( 1 /Q ) x l0 0 0 Numbe r o f Samples SEM 1.5 3* 6* 12 24 9.2 1 5 .0 4 1. 73 0 . 79 0 .4 3 240 307 248 249 268 0 .2 1 0. 11 0 .0 4 0 .0 2 0 .0 1 10 .62 6. 15 2 .2 5 0. 78 0. 58 52 48 47 50 53 0. 71 0 .2 5 0. 15 0 .0 5 0 .0 4 20 26 SEM, Standard * S i g n i f l e a n t e r r o r o f the d i f f e r e n c e . mean. TABLE 7b. Same as Table 2a fo r Time Window 30-60 s in R egion T Foresho ck Af te r s h o c k D i f f e r e n c e in (1/Q ) Be tween F oresh ock s and A f t e r s h o c k s , ” , Frequency Hz ( 1 /Q ) x l0 0 0 Numbe r of Samples SEM ( 1 / Q ) x 1000 Numbe r o f Samples SEM 1.5 3 6 12* 24 7.9 1 3. 31 1. 24 0 .6 9 0 .4 1 316 36 5 326 419 329 0. 17 0 .0 8 0 .0 3 0 .0 2 0 .0 1 7.91 3. 53 1 .1 4 0 .6 1 0 .4 3 68 62 49 71 68 0. 29 0. 21 0 .0 7 0 .0 2 0 .0 2 12. 3 SEM, Standard e r r o r o f the mean. * S i g n i f i c a n t d i f f e r e n c e . 281 282 ( 1 /4 ) M 0 0 0 ( 1 / Q ) M 0 0 0 ( ! / < » ) • 1 0 0 0 f i n • Histograms •>( coda < j~ 1 lor d i f f e r e n t freq u en cy bands with s t a t i s t i c a l l y s ig n if ic a n t 11 I i < ■ c < ■ in i be i ween f hi cs Inn k s ami a l t e r s b u c k s In the Long V alley ca ld era. Shaded area , a ftersh o ck s; in.■ ,I,.id. I ,ire.i, I, i r e n Ini i k u , ,n row, mean for f o res bock s ; arrow with a superimposed c i r c l e , mean for ,i t i * • i •» 1 1 > < . k b . Hu- tw.ij i ( c- ij., n -jo tjO ) give the reg io n ( I ) , the frequency (3 Hz) and the time u l luluw ( 10-61) s ) . 351^ Peng et a l . : Temporal Change* In Coda Peng e t a l . : T em poral C hanges In Coda Q 3515 I ! r o II o o 1 I u’ U - ' F ig . 5. Temporal v a r i a t i o n o f coda Q-1 f o r th e d ata s e t shown In F ig u r es 4. The arrow I n d i c a t e s che tim e of che main sh o c k . The means fo r f o r e s h o c k s and a f t e r s h o c k s are shown by dash ed l i n e s . betw een s o u r c e and r e c e i v e r . Four s e p a r a c e r e g io n s ( I , I I , I I I , and IV w ith th e a re a 15x40 km2 , 15x20 km2 , 10x20 km2 , 20x20 km2 , r e s p e c t i v e l y ) are grouped as shown by th e dashed l i n e s in F lg u e r s 1, and two o ch er a re a s S ( s o l i d l i n e ) and T ( d o t t e d l i n e ) are a l s o c o n s id e r e d . In. ord er to redu ce the b ia s due to d i f f e r e n t s p a t i a l c o v e r a g e , we f u r t h e r s u b d iv id e d r e g io n I i n t o I ' and I" as shown In F igu re 3. W e a p p ly a s t a t i s t i c a l c e s t of s i g n i f i c a n t Co che d i f f e r e n c e s becw een coda Q_ l b e fo r e and a f t e r che main shock f o r e a c h d a ta s e t in th e above d e f in e d r e g i o n s . W e a l s o s t u d ie d che s i g n i f i c a n c e of d i f f e r e n c e in coda Q“ 1 b etw een d i f f e r e n t r e g i o n s . In a l l th e s i g n i f i c a n c e t e s c s we used Qc _ l in s c e a d o f Qc b eca u se th e form er more c l o s e l y f o l l o w s a G a u ssia n d i s t r i b u t i o n than Che l a c c e r . We u se che method o f F is h e r and Y aces [1 970 ] by form ing che f o l l o w i n g s t a t i s t i c s : * 1 ~ * 2 d -------------- ( 4 ) * i Si , -------- / N 1 - 1 where mean of coda Q~1 f o r group i; sta n d a rd e r r o r of the mean f o r group 1 : Oi stan d ard e r r o r of a l l sam ples in group number o f sam ples In group i . T h is method i s a p p r o p r ia t e fo r the d i f f e r - - two means f o r which th e e r r o r s are due to • • c a u s e s , so th a t e s tlm a c e s of v a r ia n c e cannot p r o p e