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The study of temporal variation of coda Q⁻¹ and scaling law of seismic spectrum associated with the 1992 Landers Earthquake sequence
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The study of temporal variation of coda Q⁻¹ and scaling law of seismic spectrum associated with the 1992 Landers Earthquake sequence
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THE STUDY OF TEMPORAL VARIATION OF CODA Q -l AND SCALING LAW OF SEISMIC SPECTRUM ASSOCIATED WITH THE 1992 LANDERS EARTHQUAKE SEQUENCE by Xiaoling Liu A Thesis Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree Master of Science (Geological Sciences) May 1995 Copyright 1995 Xiaoling Liu UNIVERSITY O F SO UTH ERN CALIFORNIA TH E GRADUATE SC H O O L UN IV ER SITY PARK LO S A N G ELES. CA LIFO R N IA 9 0 0 0 7 This thesis, written by under the direction of hjd.Ki...Thesis Committee, and approved by all its members, has been pre sented to and accepted by the Dean of The Graduate School, in partial fulfillment of the requirements for the degree of X/A oU aj& L/C Scinnot D ta * THESIS COMMITTEE Ckairman s p A s t!__ Acknowledgement I would like to thank my advisor, Professor Kei Aki for being extremely patient and generous with me. W ithout his encouragement and sharing of stimulating ideas, this thesis would not be possible. I would also like to thank Professor Charles Sammis for introducing me to USC and guiding me throughout my first two years there. I am also grateful to Professor Ta-liang Teng for his invaluable advice and generous help and support. I also thank Professor Thomas Henyey and Steve Lund for their help and support throughout my years of graduate study at USC. My special thanks go to Rene Kirby for offering me tremendous help and support during my graduate study at USC. I would like to thank Su Feng for offering me her program to calculate coda Q, Yong Gong Li for providing me w ith the valuable data set and stimulating ideas. I am grateful to David Adams, Hong Ping Ouyang, Xiaofei Chen, Stewart Koyanagi for programing assistances. I also benefit tremendously from discussion with Rachel Abrocombie, Anshu Jin, Periklis Beltas, Michael Forrest, and Gretchen Murawski. I learned a lot from Linji An, Jin Wang, Jiang Qu, Jinbo Chen, James Chin and Chengping Lee. I also thank Mushtag Khan for his assistance at USC. ii Table o f Contents Chaper Page Acknowledgement.........................................................................................ii List of Figures.................................................................................................iv List of Tables..................................................................................................vii Abstract............................................................................................................viii I Introduction............................................ 1 II Temporal Variation of Coda Q“1 In A ssociation With the Lander's Event 2.1 Introduction...............................................................................4 2.2 The Landers Earthquake Sequence of 1992 and Su’ s study for the epicentral area of North Palm Springs earthquake of 1986.......................................................................................9 2.3 Method of analysis...................................................................10 2.4 Results....................................................................................... 12 2.5 Summary.................................................................................. 14 III Scaling law of seism ic spectrum for the Landers earthqauke sequence of 1992 3.1 Introduction........................................................................... 42 3.2 Data......................................................................................... 45 3.3 Method of analysis..................................................................46 3.4 Results.....................................................................................79 3.5 Summary................................................................................ 80 List of Figures Figure Page Chaper II 1 Map showing the region used in Su’ s coda Q~1 analysis. This same area is also used in our analysis........................................... 29 2 Map showing the epicenters of Joshua Tree, Landers, and Big Bear earthquakes............................................................................ 30 3 Coda Q-l vs. time obtained by Su for time window of 10-20 sec. in mainshock region........................................................................... 