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Modeling and imaging asperities on a fault plane and characterizing spatial and temporal patterns of precursory seismicity

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Modeling and imaging asperities on a fault plane and characterizing spatial and temporal patterns of precursory seismicity

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Content M O D ELIN G A N D IM A G IN G ASPERITIES ON A F A U LT PLANE AN D CHAR AC TER IZIN G SPATIAL A N D TEM PORAL PATTERNS OF PRECURSORY SEISM ICITY by Youlin Chen A Dissertation Presented to the FA C U LTY OF THE G RADUATE SCHOOL UN IVER SITY OF SOUTHERN C A LIFO R N IA In Partial Fulfillm ent o f the Requirements for the Degree DOCTOR OF PHILOSOPHY (GEOPHYSICS) May 2004 Copyright 2004 Youlin Chen Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. UMI Number: 3140450 INFORMATION TO USERS The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleed-through, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. UMI UMI Microform 3140450 Copyright 2004 by ProQuest Information and Learning Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. ProQuest Information and Learning Company 300 North Zeeb Road P.O. Box 1346 Ann Arbor, Ml 48106-1346 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Dedication To M y wife Yufang Rong And M y parents Peishan Chen and Tongxia Bia Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Acknowledgements I owe a great deal o f thanks to the many individuals for the dissertation, which would have not been completed without the support, encouragement, advice, assistance, love, and good humor o f fam ily, friends, and colleagues, here in the United States and back in China. It is my privilege to express my gratitude to the numerous persons for their various capacities in my Ph.D. education completion. First and foremost I must thank my w ife Yufang for her understanding, love and encouragement in all the time since we fell in love. Her support and encouragement was in the end what made this dissertation possible. M y parents, Tongxia and Peishan, receive my deepest gratitude and love for their dedication, love and comfort to my life and studies. I also thank my younger sister, JiaYin, for her taking care o f my parents in China. I am deeply in debt to my advisor, Charles G. Sammis, for his constructive and patient guidance and encouragement, and for his continuous supporting throughout my graduate studies. It is not often that one finds an advisor and colleague that always finds the time for listening to the little problems and roadblocks that unavoidably crop up in the course o f research. H is academ ic and e d ito ria l advice has taught me innumerable lessons and insights on the academic research and prepared me for future iii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. challenges. I am also grateful to Judy and Charlie for hosting the Thanksgiving party every year for us, which always gives me a sweet feeling o f home. M y thanks also go to my other committee members, Professor Thomas H. Jordan, Ta-liang Teng, Yehuda Ben-Zion, and Muhammad Sahimi for providing many valuable advices and comments on my studies. Specially, for Professors Ta-liang Teng and Yuhuda Ben-Zion, I am indebted to their long-term advice and constructive discussions. I also thank the numerous persons in my home department and in other facilities who have ever given me lots o f academic helps. In particular, thanks to Dr. Zheng-Kang Shen in U C LA, Yuehua Zeng in Univ. o f Nevada - Reno, Lucile Jones in USGS, David D. Bowman, Yong-Gang L i and Lupei Zhu. I appreciated the friendship o f Yunfeng Liu, Zhigang Peng, Shoshana Levin, Liangjun Chen, and Po Chen. Many interesting and good-spirited discussions between us often gave me new ideas to my research. I would also like to express my thanks and appreciation to my alumni, Yueqiang Huang and Cheng-Ping L i, for their help and truly friendship at the very beginning time in USC. Finally, I thank Cynthia Waite, Vardui Ter-Simonian, John McRaney, and John Yu for their care and assistance during my graduate study at the Department o f Earth Sciences. Thanks again to you all. IV Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table of Contents D edication...................................................................................................................................ii Acknowledgements..................................................................................................................iii List o f Tables.............................................................................................................................vi List o f Figures..........................................................................................................................vii A bstract....................................................................................................................................xiii 1 Introduction......................................................................................................................... 1 2 Asperity Model for Earthquakes...................................................................................... 6 2.1 Introduction............................................................................................................... 7 2.2 Analytical Asperity M odels.................................................................................. 13 2.3 A Numerical Asperity M o d e l...............................................................................23 2.4 Results o f Numerical Sim ulation.........................................................................25 2.4.1 Numerical Simulation o f Solid A sperities........................................... 26 2.4.2 Kinematics o f Asperity R upture............................................................. 30 2.4.3 Numerical Simulations o f Asperity C lusters....................................... 30 2.5 Diseussion................................................................................................................37 3 A High Frequency View o f 1999 Chi-Chi, Taiwan, Source Rupture and Fault M echanics.........................................................................................................................41 3.1 In tro d u c tio n ......................................................................................................................... 42 3.2 High Frequency Seismic Records........................................................................47 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 3.3 Locating High-Frequency B ursts.........................................................................53 3.3.1 Fault M odels...............................................................................................54 3.3.2 Data Processing..........................................................................................58 3.3.3 M ethodology.............................................................................................. 63 3.3.4 Results......................................................................................................... 66 3.4 Relocating Asperity Sources................................................................................ 78 3.5 Estimating the Sizes o f Sub-Events.....................................................................79 3.6 Discussion................................................................................................................82 3.7 C onclusion...............................................................................................................91 4 Spatial and Temporal Patterns o f Regional Seismicity Preceding the 1992 Landers, California Earthquake.....................................................................................................94 4.1 Introduction............................................................................................................. 95 4.2 The Seismic C atalog..............................................................................................99 4.2.1 M inim um Magnitude o f Completeness............................................... 100 4.2.2 The Declustered C atalog........................................................................103 4.3 Seismicity preceding the Landers earthquake................................................. 105 4.3.1 Changes in a- and b-value......................................................................105 4.3.1.1 Changes in a- and b-values with time in circular regions .... 108 4.3.1.2Changes in a- and b-values w ith tim e in regions o f stress accum ulation......................................................................................I l l VI Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4.3.2 Changes in the cluster statistics.......................................................... 118 4.3.3 Migration o f seismicity toward the epicenter......................................123 4.4 Conclusion and Discussion................................................................................130 5 Conclusions and discussions........................................................................................ 133 B ibliography........................................................................................................................... 140 Vll Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. List of Tables Table 3.1 Stations, accelerometers, and data inform ation................................................52 Table 3.2 Parameters o f the Chelungpu fault m o d el.........................................................55 Table 3.3 Velocity model for Taiwan re g ion ......................................................................59 Table 3.4 the observed and estimated aftershocks in first five days after the Chi-Chi m ainshock.................................................................................................................................91 Vlll Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. List of Figures Figure 2.1 An analytical asperity model for constant remote stress............................... 13 Figure 2.2 An analytical asperity model for constant remote displacement..................18 Figure 2.3 A numerical asperity m odel................................................................................24 Figure 2.4 Numerical simulation o f the slip deficit distribution on the asperity cluster and its surrounding creeping areas just prior to an event................................................. 27 Figure 2.5 The slip distribution for two models having the same asperity but different fault sizes.................................................................................................................................. 28 Figure 2.6 Kinematical rupture scenarios............................................................................29 Figure 2.7 Comparison o f the slip distribution on a composite asperity w ith that on a solid asperity having the same radius.................................................................................. 31 Figure 2.8 The average slip U a on an asperity as a function o f radius ra for both solid asperities and asperity clusters.............................................................................................. 33 Figure 2.9 The repeating period T o f asperity events vs. the average slip ............... 34 Figure 2.10 Stress drop distribution for an asperity cluster having /> = 0 .1 7 ................35 Figure 2.11 The average stress drop as a function o f the radius the o f asperity cluster for all m odels............................................................................................................................37 Figure 3.1 The time frames at 11, 14, 19, and 20 sec taken from the Chi-Chi movie that documents the ground motion for the E-W component observed at the surface by Shin and Teng, 2001 ............................................................................................................... 45 Figure 3.2a The accelerograms o f three components for station T075 ......................... 50 Figure 3.2b The accelerograms o f three components for station T084 ......................... 51 IX Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 3.3a Single-plane fault model for the Chelungpu fa u lt........................................ 56 Figure 3.3b Multi-plane fault model for the Chelungpu fa u lt..........................................57 Figure 3.4 The calculated travel time curve for P-waves against the epicentral distance......................................................................................................................................60 Figure 3.5 The amplitudes o f S-wave initiated from the Chi-Chi hypocenter against the hypocentral distance................................................................................................................62 Figure 3.6 The cartoon illustrates the brute-force algorithm to locate sub-events by searching the modeled Chelungpu fa u lt.............................................................................. 65 Figure 3.7 The located asperity sources obtained from the single-fault plane model from the E-W com ponent.......................................................................................................68 Figure 3.8 The located asperity sources obtained from the m ulti-fault plane model from the E-W com ponent.......................................................................................................69 Figure 3.9 The located asperity sources obtained from the m ulti-fault plane model from the N-S com ponent........................................................................................................70 Figure 3.10 The located asperity sources obtained from the m ulti-fault plane model from the vertical component..................................................................................................71 Figure 3.11 The rupture episodes o f asperity sources from the m ulti-fault plane model o f the E-W component............................................................................................................75 Figure 3.12 The rupture episodes o f asperity sources from the m ulti-fault plane model o f the N-S component.............................................................................................................77 Figure 3.13 The depth o f asperity sources in group G after relocation..........................79 Figure 3.14 The spatial distribution o f magnitudes o f sub-events..................................83 Figure 3.15 The frequency-magnitude relation o f sub-events.........................................85 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 3.16 The origin time o f identified asperity sources vs. their hypocentral distance to the Chi-Chi m ainshock.......................................................................................86 Figure 3.17a The data w ithin the shaded region in Figure 3.16a (the E-W component) are fitted by modified O m ori’s la w ...................................................................................... 88 Figure 3.17b The data w ithin the shaded region in Figure 3.16b (the N-S component) are fitted by modified O m ori’s la w ...................................................................................... 89 Figure 4.1 The minimum magnitude o f completeness....................................................101 Figure 4.2 Frequency-magnitude relation o f the raw catalog data w ithin a circular re g ion ....................................................................................................................................... 106 Figure 4.3 The changes o f b- and a- value as a function o f time for four selected circular regions centered at the Landers...........................................................................109 Figure 4.4 The Coulomb stress field before the Landers earthquake..........................112 Figure 4.5 The changes o f b- and a- value as a function o f time w ithin four selected positive CFS contours o f pre-Landers stress file d ......................................................... 114 Figure 4.6 The changes o f b- and a- value as a function o f time for four selected negative CFS contours o f pre-Landers stress file d .......................................................... 115 Figure 4.7 The cumulative number o f events against time in positive and negative pre-Coulomb stress lobes..................................................................................................... 116 Figure 4.8 The ratio o f the number o f clustered events to the total events..................118 Figure 4.9 Smoothed seism icity rate o f independent events and equivalent events....................................................................................................................................... 120 Figure 4.10 Flistogram and smoothed seismicity rate for small clusters and for large clusters.....................................................................................................................................121 Figure 4.1 la The number o f cumulative events w ith time counted in four CFS contour intervals using raw data........................................................................................................ 125 XI Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 4.1 lb The number o f cumulative events w ith time counted in four CFS contour intervals using declustered data.......................................................................................... 126 Figure 4.12a The number o f cumulative events w ith time counted in four annular or circular regions centered the Landers using raw data......................................................127 Figure 4.12b The number o f cumulative events w ith time counted in four annular or circular regions centered the Landers using declustered data.........................................128 X II Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ABSTRACT First, quasi-static models were used to explore the failure o f a strong stuck asperity on an otherwise creeping fault plane. They produced the temporal scaling observed at Parkfield. However such scaling requires the constant density o f unit asperities w ithin the cluster. It rules out the Cantor dust fractal model suggested at Parkfield. Although the average stress drop for asperity models decreases with earthquake size, it is significantly lower over the entire rupture area, equivalent to that estimated from spectral analysis. The fracture energy is estimated to be G > 10’ J/m^, near the upper lim it o f estimates on the San Andreas Fault. Next, the rupture process o f the 1999 Chi-Chi, Taiwan earthquake was explored from high-frequency near-field strong-motion seismograms. The entire mainshock was resolved into a sequence o f distinct bursts in high frequency, each o f which corresponds to a sub-event from an asperity. Their origin times, locations and magnitudes were determined from a pre-determined Chelungpu fault. The first appeared sub-events follow the Chelungpu rupture propagation at a velocity o f 2.0 km/s. Later sub-events can be interpreted as aftershocks that begin before the rupture has terminated. These sub-events have the Gutenberg-Richter 6-value o f 1.0. Spatially, the larger sub-events are located at greater depth, while the small sub-events are only located at shallower depths. Overall, they accord w ith results o f waveform inversions. Xlll Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Finally, the Gutenberg-Richter a- and b- values, cluster statistics, and the migration o f seismicity were measured as functions o f magnitude, space, and time before the 1992 Landers California earthquake using raw and declustered catalogs. The pronounced increase in a-value for distances less than 120km to the Landers as well as its un-correlation w ith changes in 6-value indicate an increase o f events at all magnitudes. More and larger clusters were formed w ith time before the Landers mainshock, which reflected smoother and more spatially correlated regional stress fields before a large event. Foreshock migration towards the Landers mainshock was observed in the active stress lobes defined in the stress recovery model, but not in randomly selected regions. X IV Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C h a p t e r 1 Introduction This dissertation consists o f three papers that explore the nature o f heterogeneity in earthquake physics. The first, hereafter referred as paper I, has been published in Bull. Seim. Soc. Am.. The second (paper II) w ill be submitted to the J. Geophys. Res.. The third one (paper III) was submitted to Geophys. J. Int.. Paper I and II focus on heterogeneity in the form o f asperities on a fault plane, while paper III explores spatial and temporal patterns in regional seismicity. Paper I was motivated by the unusual spatial, temporal and magnitude distribution o f seismicity observed on the creeping section o f San Andreas fault, California. The primary objective o f paper I was to use analytical and numerical asperity models to explain these observations. By numerically simulating the failure o f a strong stuck asperity on an otherwise creeping fault plane, the numerical model produced the same slip distribution as analytical asperity models, which, for a constant loading rate, produced repeating events having a period T that scales w ith moment Mo as T < x , the scaling relation observed at Parkfield. When the asperity is a composite o f smaller hard unit asperities, only clusters with a fixed asperity density follow the observed T oc scaling, which rules out the fractal spatial distribution (Cantor dust) o f Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. unitasperities at Parkfield suggested by Sammis et al. (1999). Theoretically, the stress drop for asperity models is not independent o f seismic moment but decreases with earthquake size. For solid asperities, the average stress drop on the asperity is on the order o f 100 MPa, well below the theoretical strength. Moreover the average stress drop over the entire rupture area is significantly lower, equivalent to that estimated from seismological spectral analysis. This solved the paradox o f abnormally high stress drops for the smallest events derived from the circular crack model. The energy release rate for asperity events is estimated to be > 1.4 x 10’ J/m^. Since it is near the upper lim it o f estimate using parameters from large events on the San Andreas fault, the asperity model may provide another way to estimate the energy release. Paper II was motivated from the stochastically distributed asperity sources and delayed ruptures observed in the 1999 Chi-Chi, Taiwan earthquake. However this distribution in space and time o f asperities can not be recognized in the detailed mappings o f slip history obtained from waveform inversions which used only low- frequency information. Using the high-frequency near-field strong motion data from the Chi-Chi earthquake. Paper 1 1 identified a sequence o f distinct sub-events, each o f which corresponds to an asperity source lying on the Chelungpu fault rupture. The locations and origin times o f these sub-events determined from high-frequency arrivals showed that these asperity sources follow the Chelungpu rupture propagation history at a velocity o f about 2.0 km/s, but there also exist stochastic jumps and significant delays, which may be interpreted as aftershocks that occur during the Chi- Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Chi mainshock. Spatially these asperity sources appear in groups, most o f whieh are located at shallow depth along the Chelungpu surface trace. Asperities located at great depth suggest a non-planer rupture surface w ith dip increasing to the east. An asperity group or combined groups correspond to the large asperities presented in source inversion studies. When the size o f each sub-event was determined, the frequency- magnitude distribution o f these sub-events has b-value equal to 1.0, which implies that the asperity sources have a fractal distribution. In space, the large sub-events are located at greater depth in accord w ith the seismogenic layer, while the small sub events are only located at shallower depth where large events can not be generated. Paper III turns to the study o f regional seismicity prior to the 1992 Landers, California earthquake. Currently there are four physical models that ean explain the accelerating seismic moment release observed in a period prior to a great earthquake: (1) The damage mechanics model, (2) the critical point model, (3) the stress recovery model, and (4) the generalized aftershock model. Prior studies designed to test the applicability o f these four models usually suffered the problem o f very poor statistics, because only a few intermediate precursors were used. In paper III, the myriad o f smaller events were used to improve these statistics, and thus sharpen distinctions between the proposed models. Specifically, this paper focus on exploring changes in a- and 6-value, changes in the cluster statistics, and spatial migration o f seismicity using both raw and declustered catalogs. For the raw catalog, the a-value o f regional seismicity increased over a large portion o f southern California to distances o f i?