r ly be p o o le d . T h is i s e x a c c ly the case coda Q~* m easurem ents were tak en from a lar<e number o f s e ism o g ra m s. We c o n s id e r che di::~r~- - betw een two means to be s i g n i f i c a n t when d .0 e q u a tio n (4) e x c e e d s th e c r i t i c a l v a lu e s for d i f f e r e n t s e t s o f s a m p lin g numbers g iv e n bv Sukhatme [193 8) at th e 95Z c o n f id e n c e level. O th e r w ise , th e d i f f e r e n c e i s c o n s id e r e d to be s i g n i f i c a n t . In o ch er w o rd s, the c r i t i c a l v a l u e s 283 3516 Peng e t a l . : T em p oral Changes in Coda Q IT <— ^9- i I w ftfnna ja # ■ < - < © - 2 8 4 OOOI.(0/t> 0001.(6/1) Peng ec a l . : T em po ral Change* In Coda Q 3517 M 1* m ( I i/a m im * On* F ig . 7. Temporal v a r i a t i o n o f coda Q~1 f o r th e d ata s e c shown in F ig u r e 6. of d depends not o n ly on th e sam pled numbers of coda Q- * - fo r fo r e s h o c k s and a f t e r s h o c k s but a l s o v a r i e s as the s c a l e f a c t o r s ( 8 ) , where S i ta n 8 - — (6 ) s 2 C o n s e q u e n tly , t h e s e p aram eters c o n t r o l the c r l c i c a l v s lu e of d in e q u a tio n (4 ) f o r each s i g n i f i c a n c e t e s t . T ab les 2a-7b l i s t t h e s e p ara m eter s in d e t a i l when th e d i f f e r e n c e i s s i g n i f i c a n t . R e s u lt s Most of our e s r t h q u s k e s (a t l e a s t 857!) o cc u r r e d in r e g io n s I I . I l l , and IV, w ith many c l u s t e r e d s o u th o f che Long V a lle y c a ld e r a and n o r th w e st of Bishop ( r e g i o n s II and IV ). F ig u r e 3 shows the d i s t r i b u t i o n o f m id p o in ts f o r f o r e s h o c k s and a f t e r s h o c k s f o r two d i f f e r e n t tim e w indow s. We s e s t h a t the m id p oin t d i s t r i b u t i o n s are n e a r ly che same f o r d ata from both f o r e s h o c k s and a f c e r s h o c k s . Comparison of coda Q"1 b etw een f o r e s h o c k s and a f t e r s h o c k s i s made fo r r e g io n s I, I ' , I", I I , i l l , IV, S, and T in T ab les 2a-7b where th e mean coda Q_ l , the number of sam ples used to c a l c u l a t e che mean, and che sta n d a rd e r r o r of che mean are shown f o r each freq u en cy band. When th e d i f f e r e n c e in Che mean v s lu e b etw een f o r e s h o c k and a f c e r s h o c k i3 s i g n i f i c a n t at Che 95? l e v e l , che p e r c e n ta g e change in coda Q- * i s shown in che l a s t column. The d i s t r i b u t i o n s of o b se r v e d coda Q-1 in the form o f h isto g ra m s and tem p oral v a r i a t i o n from A p r il 1984 to January 1985 are shown in F ig u r es 4 -1 3 f o r che c a s e s in w hich s i g n i f i c a n t d i f f e r e n c e s b etw een fo r e s h o c k s and a f t e r s h o c k s were found bv Che s i g n i f i c a n c e c e s t . W e found a c o n s i s t e n t p sc c e r n of che ch sn g e in coda Q” 1• The coda Q“ 1 In c r e a s e d a f t e r che main shock in r e g io n s I I , I I I , and IV fo r Che tim e window 20-45 s , but i t d e c r e a s e d f o r a l l che windows in r e g io n I which was l o c a t e d f a r t h e s t from th e main shock e p i c e n c e r . The change i s 20-3 0 ? when s i g n i f i c a n t . A s i m i l a r 285 3518 Peng e c a l . : T e m po ral Change* In Coda Q < - « 3 I i 91 01 jo # 2 8 6 ( I / W I 0 0 0 ( l /g ) M 0 0 0 Peng et a l . T em poral Change* in Coda Q 3519 [ n e a r -s o u r c e I n c r e a s e of coda Q~l a f t e r the o