31 4 Same as 3, but for time window of 15-40 sec.................................32 5 Coda Q"1 vs. time obtained by us in region 1 for time window of 10-20 sec......................................................................................33 6 Same as 5, but for time window of 15-40 sec.................................34 7 Coda Q"1 vs. time obtained by us in region 2 for time window of 10-20 sec......................................................................................35 8 Same as 7, but for time window of 15-40 sec.................................36 9 Coda Q“1 vs. time by Jin for the Southern California area.................................................................................................. 37 10 Coda Q-l vs. time by us in region 3 for time window of 15-40 sec......................................................................................38 11 Same as 10, but for time window of 20-45 sec................................39 12 Map showing quarry site and stations used by Ouyang............................................................................................ 40 13 Mean of coda Q"1 vs. time by Ouyang using quarry blasts.............................................................................. .41 Chapter III 14 Figure showing displacement and acceleration amplitude spectra of the omega square model........................................................... 61 15 Map showing the locations of 10 sites used to record Lander's aftershocks............................................................................................. 62 16 Map showing the distribution of stations at site 8............................. 63 17 Map showing the location of station EDCY used in the study of Joshua Tree aftershocks....................................................................... 64 18 Mean value of normalized coda spectrum value vs. mean of moment for earthquakes occuring inside the fault zone recorded at station 0500. Time window is 10-15sec.......................................................... 65 19 Same as 18, but for earthquakes off the fault zone............................. 66 20 Same as 18, but for S wave....................................................................67 21 Same as 19, but for S wave....................................................................68 22 Same as 18, but for station 0503............................................................ 69 23 Same as 22, but for earthquakes occuring off the fault zone.................................................................................................70 24 Same as 22, but for S wave.....................................................................71 25 Same as 23, but for S wave.....................................................................72 26 Same as 18, but for station 0489............................................................. 73 27 Same as 26, but for earthquakes occuring off the fault............................................................................................. 74 28 Same as 26, but for S w ave...................................................................75 29 Same as 27, but for S wave.......................................................................76 30 Mean value of normalized coda spectrum value vs. mean of moment for earthquakes recorded at station EDCY...........................77 31 Same as 30, but for S wave.....................................................................78 vi List of Tables Table Page 2.1 Earthquakes used in the study of coda Q 'l in region 1 for time window of 10-20 sec.........................................................16 2.2 Same as 2.1, but for 15-45 sec window........................................... 18 2.3 Same as 2.1, but for region 2........................................................... 23 2.4 Same as 2.2, but for region 2........................................................... 23 2.5 Earthquakes used in region 3 for time window of 15-40 sec......................................................................................24 2.6 Same as 2.5, but for time window of 20-45 sec.............................. 26 3.1 Earthquakes used at station 0500 for the Landers sequence.........................................................................................50 3.2 Same as 3.1, but for station 0503....................................................51 3.3 Same as 3.1, but for station 0489....................................................52 3.4 Earquakes used at station EDCY for the Joshua Tree sequence.........................................................................................52 3.5 Results of least square fitting of two models to Landers and Joshua Tree data. R1 and r2 are the sum of the residue squares. A1 and a2 are constants needed for two models to fit the data in a least square sense..............................................................................................54 Abstract Temporal variation of coda Q"1 and scaling law of seismic spectrum were studied for the Landers earthquake