=250 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. km from the Landers earthquake. However, only for regions w ith i?<125 km, a- and b- vaiues are relatively uncorrelated indicating a uniform increase in activity at all magnitudes. For the declustered catalog, the a-value not only showed no systematic variation in time, but was almost perfectly correlated w ith the Z)-value for all radii R. This implies that the increase in the number o f aftershocks is associated w ith the increase in the number o f intermediate events that produce the accelerating seismicity. When this analysis was limited to the active lobes predicted by the stress recovery model, for the raw catalog, the boundary between the correlated and uncorrelated regions was again at about 125 km, but there was no improvement in this pattern over that obtained using circular regions. The fraction o f events belonging to clusters increased steadily from 1972 until the Landers earthquake. The number o f clusters per year also increased during this time period while the number o f independent events per year decreased until about 1989 and then increased during the two years before the Landers event. The number o f clusters plus independent events per year remained approximately constant until 1989, then increased markedly between 1989 and the 1992, Landers event, due to an increase in both clusters and independent events. Finally, the number o f large clusters (« > 5 events) associated w ith large and intermediate earthquakes increased steadily up to the time o f the Landers earthquake, while the number o f small clusters (n < 5 events) associated w ith irregular small events remained approximately constant all time. The only evidence for the stress recovery model is that the predicted seismicity migration were observed in the active Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. regions specified in this model where accelerated seismicity occurred first on the outskirts o f the critical region and moved systematically inward toward the Landers faults. Paper List: Paper I: Chen, Y. and C. G. Sammis, Asperity Models for Earthquakes, Bull. Seism. Soc. Am. 93, 1792-1802, 2003. Paper II: Chen, Y., T. Teng, and C. G. Sammis, A High Frequency View o f 1999 Chi-Chi, Taiwan, Source Rupture and Fault Mechanics, submitted to J. Geophys. Res., 2004. Paper III: Chen, Y. and C. G. Sammis, Spatial and Temporal Patterns o f Regional Seismicity Preceding the 1992 Landers, California Earthquake, submitted to Geophys. J. Int., 2004. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Chapter 2 Asperity Models for Earthquakes Abstract A quasi-static numerical method was used to simulate the failure o f a strong stuck asperity on an otherwise creeping fault plane. The numerical model produced the same slip distribution as analytical asperity models, which, for constant loading rate, produced repeating events having a period T that scales with moment Mo as T oc , the scaling relation observed by Nadeau and Johnson (1998) at Parkfield. When the asperity is a composite o f smaller hard “ unit asperities” , we still find T oc , but the constant o f proportionality depends on the density o f unit asperities within the cluster. Since, only clusters w ith a fixed asperity density follow the observed T cc scaling, this result rules out the fractal spatial distribution (Cantor dust) o f unit asperities at Parkfield suggested by Sammis et al. (1999). For solid asperities, the average stress drop on the asperity is on the order o f 100 MPa, but the average stress drop over the entire rupture area is significantly lower, equivalent to that estimated from spectral analysis. However, the stress drop for asperity models is not independent o f seismic moment, but decreases with earthquake size. The energy Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. release rate for asperity events is estimated to be G > 10’ J/m^, near the upper lim it o f estimates by L i (1987) using parameters from large events on the San Andreas Fault. 2.1 Introduction Seismicity in the creeping section o f San Andreas Fault in central California has interesting spatial and temporal characteristics. A t the northern end o f the creeping section near San Juan Bautista, Rubin (1999) observed lines o f hypocenters extending up to several kilometers. A t the southern end near Parkfield, Nadeau et al. (1994, 1995) and Nadeau and M cE villy (1997), observed a hierarchical cluster structure w ith less well-developed lineations. The Parkfield catalog contains sequences o f “ repeating earthquakes” characterized by nearly identical waveforms, hypocenters, magnitudes, and recurrence intervals. Such repeating events have been observed at many other locations in the creeping section (Ellsworth and Dietz, 1990; Vidale et al., 1994; Marone et al., 1995). Nadeau and Johnson (1998) determined the scalar seismic moment Mo for events comprising 53 repeating sequences o f between 3 and 13 events each, and found a power law scaling relation T < x between the repetition period T and the scalar seismic moment. Nadeau and Johnson (1998) used their measurements o f Mo and T to estimate source parameters o f the repeating events. The average moment-rate for each sequence Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. was determined = {M q) I { t ) . The observed surface slip rate was used for the average slip rate on an asperity in the basic definition o f scalar moment Mg =G Au to estimate the average area (v4) o f events in each sequence as (^A) = where G is the shear modulus. Note that we use braces to denote an average over events in a repeating sequence and a bar to denote the spatial average over the slip surface o f an individual event. The use o f in the equation for moment is an approximation since, strictly speaking, should be equated to the maximum displacement during an event. This approximation was subsequently dropped in a proper elastic analysis o f an asperity by Johnson and Nadeau (2002) and in this paper. However, follow ing Nadeau and Johnson’s (1998) original analysis for the moment, the average displacement can be found from the known value , and the average scalar moment o f events in a repeating sequence as(w) = (M g )/ G (h ) . The stress drop was estimated using the equation for a circular crack (see, e.g., Kanamori and Anderson, 1975) r ^3/2 G (A c t ) = — = (M „) • 3 /2 < \ ■ (2-1) Using the observed values o f (M q^ and , this analysis yielded the surprising result that the average stress drop decreases w ith earthquake size as (Act) q c ( M q ) ' , which is at odds w ith estimates based on seismic spectra that find constant (or slightly Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. decreasing) stress drop consistent w ith established scaling relations for large earthquakes (Abercrombie, 1995; Hardebeck and Hauksson, 1997). Moreover, Nadeau and Johnson (1998) inferred that the stress levels reach 2 GPa for the smallest events, which is more than 10 times laboratory strength. Sammis et al. (1999) pointed out that strengths on the order o f 2 GPa are not unphysical for small asperities and proposed that seismicity at Parkfield is generated by clusters o f very small strong “ unit asperities” loaded by creep on the surrounding fault plane. They showed that the spatial distribution o f hypocenters at Parkfield has a hierarchical cluster structure, which can be described as a discrete fractal “ Cantor Dust” having fractal dimension D = 1 and a discrete rescaling factor o f /? = 20. In this model, stress drop decreases w ith increasing moment as observed, since the area density o f unit asperities Pa decreases w ith slip area as oc for the case D = 1 . The failure stress Of on a slip patch containing N unit asperities is related to the average density Pa, strength ag, and areaAg o f the unit asperities as <Tf = ----- -— = (2-2) A I f the stress drop depends on this failure strength and the displacement (the stress drop need not be total), we have A c t = (7 f A ^ U„ “ P a^ o A A \ u „ J ^ P aU, (2.3) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. where is the slip on a unit asperity and uo is the slip associated w ith total stress drop ao. For the scaling relations deduced by Nadeau and Johnson (1998), o c and A c t g c , equation (2.3) predicts oc oc . Combining oc and = GAu gives o c A^'^ which in turn yields cc (Au)~^^'^ oc A~'^^, exactly the Z) = 1 Cantor dust structure observed by Sammis et al. (1999). However, while it is satisfying that the spatial structure is consistent with the observed displacement and stress scaling, it remains to show that fractal clustering produces the observed scaling T oc . In fact, a key result o f the numerical analysis presented below is that this temporal scaling does not hold for fractal clusters. The large stress drops implied by the Nadeau and Johnson (1998) analysis motivated several studies which challenged their fundamental assumption that asperities slip only as repeating earthquakes. I f this assumption is not true, then the slip rate associated w ith repeating earthquakes can not be equated to the slip rate observed at the surface, and equation (2.1) for the stress drop is not valid. For example, Anooshehpoor and Brune (2001) used their foam rubber fault simulator to create a series o f repeating events on a circular asperity surrounded by a stress-free circular annulus. A fter about 12 repeating events, the entire surface, including the asperity, slipped in a much larger event. The sequence then repeated. In this case the observed “ surface slip” is the sum o f contributions from the repeating events and the larger 10 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. system-wide event. To assign the entire observed slip to the repeating events is an error, which, according to equation (2.1), leads to an overestimate o f the stress drop. We analyze the annular crack in the next section, and find that it does not, in general, predict T oc scaling without an arbitrary assumption relating the inner and outer radii o f the stress free annulus. Beeler et al. (2001) also attacked the basic assumption by proposing that asperities might fail by a creep-hardening mechanism observed in laboratory sliding experiments on almanden serpentinite powders by Summers and Byerlee (1977). In this case, , and the displacement rate associated w ith the repeating earthquakes is only a small fraction o f the displacement rate observed at the surface. This model predicts a weak dependence o f T on Mo, but not specifically Motivated by the lineations o f hypocenters observed at the northern end o f the creeping segment, Sammis and Rice (2001) proposed that repeating events might occur at the boundary between creeping and locked fault patches. They integrated the known stress field at the edge o f an asperity to calculate the average stressing rate over a much smaller weak patch. Assuming all such weak patches fail at a constant stress level, they derived the observed T oc scaling. Moreover, they calculated stress drops on the order o f a few bars for large locked patches having a radius on the order o f 100 m. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. More recently, Johnson and Nadeau (2002) have investigated the elastic solution for an isolated asperity on an otherwise stress-free fault plane. As discussed in more detail in the next section, they found that this model gives the observed scaling T cc M q "' . Moreover, it predicts low average stress drop when slip in the stress-free region surrounding the asperity is properly included in the calculation o f moment. Although Johnson and Nadeau (2002) modeled asperities as composites o f smaller unit asperities, they did this only as means to remove the edge singularity. Their model is fundamentally different from that proposed by Sammis et al. (1999) in that their clusters all have a uniform density o f unit asperities, not the hierarchical structure proposed by Sammis et al. (1999). Also, Johnson and Nadeau (2002) ignore creep between unit asperities w ithin a cluster. In this paper, we use a numerical model to explore the scaling behavior o f seismicity produced by clusters o f asperities on a uniform ly slipping fault plane. In particular, we ask whether the hierarchical Cantor dust model also yields the observed scaling T q c , and is thus a viable model for Parkfield seismicity. The numerical model allows us to explore the effect o f creep between unit asperities in a cluster, ignored in the Johnson and Nadeau (2002) analytical study, but which becomes increasingly important as the density o f unit asperities decreases. We begin with a review o f analytical solutions for the mechanics o f a stuck asperity leading up to and in clu d in g the analysis o f Johnson and Nadeau (2002). W e then test o ur num erical 12 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. model by reproducing these analytical results before applying it to the problem o f asperity clusters. 2.2 Analytical Asperity Models Stress free C^remote Figure 2.1 An analytical asperity model for constant remote stress (Das and Kostrov, 1986). An asperity of radius is surrounded by a stress free annulus of outer radius r,.. The system is loaded at constant remote stress arem oK such that a = a rc -m o ie for r » A- 13 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Das and Kostrov (1986) analyzed the fracture mechanics o f the annular crack r ^ < r < r, shown in Figure 2.1. The region r< r^ is the asperity and the annulus r ^ < r < is stress free. They found the average stress on the asperity is related to the remote stress as - ^ = 0.8-^ (2.4) Sammis and Rice (2001) extended this analysis using the stress intensity factor for the asperity which, forr^. » , is given by Tada et al. (1985) ^ 4 ^ ^ ^ ^ re m o te ^3/2 \7T y (2.5) The asperity fails when K = Kc, where Kc is the critical stress intensity factor (a material property). These two equations can be combined to eliminate the factor {'^rcm oie^c) yicld thc average stress on the asperity at failure c r / = l . l - ^ (2.6) r„ For , the maximum displacement on the asperity when it fails, Ua, is that at the center o f a stress free crack o f radius rc in the stress field (Trem ote, which can be found using (2-7) 24 Eliminating the factor using equation (2.5) gives 14 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 6-v/^ K I— (2-8) The seismic moment can be obtained using B etti’s theorem (Kostrov and Das, 1988) remote K .s p e n ,y {>^)dS = | ^ ( ^ a s p c n ty {r)dS (2.9) where is the stress drop distribution over the asperity o f radius ra. Both integrals are over the entire crack surface 0 < r < , although = 0 for < r <r^. The integral on the left is the seismic moment for the asperity event divided by rigidity G. On the right, is known from equation (2.7). For the stress on the asperity is (Johnson and Nadeau, 2002) where v is Poisson’s ratio. Substituting (2.10) into (2.9) and integrating yields _ ^ _ 2 4 o ^ 4 G ^ G " ItiG ‘ ( 2 - v ) ^ ^ or W = » 2.49G«,r,r, (2.12) Using equation (2.8), this can be written Mo » 2.49;rG The observed scaling T oc Mg'^'’ requires Mg oc u ° , and hence cc u / . Using Z ' IG (2.13) 15 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. equation (2.8), this is equivalent to oc r j ’'^. However, we can think o f no physical reason for this scaling since is arbitrary in this model. Johnson and Nadeau (2002) proposed a physical interpretation o f for the case o f a single circular asperity on an otherwise stress free plane w ith fixed remote displacement Ua (Figure 2.2). The Johnson and Nadeau (2002) analysis is based on the analytical solution to the problem o f two elastic half spaces joined only by a penny shaped connection given by Westmann (1965) and M indlin (1949). In this problem, a far-field displacement Ua produces a stress distribution on the fault plane given by ' 2Gu„ 1 r(r) = (2 - r ^ 0 r > r (2.14) where the stuck patch has radius The “ slip deficit” u{r) is then defined as the imposed slip Ua (far from the asperity) minus the actual slip on the fault plane. On the stuck asperity, u{r) = Ua, while exterior to the asperity the slip deficit decays approximately as Mr. When the asperity fails, a slip field u{r) erases this slip deficit on and near the asperity. However, Nadeau and Johnson (2002) assume the existence o f a threshold slip value U c, below which fracture-slip is assumed not possible. This threshold slip U c occurs at a radius V c- The distribution o f slip during an event may be expressed as (see Figure 2.2): 16 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. i{r)^ UJa r < r < r (2.15) r 0 r> r „ When r = Vc, we have (2.16) Johnson and Nadeau (2002) calculate the scalar seismic moment for an asperity earthquake by integrating (2.15) over the rupture area. Assuming the integration gives (2.17) This equation is identical w ith equation (2.12) except for a constant. The difference may be due to the difference between the boundary conditions for the two models: constant remote stress in the Das and Kostrov (1986) model, and constant displacement in the Johnson and Nadeau (2002) model, or to slightly different approximations in the two derviations. Like Sammis and Rice (2001), Johnson and Nadeau (2002) also derived the result that oc , but they did not use the stress intensity factor directly. Instead, they divided the asperity area into smaller unit asperities, each o f radius ro, and neglected areas in between. Each unit asperity is stressed uniform ly at its average stress which, for those closest to the edge, can be approximated for as 0^0^ / = / (2-18) 17 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Asperity cells with radius r „ Asperity cluster with radius Va u r a a Slip shadow up to a critical radius Distribution o f slip during an event i i Figure 2.2 An analytical asperity model for constant remote displacement (Johnson and Nadeau, 2002). The asperity is modeled as a circular cluster (radius r„) of smaller asperities of radius rg. The slip deficit distribution is assumed constant within while it decays with \/r for r > ra. Slip during an event erases the slip deficit on and near the asperity, but is assumed to have a minimum value U c - This critical displacement defines a critical radius beyond which slip does not occur during an asperity event. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. This averaging removes the singularity at r = V a and gives the same result as equation (2.8), o c ^ . The exaet expression in Johnson and Nadeau (2002) is 3;r^(2-v) ^ -0-, <2-19) 16G where the constant o f proportionality depends on the size o f the unit asperity ro, which is an adjustable parameter in their model. Their approach is equivalent to using a stress intensity factor in the lim it . In addition to cc , the observed T oc sealing requires three additional ingredients: 1) u{r) ~u^,a constant over the asperity, and decreases as w(r) oc — for r r > r ^ ,2 ) a critical displacement U c exists below which u{r) = 0, and 3) T ccu^, i.e. 2 W ^ 3 the loading rate is constant. I f these conditions hold then r^ , r^ = — oc , and equation (2.17) gives cc oc u ^ u fu j oc u j". Hence T az Mq"" as observed. Having established scaling for solid asperity models, we now examine the constant o f proportionality in oc M q ”" . The observed value comes from Nadeau and Johnson (1998) who found logw„ =0.171ogMo -2 .3 6 in cgs units, which may be written - 1.45 x in mks units. The value o f c predicted by the analytical model can be found by substituting equations (2.8) and (2.16) into equation (2.17) to obtain 19 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4 r v 6y 1 k ; u, . (2.20) Setting c = C obs and solving for U c gives 4 = 7 T ' G ' r 1 ] - 4 ^ G^ ( 1 ^ U J k ‘^o b s v6j G^^E^ (2.21) where Kc has been written in terms o f the fracture energy Gc, using and E is Young’s modulus. Equation (2.21) places a constraint on Gc. The asperity model was developed assuming . For the smallest repeating events, Nadeau and Johnson (1998) infer « 1 cm. Hence we require u^, « 1 cm, which can be used in (2.21) to place a lower bound on Gc. Assuming G = 0.3 x 10'' Pa and £ ■ = 0.8 x lO " Pa, and =1 mm, equation (2.21) yields Gc> 1.4x1 o’ J/m^. This value is near the upper lim it o f previous estimates o f the fracture energy for large earthquakes on the central San Andreas Fault. Li (1987) discusses three methods for estimating Gc using geodetic observations. The first is based on the elastic brittle crack model for which Gc = creeping segment o f the San Andreas Fault in central 8/ California, 21 160 km. A maximum slip rate o f 34 mm/yr, and an average repeat time o f 160 years give = 5.44m. Taking G = 0.3x10" Pa and v = l/4 gives Gc= 3.3 X 1 0 *^ J/m^. I f seismic rupture is only occurring in the upper crust (say the upper 10 km o f a 50 km thick lithosphere), Gc should be increased by a factor o f 5 20 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. which gives Gc= 1.7 x 10^ Hw?. Similar values w'ere obtained using the J-integral method. A third method based on the anti-plane (mode 1 1 1 ) edge crack model o f L i and Rice (1983a,b) gave a maximum value o f Gc= 4x10® J/m^. The unusually large stress drops calculated by Nadeau and Johnson (1998) are a consequence o f their identification o f the average displacement u in the static moment Mg = GAu w ith displacement at the surface. As discussed above, should be equated to the actual displacement on the asperity, Following Johnson and Nadeau’s (2002) analysis, the average stress drop can be calculated by integrating equation (2.9) over the entire slip surface from r = 0 to r = = 2m'dr 0 JrJ' — 4G u r ^ a = --------------------- = r. -- 1 - ^ (2-22) T U - ^ ;r(2 -v j Equations (2.8) and (2.16) can be used to write (2.22) as Act o c . Since Mg q c , we have A c t c c Mg~'^^. Quantitatively, for v = 1/4, A c t (2.23) y l n j Using G = 0.3x 1 o ' ‘ Pa, W c < 1 mm from above, and the minimum seismic moment o f the repeating events at Parkfield (M g « 10*Nm), the maximum stress drop is 24 MPa. Since U c is assumed here to be a property o f the fault surface independent o f Mo, the stress drop decreases w ith increasing m om ent a s . These lo w average values are due, o f course, to the large area between and V c where the stress drop is zero. 21 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Even the average stress drop on the asperity itself in these analytical asperity models is lower than that originally estimated by Nadeau and Johnson (1998). W riting the critical stress intensity factor in terms o f the energy release rate in equation (2.6) for the average stress drop on an asperity gives <r‘ = 1.1-JG^.E/ . For the smallest event in Parkfield, T q = 10 cm. Using our previous estimate o f Gc = 1.4x 10^ J/m^ and £ ■ = 0.8x lO" Pa gives =2GPa. However since it is still in the laboratory scale, this value may not be physically ruled out (Sammis et al., 1999). W hile for events with V a = 10 m, ctJ = 200 MPa well below the theoretical strength. The stress is, o f course, much higher near the edge o f the asperity. Seismological spectral analysis also yields a low average stress drop for asperity earthquakes i f the rupture radius is estimated from the event duration G and rupture velocity Vr as U I v^. Kostrov and Das (1988) show that r is equivalent to V c for an asperity event, and that the asperity pulse has an anomalously large duration compared to a crack pulse o f radius V c. The circular crack formula A ct = then also gives 16r, low average stress drops. 