c c u r r e n c e of th e main shock wee a ls o ob serv ed by Tsukuda [1985] fo r th e M is a a a earth q u ake (M -6.2) in Japan. C ontrary to what was found fo r the time window 2 0 -4 5 a , a f t e r s h o c k s showed low er coda Q-1 than fo rea h o ck a in r e g io n I I I fo r th e time window 30-60 s . The r e s u l t s f o r r e g io n IT fo r the time window 3 0 -6 0 3 are i n c o n c l u s i v e b eca u se none of th e d i f f e r e n c e s were s i g n i f i c a n t . In o rd er to t e s t th e r e l i a b i l i t y o f p a t t e r n s of change in coda Q~l we regrou ped the d ata in re g io n s I I , I I I , and IV i n t o r e g io n * S (a r e a e n c lo s e d by s o l i d l i n e in F ig u r e 1) and T (a r e a e n c lo s e d by d o t te d l i n e in F ig u r e 1 en com p assin g a reas I I , I I I , and IV ). R egion s S and T e x h i b i t s i g n i f i c a n t d i f f e r e n c e s fo r b o th windows (T a b le s 6 a - 7 b ) . W e found th a t a f t e r s h o c k s showed low er coda Q~l than fo r e s h o c k s f o r th e tim e window 30-60 s fo r both S and T. T h is r e s u l t i s in good agreem ent w ith that measured from r e g io n I I I f o r tim e window 30-60 s . The d i f f e r e n c e was about 20X fo r area S and about 10X fo r a rea T. On t h e o th e r hand, fo r both S and T, a f t e r s h o c k s showed h ig h e r coda than f o r e s h o c k s f o r th e tim e window 20-45 a which i s in agreem ent w ith th e r e s u l t o b t a in e d from t h i s time window f o r a r e a s I I , I I I , and IV. In r e g io n I (Long V a lle y c a l d e r a ) , a f t e r s h o c k s showed low er coda Q “ 1 th an f o r e s h o c k s fo r both tim e windows (F ig u r e s 4 and 5 ) . T his r e s u l t i s in agreem ent w ith th e above r e s u l t fo r a r e a s in S and T fo r tim e window 3 0-60 s and th e r e s u l t s o b ta in e d in most o th e r re p o r te d c a s e s [Gusev and Lemzlkov, 1985; N ov elo-C asanova e t a l . , 1985; J in and Aki, 1986; S a to , 1 9 8 6 ]. F i n a l l y , we found th a t there was a s i g n i f i c a n t s p a t i a l d i f f e r e n c e in coda Q~l b e fo r e the main shock betw een re g io n I (Long V a lle y c a l d e r a ) and r e g io n T when th e same s i g n i f i c a n c e t e a t was a p p l ie d . S u r p r i s i n g l y , t h i s d i f f e r e n c e , how ever, d is a p p e a r e d a f t e r th e main sh o c k . More p r e c i s e l y , th e coda Q~^ a t 3 Hr fo r time window 20-45 s was 6 .8 x 1 0 “ 3 in r e g io n I (T ab le 2a) and 5 . 0 x l 0 “ 3 in re g io n I and 6 . 2 x l 0 “ 3 in reg io n T for a f t e r s h o c k s . A s i g n i f i c a n t s p a t i a l difference of about 30X not o n ly d is a p p e a r e d but changed sig n betw een Long V a lle y c a l d e r a and re g io n T. •e note th a t the tem poral v a r i a t i o n o f coda Q“ 1 (e.g., 20-45 s ) i s com parable to i t s s p a t i a l v a r i a t i o n . R egion I (Long V a lle y c a l d e r a ) c l e a r l v shows h ig h e r coda Q“l f o r f o r e s h o c k s than aftershocks. To make su re t h i s d i f f e r e n c e i s not due to d i f f e r e n c e s in th e s p a t i a l d i s t r i b u t i o n of m id p o in ts o v er the c e n t r a l p art o f the caldera as shown in F igure 3, we have f u r t h e r defined regions I ’ and I" w ith in w hich m id p oin t distributions u f o r e s h o c k s and a f t e r s h o c k s are s i m i l a r for the 20-4 5 s and 3 0-60 s w indow s, r e s p e c t i v