sequence of 1992. Our results suggest that the temporal variation of coda Q_ 1 is extremely complex and depend on selected areas. To find the effect of fault zone structure on seismic source spectra/ a study of seismic scaling law is carried out using two distinct data sets. Two source models are used to fit the data in the least square sense. Model 1 incorporates Hanks' (1974) self-similar relation between comer frequency and magnitude. Model 2 uses Li's (personal communications) empirical relation between corner frequency and magnitude determined from Joshua Tree aftershocks. The result is opposite from expected. Earthquakes in the fault zone follows self-similarity, while those off the fault shows a departure from self-similarity. Model fitting of Joshua Tree data requires a departure from self-similarity around magnitude 3 in agreement with Li’ s results (personal communications). Chapter I Introduction For a given seismic region, the spectral content of earthquake motion depends on earthquake m agnitude systematically. The m anner in w hich the spectrum changes w ith m agnitude is defined as the scaling law of seismic spectrum. An accurately determined scaling law provides us a way to predict strong m otion of a large earthquake using data from sm aller events in the sam e region. The data collection for sm aller earthquakes is m ore cost efficient, since the num ber of earthquakes increases exponentially w ith decreasing magnitude. A re earthquakes self-sim ilar, obeying G utenberg and R itcher's frequency-m agnitude relation, or are they characteristic? Is there a unique scale length th at influences earthquakes in a given region? V arious observations of Californian earthquakes' departure from self sim ilarity suggest the existence of a unique length in the earthquake process. For example, for major California earthquakes w ith similar length and w idth, the fault slip is proportional to the seismic moment rather than its cube root. This systematic deviation from self-similar scaling laws is attributed to a characteristic variation of the higher-order structure of fault zones along the transform plate boundary (Aki, 1992). A nother interesting observation is that corner frequencies of small earthquakes becom e constant for earthquakes for a certain range of m agnitude. This departure from self-similarity has been confirmed by many 1 seismologists (Chouet et al., 1978; Rautian and Khalturin, 1978). This constant corner frequency is believe to be related to the fmax of large events. The origin of fmax is still a debated issue. Papageorgiou and Aki (1983) interpreted it as due to the effect of the finite size of the cohesive zone, which is assumed to be similar to the fault zone width. The param eters inferred from the specific barrier model (Papageorgiou and Aki, 1983) implies the existence of a minimum subevent crack size of a few hundred meters for the San Andreas fault. The strong positive correlation between coda Q_ 1 and b value found by Jin and Aki (1989) covering a large region of Southern California requires the same charateristic crack size as found in a creeping zone, suggesting aseismic creep under Southern California may be occuring in small fractures of a few hundred meters (Aki, 1992). The above observations suggest fine-scale or higher order structures play an im portant role in earthquake processes. The departure of the Californian earthquakes from the self-similar scaling law demonstrates the importance of the scale length on the order of a few hundred meters to a few kilom eters in Californian earthquake processes. This scale length is consistent with the characteristic size in the creep model of Jin and Aki (1989) to explain the observed correlation between coda Q"1 and b value. The present thesis combines the investigation of temporal variation of coda Q_ 1 and the study of seismic scaling law, w ith special reference to the characteristic scale length for southern Californian earthquakes. In Chapter 2, a study of temporal variation of coda Q_ 1 is carried out in association w ith the Landers earthquake of 1992. The purpose of this work is 2 to extend Su’ s earlier work (1992) in the same area to the period from 1987 to 1992. Su studied the temporal variation associated with the N orth Palm Springs earthquake of 1986. Her study period is from 1981 to 1987. An anom alous change in coda Q"1 associate w ith the N orth Palm Springs earthquake was reported by Su (1992) for the lapse time window 10-20 second. We hope to see the same pattern as reported by Su for the Landers earthquake to further establish the physical reality of temporal variation of coda Q '1. Recently/ Li et al. (1994) identified fault-zone trapped mode, a distinct wave train w ith a relatively long period following the S waves that shows up when events and stations are both close to the fault trace. The study of fault zone trapped modes can effectively reveal the physical properties and geometry of the fault zone. In Chapter 3, we divide the Landers aftershocks data into two distinct sets. One consists of earthquakes occuring inside the fault zone, the other set consists of earthquakes occuring outside the fault zone. The purpose of this divison is to see the influence of the fault zone structure on the scaling law of seismic spectra for small events. Hopefully, the search for the link between fine scale fault zone structures and earthquake processes can help us to better understand and eventually predict earthquakes. 