22 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2.3 A Numerical Asperity Model Although Johnson and Nadeau (2002) modeled the circular asperity as a composite o f smaller unit asperities, they neglected displacements between them and approximated the displacement as a constant u{r) = for r <r^. This gave an adequate representation o f the fracture mechanics o f solid asperities, but it does not allow exploration o f the sealing properties o f composite asperities, especially as the density o f unit asperities decreases and creep between them becomes significant. We now explore the effects o f such creep using a numerical model Asperity clusters were simulated using the heterogeneous fault model developed by Ben-Zion and Rice (1993). In their model, a finite 2-D strike-slip fault is embedded in a 3-D elastic half-space as in Figure 2.3. The fault plane is represented by a vertical rectangle, which is uniform ly divided into square cells. The top o f the strike-slip fault intersects the free surface while the other three edges are driven at a constant slip rate. Each cell is modeled as a dislocation. The stress transferred along the fault due to incremental tectonic loading and failures in previous events is connected to the slip on the failed cells w ith a discrete boundary integral equation. For each dislocation only right-lateral (or left-lateral) slip and shear stress along the fault strike are considered; vertical and tensile displacements are neglected. Details o f the transition o f a cell from broken to unbroken are not included in this quasi-static brittle model. Failure o f the elementary cells is determined by a strength criterion and the time spent in the 23 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. dynamic rupture process is not simulated. A slip-weakening constitutive law is represented by a dynamic overshoot coefficient that connects static strength, dynamic strength and arrest stress. Constant V elocity ■ Strong Unit Asperities Creeping Ceils Figure 2.3 A numerical asperity model. A circular asperity cluster is located at the center o f an otherwise creeping strike-slip fault. The finite 2-D strike-slip fault is embedded in a 3-D elastic half-space. The top of the fault intersects the free surface while the other three edges are driven at a constant slip rate. The dark square cells in the circular asperity are termed “unit asperities”, and the grey cells on the fault plane, including those between the unit asperities, were designated “creeping cells”. Creeping cells simulate creep by repeatedly failing at a stress level much lower than the strength of the unit asperities. 24 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. An asperity was constructed as a cluster o f strong cells (which we term “ unit asperities” ) at the center o f the fault plane as illustrated in Figure 2.3. A ll other cells on the fault plane, including those between the unit asperities, were designated “ creeping cells” . Creeping cells were given an extremely low static strength thereby simulating continuous slip. In essence, we replaced creep by a myriad o f small earthquakes, which, when integrated over time, have the same effect as creep in loading the unit asperities. The fault model in this simulation is “ inherently discrete” , as classified by Rice (1993), since the size o f an elementary cell is always larger than the dimension o f the slip weakening zone and cells can fail independently. In our simulations, we required all the cells in asperity cluster (strong and creeping) to fail in a single time step. We forced this by severely weakening all cells in a cluster once any one o f its unit asperities failed. Finally the physical size o f the fault patch and the elementary cell are not important in this elastic model because there is no intrinsic length scale (e.g., the effects o f visco-elasticity in the lower crust and upper mantle are not considered). 2.4 Results of Numerical Simulations I f the asperity area is entirely occupied by unit asperities, we call it a “ solid asperity” . I f this area is occupied by a combination o f strong and weak cells, we call it 25 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. an “ asperity cluster” . Asperity clusters are characterized by the density o f asperity cells p = n! N , where n is the number o f unit asperities, and N is the total number o f cells in the cluster. The density o f asperities can also be expressed as p = / r j ' , where denotes the scale o f elementary cells, and V a denotes the radius o f the cluster. Clearly A is a measure o f the size o f the cluster. We organized our calculations into 3 sets, each o f which fixes one parameter in the equation p = n! N . Set A has a fixed density p o f unit asperities, set B has fixed size A, and set C has a fixed number n o f unit asperities. Solid asperities are a special case o f set A w ith a fixed asperity density equal to 1. 2.4.1 Numerical Simulation of Solid Asperities We first simulated solid asperities in order to validate our numerical approach. Figure 2.4a is a typical result. Slip on the asperity is uniform w ith less than 5% variation, and decreases w ith distance from its edge. Figure 2.4b shows that the numerical model gives the expected u{r) oc 1 / r dependence o f slip in the creeping area (equation 2.15), except near the edge o f the fault patch, where u(r) drops steeply to zero. This arises because the fixed (during an earthquake) model boundaries are reached. To verify that this is a boundary effect, we doubled the area o f the fault, but left the asperity unchanged. For this larger model, the region for which w(r) q c 1 / r 26 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (a) -2 1000 0 -4 10 i I middle row along Z | : middle row along X gio" slope 2 ;^10 1 10 .0 1 •2 10 r (km) from the center of asperity cluster Figure 2.4 Numerical simulation of the slip deficit distribution on the asperity cluster and its surrounding creeping areas just prior to an event, (a) 3-D view of the slip distribution, (b) Slip vs. distance from the center of an asperity cluster. Note the slight asymmetry in the vertical and horizontal directions, and that the slip distribution deviates from Mr when it approaches the fault boundary. 27 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. extends to larger r (Figure 2.5). The finite fault plane also means that the condition assumed in the analytical models is not satisfied, and we cannot numerically integrate the slip to compute seismic moment. However the numerical simulation produced oc ^ and, o f course, a repeat period T <xu^, which are, together with the assumption o f Uc, the key requirements for T cc scaling. 10 Large Model Normal Model 3 E 10 slope = - X I 1 10 ■ 2 0 r (km) from the center of asperity cluster Figure 2.5 The slip distribution for two models having the same asperity but different fault sizes. The larger is tw ice the size o f the faults used in this study. As expected, the Hr decrease in displacement extends to a larger radius in the larger model. The boundary effects do not propagate far into the model. 2 8 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. J ( . ) « . - n .... ■ 1 y i ; o. t400 1 ?====.. ID ; 1 eoe ^ 400 o 200 0 —I . 1 Figure 2.6 Kinematical rupture scenarios. For both solid and composite asperities, fracture nucleated at the edge and then circled the boundary, next propagated inward from all directions, finally fracturing the central area, (a) the stress transformation during the dynamic rupture process. Once the entire asperity ruptured, stress on the asperity dropped, (b) the slip distribution during the dynamic rupture process. Once the entire asperity ruptured, it extended well into the surrounding creeping area. 29 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2.4.2 Kinematics of Asperity Rupture In our simulations, we required all the cells in an asperity cluster to (strong and creeping) to transit from stable to dynamic slip in a single time-step. Although we did not explicitly explore the time-dependent process o f dynamic rupture at the crack tips, we examined the kinematical rupture scenario (Figure 2.6a and b). Using an “ interior loop” algorithm described in Ben-Zion and Rice (1993), asperities were failed in order o f their proxim ity to failure, taking into account stress transfer from previously failed cells. For both solid and composite asperities, fracture nucleated at the edge and then circled the boundary. The fracture then propagated inward from all directions, finally fracturing the central area. Slip also followed this spatial pattern. Once the entire asperity ruptured, stress on the asperity dropped (Figure 2.6a), and slip extended well into the surrounding creeping area (Figure 2.6b). This fracture scenario was also observed for constant stress loading by Das and Kostrov (1983, 1986) who named it the “ double encircling pincer” . 2.4.3 Numerical Simulations of Asperity Clusters Since our numerical model reproduced the analytical results for a solid asperity, we now use it to explore the scaling behavior o f asperity clusters. We begin w ith the 30 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (a) E j s e : n ' Solid Asperity Asperity Cluster (p = 0.3) 2 # E " ^ 4 Nf 6 0 X(km) 500 1000 1500 Displacement (mm) 0 X(km) 200 400 600 800 Displacement (mm) 1 10' C o •XS 3 r9 w i= > . a -io ' C O £ 2 Solid Asperity Asperity Cluster (p = 0.3)i n a ^ i: ; slope = -1 10 10 10*^ 10° r (km) from the center of asperity cluster 10 Figure 2.7 Comparison o f the slip distribution on a composite asperity with that on a solid asperity having the same radius r„. (a) shows the entire slip field while (b) shows a cross-section through the center o f the asperity. The slip distributions both show approximately constant slip on the asperity and a 1/r decrease in the surrounding creeping area. The am ount o f slip is less for the asperity cluster because creeping cells within the asperity load the unit asperities and they fail at a lower total displacement deficite. During an event, slip on the creeping cells within the cluster is only slightly less than that on the hard cells. 31 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. distribution o f slip during an event. Figure 2.7 compares the slip field during an event on a composite asperity w ith that for a solid asperity w ith the same size The slip on the creeping cells w ithin the cluster is a bit lower than that on the unit asperities since, being weaker, they have had several small creep simulating events between major cluster-wide events. Hence, the slip deficit on creeping cells w ithin a cluster is smaller and they move a bit less during a cluster-wide event. This leads to some confusion as to how average slip during an event is to be defined. We can define as the average over asperity cells and as the average over all cells in the cluster. Naturally, , but both are less than Ua on a solid asperity having the same r^. This is because creeping cells w ithin an asperity increase the stress concentration on the unit asperities causing them to nucleate a cluster-wide event more often, but w ith less displacement on the constituent unit asperities. As illustrated in Figure 2.8, the scaling oc ^ is only true for members o f model set A where p is held constant (which includes solid asperities). For sets B and C, the average slip increases with asperity density. For set C where n is held constant, this results in a decrease in Ua w ith increasing The question o f whether the average slip is proportional to the repeating period depends on how the average slip is defined. The average is exactly proportional to the repeating period T, and the ratio o f to T is just the imposed loading rate in our simulations (Figure 2.9a). However, does not scale linearly w ith T (Figure 2.9b). 32 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. For slip to be proportional to the repeating period, the slipped area must remain locked between events and release its accumulated strain only during earthquakes. Because includes pre-slipped creeping area, it is not proportional to the repeat period T. 3.4 Model set A1 (p = 1.0): slope = 1/2 3.3 3.2 Model set B (r^ or N Is fixed) O Model set A (p = 0.25): slope = 1/2 T 2.9 2.8 Model set C (n is fixed) 2.7<- -0.5 -0.4 -0 .3 0.2 Figure 2.8 The average slip on an asperity as a function of radius for both solid asperities and asperity clusters. Only models having fixed asperity density display : scaling. 33 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 60 Solid Asperity 55 50 45 Asperity Cluster 40 35 30 25 slope = 1/35 (mm/yr) 2000 1000 1500 Average slip on unit asperities (mm) 60 Solid Asperity 55 50 45 Asperity Cluster 40 35 slope = 1/35 (mm/yr) . 30 25 20 1 :00 400 600 800 1000 1200 1400 1600 1800 2000 Average slip on all cells in asperity cluster [Ug(mm)] Figure 2.9 The repeating period T of asperity events vs. the average slip (a) If is averaged over the asperity cells only, it is proportional to the repeating period T, and the ratio uJT is the given loading rate, (b) I f the slip is averaged over the entire asperity cluster including the creeping cells, it is not proportional to T. 34 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Stress drop scaling for composite asperity models is also sensitive to the density o f unit asperities since the creeping cells w ithin the cluster are essentially stress free. The stress distribution on a composite asperity (and hence the stress drop) is a maximum at the edge and minimum at the center (Figure 2.10), but it cannot be exactly described by equation (2.14), which was derived for the solid asperity. 1800 1600 ■ 1400 ra X ) 1200 ■ c .2 I 1000 1 8 0 0 o "O (/} CO C D 600 ■ 400 - 200 0 -2 m m Asperity cluster (p = 0.17) T“ •% X : •» t* I*.* «*, • % rnmtM -1.5 -1 -0.5 0 0.5 1 r (km) from asperity center 1.5 Figure 2.10 Stress drop distribution for an asperity cluster having p = 0.17. Ail creeping cells, within or surrounding the asperity cluster, are almost stress free. The stress distribution on the unit asperities is still m axim um at the edge and m inim um at the center, hut it cannot he exactly described by equation (2.14). 35 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The average stress drop on the asperity is the average stress drop on the unit asperities times their density p. Figure 2.11 shows the average stress drop on the unit asperities as a function o f for all model sets. For the solid asperities, this average is just we have discussed in section 4.2, and then «: . However for the composite asperity models, such scaling does not exist for two reasons. First, since equation (2.14) no longer holds, the consequent sealing rn^ruv > s no longcr valid. Second, the average slip does not scale w ith the size ra o f asperity cluster for model sets w ith variable p. Specifically, the average stress drops are roughly constant for model set C where the number o f asperity cells is fixed, while for model set A and model set B the average stress on the unit asperities decreases as the number o f asperity cells increases. From Figure 2.11, we see that the average stress drop on the unit asperities for a composite model can be much higher than for a solid model w ith the same This is because the outer asperities in a solid cluster support the load and shield the inner ones. In a composite asperity, on the other hand, creeping cells w ithin the cluster also load the inner asperities resulting in a larger average load on the unit asperities. For connected sub-clusters o f unit asperities within the cluster, the local stress state is described by equation (2.14). However, because o f creep between connected sub-clusters, equation (2.14) does not hold for the entire cluster. 36 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1 2 0 0 Model set B (r, or N is fixed) 1100 Model set A (p = 0.25) 1000 900 Q . O 800 1 /5 W C D 700 to < D 03 C 3 600 0 5 > < Model set C (n is fixed) 500 400 ■ Model set A1 (p = 1.0): A ct 0.8 0.6 0.4 r (k m ) 1.2 Figure 2.11 The average stress drop as a funetion of the radius the of asperity cluster for all models. Only the stress drops of solid asperities show A ct cc 1/r^ scaling. 2.5 Discussion The scalar seismic moment o f an event that ruptures a stuck asperity on an otherwise stress-free fault surface has the form Mn = k G u r r where the constant k 37 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. depends on the boundary conditions. For a fixed remote displacement Ua, Johnson and Nadeau (2002) show k = A, while for constant remote stress, we used B etti’s theorem to show that k ^ 2 .5 . In both cases, displacement on the asperity during an event scales as cc and we have M g oc . Since, for constant loading, the repeat time T o f asperity events is proportional to w «. The scaling between T and Mn is determined by the scaling o f rc w ith Ua. Johnson and Nadeau (2002) define by assuming the existence o f a minimum displacement U c which, for the \/r decrease in displacement beyond the asperity, leads to /u ^. Hence oc u j , M g oc u j ' , and r oc oc as observed by Nadeau and Johnson (1998). It is important to note that their basic measurements for the repeating sequences are (T) and (M q) , which are independent o f any assumptions. Their determination o f depends on their assumption that asperities only slip during an earthquake, but is independent o f any model. Fitting their observed relation between ( m „ ) and ( M g ) to the analytical asperity model placed a constraint on the fracture energy, G> 10^ J/m^, which is consistent w ith previous estimates based on models for large events on the San Andreas fault. Our numerical simulations found that only clusters w ith fixed asperity density (which includes solid asperities) yield the scaling relations between displacement and asperity size required to produce the observed pow er la w scaling between repeat tim e and scalar moment. Hence, if the asperities at Parkfield are clusters o f smaller unit 38 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. asperities, they must all have the same density. This unlikely circumstanee effectively rules out the Cantor dust fractal model proposed by Sammis et al. (1999) which assumed that larger earthquakes sweep over more o f the fractal pattern and thus break a lower density o f unit asperities. For the solid asperity model, the average stress drop still decreases with earthquake size as M~^'^. Average stress on the asperity itself can be as high as 100 MPa, but when the stress drop is averaged over the entire rupture area, it is reduced to less than 30 MPa. These low stress drops are equivalent to those found by seismological spectral analyses, which see the entire slip history. The creeping cells within a cluster increase stress concentration on its constituent unit hard asperities. Hence composite asperities fail at a lower average stress than solid asperities having the same radius Stress redistribution by the creeping cells also leads to a spatial distribution o f stress drop over an asperity cluster which is not the same as that over a solid asperity. Having ruled out a Cantor dust o f unit asperities, it appears that repeating events at Parkfield events are probably due to the repeated failure o f solid asperities o f various sizes. However, the fractal hierarchy found by Sammis et al. (1999) is an observation, so we are left w ith the question o f how to reconcile the observed spatial, temporal, and magnitude distributions. One possibility is that the asperities are “ knockers” , isolated blocks o f very strong high-grade metamorphic rocks such as 39 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. blueschist that are commonly observed in Franciscan terrain (Coleman and Lanphere, 1971; Karig, 1979). In its central creeping section, the San Andreas separates two quite distinct geologic materials w ith very different velocities and attenuation properties, the Salinian block on the southwest and Franciscan assemblage on the northeast. The Franciscan formation has been hypothesized to produce the creep, which may be resisted locally by the knockers. The shape o f exhumed knockers is ellipsoidal with sizes ranging from several meters to tens o f kilometers. One hypothesis that could explain the different hypocenter distributions at the two ends o f the creeping section is that these knockers experience rolling and fragmentation in the fault zone under shear flow. Repeated fragmentation produces the nested clusters (Cantor Dust) when shear flow is small. When the shear flow is large, the fragments are aligned into streaks. This interpretation implies that shear flow is larger at the North end. Neither the physical fragmentation process o f knockers nor their distribution under shear flow has been studied. A comprehensive model o f the fragmentation and transport o f knockers may be required to explain the observed spatial distribution o f seismicity and variations in b-value. 40 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Chapter 3 A High Frequency View of 1999 Chi-Chi, Taiwan, Source Rupture and Fault Mechanics Abstract High-frequency band-pass filtering o f broadband strong-motion seismograms recorded immediately adjacent to the fault plane o f the 1999 Chi-Chi, Taiwan earthquake reveals a sequence o f distinct bursts, each o f which can be considered as a sub-event from an asperity source o f the Chi-Chi mainshock. These bursts collectively make up the entire mainshock accelerogram. Each burst may have released a significant portion o f the total energy release o f the Chi-Chi mainshock. Many o f these bursts contain quasi-periodic sub-bursts w ith periods on the order o f a few tenths o f a second. Most bursts occur well behind the propagating rupture front. Detailed pictures o f these asperity sources do not appear in conventional slip-map studies, presumably because o f the low-pass filtering used in these waveform inversions. We directly used the high-frequency data to determine the origin times, locations and magnitudes o f these sub-events. The first asperities to rupture in a given location follow the Chelungpu rupture propagation history at a velocity o f about 2.0 km/s. Later asperity 41 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. events at a given location can be interpreted as aftershocks that begin before the Chi- Chi rupture has terminated. Spatially these asperity sources appear in groups, most o f which are located at shallow depth along the Chelungpu surface rupture and are consistent with the large asperities presented in source inversion studies. Asperities located at great depth suggest a non-planer rupture surface w ith dip increasing to the east. The frequency-magnitude distribution o f these sub-events has b-value equal to 1.0. In space, the larger sub-events are located at greater depth, while the small sub events are only located at shallower depths. 