e l y . \ com p arison betw een a f t e r s h o c k s and foresnocks for r e g io n s I' and I" i s shown in F ig u r e s 6 and ’ i-d . a g a in , i s c o n s i s t e n t w ith th e r e s u l t obtained ■- m r e g io n I . This e x c lu d e s th e p o s s i b i l i t y :nat g r e a t e r co v era ge o f m id p o in ts ov er che centra: :art of th e c a ld e r a in re g io n I by fo r e s h o c k s than a f t e r s h o c k s i s r e s p o n s i b l e f o r th e result of tem p oral v a r i a t i o n in coda Q” 1. It Is a l s o i n t e r e s t i n g to n o t e th a t th e s p a t i a l variation in coda Q“ l has th e same m agnitude as chat of temporal v a r i a t i o n f o r s e v e r a l r e g i o n s . For exam p le, compare r e g io n s I ' snd I I f o r th e 2 0 -4 5 s window at 287 3520 Peng ec a l . : T em po ral Changes in Coda Q C M i l / S *m . Vi mm Cmtm 1 /e A m r w - m i ) o o 3 II < • S , § ft o 1 1 C«4ft I / S v » T ta * ( 1 B - W D C** 1 /% m T te* C1I e e l « 9 1M 4 s«m 4 tiMtute C«4a I / S m T te * QOS-SOW) 7 S 9 10 11 12 1 2 M mU l*** S ah a* * W * * ? l«nb4M*a« M t 1/S m r\ m m e « V o t ii F ig . 9. Temporal v a r i a t i o n o f cod* Q-1 f o r che d a ta s e t shown in F igu re 288 Peng e t a l . : T em poral Changes In Coda Q 352 1 ;VJ-<!045 0 2 4 6 8 10 12 14 16 ( 1/Q)" 1000 F ig . 10. Same as F igure 3 fo r fo reah o ck a and a f t e r s h o c k s In re g io n IV. 3Hz. R egion I' shows h ig h e r coda Q~l fo r f o r e s h o c k s than r e g io n II and low er coda Q_ l fo r a f t e r s h o c k s than r e g io n II ( T a b le s 2b and 3 a ) . The d e c r e a s e of coda Q“ ‘ w ith tim e f o r re g io n I' and th e I n c r e a s e fo r r e g io n II are s i g n i f i c a n t . A s i m i l a r p a t t e r n o f change In coda Q-1 can be seen betw een r e g io n s I" and T fo r the time window 3 0-60 a (T a b le s 2d and 7 b ). D is c u s s io n and C o n c lu sio n From th e r e s u l t s which p a ssed th e s i g n i f i c a n c e t e s t at 95S l e v e l we found th a t coda fo r a f t e r s h o c k s Is h ig h e r than th a t fo r fo r e s h o c k s in th e area c l o s e to th e e p i c e n t e r o f the main shock but low er than th a t f o r f o r e s h o c k s in the area f a r t h e r away from th e e p i c e n t e r . T h is p a tt e r n o f change can be e a s i l y s e e n from F ig u r es 8 -1 3 . T his i s a r e m in is c e n t o f M o gl's doughnut p a t t e r n of p r e c u r so r y s e i s m i c i t y [K anam orl, 1981; Mogi , 1 9 8 5 ], in which an a rea of q u i e s c e n c e is surrounded by an a c t i v e zo n e. In M o gl's model an earth q u ak e w i l l in d u ce cr a c k s or o t h e r w is e make the su rrou n d in g medium l e s s co m p e te n t, which w i l l in turn e l e v a t e th e coda Q~1 . T h ere fo re we may e x p e c t th a t the a re a of q u i e s c e n c e has low coda Q_ l and th e active Cads Q vs. Tima (IV3-204S) S I' Month Round Vallsv Earthquake (M-S.7) F ig . 11. Temporal v a r i a t i o n o f coda Q-1 fo r th e d a ta s e t shown in Figure 10. 