3 Chapter II Temporal variation of coda Q '1 associated with the Landers earthquake of 1992 2.1 Introduction Seismic waves arriving after the passage of all direct body and surface waves are defined as coda waves. The decay rate of the coda amplitude supplies information on the average attenuation in the crust over the region of propagation paths for the back-scattered waves composing the coda. Since a deterministic interpretation of high frequency seismic waves is difficult because of their extreme sensitivity to lateral heterogeneities; a statistical approach was adopted by Aki (1969) by modeling the seismic coda waves of local earthquakes as backscattering waves from randomly distributed heterogeneities. This approach involves a handful of statistical parameters to characterize the medium for interpreting observations. Since coda waves lie in the later portions of a seismogram, they travel longer, encountering a greater variety of heterogeneities along the way. Therefore some of their properties can be considered as averaged over many sam ples of heterogeneities. The decay rate of coda waves for a given frequency is independent of source and receiver location and the particular path connecting the source and receiver. Evidence supporting the stability of coda decay rate is given by Aki (1969), Tsujiura (1978), Rautian and Khalturin (1978). Aki (1992) proves theoretically that an elastodynamic displacement field composed of both P and S waves will contain a greater fraction of S 4 waves w hen it is scattered by increasingly heterogeneous regions. This result suggests the dominance of S waves in the coda part of a seismogram, further confirming the conclusion of Aki (1980) on the com position of coda waves based on the observation of similar attenuation and site amplification for S and coda waves. It can explain w hy the decay rate is not m uch different between local earthquakes and quarry blasts for later coda as found by Su et al. (1991), because S waves will dom inate the later coda for any sources. It also supports unusual findings by Koyanagi et al. (1991) that the T phase observed on the Island of Hawaii converted from acoustic waves in the ocean shares sim ilar propagation velocity and site am plification as those of S waves. Futherm ore, it also renders the validity of using the energy transport equation w ith a single propagation velocity to investigate energy distribution from a point source by Zeng (1991). M any analyses and interpretations of coda w aves incorporate separating source, site and path effects of the pow er spectrum of coda waves. The pow er spectrum P(co 1 1 ) of coda waves at the lapse time t (measured from the earthquake origin time) can be written as, P(o) I t)=source(co) • site(co) • C(co 11 ) (1) w here C(co 11 ) is common to all sources and sites. The separability of the three effects has been confirmed empirically for various parts of the world (Herraiz and Espinoza, 1987). The assum ption of common path effect for all source and receiver pairs w ithin a region is reasonable because coda waves reflect the average properties of the medium they sample. One im portant application of the fundam ental separability of coda waves is the spectral ratio technique. 5 The spectral ratio method with data from a single station provides an easy way to separate source effect from the path and recording site effect since the common path and site terms are eliminated w hen taking the ratio of two spectra. Chouet et al (1978), Phillips (1985) and M ayeda (1991) use this fundamental separability for coda waves to isolate source and site effects. The site amplification factor determ ined by this m ethod does not require the knowledge of the geology, velocity structure and so on. Recently Li et al. (1992) used coda waves in eliminating source and site effects from the fault zone trapped modes of Landers aftershocks successfully. Coda Q '1 is a measurable geophysical param eter well correlated with seismicity. Spatial correlation betw een coda Q '1 and seismicity is well established. Tectonically active regions show high values of coda Q '1 while stable regions show low Q"1. Coda Q’1 is frequency dependent with low Q"1 at higher frequencies. This frequency dependence weakens from active regions