3.1 Introduction The 1999 Chi-Chi, Taiwan, earthquake (M w = 7.6) was the largest earthquake to strike Taiwan in the 20^'’ century. Geological and geophysical studies as well as field observations have shown that this earthquake ruptured about 85km o f the Chelungpu fault w ith complicated surface faulting. Most o f the length o f the fault rupture strikes in nearly north-south direction, dips to the east at a shallow angle (20° - 30°), and is dominated by thrust motion. A t the northern end, the fault trend bends toward the east and exhibits significant strike-slip motion (Lee et al., 2000). The Chi-Chi earthquake also generated unprecedented high-quality near-field strong motion data recorded by a dense network operated by the Central Weather 42 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Bureau o f Taiwan (CW B). In addition to teleseismic and GPS data, a number o f studies have addressed source parameters and source process. Generally, ground motions exhibit a major change between the southern and northern segments o f the Chelungpu fault. Ground motions at the southern segment showed large accelerations but small displacement and slip velocity, while at the northern segment, they showed large displacement (over 9m) and an unusually large slip velocity o f over 4m/see (Chung and Shin, 1999; Huang et al., 2001; Wu et al., 2001). During the mainshock, a total moment o f 3.38 x 10^° Nm (Harvard C M T solution) was released over about 30 - 40 see w ith an average rupture velocity o f 2.5 -2 .6 km/sec (W u et al., 2001; Ma et al., 2001; Zeng and Chen, 2001). The moment release rate peaked between 19 and 25 sec (Chi et al., 2001). Some large asperities were found from detailed mappings o f spatial and temporal distributions o f displacement and slip velocity inversion. From the velocity waveform inversion o f strong motion data, Chi et al. (2001) found that the source is composed prim arily o f three large asperities. The first one is located near the hypocenter, 30 km extending to the north, and its slip is mostly thrust. The second is located at shallow depth near the northern end o f the rupture. Slip on this asperity is oblique and shows a temporal rotation o f the rake from pure thrust to strike slip with large ground velocity. The third is located at the southern end o f the rupture. The former two asperities were also found by other studies, but they may not be distinguishable (e.g. Ma et al., 2001; Zeng and Chen, 2001). A ll three asperities were shallower than 10- 15km (W u eta/., 2001). 43 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The Chi-Chi mainshock triggered over 700 strong-motion stations across the island w ith an average station spacing o f 5km. Shin and Teng (2001) used more than 400 records around the Chelungpu fault to construct a movie o f surface motions during the rupture. This movie is a direct presentation o f the time averaged (~lsec) and spatially interpolated (<5km) record acceleration. It does not involve a crustal velocity model or wave propagation theory. Figure 3.1 gives a few o f typical time frames o f the movie. In each frame, the expanding circle gives the reference S-wave front calculated from a local velocity model, the thick cross indicates the Chi-Chi mainshock epicenter, and the time after the origin time is given at the top o f each frame. The observed wavefront appears to significantly depart from the calculated S- wave front to the east and southwest due to crustal heterogeneity. Any surface motion larger than 600 gal (blue patches) probably reflects energy release from a large asperity located directly below the large surface acceleration. Compared to images o f slip on the fault plane, many more asperities are identified in this movie. Furthermore the movie events appeared to jum p about in space and time without an orderly progression. Some occurred at times significantly later than that would be expected from rupture propagation (the predicted rupture front would be close to S wavefront with the rupture velocity about 0.8 times o f the S-wave velocity). Direct observation o f surface motions suggest a more discontinuous rupture propagation for the Chelungpu fault, which may depart significantly from a uniform propagating fault model. On the other hand, those later energy releases may also 44 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. EW:011 Sec. EW:014Sec. 25 Qt24 ■a 25 22 - 7 _ 600 1 600 450 1 400 360 1 300 1 250 200 : 1 • H * 150 100 80 / X -■ 50 25 10 5 120 121 Longitude 122 EW:019 Sec. 400 360 300 250 200 150 100 22- 25 122 Longitude 25 0)24 3 '25 22 'u / 'M ' / ’ 4 .... H 600 500 450 if im H H 360 H 250 M l 200 \ ' / '■ 150 '"V.., / 100 '■ 80 -i 50 25 10 5 120 1 21 122 Longitude EW:020 Sec. 25 600 500 460 400 350 300 250 200 100 22 122 120 Longitude Figure 3.1 The time frames at 11, 14, 19, and 20 sec taken from the Chi-Chi movie that documents the ground motion for the E-W component observed at the surface by Shin and Teng, 2001. The color bar in each frame gives the ground acceleration in gal. The thick plus sign indicates the epicenter of the Chi-Chi mainshock. The circle indicates the calculated S-wave front. 45 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. reflect aftershock sequences that cannot be distinguished from the Chi-Chi mainshock. However, the details o f these asperity sources are impossible to differentiate w ith the spatial and temporal distributions o f displacement or slip velocity derived from the broadband near-field strong motion seismograms, nor is this differentiation possible using teleseismic broadband and GPS data (Ma et al., 2001; Wu et al., 2001; Zeng and Chen, 2001; Oglesby and Day, 2001; Chi et al., 2001). Current waveform inversion studies typically are based on low-passed velocity or displacement time series numerically integrated from strong-motion accelerograms. The low-pass filter is usually significantly less than IH z due to the low resolution o f the earth model and a poorly known site response. The absence o f asperity sources in waveform inversion studies, and to a lesser extent in the movie construction, is simply due to the loss o f high-frequency information in the low-passed input waveforms. In this study, we w ill image the asperity sources at high-frequeney using the near field strong-motion accelerograms. A fter high-pass filtering, the entire rupture process o f the Chi-Chi mainshock is resolved into a sequence o f high-frequency bursts, which probably originate from the rupture o f asperities. By comparing the observed and calculated arrival times o f these sub-events, we used a brute-force method to compute asperity locations in a modeled fault plane simulating the Chelungpu rupture. Next we estimated the relative sizes o f these sub-events assuming that the total seismic moment was released through these sub-events. Once the high-frequeney bursts corresponding to each asperity source were determined, the asperity sources were relocated on a less 46 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. constrained fault surface. Finally, the spatial, temporal and size distribution for these located asperities was determined. 3.2 High Frequency Seismic Records The wealth o f the Chi-Chi data not only allows more precise study for the rupture process and dynamic faulting o f a large earthquake, but also provides an opportunity to address new questions concerning the physics o f the earthquake source. We selected 49 stations in adjacent to the Chelungpu fault rupture for this study. As listed in Table 3.1, these stations are equipped w ith Teledyne Geotech A900 (or A900A) or Terra Tech IDS (or ID SA) accelerometers. Both types o f instruments have a nominal flat response from DC to 50 Hz and are capable o f recording a fu ll scale o f ± 20. The output o f these accelerograms has a 16-bit resolution and is digitized at 200 or 250 samples/sec. Table 3.1 also gives the group quality to which each accelerogram belongs (QG), the origin time correction (Time_Corr), and the time shift (Time_Shift), which w ill be discussed in the next section. Stations very close to a seismic source are able to record the radiated wave energy in high-frequency band. A fter prelim inarily analyzing high-pass filtered accelerograms, we observed unusual and intriguing phenomena from high-frequency waveforms. As examples. Figure 3.2 shows the original and processed accelerograms for stations 47 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. T075 and T084. In each record, the top trace shows the first 40 seconds o f the original broadband accelerogram. Suceessive traces show the band-pass filtered accelerograms at progressively higher frequency bands beginning at 10-20 Hz and ending at 40-50 Hz w ith the same time span. The time axis o f each trace is referenced to the Chi-Chi mainshock, and a few seconds o f pre-P wave recordings are included. The filtered waveforms are produced from a 4th-order Butterworth filter and zero-phase shift. Some intriguing observations from these high-frequency waveforms are summarized as follows. 1. Obviously, a single 40-second long broadband record has been resolved into a sequence o f distinct individual arrivals at high frequency. These bursts are very probably interpreted as high-frequency signal arrivals radiated from asperity patches lying on the fault rupture, and each source radiation burst corresponds to a sub-event. 2. For an individual component, some high-frequency bursts may appear in all band-pass filtered accelerograms, but their relative amplitudes in each accelerograms may not have the same ratios. Some bursts, however, only appear in lower or higher frequency bands. This implies that their corresponding asperity sourees have different magnitude sizes and dominant spectra. The burst only shown in lower frequency band may correspond to a source w ith large magnitude but far from its recording station. Its high-frequency components thus have completely decayed out. On the other hand, the burst only shown in higher frequency bands may correspond to a very small source which is located very close to its recording station. 48 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 3. The high-frequency bursts may not have to appear in all three recording components. This implies that the corresponding asperities may have different preferred slip directions. 4. The high-frequency bursts appear through the entire rupture process o f the mainshock, which indicates long time delays existing after the predicted arrival times o f a rupture front initiating at the hypocenter. Although it may not be surprising that a large earthquake is formed by a cascade o f sub-events, the high-frequency waveforms suggest more discontinuous rupture propagation than the orderly progression o f a large rupture process previously assumed. 5. The main seismic energy propagating to the earth’s surface must be in the form o f S-waves. In original accelerograms, the amplitude o f initial P-wave is usually 5 to 10 times smaller than o f initial S-wave. The wave amplitudes are heavily reduced after high-frequency band-pass filtering because these frequency bands are far beyond the corner frequency in spectra. However the resultant waves still have amplitude levels comparable to the initial P-waves, this indicates that they must be S-waves. 6. Many o f the individual arrivals appear to be composed o f multiple sharp arrivals w ith similar waveforms as shown in the expanded sections for the multiple bursts segments in Figure 3.2. These multiple bursts have progressively decreased or increased amplitudes and evenly spatial period, which are probably interpreted by stick-slip instability at high loading rates as in the case o f an asperity being loaded by fault slip during an earthquake. Furthermore, these multiple bursts can appear in any 49 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. I A ^ I ^ I ' i ■ i i Figure 3.2a The accelerograms of three components for station T075. In each component, the top trace is the original accelerogram, and the following traces are processed accelerograms pass-filtered at 10-20Hz, 20-30Hz, 30-40Hz, and 40-50Hz respectively. The two multiple-burst segments with quasi-repeating periods (shaded regions in the 40-50Hz filtered trace for the N-S component) are expanded and plotted at the bottom. At the left-top corner are plotted the location of station T075 (triangle) to the Chi-Chi mainshock epicenter (pentagon) and the Chelungpu surface rupture (thick line). 50 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. > , t “ I I : t . 11 S " J J . i ■ * k « > X / V I • ■4 * - F igure 3.2b The accelerograms o f three components for station T084. The pictures are the same as in a) except that the expanded multiple-burst segments are in the 20- 30Hz fdtered accelerogram for the E-W component. 51 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. high-frequency band and any directional component. For instance, pronounced repeating bursts appear at frequency band 40-50 FIz in N-S component (Figure 3.2a), and at frequency band 20-30 Hz in E-W component (Figure 3.2b). Table 3.1 Stations, accelerometers, and data information Code Latitude Longitude Elevation Accelero meter Type QG Time_ Corr Time Shift n n (km) (sec) (sec) C006 23.5815 120.5520 0.200 ID SA B 4.501 0.2597 COlO 23.4653 120.5440 0.205 IDSA B -3.654 0.0841 C024 23.7570 120.6062 0.085 A900 B 2.053 0.5051 C028 23.6320 120.6052 0.295 A900 B 0.000 0.0112 C029 23.6135 120.5282 0.105 A900 B 0.000 -0.5084 C034 23.5212 120.5443 0.140 IDSA B 8.674 0.1569 C035 23.5200 120.5840 0.230 A 900A B 1.817 0.1649 C041 23.4388 120.5957 0.230 A900 B 0.000 0.9921 C074 23.5103 120.8052 2.413 A900A B 0.000 0.2482 COSO 23.5972 120.6777 0.840 A900A B 1.304 0.4136 C lO l 23.6862 120.5622 0.075 A 900A B 0.000 0.1497 T048 24.1800 120.5888 0.160 A900 B -1.593 0.4548 T050 24.1815 120.6338 0.089 A900 B 0.000 -0.1831 T051 24.1603 120.6518 0.068 A900 B 154.996 0.4762 T052 24.1980 120.7393 0.170 A900 B 0.000 -0.5509 T053 24.1935 120.6688 0.127 A900 B -1.114 0.4294 T054 24.1612 120.6750 0.097 A900 B 73.735 0.4445 T055 24.1392 120.6643 0.090 A900 C -2.153 0.5084 T056 24.1588 120.6238 0.062 A900 B -1.623 0.4584 T057 24.1732 120.6107 0.049 A900 B -2.551 0.4320 T060 24.2247 120.6440 0.138 A900 B -1.270 0.3995 T061 24.1355 120.5490 0.030 A900 B 0.000 0.9045 T063 24.1083 120.6158 0.039 A900 B 63.718 0.5235 T064 24.3457 120.6100 0.037 A900 B 0.000 0.8022 T065 24.0588 120.6912 0.048 A900 B 0.000 0.0478 T067 24.0912 120.7200 0.073 A900 B 0.000 -0.1382 T068 24.2772 120.7658 0.276 A900 B -1.050 0.2985 T071 23.9855 120.7883 0.187 A900 B 0.000 0.5048 T072 24.0407 120.8488 0.363 A 900 A 0.000 0.3911 T074 23.9622 120.9618 0.450 A900 A 0.000 0.2792 T075 23.9827 120.6778 0.096 A900 A 0.000 0.0866 T076 23.9077 120.6757 0.103 A900 B 0.000 0.0014 52 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table 3.1 continued T078 23.8120 120.8455 0.272 A900 A 0.000 -0.0920 T079 23.8395 120.8942 0.681 A900 A 0.000 -0.0164 T082 24.1475 120.6760 0.084 A900A B -1.522 0.4845 T084 23.8830 120.8998 1.015 A900A A 0.000 0.1029 T087 24.3482 120.7733 0.260 A900A B 0.000 1.2349 T088 24.2533 121.1758 1.510 A900A B 0.000 0.9905 T089 23.9037 120.8565 0.020 A900A A 0.000 0.0041 TlOO 24.1858 120.6153 0.100 A900 B -1.581 0.4074 T102 24.2493 120.7208 0.188 A900 B 0.000 -0.5355 T103 24.3098 120.7072 0.222 A900 B 0.000 0.4694 T104 24.2455 120.6018 0.213 A900 B 6.203 0.3771 T109 24.0848 120.5713 0.023 A900 B -1.795 0.5306 T116 23.8568 120.5803 0.049 A900 B -2.382 0.6037 T122 23.8128 120.6097 0.075 A900 B -3.061 0.5250 T129 23.8783 120.6843 0.110 A900A A 0.000 0.1263 T136 24.2603 120.6518 0.173 IDS B 2.771 0.3266 T138 23.9223 120.5955 0.034 ID S A B -8.589 0.6334 3.3 Locating High-Frequency Bursts Due to the jo in t action o f high-pass filtering by data processing and low-pass filtering by the earth itself, the separation o f the burst arrivals in space and time permit us to locate these individual burst events directly. The difficulty in this problem is that associations o f bursts in different records are unknown. Moreover bursts o f sources can arrive in different time order at different stations. Our burst association problem then becomes one similar to the location o f a dense pack o f aftershocks often happened immediately after large mainshocks. In order to locate those aftershocks, a brute-force method is usually used to compute all possible origin times and locations in a source volume outlined by the later aftershock distribution. Our event location 53 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. problem is perhaps simpler, because we can assume, at least at first, that all energy bursts are originated from asperity patches lying on a known Chelungpu fault plane. Once the bursts corresponding to each asperity have been identified, we can relax this assumption and allow asperity patches to lie in a broader fault zone so as to refine their spatial-temporal distribution. 3.3.1 Fault Models Since the Chi-Chi earthquake ruptured approximately a 85km segment o f the Chelungpu thrust fault, and most o f the length exhibits a strike o f about 3° to 5°, and a dip o f about 29° to the east (Lee et al., 2000), we first modeled the Chelungpu fault using a single plane o f 80km long, 3° in strike, and 50km wide in a 29° dipping plane to the east. The location o f the fault plane is carefully chosen to w ell coincide with most o f the surface rupture (Figure 3.3a). The Chelungpu surface rupture exhibits a complicated faulting geometry especially at the northern end where the faulting trend bends toward the east and at the southern end where the faulting trend bends toward southeast. The calculated travel time o f asperities located at the modeled fault plane is very sensitive to the orientation o f the fault plane. A simple calculation showed that, at a distance o f 20 km, 1 km variation in depth would lead to 0.3 sec variation in travel tim e, w h ic h is considered too large an uncertainty in th is study. In order to avoid this problem, we introduced a multi-plane rupture model which is comprised o f five 54 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. rectangle planes w ith different orientation, strike, dip angle, and dimensions to closely match the geometry o f the Chelungpu rupture (Figure 3.3b). The parameters o f the two models are listed in Table 3.2. In fact the parameters o f the multi-plane model are chosen and adjusted from the field observation and the preliminary results o f the single plane fault model. In both fault models, each fault plane is discretized into 1km x 1km patches, each o f which is regarded as a potential asperity source. To locating high-frequency bursts, the fault model, as well as the Chi- Chi mainshock occurrence time at 1999/09/20 17:47:15.85, epicenter at 23°51.I5’N I20M 8.93’E, and focal depth at 8.0km (determined by CW B) w ill be input into an algorithm as known parameters. Table 3.2 Parameters o f the Chelungpu fault model Single plane model Strike ( ° ) 3.0 Dip (°) 29.0 Dimension (km ^km ) 80.0 X 50.0 Multi-plane model Fault planes from south to north Strike (° ) Dip (°) Dimension (km xkm ) A 45.0 29.0 11.5 X 30.0 B 3.0 29.0 31.9 X 50.0 C 5.0 25.0 15.0 X 53.0 D 3.0 29.0 23.1 X 50.0 E 65.0 25.0 15.0 X 20.0 55 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. T087. 24.3 T0S3. Tio; 24.2 T04< T063. TO {i 24.1 T io a TOSSi T07{ ^ 23.9 23.8 23.7 C101, 23.6 C006. C 0 3 ^ C 0 3 ^ 23.5 121.2 121.1 121 120.9 Longitude 120.8 23.4 120.7 120.6 120.5 Figure 3.3a Single-plane fault model for the Chelungpu fault. The fault plane is divided into patches with dimension o f 1km x 1km. The parameters o f each fault plane are listed in Table 2. The triangles indicate the distribution o f used stations, and the station names are also labeled. 56 Reproduced with permission of the copyright owner . Further reproduction prohibited without permission. 24.4 T087. 24.3 T - 1 3 % 24.2 T04i 24.1 T07I ...................... ^ 23.9 23.8 C028. 23.8 23.5 C Q 1 5^ C 0 4 -^ 121.2 121.1 1 2 1 120.9 Longitude 120.8 23.4 120.7 120.6 120.5 Figure 3.3b Multi-plane fault model for the Chelungpu fault. Each fault plane (A-E) is divided into patches with dimension o f 1km x 1km. The parameters of each fault plane are listed in Table 2. The triangles indicate the distribution of used stations, and the station names are also labeled. 57 Reproduced with permission of the copyright owner . Further reproduction prohibited without permission. 3.3,2 Data Processing We have selected 49 stations around the Chelungpu surface trace from 441 digital strong-motion records processed and disseminated on CDROM by Lee et al. (2001). The selection criterion is that the distance from the station to the Chelungpu fault plane (not the mainshock hypocenter) must be less than 20 km. The distribution o f these stations is also shown in Figure 3.3. Recorded data files on CDROM have been organized into four quality groups (A to D from the best to the worst) based on if pre event and/or post motion data are long enough, if any component was unrecorded, and if they have other defects such as noise spikes. Most o f our selected records are fallen into quality group A and B indicating “ excellent” to “ good” quality (Table 3.1). A ll aceelerographs recording quality A data have accurate absolute tim ing synchronized by their own GPS clocks. Most o f the remaining aceelerographs are not equipped with GPS tim ing devices, but the relative times are based on their internal clocks. The apparent tim ing errors resulted from internal timings or bad GPS timings have been corrected, so that the near-field Chi-Chi mainshock records are good to 1 second at epicenter distance less than 50km (Lee et al., 2001). The time corrections are listed in Table 3.1. A redundant check is still necessary because the local velocity m odel used in this study w o u ld be d iffe re n t fro m the T aiw an regional m odel used in time correction. We adopted a 1-D velocity model from the tomography study o f Ma 58 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. et al. (1996) for the southwestern Taiwan region (Table 3.3). It is also the veloeity model used in Ma et al. (2001). Table 3.3 Velocity model for Taiwan region Thickness (km) Vp (km/s) Vs (km/s) 1.0 3.50 2.00 3.0 3.78 2.20 5.0 5.04 3.03 4.0 5.71 3.26 4.0 6.05 3.47 8.0 6.44 3.71 5.0 6.83 3.95 5.0 7.06 3.99 15.0 7.28 4.21 H a lf Space 7.87 4.45 We first generated a P-wave reference travel-time curve using the local P-wave velocity model, and check the curve against the P-wave arrival time from all selected stations (Figure 3.4). For the stations w ith GPS tim ing (solid squares in Figure 3.4), the mean difference between the observed P-wave travel time (observed P-wave arrival time subtracts mainshock origin time) and the calculated travel time is 0.13sec, w ith a standard deviation o f O.lSsec. The scatters o f other stations are larger than those for the stations w ith GPS timing. In addition to clock errors, the scatters could also be resulted from lateral heterogeneity, stations elevation, and difficulty in observing the initial onset due to the emergent nature o f the P waveforms. To make the wave propagation self-consistent coherent w ith the local velocity model, we 59 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. applied a time shift to the original records by lining up the P-wave arrival w ith P-wave reference travel-time curve at corresponding epicentral distances. The time shifts are also listed in Table 3.1. Since only travel times are involved in this study, the uncertainty introduced by velocity model and site response would be smaller than that o f waveform inversion in high frequency. o 0) (1 ) E o > (0 12 10 8 6 4 2 0 10 30 50 60 0 20 40 Epicentral distance (km) Figure 3.4 The calculated travel time curve for P-waves against the epicentral distance. The observed travel time of initial P-wave of the Chi-Chi mainshock at each used station (solid and open squares) is also plotted at the corresponding epicentral distance. The solid squares indicate the stations having GPS timing. As shown in Figure 3.2, a myriad o f bursts appear on the high-pass filtered accelerograms. Some o f these bursts might be scattered waves due to small scale obstacles, so that we have to use some c rite ria to p ic k up d irect burst arrivals. In order to find out the distance through which the radiated high-frequency energy can still be 60 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. recognizable, we consider the spatial attenuation due to material absorption, where the amplitude exponentially decays (A ki and Richards, 1980) as; A (r) = A ,e~^ (3.1) w h e re /is frequency, r is distance from source to receiver, Q is quality factor, and v is velocity. We temporarily avoid geometrical spreading, site effects, and source effects here. The attenuation o f S-waves band-pass filtered at 10-20Hz, 20-30Hz, 30-40Hz and 40-50Hz is illustrated in Figure 3.5, where the maximum amplitude o f horizontal component during the first 2 seconds after S-wave arrivals is plotted against hypocentral distance. We assume that this short duration o f S wave is initiated from the Chi-Chi hypocenter, but the follow ing arrivals may be the result o f the superposition o f rupture pulses from other sources (Chen et al., 2001). The theoretical decayed amplitudes calculated from equation (3.1) are also plotted in Figure 3.5. In equation (3.1), v = 3.21 km/s is the average S-wave velocity o f the crust in Taiwan, Q = 250 is taken from velocity models for seismic source inversion studies (e.g. Wu et a i, 2001; Chi et al., 2001), and/ uses the mean frequency for each band-pass window. A t least up to 40km, the observational data follows an exponential decay well. The data at the four closest stations deviate significantly from what the theory predicts probably due to the effects o f radiation patterns as introduced by the location errors. In general, lower frequency data are less scattered than higher frequency data, we thus choose the 20-30Hz frequency band to implement bursts locating. For the S-wave band-pass filtered at 20-30Hz, we found its amplitude approximately attenuated by 61 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. one order every 20km propagated. Since the bursts whose amplitudes are l/IO o f the maximal amplitude are still recognizable in each station, we set this amplitude level as a threshold, and pick up all bursts whose amplitudes are higher than this threshold. These bursts contain the high-frequency energy radiated from all possible asperity sources in a region about 20 km from their recording station. 