2 8 9 3522 Peng e t a l . : T em po ral Change* in Coda Q < — 290 (l/QJMOOO (l/Q)*1000 Peng e t a l . T em poral Change* In Coda Q 352 3 § " £ zone has h ig h cod* Q- 1 b e f o r e che main shock . A f te r che main sh o c k , how ever, che r e g io n of a f t e r s h o c k s in che im m ediate v i c i n i t y of che main sh ock f a u l c zone becomes h ig h in coda Q- 1 , and che a c t i v e zone o f th e doughnut may become q u i e t and low in coda Q- 1 . Thus che s p a c i s l and tem poral p a t t e r n o f cod* Q-1 v a r i a t i o n ob served in che Msmaoth Lakes- B ish op area i s in hsrmony w ith the g e n e r a l id e a d e v e lo p e d f o r th e s e i s m i c i t y p r e c u r s o r , a lth o u g h we do n ot have ob viou s s e i s m i c i t y p r e c u r s o r s in che c a s e o f che Round V a lle y ea r th q u a k e . W e a l s o found t h a t che v a lu e o f coda Q_1 o b t a in e d by a s i n g l e measurement shows a la r g e v a r ia n c e aa e v id e n c e d in h isto g ra m * of F ig u r es 4, 6, 8, 10, and 12. From t h e s e h isto g ra m s we can not f in d a s im p le g e o g r a p h ic v a r i a t i o n * in coda Q-1 v a l u e s . The la r g e v a r ia n c e r e q u ir ed a la r g e number o f measurmencs f o r d e t e c t i n g sm a ll d i f f e r e n c e in coda Q“ 1 as shown in T ab le 2 a -7 b . The o b served la r g e v a r i a t i o n may be a t t r i b u t e d to the n atu re o f s c a t t e r i n g s o u r c e s in th e l i t h o s p h e r e . Probab ly a s m a ll number of s t r o n g s c a t c e r e r s d om inate che coda in s e l s m i c a l l y a c t i v e z o n e . W e are p la n n in g a Monte C arlo exp er im en t t o s im u la t e coda to stu d y th e cau se of Che la r g e v a r ia n c e in o b se rv ed coda In c o n c l u s io n , che doughnut model which was Invoked fo r e x p l a i n i n g p r e c u r s o r y s e i s m i c i t y p a t t e r n * ap pears to e x p l a i n , at l e a s t fo r the Mammoth L a k es-B lsh o p a r e a , th e ob se rv ed coda Q-1 v a r i a t i o n a a s o c ia t e d w ith che Round V a lle y e a r th q u a k e . I t a l s o h e lp s to r e c o n c i l e c o n f l i c t i n g r e s u l t s re p o r te d in p u b lis h e d c a s e s t u d i e s o f che coda Q-1 p r e c u r s o r . In t h i s stu d y we found a r e s u l t s i m i l a r to th a t o f Tsukuda [1985] fo r a re a s n ear to che main shock l o c a t i o n and sam pled by s h o r t la p s e tim e . On Che c o n t r a r y , fo r Chose r e g io n s w hich are f a r t h e r away from th e main shock e p i c e n t e r and sampled by lo n g la p s e tim e , our r e s u l t i s c o n s i s t e n t w ith t h e s e r e p o r ts from och er p u b lis h e d c a s e s . W e s e e c l e a r l y and c o n s i s t e n t l y th a t coda Q~1 d e c r e a se d coward che end fo r both 2 0 -4 5 s and 3 0-60 s in r e g io n I and in c r e a s e d coward che end fo r 20 -4 5 s but n o t f o r 3 0 -6 0 s In r e g io n s I I , I I I , and IV. It i s , h ow ever, d i f f i c u l t to c e l l when che change o cc u r r e d b eca u se of la r g e v a r ia n c e o f d aca. In t h i s c a s e , th e o n ly p o s s i b i l i t y was h y p o th e s is t e s t i n g . W e ch ose che n u l l h y p o t h e s is th a t coda Q-1 In che 8 months b e fo r e che earth q u ake was eq u al to che coda Q-1 in che 2 months f o ll o w i n g che e a r th q u a k e . The h y p o t h e s is was r e j e c t e d by the s i g n i f i c a n t t e s t . A major p u z z le , h ow ever, remains about coda Q-1 i f t h i s ob se rv ed tem p oral change i s r e a l . The o b se rv ed tem p oral change s u g g e s t s chat h e t e r o g e n e i t i e s r e s p o n s i b l e f o r che s c a t t e r i n g and a t t e n u a t i o n o f coda waves are c r a c k -r e la c e d because o n ly c h in cra ck s can respond s e n s i t i v e l y to a sm all s t r e s s c h a n g e. Ac d ep th s where