to stable regions (Herraiz and Espinosa, 1987). Jin and Aki (1988) found evidence for migration of high coda Q-1 region coincident with the migration of seismicity in North China on the scale of a few hundred kilometers during several hundred years. They first attributed coda Q '1 to the fractured state of the brittle part of lithosphere related to seismicity. However, the low coda Q_ 1 observed during the aftershock period as well as the high Q_ 1 on the gulf coast, which is attributed to growth fault (aseismic fracture), suggest that coda Q -1 may be a measure of creep fracture in the ductile part of lithosphere. Therefore the study of temporal variation of coda Q_ 1 can provide us with crucial inform ation on im pending earthquakes, since the brittle p art of lithosphere is thought to be loaded by the deformation in the ductile part (Jin and Aki, 1989). 6 Temporal correlation between coda Q~1 and seismicity is more complex than spatial correlation. Chouet (1979) first reported a significant temporal change in coda decay at Stone Canyon, California. Since then many studies of temporal variations of decay of coda Q have been undertaken in regions where a large earthquake took place. The accumulation of stress in the vicinity of a major event modifies the way coda waves are scattered and attenuated. An increase in coda Q_ 1 has been observed by many authors before a large earthquake (Wyss, 1985; Gusev and Lemzikov, 1985; Novelo- Casanova et al., 1985; Jin and Aki, 1981; Sato, 1986). An opposite pattern was found in Japan (Tsukuda, 1988). Peng et al. (1987) and Su (1989) found a more complex pattern. Near the mainshock region, coda Q 1 was higher before the occurrence of an earthquake. For regions farther away, an opposite pattern or no significant change of coda Q-1 was observed. There was no major earthquake associated with the temporal change of coda Q'1 found by Chouet at Stone Canyon. Some anomalous changes in coda Q in southern California were found not correlated with major earthquakes (Jin and Aki, 1989). Jin and Aki (1989) found an impressive and systematic temporal change in coda Q_ 1 in southern California from 1933 to 1987. The coda power spectrum was fitted by the following formula. ln{P(o) I t) ta} = C(co) - bt (2) C(co) is independent of t and determined by source and site effects for a given co. Sources of bias that could lead to the fictitious change in coda Q_ 1 such as instrum ental effects, distributions of earthquake hypocenters, variations in focal mechanism of earthquakes were examined and dismissed. 7 Coda Q-l were found to correlate positively with b value determined from earthquakes with magnitude >3 at a confidence level of 0.974, suggesting the physical reality in both parameters, since the two data sets were completely independent. However, correlation between coda Q"1 and b value was not consistent, sometimes positive as for southern California, but negative in other cases. Three physical models were proposed by Jin and Aki (1989) to account for temporal variation in coda Q"l; (1) fractal model, (2) dilatancy-diffusion model, (3) creep model. The fractal model fails to explain the observation in two ways: (a) it predicts a correlation between the decay constant a in equation 2 and b value which is not observed, (b) The fractal model also suggests intensified clustering and localization of fractures contrary to the observation that coda Q"1 tends to decrease im m ediately before the earthquake (declustering or antilocalization). The dilatancy-diffusion model predicts correlation between increasing coda Q 'l with seismic quiescence. Dilatancy reduces the pore pressure and increases the frictional strength of a fault. Dilatancy also increases coda Q "l. This model contradicts w ith the observation by Robinson (1987) that low coda correlates with low rate of seismicity. The creep model is preferred because it can explain both positive and negative correlation between coda Q“1 and b value. Aseismic creep increases the crack density and coda Q"l. Assuming the creep fracture has a certain predominant crack size, the occurrence of those earthquakes with the comparable size are enhanced. If this critical magnitude Mc is in the lower part of the m agnitude range used in estimating b value, the enhanced seismicity will show an increase in b. If Mc is in the upper part of the magnitude range, it will decrease b (Jin and Aki, 1989). 