1 0 A. 1 0 -2 0 H z 2 0 -3 0 H z ▼ 3 0 - 4 0 H z 4 0 -5 0 H z ,2 10 ' V ,D 10 Q. -1 1 0 1 0 1 0 40 30 10 Hypocentral distance (km) Figure 3.5 The amplitudes of S-wave initiated from the Chi-Chi hypocenter against the hypocentral distance. The amplitudes are for horizontal components and have been pass-filtered at 10-20Hz (up triangles), 20-30Hz (circles), 30-40Hz (down triangles), and 40-50Hz (diamonds). The theoretical amplitudes calculated by eqn. (1) for the four frequency bands are also plotted (thick lines). Each burst is comprised o f a few oscillations as shown in the expanded accelerograms in Figure 3.2. For sim plicity, we use the peak location o f the oscillations as the burst arrival time, because it is easier and more accurate to pick up 62 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. than the initial time. Since the duration o f each burst is less than 0.4 seconds, replacing initial time w ith peak time does not significantly affect the final results. We use individual directional component to locate bursts, and the final results are based on all three directional components. 3.3.3 Methodology In this study, the unassociated arrival times o f high-frequency bursts are used to determine their source locations and original times on the modeled fault plane. We have developed an algorithm to do this by brute force as illustrated in Figure 3.6. For each patch w ith dimension o f 1km x 1km on modeled fault planes, we calculate the travel time to each recording station. Beginning w ith the origin time for the Chi- Chi mainshock, we calculate the predicted arrival time at each station for an sub-event with origin time tg + y'A/on each patch. The time delay A? between two neighboring origin times is set to 0.1 sec. We call the array o f calculated arrival times where i indexes the asperity patch,y indexes the origin time, and k indexes the station. A t the station, we have a vector o f the observed arrival times o f the bursts. We write (tobsili the observed arrival time o f the n''^ burst at station k. For each asperity i and origin time j, we now compare its predicted arrival times w ith the nearest observed arrival at the station by calculating their time difference 63 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. as = it Y. - ( t Y V o h .s /m i n V calc )ij optimal origin time and location for each event as = 1 ________ N , . We then form a functional Wij that is minimized to find the ^ (3-2) k=\ where is a weighting factor and the summation is over all stations. Due to the fact that the earth is a low-pass filter, we do not expect that the radiated high-frequency energy would be received by all stations. Considering the media absorption and geometrical spreading, we use a weighting factor having a form o f 1 - - (3.3) r We still set v = 3.21 km/s, the mean o f the local S-wave velocity, and/ = 25 Hz. Since the goal o f weighting factor is to emphasize recordings at neighboring stations, we set Q - 100, a value lower than in some crustal models. In fact Q = 100 to 250 may all be appropriate values to the shallow crust in the source area. As an efficient weighting factor, gives a strong weight to neighboring stations and a light weight to far stations. Therefore only the records at neighboring stations contribute significantly to Wij, while the records at far stations contribute almost nothing to W j no matter their observed arrivals match the predict arrivals well or not. The form o f the weighting factor is more important than the particular parameter values. Different parameter values w ill systematically increase or decrease all values o f functional Wj, but the 64 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. final results w ill not be ehanged if only aecordingly inereasing or deereasing the selection threshold. The arrival time o f the d burst at station k, (tohsfn ■ The calculated arrival time from patch i at timeyAt to station k, . The nearest arrival time to the calculation, (t„hsf\ station patch i at [me /At Figure 3.6 The cartoon illustrates the brute-force algorithm to locate sub-events by searching the m odeled Chelungpu fault. 65 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Using Wij only is not enough to locate asperity sources. I f a source is very close to a single station but very far away from all other stations, m ultiple source locations having the same distances to that single station would result. These multiple sources cannot be discriminated from the Wy. We thus require extra criteria to constrain asperity sources. First, we require at least iV(>2) stations w ithin a distance D receiving signals from a potential source. Next, for these stations receiving signals w ithin Z), their individual time difference between observed arrival and calculated arrival must be less than T. The above amplitude attenuation analysis helps us to determine these parameters. The threshold distance D is set to 20km, the maximal distance through which the attenuated energy bursts can still be recognizable at a receiver. W ithin the station coverage o f Z) = 20km, we request at least Z /= 4 stations receiving the signals. Since the mean difference between observed travel time and calculated travel time is 0.13sec for the stations w ith GPS timing, and the other stations have been performed time correction and time shift by the P-wave travel-time curve, the time threshold T o f 0.1 ~ 0.2 sec is found to be appropriate. 3.3.4 Results The 80 km x 50 km single-fault model plane results in 4000 grid patches w ith the dim ension o f 1km x 1km. T im e delays fo r each asperity source are com puted up to 40 sec w ith 0.1 sec in step. Therefore, totally 1.6 m illion potential spatial and temporal 6 6 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. sources w ill be searched and the resultant functional Wjj has a very wide range. Only about 500 optimal solutions which have small values o f Wij and pass extra conditions are selected. As shown in Figure 3.7, the asperity sources identified from the E-W component are projected on the free surface. The entire rupture process is divided into a few o f episodes w ith five seconds each in duration, and the asperity sources belonging to different episodes are indicated by different symbols. Note that all optimal solutions for significant radiations are concentrated in the first 25 sec, and almost all identified asperity sources are located at shallow depth. The Chelungpu fault has about 30” dipping to the east, thus they are shallower than about 1 2 -1 3 km. This result is also consistent w ith other broadband seismic source studies for the Chi- Chi earthquake (e. g. Ma et al. 2001; Zeng and Chen, 2001; Chi et al. 2001). Because most asperities are only a few o f kilometers deep along the Chelungpu surface rupture, the geometry o f the fault model becomes important. In particular, the asperities found on edges o f the fault model plane, mainly those at the northwest and southwest corner, would be artifacts due to the inconsistency between the fault model plane and the real fault trace geometry. We therefore also used the multi-plane fault model. The follow ing results are based on the multi-plane fault model. The asperity sources determined from three-component seismograms are projected on the free surface as shown in Figure 3.8-3.10 respectively, and the asperities belonging to different episodes are indicated by the same symbols as in Figure 3.7. Generally the temporal and spatial distribution o f located asperities 67 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 24.4 E-W component 0-5 s 5-10 s 10-15s 4 15-20S 20-25 s 0) 24 ■a 23.9 P 23.5 120.6 120.65 120.7 120.75 120.8 120.85 120.9 120.95 121 121.05 121.1 Longitude (deg) Figure 3.7 The located asperity sources obtained from the single-fault plane model are projected on the Earth’s surface. The asperities in 5-second episodes are plotted by different symbols. The rectangle indicates the fault plane. 68 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 24.4 24.3 24.2 24.1 O ) O 24 2 , o; ■ o 3 ■ 4 -1 ■'5 23.9 re 23.8 23.7 23.6 23.5 E-W component 5-10 s 10-15s 5-20 s 20-25 s xW<xX X X X X--X V F V ■ ) ■ ■ ■ f V V V -f- ■ f V. •tv V 4. G V 4 - 1 " ★ -r V V V ■ f -i- V , 4. V « « XfH-' ■ + J L 120.8 120.7 120.8 120.9 Longitude (deg) 121 121.1 Figure 3.8 The located asperity sources obtained from the multi-fault plane model for the E-W component are projected on the Earth’s surface. The asperities in 5-second episodes are plotted using the same symbols as in Figure 7. Seven asperity groups (from A to G) are formed as indicated by shaded regions. 69 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. N-S component 24.4 0-5 s X 20-25 s 24.3 X X 24.2 24.1 O) -S 23.9 23.8 ■iv 23.7 23.6 23.5 < — 120.6 121.1 120.9 121 120.7 120.8 Longitude (deg) Figure 3.9 The same as Figure 8, but for the N-S component. 70 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Vertical component 24.4 0 '5 s 5-10 s 10-15s 15-20s 20-25 s 24.3 24.2 24.1 U i G V 23.9 23.8 23.7 23.6 23.5'— 120.6 121 121.1 120.7 120.8 120.9 Longitude (deg) Figure 3.10 The same as Figure 8, but for the vertieal eomponent. 71 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. approximately follows the Chelungpu rupture history. Temporally, the rupture initiates from the hypocenter, and then bi-directionally propagates toward the north and south. However, significant jumps in slip are also found among these asperity sources. Spatially, these asperities appear in groups as indicated by the shaded regions (asperity patches A - G) in Figure 3.8-3.10. Individual asperity group or combined nearby groups correspond to a large asperity found in source inversion from low-frequency seismic data. The consistency suggests the reliability o f the high-frequency burst study. Clearly, small asperities as outlined by high-frequency bursts give a much detailed picture describing the manner w ith which such a large (80 km x 50 km) rupture is generated. The asperities identified from three-component data have shown consistent temporal and spatial distribution. The results from horizontal components can be compared w ith the movie o f surface motions (Shin and Teng, 2001). The locations and arrival times o f observed large energy release (ground acceleration larger than 600 gal) on the surface are read from each movie frame. Assuming that these energy releases originate from right below locations on the down-dip fault plane, they w ill take about 3 - 4 seconds to reach the surface at a depth o f 10 ~ 12 km. The identified asperity sources are plotted in 5-sec episodes. The major energy releases read from the movie are also plotted in the corresponding episode by subtracting their proper travel times (solid circles in Figure 3.1 la-e and 3.12 a-e), and their arrival times are labeled along with the symbols. In both horizontal components, the origin times and locations o f the 72 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. identified asperity sources approximately accord w ith the major energy releases. The detailed comparison is shown by the results obtained from the E-W component (Figure 3.1 la-e). In the follow ing discussion, we use the word “ energy release” to denote the large ground acceleration, and “ asperity” to denote the source o f each sub event. The movie showed that observable motions o f the Chi-Chi nucleation emerge at the surface 3 sec after its origin time. The energy release continues until it reaches to the first largest asperity rupture observed about 14 km to the west o f the epicenter at 11 sec (Figure 3.1). In the first two episodes before 10 sec (Figure 3.1 la and b), asperities are found at very shallow depth a few o f kilometers to the west o f the hypocenter and at the kink o f the Chelungpu surface trace to the north. This indicates a rupture propagation northward in the first 10 sec. More asperities as well as large energy releases are observed in follow ing episodes starting at 10 sec. During the follow ing episode from 10 to 15 sec (Figure 3.1 Ic), the rupture propagates in all directions on the Chelungpu fault plane, leading to the slip over asperities in distance from 10 to 20 km around the Chi-Chi hypocenter. In this time episode, the rupture was not only constrained at shallow depth, but also reached to the depth o f about 12 km. A ll major energy releases are found to the north o f the hypocenter, and each can correspond to an identified asperity. On the other hand, much more asperities than the major energy releases are identified in this study. The asperities to the north o f the hypocenter slipped at about 12 sec after the initiation, and they are also found in some 73 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. seismic source inversion studies (e.g. Ma et al., 2001; Wu et at., 2001). The rupture continues to propagate in follow ing episodes from 15 to 25 sec (Figure 3.1 Id and e). However, the propagation mainly concentrates on shallow depth towards the north and south along the fault surface trace, but it stops continuing to propagate eastward deeper than 12 km. The delay ruptured asperities can still be found at the depth o f about 12 km around the hypocenter in episode 15 to 20 sec. Again major energy releases are observed near some identified asperities. Most asperity groups are located at shallow depth from the north to south, but only one major energy release (at 27 sec) is observed to the north because no high peak ground acceleration was reported to the north where the Chelungpu surface trace curves to the east. One major difference o f the identified asperities from the large energy releases is at the region near the central range mountains. Asperity group G is found a few kilometers to the southeast o f the hypocenter in episode o f 15-20 sec (Figure 3.1 Id), but no major energy releases are observed in corresponding times and locations. On the contrary, no asperities are identified to the east o f the hypocenter to reflect the observed major energy released after 25 sec. They may reflect the same asperity sources, but the difference in the two types o f studies is probably due to the bad station azimuth coverage on the hangingwall, at which the asperities are more d ifficult to identify and the major energy releases are obtained from spatial interpolation w ith data from stations farther on the east coast o f Taiwan. 74 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. E p is o d e a: 0 -5 s e c E p is o d e b: 5 -1 0 s e c E p is o d e c: 1 0 -1 5 s e c w - ■ J ■ J T 4 ^ i k - I ; 4 ■J ■ : . ^ E p is o d e d : 1 5 -2 0 s e c / W ■ E p is o d e e: 2 0 -2 5 s e c Longitude (deg) Figure 3.11 The asperity sources obtained from the multi-fault plane model for the E- W component are projected on the Earth’s surface and plotted in 5-second episodes (from episode a to e) individually. The m ajor energy releases (> 600 gal) read from the Chi-Chi movie are also plotted (solid circles) and their arrival times are labeled with their symbols. 75 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The temporal and spatial distributions o f asperities identified from N-S and vertical components are similar to that from E-W eomponent, but some differences also exist in the N-S and vertieal components. The episodes o f asperity appearance for the N-S component are shown in Figure 3.12a-e. The major difference between two horizontal components exists in the asperity group G to the north o f the hypocenter. Temporally, most asperities in this area are identified in 10-15 sec from E-W component (Figure 3.11c), while they concentrate in 15-20 sec for N-S component (Figure 3.12d). This suggests that the rupture velocity in E-W direction is faster than in N-S direction, probably due to the crustal heterogeneity. The asperity group F does not explicitly appear in the vertical component (Figure 3.10). This is to be expected that the slip o f deeper asperities is dominantly in the E-W thrust. Therefore the number o f identified asperities from N-S and vertical components is less than from E-W component under the same sub-events selection condition. Sim ilarly the number o f recognizable major energy releases from N-S component is also less than from E-W component. Moreover, the major energy releases observed after 25 sec from E-W component do not appear in N-S component. In the same area, no asperities are found after 25 sec from N-S component either (Figure 3.12e). 76 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. E p is o d e a; 0 -5 s e c E p is o d e b: 5 -1 0 s e c E p is o d e c: 1 0 -1 5 s e c . ; . ■ r' ■ ■ \ / - \ ^ j ■ \ ; • E p is o d e d: 1 5 -2 0 s e c E p is o d e e: 2 0 -2 5 se c Longitude (deg) Figure 3.12 The same as Figure 11, but for the N-S component. 77 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 3.4 Relocating Asperity Sources Once the association algorithm has been applied to separate groups o f potential arrivals from particular sources and preliminary locations are obtained, these locations can be refined using a standard location algorithm. Since the asperity sources may lie in a broader fault zone instead o f a single fault plane, we w ill find the optimal location and origin time for each source by searching a domain centered at each preliminary location and origin time. The searching process hierarchically changes from wide range and rough step to narrow range and fine step; so that the precision o f final location uncertainty w ill be less than 1km in horizontal direction, 0.5 km in depth and 0.1 sec for origin time. Generally, most asperities do not significantly change their locations and origin times except the deep ones in fault patch G. The origin times o f these asperities do not change much, but they moved southward in horizontal, and moved deeper than the pre-determined fault plane. Since fault patch G is located at segment B o f the m ulti plane fault model, the depth variation obtained from the E-W component for segment B is plotted in Figure 3.13. This suggests a non-planer rupture plane at the south o f the Chelungpu fault, which may has a larger dipping angle at depth. 78 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 0 2 4 6 8 V ! 14 16 18 20 25 20 10 15 0 5 -15 -10 -5 Distance to Chi-Chi epicenter (km) Figure 3.13 The depth of asperity sources in group G after relocation. The thick line indicates a fault surface with 29° dipping to the east. 3.5 Estimating the Sizes of Sub-Events Traditionally, there are three types o f measures concerning the size o f an earthquake: radiated seismic energy, scalar seismic moment, and magnitude. The seismic energy considers the total energy summed over all frequencies. The seismic moment is physically related to the final static displacement o f an earthquake. The magnitude is assumed related to the seismic energy release, so that it measures the 79 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. maximum amplitude o f band-passed seismograms covering the corner frequency in the source spectrum. Unfortunately, we cannot directly determine the size o f sub events using these three measures because we do not have enough required information o f these sub-events. In particular, since we have no idea o f the frequency information other than that w ithin the 20 to 30Hz frequency band on source spectra, it is impossible to measure the seismic energy and moment by the conventional methods. Moreover, the frequency from 20 to 30 Hz must be far beyond the corner frequencies o f these sub-events if they have magnitudes about 6 as supposed by Shin and Teng (2001). In this study, however, we w ill infer the size o f the sub-events using the follow ing method under some assumptions. Generally, the Ath station local magnitude, M J J i), is defined as (Richter, 1935): M , {k) = log A ,^ - log A,, = log(^, / ^ „ ), (3.4) where Ak is the maximum amplitude in microns recorded by standard a Wood- Anderson torsion seismograph (with static magnification o f 2800, natural period o f 0.8 second, and damping factor o f 0.8) on station k. The amplitude correction Ao is used to register amplitude to an epicentral distance o f 100km. The value o f amplitude o f seismic wave at hypocentral distance r is a combined result o f material attenuation, geometrical spreading, and site effect. The Ak(r) can be written as: (3.5) rS Tlf where y = — is the attenuation coefficient, 5” is a site-dependent constant, and C is an Qv 80 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. amplitude registered at a reference distance. In practice, the final magnitude is the arithmetic average o f station magnitude over Ns stations, and the corresponding amplitude A is thus the geometric average o f Ak over Ns stations, A = Y [A , . (3.6) V ^ = 1 The seismic moment and magnitude scale relation can be written as lo g ( M j = 6 M ^ + a , (3.7) then ={a / aJ AON (3.8) Using the empirical relation between local magnitude and moment magnitude for Taiwan seismicity, =0.193 + 0.993M „ (Chang et al., 2001), as well as moment and moment magnitude relation, lo g (M „) = 1.5M „ + 9.105 (Mo in unit Nm) (Hanks and Kanamori, 1979), we find out b = 1.511 and a = 8.814. In order to infer the size o f the sub-events represented by high-frequency bursts on accelerograms, we make two assumptions. First we assume that the moment o f the Chi-Chi mainshock is totally released through identified sub-events, thus M „ = f ^ M S j) = Z ( A ( j ) / A y - \ 0 ^ = \ 0 ^ f ^ C { j y . (3.9) M .M ,/= ! Second, we assume that the relative ratios o f displacement amplitudes C(j) o f these sub-events are the same as those o f the acceleration amplitudes a(j), i.e., C (l): C(2): C (3):...: C (y ):... = a ( l) : a(2) : a (3 ):...; a ( j) :... 81 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C{j) = p-a{j), (3.10) where, a{j) is the acceleration amplitude which has been calibrated using equation (3.5). Due to the high-frequency band used in this study, some results o f attenuation studies for Taiwan regions (e.g. Chang et al., 2001) may not be applicable in this study. Following the method presented in Shin (1993), we determined y and S using the high- frequency data in this study. A fter calibrating the acceleration amplitude, we first solved the constantp by substituting equation (3.10) into equation (3.9), and then calculated the moment and local magnitude o f each sub-event from equation (3.7) and (3.8). 