we presume th a t the s c a t c e r e r s e x i s t , t h e s e cr a c k s must be kept open by h ig h pore p r e s s u r e . S in ce f l u i d w i l l have fintce v i s c o s i t y , i n t r i n s i c Q o f S waves w i l l be low. From che r e s u l t s shown a b o v e, che coda Q-1 i s alw ays l e s s Chan 0 .0 0 1 fo r fr e q u e n c i e s h ig h e r than 10 Hz. M u lt ip le s c a t t e r i n g [ e . g . , Gao ec a l . , 1983; W u and A kl, 1985; F rank el and C la y to n , 1986] can cau se ap paren t low coda Q- 1 in Che r e s u l t *291 (i/Vt-ina (i/W M 352M Peng ec a l . : T em poral Changaa in Coda 0 m O 4 ! — -* - - J '• • i *r i, a ii u cmi Tte» fna to tm C M i U* m Ttea ( hilliihi HMf) 8 « « © Co* V /l « f c Tto pMMft C M i I/* m Ite (Ill-ION) L-* a F ig . 13. Temporal v a r i a t i o n of coda $ - i f o r tha d ata s e t shovn in F igure 12. 2 9 2 Peng e t a l . : T em p oral Changea In Coda Q 5525 o b ta in e d by th e coda m ethod, but th e agreem ent betw een coda Q -1, measured u s in g s i n g l e - s c a t t e r i n g model and Q~* o f S waves measured by an Ind ep en d en t method [ e . g . , Akl 1980a] ia u s u a l l y e x c e l l e n t fo r h ig h f r e q u e n c i e s and s h o r t la p s e t im e s . Of c o u r s e , th e s e p a r a t io n o f i n t r i n s i c and s c a t t e r i n g Q- ^ may p r o v id e some c l u e t o th e above problem . It i s , h ow ever, d i f f i c u l t in p r a c t i c e to a p p ly any m u l t i p l e - s c a t t e r i n g models to a c t u a l d a ta b eca u se th e s e p a r a t io n o f i n t r i n s i c and s c a t t e r i n g Q” 1 I n t r o d u c e s a s e v e r e n o n u n iq u en ess in d e te r m in in g t h e s e p aram eters from th e d a ta . A ck n ow le d g m e n ts. We thank S t e v e R o eck er, Bruce J u l i a n , C a ry l M ic h s e ls o n , and Jsmes W. Dewey f o r t h e i r c a r e f u l r e a d in g s o f che m a n u scr ip t and v a lu a b le comments. An anonymous r e v ie w e r i s a l s o a p p r e c i a t e d fo r s u g g e s t i n g th e im provem ents o f che f i g u r e s . T h is work was s u p p o r ts by U .S. G e o lo g ic a l S urvey g r s n t s 1 4 -0 8 - 0 0 0 1 -A -0036 and 1 4 - 0 8 - 0 0 0 1 - G - 1195. R e fe r e n c e s A k i, K. , A n a ly s is o f Che s e i s m i c coda of l o c a l e a r th q u a k e s as s c a t t e r e d w a v es, J . Geophys. R ea. , J74, 6 1 5 -6 3 1 , 1969. A k i, K. , A t t e n u a t io n o f sh e a r -w a v e s in the l i t h o s p h e r e f o r che f r e q u e n c i e s from 0 .0 5 to 25 Hz. Ph ys. Earth P l a n e t . I n t e r . , 21, 5 0 -6 0 , 1980a. A ki, K ., S c a t t e r i n g and a t t e n u a t i o n o f sh e a r waves in che l i t h o s p h e r e , J . Geophys. R e s ., 85, 6 4 9 6 - 6 504, 1980b. A kl, K . , and B. C houet, O r ig in of coda waves: S o u r c e , a t t e n u a t i o n and s c a t t e r i n g e f f e c t s , J . G eoph ys. R es. , 80, 3 3 2 2 -3 3 4 2 , 1975. C hou et, B . , Temporal v a r i a t i o n in che a t t e n u a t io n o f e a r th q u a k e coda n ear Stone Canyon, C a l i f o r n i a , Geophys. R es. L e t t . , 6 , 143 -1 4 6 . 