8 2.2 The Landers earthquake sequence of 1992 and Su's study for the epicentral area of North Palm Springs earthquake of 1986 The Landers earthquake (Mw 7.4) of June 28, 1992 was preceded by Joshua Tree earthquake (Mw 6.1) of April 23, 1992 and followed by Big Bear earthquake (Mw 6.4) of June 28, 1992. A study of temporal change of coda Q '1 was carried out in association w ith Joshua Tree, Landers, Big Bear earthquakes using small local earthquakes recorded by Caltech-USGS seismic network, Su (1990) studied the temporal change of coda Q_ 1 associated with the occurrence of the North Palm Spring event on July 8, 1986. Her study area was enclosed by 115°55' and 117°30' longitude, and 33°30' and 34°30' latitude (fig. 1), covering a period from 1982 to 1987. Since the epicenters of Joshua Tree (33°58’ N, 116°19'w) , Landers (34°12'N, 116°26'W), Big Bear (34°12’ N, 116°50'w) earthquakes are included in her region of study (fig. 2), the new data enables us to extend Su's work to see any precursory change in coda Q_ 1 for these earthquakes. We hoped to find the consistent precursory pattern of temporal variation of coda Q"1 before Landers event similar to the one reported by Su in association with North Palm Springs event. As pointed out earlier, an anomalously higher value of coda Q"1 was found for a certain period before a major earthquake in many cases. To further establish the physical reality of temporal variation of coda Q'1, we hope to see that coda Q_ 1 starts to increase steadily sometime after the North Palm Springs earthquake and then decrease before the onset of the Landers earthquake sequence in this area. Three different regions are used in this study. Region 1 is chosen to be the same as Su's expanded area (115°55' to 117°30' longitude, 33°30' to 34°30' latitude). Region 2 is the same as Su's main shock area (116°35' to 116°45' 9 longitude, 33°57' to 34°02' latitude). Region 3 is the same as one of the areas (116°10' to 116°50’ longitude, 33°10' to 33°50' latitude) for which Peng made coda Q '1 measurement for the period 1982 to 1988 (1989). Over four hundred earthquakes of magnitude range 2.0 and 2.8 in the study area are chosen to avoid saturation and insure good signal to noise ratio. The cusp number and magnitude of the earthquakes used in the above three areas for different time windows are listed in table 2.1 through table 2.6. The seismograms are visually checked to make sure they are free of recording problems. 2.3 M ethod of analysis Following Aki and Chouet (1975), we define coda Q_ 1 by assuming that coda waves consist of backscattered S waves, and the first Born approximation is valid. To include the effect of m ultiple scattering, sim ultaneous determination of intrinsic coda Q_ 1 and scattering coda Q"1 is required, resulting in non uniqueness and large errors for both parameters (Wu and Aki, 1988). To avoid the effect of possible differences in relative contribution of multiple scattering among different time windows, we fix the window in our study of temporal variation in coda Q_ 1 . To avoid contamination of forward-scattering waves, the beginning of the time window are chosen as the twice the S wave travel time (Rautian and Khalturin, 1978). Seismograms are screened for saturated data. Following Su (1990), the power spectrum is calculated using the fast Fourier transform for successive overlapping time windows. The noise spectrum is subtracted from the coda spectrum and corrected for instrument response. When signal to noise ratio falls below 2, the window is terminated. The power spectrum is averaged over octave frequency bands centered at 1.5, 3.0, 6.0 and 12.0 Hz. Rewriting equation 1, we have ln{P(colti)ti2} = c(co)-bti (3) where b = co/Qc = 2 n f Qc-1, P(co I q) is the power spectrum centered at frequency to and lapse time q is measured from the origin time to the mid point of the ith moving window. The linear regression method is applied to equation 3 to obtain Qc_ 1 at a significant level of 95%. Those data with regression correlation coefficient less than required are excluded. In Su's work, the region (fig. 1) was divided into a mainshock area (116°35' to 116°45' longitude, 33°57' to 34°02' latitude) centered on the epicenter of the North Palm Spring earthquake and a "surrounding" area. She found that the value of coda Q_ 1 reaches its peak before the occurrence of the North Palm Springs event and it starts to decrease afterwards in the mainshock region, while the value of coda Q"1 remained essentially the same in the "surrounding" area (Su, 1991). This m otivated her to focus measurement of coda Q_ 1 in the mainshock region. Since the Landers event was preceded by Joshua Tree and followed by Big Bear events, it is difficult to zoom in on one "mainshock" area. Instead, the whole region (mainshock plus surrounding region in fig. 1) was used in my first analysis. Coda Q '1 was measured for two lapse time windows of 10 to 20 sec. and 15 to 40 sec. from 1987 to 1992 to compare with Su's results. 