3.6 Discussion The data from the E-W component were used to estimate moments and local magnitudes o f sub-events. The largest sub-event had M i = 7.0, and the smallest had M l = 4.8. Figure 3.14 shows the magnitude distribution in space, where the sub-events are distinguished every 0.5 unit from magnitude 5.0 to 7.0. Note that the sub-event magnitudes increase w ith depth. Specifically, almost all largest sub-events {M i > 6.5) are at depth larger than about 12 km, approximately the lower boundary o f seismogenic layer. The sub-events from 6.0 to 6.5 are found at depth o f about 9-10 km. The small events whose magnitudes are less than 5.5 are all located above 2 km. 82 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 24.4 M>=6.5 6.0<=M <6.5 5.5<=M <6.0 5.0<=M <5.5 M<5.0 « 24 ^ 23.9 nj 120.6 120.7 120.8 120.9 Longitude (deg) 121.1 Figure 3.14 The spatial distribution of magnitudes of sub-events. 83 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Because the rupture at the unstable seismic region has higher probability to develop into a large event (Scholz, 1990), large earthquakes usually nucleate in the seismogenic layer from about 2 km to 11 km. On the contrary, the very shallow region is seismically stable, so that only small sub-events can be created. Figure 3.15 shows the frequency-magnitude distribution o f these sub-events. The logarithm cumulative number is linearly distributed w ith magnitude except at the higher and lower magnitude ends. A t the lower magnitude end, the cumulative number curve flattens at about M l = 5.2 due to the incompleteness o f sub-event catalog. Obviously, not all small sub-events can be identified in this study because the high-frequency bursts whose amplitudes are less than 1/10 o f the maximum one were discarded. A t the large magnitude end, the cumulative number also departs from the linear trend due to the finite energy release. Using the maximum likelihood estimate based on tapered Gutenberg-Richter law (Kagan, 2002), we found that b-value is equal to 1.0 and tapered at the corner magnitude o f M l = 6.7, from which the cumulative number decreases exponentially. In terms o f the geometrical interpretation for Zi-value (King, 1983), b = 1.0 implies a planar spatial distribution w ith fractal dimension D = 2b = 2 . The rupture velocity during the development o f the Chi-Chi earthquake can be estimated from the locations o f the asperities. The origin times o f asperity sources are plotted as a function o f their hypocentral distances to the Chi-Chi initial point in Figure 3.16 (Results from the E-W component are shown in part a, and results from N- S component are shown in part b). Corresponding to each hypocentral distance, the 84 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. v > 0 ^ > 0 > o a; £1 E 3 C V > J S 3 E 3 o ,3 10 Iog/V=rlv07 A^ + 8.11 ,1 10 10 7 6.5 5.5 6 5 Magnitude Figure 3.15 The frequency-magnitude relation of sub-events. The maximum likelihood estimation (M LE) based on Tapered Gutenberg-Richter model (solid line) is used to fit the data. The obtained parameters are = 1.0, a = 8.1, and m, (the magnitude from which frequency-magnitude distribution tapers) = 6.7. origin times o f asperities appear in clusters, but the earliest origin time increases with hypocentral distance. The slope o f the earliest origin times indicate the inverse o f the rupture velocity. Fitting the earliest origin time o f asperities (indicated as plus signs) identified from the E-W component, we found the rupture velocity o f about 2.06 km/s. It has no significant difference from the N-S component, where rupture velocity is about 2.01 km/s. Note that extending the line to shorter times gives an intercept at about 8-9 km, not the origin. This suggests that the major Chi-Chi rupture starts at about 8 km from the Chi-Chi hypocenter 2.5 sec later than the Chi-Chi origin time. As indicated in Figure 3.16a, connecting the earliest asperity origin time to the origin 85 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. a: Asperities located from E-W component 0> 25 ~ 20 Q. V„ = 5.51 20 30 40 Distance to the Chi-Chi epicenter (km) b: Asperities located from N-S component 0) 25 1‘ ~ 20 f * V„ = 5.58 Distance to the Chi-Chi epicenter (km) F igure 3.16 The origin time o f identified asperity sources vs. their hypocentrai distance to the Chi-Chi mainshock. A rupture velocity is obtained by linearly fitting the earliest asperities (plus signs). The inverse o f the slope o f a line connecting the hypocenter to the closest asperity on the rupture front is considered as P-wave velocity, a) Results for the E-W component, b) Results for the N-S component. 86 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. point (the hypocenter), we obtain a straight line w ith a slope equal to 1/5.51, which is approximately equal to the inverse o f P-wave velocity o f the Taiwan crust. Therefore we suggest that the initial rupture at the hypocenter did not develop to a large earthquake. Instead, it was initiated about 8 km away and 2.5 sec later when the P- wave from the hypocenter arrives at this first major asperity position. Since most asperity sources do not change their locations and origin times after relocation, they do not significantly affect the rupture velocity measurement. We should also note that most asperities ruptured later than the earliest asperity origin times. These later asperities w ith the same hypocentrai distances form clusters. They reflect delayed ruptures o f asperities at the nearly same distances and/or repeated slips o f already ruptured asperities. Each cluster represents an aftershock sequence o f the earliest rupture at this distance. Using the cluster in shaded area in Figure 3.16, we first calculated the occurrence time o f each aftershock relative to its initial rupture time by subtracting the initial rupture time from its absolute occurrence time, and then we bin the number o f these aftershocks every 0.5 sec. The binned data can be fitted using a modified O m ori’s law: — = 7 - ^ (3.11) dt {t + cY Because coefficient ^ is a function o f the minimum magnitude o f completeness, we only select the sub-events larger than M i = 5.2 considering the completeness o f identified sub-events. As shown in Figure 3.17a, the maximum number o f sub-events appears at about 7.5 sec, so that we may shift time axis to the right by a constant c = 87 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 7.5 sec, and the other two parameters w ill be determined by linear fitting equation (3.11) in logarithm scale. The fitting results give thatp = 1 and logiod = 0.93. Using the same cluster shown in Figure 3.17b, which is derived from the N-S component, we obtained a sim ilarp-\a\ue but logiod = 1.05. However, the other clusters do not follow O m ori’s law probably due to the incompleteness o f sub-events. T3 c a 0 25 < U V) k - 2 0 < 1 ) Q . « 15 - 9 1 2 5 < 1 ) I " . 2 z dt ■ ■ L ilI l 4 6 8 10 12 Time (sec) after mainshock 14 16 18 Q . ooo o Time (sec) Figure 3.17a The data within the shaded region in Figure 3.16a (the E-W component) are fitted by modified Omori’s law. The obtained parameters are also shown in the figure. 88 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. dt ^ i_ 2 0 4 6 8 10 Time (sec) after mainshock 14 16 Q . OO o o OCD Time (sec) Figure 3.17b The data within the shaded region in Figure 3.16b (the N-S component) are fitted by modified Omori’s law. The obtained parameters are also shown in the figure. Using these p and A values, we may be able to estimate the number o f the Chi-Chi aftershocks per day and compare it w ith the real catalog. The first aftershock o f the Chi-Chi earthquake occurred at 144 sec after the mainshock origin time. From Taiwan catalog, the number o f aftershocks per day for events w ith magnitude from 4.8 to 5.2 is accounted individually. The first five days’ data are listed in Table 3.4. Because the p and A values are determined per second, in order to obtain the number o f events per 89 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. day, we integrated equation (3.11) over one day period. In order to compare w ith the aftershock catalog, the number o f aftershocks in the first day must be derived by integrating after 144 sec. We also estimate the number o f aftershocks before 144 sec by integrating from 7.5 sec to 144 sec. The results derived from two horizontal components are also listed in Table 3.4. From the second day, the estimated number o f aftershocks is approximately equal to the number o f aftershocks equal to and larger than magnitude 4.9 in Taiwan catalog. This implies that we over-estimated the size o f identified sub-events. As presented in Chi et al. (2001), the total seismic moment was released during about 40 sec. However the identified sub-events in this study constrained in first 25 sec, so that only 1/2 to 2/3 o f the total moment was released through those identified sub-events. This w ill reduce magnitude 0.2 unit on average. For the first day, the estimated number o f aftershocks is much more than that in catalog even though the first 144 sec is not accounted. This inconsistency suggests that some aftershocks larger than M i = 4.9 are lost from the catalog. Some studies (e. g. Ma et al. 2001; Wu et al. 2001) have shown that most aftershocks occurred in regions where no displacement occurred during the Chi-Chi mainshock. However, our results im ply that some unidentified aftershocks are probably located at asperity regions when most o f stress was released during or immediately after the mainshock. 90 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table 3.4 the observed and estimated aftershocks in first five days after the Chi-Chi mainshock Catalog Day 1 Day 2 Day 3 Day 4 Day 5 M l = 5.2 23 4 3 0 0 M l = 5.1 35 6 3 2 1 M l = 5.0 38 6 4 2 2 M l = 4.9 52 7 4 2 2 M l = 4.8 62 8 5 2 2 Estimated < 144sec > 144sec Day 2 Day 3 Day 4 Day 5 E-W 36.9 81.1 9.0 5.3 3.8 2.9 N-S 34.9 74.0 8.3 4.9 3.5 2.7 3.7 Conclusion From the high-frequency bursts on accelerograms band-pass filtered at 20-30 Hz, about 500 sub-events were identified from the data o f three directional components individually. Each sub-event corresponds to one asperity source. The results from the horizontal and vertical component are similar in general but some differences exist. These asperities are by no means randomly distributed in time and space, nor do they have the form o f a propagating rupture. Temporally, asperity sources first slip when the rupture front arrives at a velocity o f about 2.0 km/s. The delayed or repeated asperities appear to be aftershocks that occurred during the Chi-Chi mainshock. 91 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Spatially, the asperity sources appear in groups. Seven asperity patches are found from horizontal components, and six from the vertical component. Among these patches, five o f them are located at very shallow depth along the Chelungpu surface trace. The deep asperity patch (patch F) to the north o f the Chi-Chi hypocenter was not found using the vertical-component data. This indicates that the asperities at this area mainly ruptured as an E-W thrust. Individual asperity patches or combined asperity patches were also observed in previous seismic source studies for the Chi-Chi earthquake which used low frequency data. Furthermore the detailed picture o f each asperity patch has been recognized in this high frequency study. This consistency may provide additional constraints to the normal seismic source inversions by using information at the high frequency end that is usually filtered out due to the uncertainty in the earth model. Assuming that the total seismic moment was released through the identified sub events and their acceleration amplitudes have the same proportionality as their displacement amplitudes, we have inferred the local magnitude o f each sub-event. The frequeney-magnitude distribution o f these sub-events well follows the Gutenberg- Riehter relation. A tapered Gutenberg-Riehter sealing model can fit the data segment whose magnitude is larger than the minimum magnitude o f completeness. Spatially, the large sub-events are located at greater depth consistent w ith the seismogenie layer, while the small sub-events are only located at shallower depth where large events can not be generated in general. 92 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. A fter relocating the identified asperities by relaxing them into a more loosely constraint instead o f a planar surface, we found that only the deep asperities in the patch G significantly changed their locations. In particular, they might be located deeper than the 29° east-dipping fault plane. This suggests a thick non-planer rupture zone at the south o f the Chelungpu fault, which has a larger dip at depth. 93 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Chapter 4 Spatial and Temporal Patterns of Regional Seismicity Preceding the 1992 Landers California Earthquake Abstract The Gutenberg-Riehter a- and b- values, cluster statistics, and the migration o f seismicity were measured as functions o f magnitude, space, and time before the 1992 Landers California earthquake using both raw and declustered catalogs. A pronounced increase in a-value was observed in circular regions centered at the Landers epicenter as well as in active lobes defined by the Bowman and King (2001) stress recovery model. For distances less than about 120km, this increase in a-value does not correlate w ith changes in Z)-value indicating an increase o f events at all magnitudes. Clustering increased w ith time before the Landers mainshock resulting in more and larger clusters. These observations can be interpreted as evidence supporting the critical point concept for earthquakes in terms o f a regional stress field that becomes smoother and more spatially correlated before a large event. Foreshock migration towards the Landers mainshock was observed in the active stress lobes defined by the Bowman 94 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. and K ing (2001) model, but not in the surrounding regions or in randomly selected regions. 4.1 Introduction There is mounting evidence that large earthquakes are preceded by a period o f accelerating seismic moment release (Keylis-Borok and Malinovskaya, 1964; Sykes and Jaume, 1990; Bufe and Varnes, 1993; Bowman et al., 1998; Jaume and Sykes, 1999). This increase has been shown to be due mostly to an increase in the number o f intermediate-size events over a wide area surrounding the epicenter o f the main event. The accelerating seismicity is commonly fit to a “ time-to-failure equation” o f the form = A - B { t f - t y (4.1) where £, is the energy o f the i‘^ event and a determines the measure o f seismicity (0 for event count, 1/2 for B enioff strain, or 1 for energy). The B enioff strain is usually chosen because it is a compromise between the energy (or, equivalently, the seismic moment), which is dominated by the largest events and the event count, which is dominated by the smallest. It is also common practice when using a = 1/2 to include in the sum only those events w ithin 2 magnitude units o f the mainshock. This restriction is required to focus the analysis on intermediate-sized events since the B enioff strain is also dominated by smaller events, although not as much so as the event count. Using 95 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. the energy in (1) also focuses on the largest events but, because o f the large energy difference between events o f similar magnitude, the cumulative energy is a rougher function than the B enioff strain and more difficult to fit to equation (4.1). On the right hand side o f equation (4.1), ty is the time o f the mainshock, s is typically about 0.3, and A and B are adjustable parameters. Optimization o f the fit o f the accelerating B enioff strain to equation (4.1) w ith respect to region size has shown that the radius R o f the optimal region scales w ith the magnitude o f the large event as \ogR cc-^m^ (Bowman e/a/., 1998). This is equivalent to R x L w h e re ! is the fault length. Several physical models have been proposed to explain these observations: (1) a damage mechanics model, (2) a critical point model, (3) a stress recovery model, and (4) a generalized aftershock model. For the damage mechanics model, positive feedback between fracture damage (as evidenced by seismicity) and stress concentration produces accelerating seismicity before a great earthquake (Sammis and Sornette, 2002). In the model explored by Ben-Zion and Lyakhovshy (2002), this feedback occurs as the result o f a lowered elastic modulus in damaged regions that concentrates strain and accelerates damage accumulation. They found that their model produced an increase in intermediate events and the time-to-failure equation (4.1) with w=0.3. The c ritic a l p o in t m odel interprets the observed increase in event size as evidence that the regional stress field becomes smoother before a large event. Sornette and 96 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Sammis (1995) pointed out that equation (4.1) is the expected behavior o f a system approaching a critical phase transition. From this perspective, the observed increase in event size reflects a growing correlation length in the stress field. The idea is that patches o f crust in which the stress exceeds some threshold become larger through time so that an event, once nucleated, has a better chance o f growing large late in the seismic cycle. Zoller et al. (2001) supported this view by using a 3-point correlation analysis to directly document the growing correlation length. In the stress recovery model, seismicity increases as a result o f the stress increase mostly in those areas where it w ill be released during the main event. Bowman and King (2001) have developed a model in which a simple dislocation is used to calculate the spatial and temporal distribution o f the stress accumulation needed to produce a specified large earthquake under the assumption o f constant tectonic loading by slip on a ductile extension o f the fault at depth. In their model, the probability o f an intermediate precursory event is determined by the difference between the regional stress and a threshold value. The difference between this model and the critical point model is subtle. The critical point model assumes uniform tectonic loading (uniform regional strain). Correlation length increases as the average stress level rises and as a result o f stress redistribution by the smaller events (see Sammis and Smith, 1999; Ben- Zion, 1996). In the stress recovery model, tectonic loading occurs by slip on the deep extension o f the fault plane responsible for the large event. It is not spatially uniform, but occurs in areas where the stress was released by the last large event, and w ill be 97 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. released again by the coming large event. The accelerating seismicity occurs preferentially in these areas. The increase in event size is again due to an increase in correlation length, but in this case correlation length grows due to percolation as the average stress level rises. One prediction o f the stress recovery model is that intermediate events should occur first on the outskirts o f the critical region, where stress first reaches the threshold, and then migrate toward the future epicenter o f the great event. Using a statistical approach, Helmstetter et al. (2002) show that accelerating seismicity before a large event can result from the combination o f the Gutenberg- Riehter law for the frequeney-magnitude distribution and O m ori’s law for the rate o f aftershocks. In their model the definition o f an aftershock is generalized to allow events o f all sizes, including those larger than the mainshock. From this point o f view, a cluster o f intermediate events makes a large event much more probable. Hence, large earthquakes tend to be preceded by a cluster o f intermediate seismicity. Unlike the other models, this one does not assume that a special state o f the crust is necessary for a large event. Accelerating seismicity results from a cascading instability in the stress transfer that produces aftershocks. Since each o f these four models explains the observed temporal clustering o f intermediate-size events before a great earthquake, the question naturally arises as to whether it is possible to decide, based on the seismicity data, whether one is better than the others. There are, for example, differences in the predicted temporal and 98 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. spatial distribution o f the intermediate sized events. Although both the stress recovery and the statistical models predict a migration o f epicenters toward the ultimate site o f the large event, only the stress recovery model predicts a spatial “ lobed” pattern. However, any such test suffers from the problem that there are only a few intermediate precursors, and the statistics are necessarily poor. We would like to be able to use the myriad o f smaller events to improve these statistics, and thus sharpen distinctions between the proposed models. In this paper, we explore the spatial and temporal evolution o f small events that precede the 1992 Landers, California earthquake. We then compare these observations w ith the predictions o f each o f the above models to see if the small events can 1) distinguish between the models and 2) improve the statistical significance o f precursory patterns. We w ill explore changes in a- and 6-value, changes in the cluster statistics, and spatial migration o f seismicity using both raw and declustered catalogs. 4.2 The Seismic Catalog Our seismic catalogs were taken from SCSN (Southern California Seismographic Network), a jo in t project o f California Institute o f Technology and USGS (U. S. Geological Survey). This network monitors and records events in the entire southern California region from 29°N to 4 I°N latitude and from I I2°W to I23°W longitude. 99 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The catalog is distributed by SCEC (Southern California Earthquake Center), and is available from 1932 to date. From A p ril 1, 1983 to July 14, 1983, the SCEC database is missing 3.5 months o f data due to station updates. To compensate for the missing data in this period we used the ANSS (Advanced National Seismic System) composite catalog in southern California regions. Using this combined catalog we explored 20 years southern California seismicity before the 1992 Landers earthquake. 4.2.1 Minimum Magnitude of Completeness The minimum magnitude o f completeness, rU c, is an important parameter for seismicity studies, especially when the analysis includes small earthquakes. Regional Me usually decreases w ith time as the number o f seismographs increases and data processing improves. It also varies spatially due to the heterogeneity o f station deployment. There are many studies addressing the completeness problem (Rydelek and Sacks, 1989, 1992; Gomberg, 1991). We determined trie using a simple method developed by Wiemer and Wyss (2000) and implemented in their ZM AP software (Wiemer, 2001). Their method is based on the assumption that the frequeney- magnitude distribution (FM D ) is given by the Gutenberg-Riehter (GR) relation down to the lowest magnitudes. Abercrombie and Brune (1994) found that the GR-FM D holds down to at least m = 0, so any deviation o f the data from GR at small magnitude 100 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. is ascribed to incompleteness in the catalog. Hence, rric is defined as the magnitude at which smaller events deviate from the GR distribution by a specified amount, which ZM AP expresses as a confidence level. 35 30 - c 2.5 1.5 0.5 Magnitude 2005 1985 1990 Time (yr) Figure 4.1 a) The percentage of catalog data not following Gutenberg-Riehter relation (residues) at all magnitude levels for the southern California region. A tm = 1.5 the residue is 10% (thus 90% confidence), and at w = 2.0 it is only 5% (a confidence of 95%). b) The minimum magnitude of completeness as a function of time for different confidence limits. 