1979. F i s h e r . R. A ., and F. Y a te s , S t a t i s t i c a l t a b l e s fo r B i o l o g i c a l A g r i c u l t u r a l and M edical R e s e a r c h , pp. 1 -1 4 6 , H afn er, 1970, D a rie n , Conn. F r a n k e l, A ., and R. W. C la y to n , F i n i t e d i f f e r e n c e s im u l a t i o n s of s e i s m i c s c a t t e r i n g : I m p l ic a t i o n s f o r th e p r o p a g a t io n o f s h o r t - p e r i o d s e i s m i c w aves in the c r u s t and m odels of c r u s t a l h e t e r o g e n e i t y , J _ . G eophys. R es. , 9 1 , 6 4 6 5 -6 4 8 9 , 1986. Gao, L. S ., L. C. L ee , N. N. B isw a s, and K. Aki, C omparison o f t h e e f f e c t s betw een s i n g l e and m u l t i p l e s c a t t e r i n g on coda waves f o r l o c a l e a r th q u a k e s , B u l l . S e i s a o l . Soc. A m .., 73, 3 77 - 3 8 9 , 1983. G usev, A. A ., and V. K. Lem zikov, P r o p e r t ie s of s c a t t e r e d e l a s t i c waves in th e l i t h o s p h e r e of Kamchatka: P aram eters and tem poral v a r i a t i o n , T e c t o n o p h y s l c s , 1 1 2 , 1 3 7 -1 5 3 , 1985. J i n , A ., On th e d u r a tio n of coda waves and the b a c k - s c a t t e r i n g c o e f f i c i e n t , in P r o c e e d in g s of th e Symposium on S eism o lo g y in C h in a , S e i s m o l o g i c a l P u b lis h in g House, S h a n g h a i, P e o p l e ' s R ep u b lic o f C hina, 1981. J i n , A . , and K. A kl, Temporal change in coda Q b e f o r e th e Tangshan ea r th q u a k e o f 1976 and th e H aich en g ea r th q u a k e o f 1975, J _ > G eophys. R es. , 2 1 , 6 6 5 - 6 7 3 , 1986. Joh n so n . P ., and S. W. S te w a r t, Caltech-USGS s e i s m i c p r o c e s s in g s yste m (CUSP): User d o c u m e n ta tio n , U .S . G e o l. Surv. O p en -F ile R ep., in p r e s s , 1986. J u l i a n , B. R ., and S. S lp k ln , Earthquake p r o c e s s e s in th e Long V a lle y a r e a , C a l i f o r n i a , J . Geophys. Rea. , 9 0 , 11 , 155-1 1, 169, 1985. ~ “ Kanam orl, H ., The n a tu re o f s e i s m i c i t y p a tt e r n s b e f o r e la r g e e a r th q u a k e s , in Earthquake P r e d i c t i o n , An I n t e r n a t i o n a l Review, Maurice Ewing S e r . , v o l . 4, e d it e d by D. W . Simpson and P. G. R ic h a r d s , pp. 1 -2 0 , AGU, W ashington, D .C ., 1981. K opnichev, Y. F . , M odels fo r th e fo rm a tio n o f the coda of the l o n g i t u d i n a l w ave, ( D okl. Akad. Nauk. SSSR, E n g l. T r a n s l . ) , 2 3 4 , 1 3 -1 5 , 1977. Lee, W . H. K ., K. A k i, B. C hou et, P. Joh nson , S. Marks, J . T. Newberry, A. S. R y a ll, S. W . S t e w a r t, and D. M. TottIngham , A p r e lim in a r y stu d y o f coda Q in- C a l i f o r n i a and Nevada, B u l l . S e la m o l. S o c . Am., in p r e s s , 1986. Mogi, K ., Earthquake P r e d i c t i o n , pp. 1 -355 , Academic P r e s s , 1985, O rla n d o , F l o r id a . N o v elo -C a sa n o v a , D. A ., E. Berg, V. Hsu, and C. E. He I s l e y , T lm e -sp a ce v a r i a t i o n s e is m ic S-wave coda a t t e n u a t i o n (Q- 1 ) and m agnitude d i s t r i b u t i o n f o r th e P e la ta n e a r th q u a k e , Geophys. R es, L e t t . , 12, 7 8 9 -7 9 2 , 1985. R a u tla n , T. G ., and V. I . K h a lt u r ln , The use of coda fo r d e t e r m in a tio n o f th e ea r th q u a k e sou r ce sp e ctru m , B u l l . S e l s m o l . S o c . Am., 68., 9 2 3 -9 4 0 , 1978. Rhea, S . , Q d eterm in ed from l o c a l e a r th q u a k e s in th e South C a r o lin a c o a s t a l p l a i n , B u ll. Seism . S o c . Am., 2 2 - 2 2 5 7 -2 2 6 8 , 1984. R oeck er, S. W ., 3. T u ck er, J. King, and □. H a t z f e ld . E s tim a te s o f Q in C en tra l A sia as a f u n c t io n of freq u en cy and d ep th u s in g th e coda o f l o c a l l y reco rd ed e a r th q u a k e s . Bu1 1 . Se 1 s mo 1 . S o c . Am., _72, 1 2 9 -1 4 9 , 1982. S a