2.4 Results For the time window of 10 to 20 sec., Su (1990) found coda Q '1 peaks and then starts to decrease before the onset of the major events at all frequencies. The peak at higher frequencies is stronger and lies closer to the occurrence time of the major events (fig. 3). The mean of coda Q-1 * 1000 from 1987 to 1992 in region 1 (equivalent to Su’s m ainshock plus surrounding region) is shown in figure 5. If we put together figure 3 and figure 5, we found the usual precursory pattern for 1.5 Hz and 3 Hz. For 1.5 Hz, coda Q_ 1 * 1000 is around 11 (fig. 3) at the end of 1986 and reaches about 14.5 (fig. 5) in the middle of 1990 and starts to decreases to 11 at the beginning of 1992. The change in coda Q '1 is about 31.8%. For 3 Hz, coda Q '1 * 1000 is around 7 in the end of 1986 (fig. 3) and it increases steadily to about 11 in the beginning of 1991 (fig. 5) and then decreases. For 6 Hz and 12 Hz, no significant peak is found. For 6 Hz, coda Q '1 * 1000 is about 4 in 1987 (fig. 3) and increases to about 5 at the end of 1991 and decreases to about 4 in 1992 (fig. 5). For 12 Hz, coda Q_ 1 * 1000 is around 2 in the beginning of 1987 (fig. 3) and remains around 2 till the end of 1991 and then decreases to 1.5 in 1992 (fig. 5). For the time window of 15-40 sec., Su found no significant change of coda Q '1 (fig. 4). This is confirmed by our result. Coda Q_ 1 is very stable, showing no precursory pattern (fig. 6). Due to the complexity of the above pattern of temporal behavior of coda Q_ 1 , a second study was carried out in region 2 chosen to be the same as Su’ s mainshock region. O ur result on temporal variation of coda Q_ 1 for region 2 is shown in figure 7 and figure 8. Combining figure 3 with figure 7, 1 2 no significant change of coda Q_ 1 can be detected for 12 Hz and 3 Hz for the time w indow of 10 to 20 sec. For 12 Hz, coda Q"1 * 1000 is about 2 at the beginning of 1987 (fig. 3) and it continues to fluctuate around 2 till the beginning of 1992 (fig. 7). For 3 Hz, coda Q '1 * 1000 is about 8 in the m iddle of 1987 (fig. 3) and it increases to 9 and remains there till the end of 1991 (fig. 7). A slight anomalous change is found for 6 Hz (fig. 7). Comparing figure 4 with figure 8, a slight change of coda Q-1 can be found at 3Hz, 6 Hz, and 12 Hz for the time w indow of 15-40 sec. A more significant change is found at 1.5 Hz for the same window. Coda Q_ 1 * 1000 is about 10 in the m iddle of 1987 (fig. 4) and it steadily increases to about 12.5 in the end of 1991 (fig. 8). The change of coda Q_ 1 is 25%. The above tw o studies support the idea of spacially dependent tem poral change of coda Q"1. Since three major events happen in this region, the resultant picture of tem poral variation of coda Q_ 1 can be an averaged effect over the three events. If each major earthquake has its own mainshock area and surrounding area, then the precusory change of coda Q_ 1 measured for the whole region can be smoothed out. Comparing with Jin (1989)’ s result (fig. 9), the prom inent peak of coda Q_ 1 around 1987 in her result, confirmed by Peng (1989), is generally not observed in our previous two study areas. A third study is carried out in the region of 116o10’ to 116°50' longitude, 33°10’ to 33°50’ latitude. This region is chosen because Peng (1989) found a consistent pattern of tem poral variation of coda Q '1 in this region after the occurrence of the N orth Palm Springs earthquake. The temporal change of coda Q"1 is mostly positive in this region after the North Palm Spring event. For the time window of 15-40 sec, coda Q_ 1 remains very stable for frequencies 1 3 at 3.0 Hz, 6.0 Hz, and 12.0 Hz (fig. 10). For the time window of 20-45 sec, we found a very clear peak at 1.5 Hz, while the value of coda Q"1 at higher frequencies does not change significantly. The peak is about one and half years before the occurrence of the Landers events and the percentage change in coda Q_ 1 is 29.5% (fig. 11). This region is further south from the epicenter of the Landers earthquake. Therefore, the longer and later tim e w indow m ight be sam pling the mainshock region. However, no peak value of coda Q"1 is observed in 1987, suggesting again the space-dependent nature of temporal change of coda Q*1. O uyang (personal communications) studied the tem poral variation of coda Q 'l, using only quarry blasts as sources in the similar region (fig. 12). Only two stations were used by her. One of her results is shown on figure 13. Com paring figure 13 w ith figure 11, the peaks in her result appear later than those in m y plot, suggesting the tem poral variation of coda Q_ 1 is highly space-dependent. 