101 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. We measured as a function o f time and space for our data set. For the data since 1971, the southern California catalog is complete from W c = 1.5 at a confidence o f 90% and complete from rU c = 2.0 at a confidence o f 95% (Figure 4.1a). This means that at rtic = = 1.5, a simple power law can explain 90% o f the data variability, and at nic = 2.0, it can explain 95% o f the data variability. Figure 4.1b shows ruc as a function o f time at confidence level o f 95%. Except some short-period fluctuations, rric has decreased since 1980. During most o f the 1980s, rric was below 1.8. In the late 1990s, rric fell below 1.5. Our determination is consistent w ith previous studies which found that the SCSN catalog is complete atm = 3.0 since 1932 (Hilemen et al., 1973) and at m = 1.8 since 1981 (Given et al., 1989). To assure completeness, we truncated our catalog at magnitude 2.0, a few tenths above the maximum observed rric. As expected, rric is generally lower in the center o f networks than in surroundings. In the neighborhood o f the Landers event, rric is uniform ly low and it does not significantly affect our results. 4.2.2 The Declustered Catalog Because aftershock sequences dominate the spatial and temporal distribution o f small events, we produced a “ declustered catalog” by identifying and removing aftershock sequences using an a lg o rith m developed b y Reasenberg (1985). T his algorithm identifies clustered events using a spatial test based on an estimate o f stress 102 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. redistribution in the vicinity o f each earthquake and a temporal test based on O m ori’s law. I f an event falls in a stress triggering region determined by either the largest previous event or the most recent event, it passes the spatial test and becomes a candidate for membership in the cluster. For the temporal test, each earthquake sequence is modeled as a Poisson process w ith a variable arrival rate determined by O m ori’ s law. I f an event falls in the time interval in which an expected aftershock would occur w ith 99% probability, it passes the temporal test. Only if a candidate event passes both the spatial and temporal tests, does it become a member o f the cluster. This algorithm considers every event as an aftershock o f the prior event, so that the aftershocks o f aftershocks are grouped into one cluster which includes aftershocks o f the mainshock as well as foreshocks. For our catalog, about 72% o f events were identified as belonging to a cluster, and about 50% o f clusters contain at least one foreshock. The distribution is dominated by small clusters containing five or fewer events, but most o f the clustered events are members o f a few large clusters. The percentage o f clustered events found here is a bit higher than in the Reasenberg (1985) study, probably because our catalog contains a few more very large earthquakes. This algorithm removes foreshocks and aftershocks from the catalog by combining all events in a cluster into a single “ equivalent event” whose origin time is the mainshock, and whose magnitude is found from the cumulative moment o f all events in the cluster. In the subsequent analysis we w ill look at both raw and declustered catalogs. 103 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4.3 Seismicity preceding the Landers earthquake 4.3.1 Changes in a- and b-value Although straight-forward in principle, measurements o f a- and Zj-values are complicated by truncation o f the catalog at nic. The basic formula for the GR distribution is \ogN {m ) = a -b m (4.2) where N{m) is the number o f earthquakes w ith magnitude greater than or equal to m. Truncating the GR distribution at modifies equation (4.2) to \o%N{m) = a ^ -b {m - m ^ ) for m > nic (4.3) The GR equation (4.3) can be written as a Pareto distribution for scalar seismic moment M (Kagan, 2002) A ( M ) = 1 0 ''c j^ ^ ] ^ fox M > Me (4.4) where /3 = ^ b . Fitting equations (4.3) or (4.4) to seismic data determines the three parameters, b (or P), a (or Uc), and nic (or M :) in equations (4.3) and (4.4). We used the results in the previous section to determ ine and w e found the other tw o parameters using least-squared analysis (LS) or a maximum likelihood estimate (M LE) 104 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (A ki, 1965). LS finds a and b together, while M LE only gives the 6-value, and the corresponding a value is estimated using least squares analysis. More complicated models also consider deviations from the GR power law relation at large magnitude. In this study, we consider the tapered GR relation, which has an exponential taper applied to the cumulative number o f events (Kagan, 2002) A (M ) = 10^‘^ f - ^ l exp ' for M c < M < o o (4.5) \M J \ M tcm ^ where Mtcm corresponds to the “ tapered corner moment” . For M < , the small earthquakes obey a GR power law. For M > , the distribution o f large earthquakes decays exponentially. Kagan (2002) gives a method for estimating and simultaneously using the likelihood function. In order to measure a- and 6-values accurately and objectively, we used LS analysis based on the GR model and a M LE analysis based on both the GR model and the tapered GR model. The LS analysis chooses the straightest segment in distribution, thus becomes an im plicit parameter. The M LE method, however, is more sensitive to small magnitudes because o f their larger number, and the behavior at large magnitudes is not as important. We adjusted m ^. to minimize differences between the a- and 6-values measured using the three different methods. In most cases M LE method results in very similar a- and 6-values for all distributions (3), (4), and (5) (Figure 4.2). 105 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. We measured the a- and i-values in 3-year time windows moving in 1-year steps from 1976 up to the Landers earthquake. The space domain on which the a- and b- values were measured was chosen in two different ways. First, we examined circular regions centered at the middle o f Homestead Valley fault (not the mainshock epicenter) with different radii. Second, we examined regions bounded by stress-transfer contours calculated using the Bowman and King (2001) stress recovery model. w c o > a > E J T B 3 E 3 o Magnitude Figure 4.2 Frequeney-magnitude relation of the raw eataiog data within a circular region centered on the Landers earthquake with R = 50km in a 3-year period from 1980 to 1983 (fold line). Three methods are used to measure b- and a- values: the maximum likelihood estimation (M LE) based on Tapered Gutenberg-Riehter model (solid line), the M LE base on G -R m odel (dotted line), and the least squared estimation (LSE) based on G -R model (dashed line). 28-Jun-1980 11:57:00 - 29-Jun-1983 05:67:00, R = 50km 10 Catalog Tappered Q-R MLE fitting G-R MLE fitting Q-R LSE fitting 3 10 2 10 1 10 0 10 ■ 1 10 3.6 4.S 1 2 2.5 3 4 1.5 106 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4.3.1.1 Changes in a- and b-values with time in circular regions We first used the raw seismic catalog to measure the a- and 6-values as a function o f time from 1976 to 1992.6, just before the Landers earthquake. A t each time point we used the previous 3 years data. This 3-year window was advanced in 1-year steps. In space we selected circles w ith different radii centered at the middle point o f Homestead Valley fault. The radii ranged from 50km to 150km in 10km intervals plus 200km and 250km. The smallest number o f earthquakes used to find a- and 6-values in any space-time window was over 1000 events, well above the 200 event threshold used by Wiemer and Wyss (1997). The data for a 50 km radius for the three year period between 1980 and 1983 is shown in Figure 4.2 with the various fits. This is a worse case since larger radii had more events during each three year interval. The a- and 6-values are plotted as functions o f time in Figure 4.3a for radii o f 60 km, 120 km, 130, and 250 km respectively. The large fluctuations before 1979 may be due to lower data quality. An increase in a-value w ith time up to the Landers mainshock was observed in some radii. We wish to see if there changes in activity level (a-value) are caused by a change in slope (6-value) or if they are uncorrelated w ith 6-value, and thus represent a change in activity at all magnitudes. We therefore calculated the cross correlation eoefficient between the time sequenees for a- and 6- value for each radius using the follow ing equation: 107 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The results are plotted as Figure 4.3c. Note that for radii less than 120km, the changes o f a-value do not correlate w ith changes o f b- value (C = 0.5-0.7). This means that the increase in a-value represents an increase in activity at all magnitudes. For radii larger than 120 km, not only does the a- value not increase monotonically with time, but the changes in a-value also correlate w ith changes in Z)-value (C = 0.8-0.95). Thus although we also observed increases o f a-value at large radii, such changes are probably due to an increase in Z)-value, which reflects a preferential increase in small events. I f we regard the abrupt increase in the cross correlation coefficient at about 120 km as the boundary between different patterns in the behavior o f a- and 6-values, it is consistent w ith the critical value o f R=125 km determined by Bowman et al. (1998) by optimization o f the fit o f the seismicity to equation (4.1). We next measured the temporal and spatial variation o f a- and 6-values using the declustered catalog. The results, summarized in Figures 4.3b and 4.3c, are quite different from those found using raw catalog. The a- and 6-values remain almost unchanged w ith time for all radii. Moreover, the fluctuations in a-value are almost perfectly correlated w ith fluctuations in b-value (C > 0.9). Hence the increase in a- value observed in the raw catalog is due to clustered events, most likely aftershocks o f intermediate events. Except for the 1992.4 m = 6.\ Joshua Tree earthquake there were no earthquakes w ith m>6 w ithin the region o f R < 150km during our study period. 108 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. R » w data □eclustered data a-value b-value a-value b-value a-value b-value a-value b-value R = 250km R= 130km R = 120km R = 60km / A K 1 ins Time (yr) ia«o ISIS Time (yr) Tapptrtd 0>R MLE O 6-RMLE -A - G-R LS E Declustered data Raw data Rc = 125km (Bowman etal., 1998) o o M H O 200 2S0 100 150 R adius (km ) o Figure 4.3 The changes of b- and a- value as a function of time for four selected circular regions centered at the Landers of R = 60km, 120km, 130km and 250km. a) b- and a- values are m easured using raw data, b) b- and a- values are m easured using declustered data, c) the cross correlation coefficients between the b- and a- values as a function of time for all circular regions in which they are measured. The raw and declustered data are both shown as indicated. 109 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. However, two large events {m = 6.2 and m - 6.6) occurred at 1987.11 w ithin R < 200km. The aftershock sequences o f these large earthquakes could extend into R<150km, but we did not observe a significant increase in o-value at for R<150km at this time. 4.3.1.2 Changes in a- and b-values with time in regions of stress accumulation Bowman and King (2001) developed a model to calculate the stress field required to produce a mainshock having a prescribed slip by displacing the fault backwards the amount that it moved in the mainshock. Their model has been applied in several seismicity studies (Bowman and King, 2001; King and Bowman, 2003; Bowman and Sammis, 2003). The pre-stress field can be established by adding the back-slip results to the preexisting regional stress (King and Cocco, 2001). In this work, we calculated the pre-stress by back-slipping the Landers event using a program developed by Zeng (2001) from the slip distribution measured by Wald and Heaton (1994). The fault plane is comprised o f three subfaults w ith different orientations. From northwest to southeast they are the Emerson and Camp Rock faults (strike 320°), the Homestead Valley fault (strike 334°) and the Johnson Valley and Landers faults (strike 355°). The pre-stress was resolved on the ruptured Landers fault determined from focal mechanics solution. We did not calculate the total pre-stress 110 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. field because the regional background stress state is unknown. However, the shape o f the back-slip stress is identical to the total stress field if the regional stress field is homogeneous. In this work we need only the shape o f pre-stress field to delim it the regions where accelerated seismicity is expected. The stress contours are plotted in Figure 4.4. This plot is not sensitive to the assumed coefficient o f friction The positive lobes are expected to be seismically active before the earthquake. The time window in which a- and 6-values were measured is the same as in the circular regions in the previous section, but the space windows were lim ited to positive lobes o f the Coulomb pre-stress field in Figure 4.4. Contours o f constant pre stress were taken as the boundaries o f space windows. Lower pre-stress contours correspond to larger windows. Our smallest space window corresponds to a stress contour o f 2.7 bar (the lobes extend to distance o f about 70 km), and our largest space window corresponds to a stress contour o f 0.035 bar (the lobes extend to about 250 km). In all space windows, there were at least 200 events, enough to accurately measure a- and 6-values (Wiemer and Wyss, 1997). We first used the raw catalog to measure a- and 6-values (Figure 4.5a) and their cross correlation coefficient (Figure 4.5c). For the contours from 2.7 bar to 0.6 bar, the a- value rose gradually until 1984, and then remained at a high level. W ithin these regions, corresponding changes in 6-value were different from the changes o f o-values, especially at the end o f the 1980s where 6-value underwent a pronounced decrease. For larger contours (corresponding to stress levels less than 0.4 bar), a- values also 111 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. increase before 1982, but this trend was well correlated w ith changes o f 6-values. From the contour o f 0.6 bar to 0.4 bar, the correlation coefficient jumps above 90%. The 0.6 bar contour is the approximate boundary between uncorrelated and correlated a- and b- values. This is consistent w ith our result for circular regions because a circle with a radius o f 120km approximately covers the regions w ithin 0.6 bar contour. f t ' - r > A , 1 VA 1/'4----- .S 34.5 -119 -118.5 -118 -117.5 -117 -116.5 -116 -115.5 -115 -114.5 -114 longitude F ig u re 4.4 The Coulom b stress field before the Landers earthquake is plotted as contours of the changes of failure stress (CFS). The circles with different radii are plotted as well (dash line). 12 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. According to the King and Bowman (2001) model, it is only these positive Coulomb regions that contribute to the observed accelerating seismicity in circular or otherwise arbitrarily shaped regions. In order to test this hypothesis, we measured a- and 6-values and their correlation coefficient in the negative lobes o f the Coulomb pre-stress field from the raw catalogue (Figure 4.6a and 4.6c). In contrast to the positive lobes, no regular changes in a- and 6-values were observed, however, their cross correlation coefficients are much lower than in positive lobes. We also used the declustered data set to measure a- and 6- values and their correlation coefficient in both positive (Figure 4.5b and 4.5c) and negative (Figure 4.6b and 4.6c) lobes. As in circular regions, the changes o f a- and 6-values did not show any regular patterns, and they were almost perfectly correlated. Again, this implies that the observed increase in a-value is mostly due to the increased aftershock sequences before the Landers mainshock. Once the aftershocks are removed, a-value is almost perfectly correlated w ith 6-value. The different patterns o f the changes in a- values in positive and negative pre-Coulomb stress lobes only weakly support the stress recovery model, because the relatively high correlation coefficients between a- and 6- values (> 70%) for the positive lobes implies that the increase in ^-values is probably due to a relative inerease in the number o f small events. In order to better distinguish between the seismicity patterns in positive and negative regions, we plotted the cumulative number o f events down to m ~ 2.0 within the outermost contours o f both lobes (Figure 4.7a and b). Although the patterns in ,13 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Raw data a a-value b-value a-value 6-value CFS=0.035bar CFS = 0.4bar a-value 6-value a-value 6-value CFS = O.Sbar CFS = 2.7bar 1} Oacluatered data 7 ^ Tim « (yr) t380 ISSd Tim e (yr) 5 5 1 n i 1 0.95 A o 0.9 - a - T^ipored G-R MLE O 6.RMLE e^Rise Declustered data ’S 0 ) |0 . 8 S o c 0.8 o Raw data 2 o Changes of Coulomb Stress (bar) Figure 4.5 The changes of b- and a- value as a function of time within four selected positive CFS contours of pre-Landers stress filed (CFS = 2.7bar, 0.6bar, 0.4bar and 0.035bar). a) b- and a- values are m easured using raw data, b) b- and a- values are measured using declustered data, c) the cross correlation coefficients between the changes of b- and a- values with time at all CFS contours in which they are measured. Results from raw and declustered data are both shown as indicated. 114 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Raw dafa Oeciuslered data a-value i}-value CFSs -0.024bar a-vaiue ® « a r A. 4 CFS = -0.047ba 6-value a-value CFS = -O.lbar * & b-value a-value A CFS » -0.2bar b-value Tim e (yr) IM S Time (yr) 5 1 ■ o ™ 0.8 it — TappefBd 6-H MLC a G-RMLE -A. G-R USE Dectustered data Raw data o o V I -1 0 '^ Changes of Coulomb Stress (bar) 2 -10 -10 o Figure 4.6 The changes of b- and a- value as a function of time for four selected negative CFS contours of pre-Landers stress filed (CFS = -0.2bar, -O.lbar, -0.047bar and -0.024bar). a) b- and a- values are m easured using raw data, b) h- and a- values are measured using declustered data, c) the cross correlation coefficients between the changes of b- and a- values with time at all CFS contours in which they are measured. Results from raw and declustered data are both shown as indicated. 15 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Raw Data 2000 1800 positive lobes negative lobes X 1800 - 1400 - Q. i2 1200 ■ 1000 800 600 400 200 1995 1990 1985 1975 1980 1970 Time (Yr) Declustered Data 900 800 > positive lobes g negative lobes 700 ^ 600 500 400 3 300 = 200 100 1995 1985 1990 1975 1980 1970 Time (Yr) Figure 4.7 a) The cumulative number o f events against time in positive (circles) and negative (squares) pre-Coulomb stress lobes defined by stress recovery model using raw data, b) Same as a) but using declustered data. 116 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. positive and negative lobes for the raw data (Figure 4.7a) are different, the cumulative numbers o f events in both lobes show periods o f acceleration, but at different times. For the declustered data, the positive and negative lobes have almost identical patterns (Figure 4.7b). The significant decrease starting at about 1979 in both curves is due to the removal o f aftershocks o f a large mainshock occurred at the boundary o f the positive and negative lobes. Since we have observed an increase in a-value and low correlation coefficient w ith 6-value from circular regions, the contradiction between the changes in a-value and cumulative events number suggests that the stress accumulation model may be too simple to represent the active regions. 4.3.2 Changes in the cluster statistics Clusters were defined using the method developed by Reasenberg (1985). As discussed in the section on a- and 6-values, this algorithm replaces each cluster with an equivalent event located at the hypocenter o f its largest event and having a moment equal to the sum o f the moments o f all its members. Independent events are those that do not belong to cluster. The clustering algorithm thus replaces Ntot events in the raw catalog w ith Neqv equivalent events and independent events. Clearly, Ntot > Neqv + Nind- W e investigate the tem poral e vo lu tio n o f three measures o f th is clustering: (1) the number o f events belonging to clusters. Nee, where Nee - Ntot - Ni„d, (2) the number 17 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. o f clusters, Nd, were Nd = Neqv, and (3) the distribution o f cluster sizes, which are obtained from the clustering algorithm. Although the catalog is complete w ith 95% confidence to nic = 2.0, we lim it our determination o f Neqv and Nnd to events w ith m > 3.0. Extending the analysis down to me would identify an artificially large number o f independent events, many o f which have aftershock smaller than me. Fraction of Events Belonging to Clusters 0.9 0.8 0.7 O z 0.6 0 > O z 0.5 0.4 0.3 0 2 < _____ ■ _____ ■ ______■ _____ ■ _____ ■ ______■ _____ ■ ----------■ _____ '--------- '— 1972 1974 1978 1978 1980 1982 1984 1986 1988 1990 1992 Time (Yr) Figure 4,8 The ratio of the number of clustered events to the total events in 1-year moving time window up to the Landers mainshock. Figure 4.8 shows that the fraction o f clustered events w ithin R=150 km o f the Landers event. Nee / Mw, increases as a function o f time from 1973 until just before the Landers event. Figure 4.9a shows the yearly rate o f both independent and equivalent earthquakes in this same region over the same time interval. Note that the number o f 18 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. dN dN, ^ clusters per year, — — = — — , increases w ith time while the rate o f independent dt dt events, , decreases. The combined rate ^ remains approximately dt dt constant (Figure 4.9b), consistent w ith the result that the a-value o f the declustered catalog does not vary systematically w ith time (Figure 4.3b). The increase in independent events after 1988 reflects an increase in total seismicity. The ratio dN / dt ------ reaches a peak in 1988, four years before the Landers earthquake (Figure d N ,„J d t 4.9c). Patterns similar to those in Figure 4.9 were observed for all regions w ith R < 150km, but the smaller numbers o f events produced larger fluctuations. The general result is that the number o f events belonging to clusters and the number o f clusters both increase w ith time approaching the Landers earthquake. We next examine the distribution o f cluster sizes, where a cluster’s size is defined as the number o f its members. In general, most o f the clusters are small: about 85% o f the clusters contain 5 or less events. However most o f the clustered events belong to the largest few clusters. The largest 15% o f all clusters contain about 87% o f the clustered events. To study the evolution o f the cluster distribution w ith time, we divided the time interval from 1973 until just before the Landers event into four intervals, each about 4.9 years long. The distribution o f cluster sizes for each time interval is shown in Figure 4.10a. The smallest bin contains the number o f clusters with 5 or less events while the largest bin contains the number o f clusters w ith 100 or 119 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. >30 m. 1995 1980 1985 1990 1970 1975 u60 «55 50 1970 1985 1990 1995 1975 1980 2.5 0.5 1970 1980 1985 1995 1975 1990 Time (Year) Figure 4.9 a) Smoothed seismicity rate of independent events ( dN.^j I d t) and equivalent events ( dN ^^Jdt). b) Combined seismicity rate of independent events and equivalent events ( + N )/ dt ). c) The ratio o f seism icity rate o f equivalent events to of independent events ( / dt)l(dN^^^ / dt)). 