to , H . , Energy p r o p a g a tio n in c l u d in g s c a t t e r i n g e f f e c t s , s i n g l e i s o t r o p h i c a p p r o x im a tio n , J _ . P h ys. E a r t h , 2 5 , 2 7 - 4 1 , 1977. S a t o , H ., A t t e n u a t io n and e n v e lo p e fo rm a tio n of th ree-c o m p o n en t seism ogram s o f sm a ll lo c a l ea r th q u a k e s in randomly inhom ogeneous l i t - . o - s p h e r e , _J. G eophys. R es. , 8 9 , 1 2 2 1 -1 2 4 1 , 1984. S a t o , H ., Temporal change in a t t e n u a t i o n i n t e n s i t v b e fo r e and a f t e r th e e a s t e r n Yamanasht e a r t h quake o f 1983 in c e n t r a l Jap an, _J. Geoph■ /s . Rea. , 9J_, 2 0 4 9 -2 0 6 1 , 1986. S c h o lz , C. H . , L. R. S y k e s , and Y. P. Aggrawal, Earthquake p r e d i c t i o n : A p h y s i c a l b a s i s , S c i e n c e , 181, 8 0 3 -3 1 0 , 1973. Sukhatme, P. V ., On f i s h e r and B eh re n 's t e s t >f s i g n i f i c a n c e f o r the d i f f e r e n c e in means of t-o normal s a m p le s , Sankhya, ^4, 3 9 - 4 8 , 1938. Tsukuda, T. , Coda Q b e fo r e and a f t e r a -sed; im-s-.i .e e a r th q u a k e , paper p r e s e n t e d a t the 23rd A ssem b ly, I n t . A ss o c , o f S e is m o l. and . th e E a r th ’ s I n t e r . , Tokyo, Aug. 1985. T s u j i u r a , M. , S p e c t r a l a n a l y s i s of the coda from l o c a l e a r th q u a k e s , 3 u l l . Earthquake • Ins t . U n iv . T ok yo, 5 3 , 1 -4 8 , 1978. W ilso n , M. , M. Wyss, and R. K o y a n a g i, Teapor i; a t t e n u a t i o n change in th e Koae f a u l t svste-a, so u th e r n H aw aii, EOS, T r a n s . ACU, 6 4 , ’hi, 1983. Wu, R. S . , S e is m ic wave s c a t t e r i n g and the small 293 3526 Peng ec a l . : Temporal Change* In Coda Q s c a l e I n h o m o g e n e ltle a In che l l c h o a p h e r e , Ph.D. c h e a t s , Haas. I n s t , o f T e c h n o l. , Cambridge, 1984. Wu, R. S . , and K. A kl, E l a s t i c wave a c a c c e r l n g by a random medium and che s m a l l - s c a l e ln h o m o g e n e lc le s In th e ll c h o a p h e r e , _J. Geophys. R e s . , 90, 1 0 , 2 6 1 - 1 0 , 2 7 3 , 1985. Wyss, M ., P r e c u r s o r s to la r g e e a r th q u a k e s , E arth quake P r e d i c t . R e s . , _3, 5 1 9 -5 4 3 , 1985. j . t, Peng and K. A k l, Department o f C e o lo g i c a l S c ie n c e s , U n i v e r s i t y o f S o u th er n C a l i f o r n i a , U n i v e r s i t y Park, Los A n g e le s , CA 90089. B. C houet, P. Joh nson , W . H. K. Lee, S. Marks, S. W. S te w a r t , and D. M. Totcingham , U. S. G e o lo g i c a l Survey, 345 M i d d le f x ie l d Road, M S 77, Menlo Park, CA 94025. J . T. N ewberry, S ie r r a C e o p h y s lc s, I n c . , P.O. Box 3886, S e s t t l e , W A 98124. A. S. R y a ll, C en ter f o r S e is m ic S t u d i e s , 1300 North 17th S t r e e t , S u i t e 1450, A r lin g t o n , VA 22209. ( R e c e iv e d A p r il 18, 1986; r e v is e d O ctober 10, 1986; a c c e p te d O ctober 13, 1 9 8 6 .) 294

Asset Metadata

Creator Peng, Jenn-Yih (author)

Core Title Spatial and temporal variation of coda Q[-1] in California

Contributor Digitized by ProQuest (provenance)

Degree Doctor of Philosophy

Degree Program Geological Sciences

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag geophysics,OAI-PMH Harvest

Language English

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c29-353018

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Rights Peng, Jenn-Yih

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