120 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 100 90 80 70 W ^ 60 O O 50 in _Q 40 E 3 30 20 10 0 a -|------------r I I 1973-1977.8 I I 1977.8-1982.7 ■ 1 1982.7-1987.6 ■ I 1987.6-1992.5 p J I 10 20 30 40 50 Cluster size 60 80 100 Small cl usters ( No. of, member events 5) / 0) 14 re 10 Large clusters ( No. of member events > S) 1995 1990 1985 1980 1975 1970 Time (Year) F igure 4.10 a) Histogram o f number o f clusters with different sizes for four continuous time periods, b) Smoothed seismicity rate for small clusters (No. of member events < 5) and for large clusters (No. o f member events > 5). 121 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. more events. In Figure 4.10b the yearly rate o f small clusters that contain 5 or less events is compared w ith the yearly rate o f larger clusters containing more than 5 events. Note that the rate o f occurrence o f larger clusters increases w ith time and that a large increase occurs in the final 4.9 years prior to the Landers event. These larger aftershock clusters are associated w ith the larger events that produce the accelerating seismicity. They may also reflect the growing correlation length in the smoother stress field hypothesized in the critical point model. 4.3.3 Migration of seismicity toward the epicenter Both the stress recovery and the statistical models predict a migration o f epicenters toward the ultimate site o f the large event, but the reasons are quite different for the two models. The stress recovery model considers a whole earthquake cycle for a segmented fault under constant tectonic loading (Bowman and King, 2001). It predicts the temporal and spatial changes o f seismicity produced by changes o f Coulomb stress field. Immediately follow ing the mainshock, the four quadrants at the ends and along side the fault (parallel and perpendicular lobes) experience increased activity (aftershocks) as the Coulomb stress in these four lobes is increased. As tectonic loading continues, the stress starts to rise in the diagonal lobes. Because the stress firs t reaches to the fa ilu re stress at th e ir outerm ost extent, the foreshocks in the diagonal lobes appear to migrate toward the epicenter o f impending mainshock from 122 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. their outer edges. The foreshocks migration predicted in Helmstetter et al. (2002) is derived from an extended O m ori’s law, where the foreshocks are expected to migrate in towards the mainshock epicenter whereas the aftershocks are expected to migrate out from the mainshock epicenter. In contrast to the stress recovery model, this model does not specify the regions where the foreshocks are expected. Because there are fewer foreshocks than aftershocks and because they are more widely distributed, statistical analyses are necessarily poor. In order to improve foreshock statistics, in this work we selected events as small as w = 2.5 from 1971 to 1992.6 (immediately prior to the Landers mainshock). We first chose those events w ithin the positive lobes o f Coulomb pre-stress field, and then analyzed the cumulative events in neighboring contour intervals w ith time approaching the Landers mainshock. The Coulomb stress contours are chosen in the same way as in measuring b- and a- values, but we combined the contour intervals w ith similar seismicity rate patterns and organized them into 4 groups. From innermost to outermost. Figure 4.1 la shows the cumulative number o f events from raw catalogue w ith time in neighboring contour intervals: - 1.68 bar, 0.40 - 1.68 bar, 0.13 - 0.40 bar, and 0.035 - 0.13 bar. In the first 3 inner contour intervals, the accelerated seismicity is systematically observed in different time periods. For the interval between 0.13 and 0.40 bar, the acceleration in cumulative events starts at 1971 or even earlier, for the interval between 0.40 and 1.68 bar, such acceleration starts at about 1977, and for the region w ithin 1.68 bar, it starts at about 1980. We did not observe any acceleration in 123 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. the outermost stress contour interval 0.035 - 0.13 bar. The jumps observed in the cumulative events are obviously caused by aftershock sequences o f large and intermediate earthquakes. In order to remove the influence o f aftershocks and investigate the background seismicity, we repeated the above work using the declustered catalogue. Foreshock migrations are clearer in the declustered catalog (Figure 4.1 lb). Both the starting and ending time o f seismicity acceleration are observed. For the interval between 0.13 and 0.40 bar, period o f accelerating seismicity starts in 1971 and ends in 1982, after which the cumulative events increase linearly w ith time. For the interval 0.40 - 1.68 bar, the acceleration period is from about 1977 to 1985.5. For the innermost contour, however, we found the seismicity acceleration period from 1979 to 1987, five years prior to the Landers earthquake. There may exist an even smaller region w ithin the 1.68 bar contour in which the acceleration period starts later than 1980 and continues until the Landers mainshock, but this is difficult to verify due to very small number o f events. In the outermost stress interval, we did not observe any acceleration. The first 3 inner stress contour intervals approximately cover a region o f R = 180km, consistent w ith other estimates o f the size o f the critical region. To compare w ith the stress specified regions, we next choose circular annular regions w ith different sizes. Here chose four regions whose radii ranges are less than 80km, 80 - 130km, 130 - 180km and 180 - 250km. These regions approximately cover the stress contour intervals defined above (Figure 4.12). Although we observed 124 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Raw data 1500 CFS>1.7bar ,1000 500 Acceleration period 1990 1995 1980 1985 1970 1975 *5 600 CFS = 0.1 - 0.4bar Aocele ration period 400 200 1970 1975 1980 1985 1990 1995 500 CFS = 0.035-O.lbar 400 300 200 100 1970 1980 1975 1985 1990 1995 Time (Yr) Figure 4.11a The number of cumulative events with time counted in four CFS contour intervals (0.035-0.Ibar, 0.1-0.4bar, 0.4-1.7bar and >1.7bar) using raw data. The acceleration period moves from outer CFS contour intervals to inner CFS contour intervals. 125 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Declustered data 1000 CFS>1.7bar 800 600 400 Acceleration period 1995 1980 1985 1990 1970 1975 1975 *-400 CFS = 0.1 - 0.4bar g 300 Acceleration period 200 100 1980 1985 1990 1995 1970 1975 400 CFS = 0.035-O.lbar 300 200 100 1970 1975 1980 1985 1990 1995 Time (Yr) Figure 4.11b The number of cumulative events with time counted in four CFS contour intervals (0.035-0.Ibar, 0.1-0.4bar, 0.4-1.7bar and >1.7bar) using declustered data. The acceleration period moves from outer CFS contour intervals to inner CFS contour intervals. 126 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Raw data 2000 R < 80km 1500 MOOO 500 1995 ^ 1970 1980 1985 1990 1975 C (U > R = 130-180km 200 1970 1980 1985 1995 1975 1990 800 R = 180-250km 600 400 200 1970 1975 1980 1985 1995 1990 Time (Yr) Figure 4.12a The number of cumulative events with time counted in four annular or circular regions centered the Landers (180-250km, 130-180km, 80-130km and <80km) using raw data. 127 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Declustered data 1000 R < 80km 800 - 600 400 ^ 200 1990 1995 1980 1985 ^ 1970 k. Q ) c 400 - 4 ) 5 300 ■ 1975 R = 80 -130km O 200 L. ^ 100 E D Z 1995 1980 1985 1990 1970 1975 300 R = 130-180km 3 § 200 O 100 1995 1970 1980 1985 1990 1975 400 R = 180-250km 300 200 100 1970 1980 1985 1990 1995 1975 Time (Yr) Figure 4.12b The number of cumulative events with time counted in four annular or circular regions centered the Landers (180-250km, 130-180km, 80-130km and <80km) using declustered data. 128 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. pronounced seismicity acceleration w ithin inner annuli (- 80km and 80 - 130km), we did not observe any indication o f foreshocks migration. Apparently earthquakes outside the contours stress aecumulation veiled the foreshocks migration. Beyond the region o f R = 130km, the eumulative events increase linearly w ith time, consistent w ith a- value measurements beyond 130km, which did not show systematical increase. 4.4 Conclusion and Discussion Where previous studies o f seismic acceleration preceding large earthquakes have focused mainly on the increase in intermediate-sized events, we have explored the evolution o f the spatial, temporal and magnitude distributions o f regional seismicity for all events down to the magnitude o f completeness o f the catalog. We focused our study on the 1992 Landers earthquake because it is the most recent large event in southern California, and therefore gives us the longest and most complete record o f precursory seismicity. The central question is whether the inclusion o f small events in the analysis yields additional insight into the phenomenon o f aceelerating seismicity. Since most small earthquakes are aftershocks, we might expect an increase in their number associated w ith the increase in the number o f intermediate events, and this is what we observed. However, we also observed precursory phenomenology that required the fu ll range o f magnitudes such as changes in the correlation coeffieient between a- and b-value, changes in cluster statistics, and the spatial migration o f 129 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. seismic acceleration. We used the Reasenberg (1985) algorithm to produce a “ declustered catalog” from the “ raw catalog” by identifying clusters and replacing each w ith an equivalent event. Studies o f the evolution o f cluster statistics were also based on the clusters identified using this algorithm. Our observations can be summarized as follows: 1. For the raw catalog, the a-value o f regional seismicity increased over a large portion o f southern California to distances o f R = 250 km from the Landers earthquake. However, the correlation between a- and 6-value increased sharply at about i? = 125 km. For regions w ith R < 125 km, a- and 6-value are relatively uncorrelated indicating a uniform increase in activity at all magnitudes. For regions w ith R > 125 km, the strong correlation between a- and 6-value indicates a systematic increase in small events. 2. For the declustered catalog, the a-value showed no systematic variation in time. Moreover, fluctuations in a-value were almost perfectly correlated w ith fluctuations in 6-value for all radii R. The implication is that the lack o f correlation between a- and 6- value for R < 125 km in the raw catalog is almost entirely due to the aftershocks o f the intermediate events that produce the accelerating seismicity. The correspondence between the boundary o f the uncorrelated region and the optimal radius for acceleration found by Bowman et al. (1998) supports this interpretation. 3. When this analysis was lim ited to the raw catalog in the active lobes predicted by the Bowman and King (2001) stress accumulation model, the boundary between 130 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. the correlated and uncorreiated regions was again at about 125 km, but there was no improvement in this pattern over that obtained using circular regions. The a- and b- value was relatively uncorrelated at all distances for the non-active lobes predicted by the stress accumulation model. The observation o f very different patterns in the active and non-active lobes suggests that they may have some physical significance, but the interpretation o f these differences is not clear. 4. For the raw catalog, the cumulative number o f events accelerated between 1970 and the Landers earthquake in both the active and non-active lobes o f the stress accumulation model, although the acceleration began a bit later in the non-active lobes. For the declustered catalog, the cumulative number o f events was virtually identical in the positive and negative lobes suggesting that the difference between these regions in the raw catalog is due to differences in clustering. The rate accelerated between about 1970 and 1982 and remained constant between 1982 and the Landers event. 5. The fraction o f events belonging to clusters increased steadily from 1972 until the Landers earthquake. The number o f clusters per year also increased during this time period while the number o f independent events per year decreased until about 1989 and then increased during the two years before the Landers event. The number o f clusters plus independent events per year remained approximately constant until 1989, then increased markedly between 1989 and the Landers event, due to an increase in both clusters and independent events. Similarly, the ratio o f the number o f clusters to the number o f independent events increased smoothly between 1972 and 1989, and 131 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. then decreased during the two years before Landers. Finally, while the number o f small clusters {n<5 events) per year remained approximately constant, the number o f large clusters {n> 5 events) increased steadily up to the time o f the earthquake. 6. The only evidence for seismicity migration occurred in the active lobes o f the o f the stress accumulation model where accelerated seismicity began first at large distances and moved systematically inward toward the Landers faults. The pattern was particularly clear for the declustered catalog. No migration was observed in the non active lobes or in circular regions. This observation also suggests that the spatial lobes predicted by the Bowman and King model may have physical significance. The most general conclusion that emerges from this study is that the clustering behavior o f the seismicity changed before the Landers earthquake. This showed up in the spatial patterns o f correlation between a- and 6-value and in the changes in cluster statistics w ith time. The increase in the ratio o f clustered to independent events and the growth o f cluster size w ith time is the expected signal o f a growth in the correlation length. It is closely related to the increase in the number o f intermediate events, but does not suffer from the statistical problems associated w ith the small number o f intermediate precursory events. The spatial patterns o f precursory seismicity predicted by the Bowman and King (1999) stress accumulation model were supported by the differences in the correlation between a-and 6-value in the active and non-active lobes and by the observation that seismicity migration only in the active lobes. 132 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C h a p t e r 5 Conclusions and Discussions Paper I develops analytical and numerical models o f stuck asperities on an otherwise creeping fault plane. The objective is to model the repeating earthquakes on the San Andreas fault near Parkfield, California. The main conclusions from Paper 1 can be summarized as the follows: 1. From both theoretical analysis and numerical simulation, the solid asperity model w ith constant loading rate produced the observed scaling between T and Mo as Toe Mg"®. 2. Fitting the observed relation between U a and Mo near Parkfield to the analytical asperity model placed a constraint on the fracture energy, Gc> 1.4 x 10’ J/m^, which is consistent w ith previous estimates based on models for large events on the San Andreas fault. This suggests that the asperity model provides another way to estimate the energy release. 3. The numerical simulations found that only clusters w ith fixed asperity density (including solid asperities) yield the observed temporal scaling relation between T and Mo- This effectively rules out the Cantor dust fractal model proposed by Sammis et al. (1999) which assumed that repeating earthquakes involve 133 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. hierarchical clusters o f asperities, where the asperity density significantly decrease w ith the size o f clusters. 4. For the solid asperity model, the average stress drop still decreases w ith earthquake size, and the scaling power depends on the area over which the average stress drop is defined. Average stress on the asperity itself can be as high as 100 MPa, but it is reduced to less than 30 MPa over the entire rupture area. These low stress drops are equivalent to those found by seismological spectral analyses. 5. The stress drop for asperity clusters does not scale w ith earthquake size. However the numerical simulations showed that the creeping cells w ithin a cluster increase stress concentration on its constituent unit hard asperities. The repeating events at Parkfield are thus most likely due to the repeated failure o f solid asperities o f various sizes. However, the fractal hierarchy found by Sammis et al. (1999) is an observation, so that these solid asperities may have a fractal distribution in space. Unlike the nested hypocenters near Parkfield, the hypocenters o f repeated events near San Juan Bautista are distributed in linear streaks up to a few o f kilometers (Rubin et al., 1999). We therefore propose a “ knocker” model to reconcile these observed spatial, temporal, and magnitude distributions. The “ knockers” are isolated blocks o f very strong high-grade metamorphic rocks (e.g. blueschists) w ith sizes from several meters to tens o f kilometers that are commonly observed in Franciscan terrain (Coleman and Lanphere, 1971; Karig, 1979). One hypothesis that could explain the 134 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. different hypocenter distributions at the two ends o f the creeping section o f the San Andreas fault is that these knockers experience rolling and fragmentation in the fault zone under increased shear flow from Parkfield to San Juan Bautista. In order to comprehensively explain these observations, the physical fragmentation process o f knockers and their distribution under shear flow w ill be studied in future works. Moreover, the comprehensive model should be able to explain the significant variations in 6-value in frequency-magnitude statistics in the vicinity o f Parkfield, in which the 6-value changes from 0.5 in the locked region to about 1.3 in the creeping region (Wiemer and Wyss, 2000). Paper II studied the seismic source for the 1999 Chi-Chi, Taiwan earthquake at very high frequencies. The main conclusions are: 1. The Chi-Chi mainshock in the broadband record appears as a sequence o f distinct individual arrivals at high frequency. Each arrival was shown to correspond to a sub-event originating at an asperity on the Chelungpu rupture. 2. These asperity sources can be separated into those associated w ith the normal rupture propagation w ith a velocity o f about 2.0 km/s, and those significantly delayed behind the rupture front. These late sub-events may be interpreted as aftershocks which occur during the Chi-Chi mainshock. 3. Spatially the asperities appear in groups. Most o f them are located at very shallow depth along the Chelungpu surface rupture. The deep asperities were located at even greater depth after relocation and are mainly dominant by the E-W thrust. 135 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4. The frequency-magnitude distribution o f the identified sub-events follows the Gutenberg-Richter relation having the 6-value equal to 1.0. Spatially, the large sub-events are found at greater depth, while the small sub-events are only found at very shallow depth. The detailed mapping o f asperity sources gave a new high-frequency view o f the rupture mechanics o f a large earthquake, and may provide useful constrains in further refinement o f seismic waveform inversion. The magnitude-time distribution o f asperities suggests that the aftershock sequence on the fault plane begins in the first few seconds after the rupture front passes. This also indicates that the rupture propagation is not as smooth as imaged previously, probably due to the high heterogeneity near the fault plane. In space the locations o f asperity groups accord w ith those recognized in seismic waveform inversions. It appears that detailed comparison between the asperity mapping in this study and the dynamic rupture field deduced by waveform inversion is needed to reveal their potential relations in space and time. Since the magnitudes o f sub-events have been estimated, such comparison may further determine the rupture area o f each sub-event based on an asperity model. A number o f high-pass filtered seismograms exhibit sharp, quasi-periodic sub events w ithin some bursts. The inherent physical mechanism may be explained by stick-slip model under a high loading rate. Unlike the low loading rate in a “ seismic cycle” documented in most slider-block analyses o f the stick-slip instability, the loading rate in this case can be as high as the fault slip rate during the Chi-Chi 136 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. mainshock. This work can be done based on the analysis for the case o f high loading rates presented by Jaeger and Cook (1976), in which the simple friction law used can be extended to include more realistic velocity- or state-weakening friction laws. Paper III used the small earthquakes before the 1992 Landers, California earthquake to test the critical point model and the stress recovery model o f precursory accelerating seismicity. As a specific case o f the critical point model, the stress recovery model predicts a specific spatial pattern for the precursory seismicity and a temporal migration o f activity towards the ultimate epicenter. The main conclusions o f Paper III are summarized as follows: 1. For the raw catalog, the o-value in the Gutenberg-Richter relation increases with time, and the variation between a- and b- values w ithin a circular region o f R = 125 km is uncorrelated. This indicates a uniform increase in activity at all magnitudes in this region. 2. For the declustered catalog, the a-value keeps constant w ith time, and a- and b- values are almost perfect correlated for all radii R. This indicates that the increase in events number is due to the aftershocks associated w ith the intermediate events that produce the accelerating seismicity. 3. The spatial and temporal distribution o f b- and a- values has no improvement in patterns predicted by the stress recovery model (Bowman and King, 2001) over that using circular regions. I f the stress recovery model really has some physical significance, this implies that the active and non-active regions may not be as 137 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. simple as that derived from the Coulomb stress calculated by reversing the slip o f the final large earthquake. 4. The fraction o f events belonging to clusters increased steadily from 1972 until the Landers earthquake. The number o f clusters per year also increased during this time period while the number o f independent events per year decreased until about 1989. For these clusters, the number o f large clusters («>5 events) increased steadily up to the time o f the earthquake, while the number o f small clusters {n<=5 events) remained approximately constant. The cluster statistics using small events confirmed the moment release acceleration observed in intermediate events. 5. The seismicity migration observed in the active regions specified in the stress recovery model indicates the physical significance o f the spatial lobes for this model. No migration was observed in the non-active lobes or in circular regions. 138 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Bibliography Abercrombie, R. E., and J. N. Brune, Evidence for a constant Z)-value above magnitude 0 in the southern San Andreas, San Jacinto, and San M iguel fault zone and at the Long Valley caldera, California, Geophys. Res. Lett., 21, 1647-1650, 1994. A ki, K., Maximum likelihood estimate o f b in the formula log N = a - b M and its confidence limits, Research Institutes, 43, 237-239, 1965. A ki, K and P. G. Richards, Quantitative seismology. Theory and methods, Vol. 1, W . H. Freeman and Company, Chapter 5, 1980. 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Creator Chen, Youlin (author)

Core Title Modeling and imaging asperities on a fault plane and characterizing spatial and temporal patterns of precursory seismicity

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