2.5 Sum m ary In conclusion, the tem poral variation of coda Q_ 1 is sensitive to the location of study area as well as to the selected time window. We found the usual precursory pattern for certain coda windows, but failed to see the same pattern at other windows in the same area. A sharper anomalous change of coda Q_ 1 is observed at lower frequencies (1.5 and 3 Hz). Complex patterns of tem poral variation of coda Q-1 are also found by Peng (1987) and Su (1992). There seems to be a mainshock region centered at the epicenter of the major earthquake, w here the usual precursory pattern can be observed. In the surrounding area, the pattern of the temporal variation of coda Q"1 can be different from the precursory-type or remain stable. In cases of multiple events like the one studied here, the energy release of one event can influence the stress distribution in another area, thus triggering another event. The resultant temporal change of coda Q '1 is an averaged effect, rendering interpretation difficult. Therefore a more systematic study covering a large area (the whole Southern California) is needed. The temporal variation of coda Q_ 1 for systemetically shifting spatial windows should be compared for any stable and consistent pattern. The optimum area or frequency used for prediction purposes can be determined empirically. Another possible explanation for the lack of clear precursor for the Landers earthquake, as seen by coda Q_ 1 , is that the Landers event may be triggered by small and moderate sized earthquakes (Abercrombie, personal communications). The Landers earthquake might have resulted from the dynamic stress associated with the rupture which is greater than the static stress responsible for coda Q'1 change. Then, the usual precursory pattern like the change in the value of coda Q*1 could not be detected easily in the case of the Landers earthquake. 1 5 Table 2.1 Cusp number and m agnitude of the earthquakes used to obtain the value of coda Q_ 1 in region 1 for time window of 10-20 sec. Cusp # Magnitude Cusp # Magnitude 612981 2.2 621284 2.2 623207 2.3 623617 2.2 630752 2.5 630942 2.5 638797 2.2 651697 2.1 652444 2.1 693925 2.1 716092 2.2 716511 2.1 716734 2.6 717321 2.0 717741 2.3 718158 2.3 719274 2.4 720787 2.3 720978 2.2 721634 2.5 721754 2.1 722169 2.2 723372 2.0 723594 2.0 723978 2.2 724619 2.4 725107 2.0 725593 2.6 725996 2.3 726647 2.3 727036 2.1 733153 2.1 733727 2.5 741832 2.6 743715 2.1 744331 2.1 744558 2.3 744777 2.3 746682 2.5 747647 2.1 751471 2.3 751495 2.2 1010176 2.1 1010804 2.1 1012700 2.4 1012947 2.4 1015263 2.1 1017156 2.3 1017266 2.1 1019748 2.2 1020510 2.1 1023074 2.1 1023302 2.2 1024076 2.1 1025056 2.1 1032007 2.3 1032184 2.0 1032517 2.3 1041173 2.0 1041806 2.0 1049139 2.2 1049915 2.2 1051721 2.5 1051723 2.2 1052650 2.0 1053250 2.5 1056359 2.1 1056985 2.3 1 6 Table 2.1 Continued 1057091 2.1 1057726 2.1 1059739 2.2 1061386 2.2 135687 2.3 141581 2.0 2005450 2.1 2007066 2.3 2008339 2.0 2009511 2.0 2012740 2.1 2014974 2.0 2018158 2.2 2019758 2.3 2025330 2.2 2028990 2.3 2031596 2.2 2032636 2.0 2033881 2.1 2035187 2.2 2036279 2.0 2039224 2.2 2046007 2.4 2049223 2.2 2053709 2.3 2055711 2.2 2056971 2.2 3018400 2.1 3047148 2.4 3053211 2.3 3061066 2.2 3064013 2.0 3073545 2.2 3074885 2.4 1057444 2.1 1058128 2.1 1059880 2.2 1062973 2.3 141386 2.4 152837 2.2 2006842 2.0 2007259 2.3 2009229 2.1 2009716 2.0 2013322 2.0 2016811 2.3 2018272 2.3 2024794 2.2 2028018 2.8 2030874 2.0 2031857 2.1 2033624 2.0 2034780 2.1 2035761 2.0 2037371 2.7 2042344 1.8 2047716 2.1 2051739 2.3 2055643 2.2 2056511 2.1 3018295 2.1 3047134 2.5 3047748 2.1 3059599 2.3 3061372 2.0 3067797 2.2 3074430 2.1 1 7 Table 2.2 Cusp num ber and m agnitude of the earthquakes used to obtain the value of coda Q'1 in region 2 for tim e w in d ow of 15-40 sec. Cusp # M agnitude Cusp # M agnitude 620548 2.3 621284 2.2 621562 2.8 623207 2.3 623617 2.2 624158 2.4 630097 2.7 630752 2.5 630885 2.4 630942 2.5 638396 2.7 638797 2.2 639095 2.6 641443 2.1 641742 2.0 642035 2.1 642448 2.2 643305 2.1 643680 2.3 644025 2.6 651697 2.1 652444 2.1 652863 2.1 663995 2.6 682368 2.5 683460 2.4 715421 2.0 715747 2.3 716092 2.2 716511 2.1 716734 2.6 717144 2.2 717321 2.0 717741 2.3 717757 2.3 717781 2.2 717846 2.6 718158 2.3 718359 2.1 718763 2.4 718977 2.1 719274 2.4 719907 2.5 720787 2.3 720978 2.2 721634 2.5 721754 2.1 722169 2.2 722334 2.2 722872 2.5 723057 2.4 723138 2.4 723372 2.0 723594 2.6 723700 2.5 723827 2.6 723978 2.2 724485 2.4 724619 2.4 724889 2.4 725107 2.0 725123 2.8 725281 2.3 725349 2.5 725593 2.6 725777 2.1 1 8 Table 2.2 Continued 725996 2.3 727036 2.1 731790 2.4 732902 2.1 733727 2.5 735307 2.5 737452 2.5 740078 2.2 740915 2.2 743298 2.1 744331 2.1 744777 2.3 746682 2.5 751471 2.3 1007362 2.5 1007835 2.0 1008838 2.0 1010176 2.1 1010804 2.1 1012700 2.4 1013918 2.5 1015568 2.6 1016514 2.4 1017266 2.1 1017638 2.3 1018511 2.0 1019515 2.3 1019748 2.2 1019980 2.3 1021133 2.1 1021560 2.1 1023074 2.1 1023762 2.1 1024076 2.1 1025056 2.1 1025484 2.2 1026119 2.0 1026455 2.6 1027392 2.4 1028922 2.3 726647 2.3 727346 2.6 732726 2.7 733153 2.1 735285 2.4 736652 2.2 737620 2.2 740249 2.4 741832 2.6 743715 2.1 744558 2.3 745253 2.5 747647 2.1 751495 2.2 1007591 2.3 1008066 2.1 1009693 2.6 1010467 2.7 1011507 2.5 1012947 2.4 1015263 2.1 1016367 2.5 1017242 2.1 1017402 2.1 1018244 2.3 1018923 2.1 1019688 2.2 1019838 2.4 1020655 2.2 1021428 2.3 1022783 2.3 1023302 2.2 1023969 2.4 1024673 2.0 1025334 2.1 1025730 2.3 1026201 2.3 1027294 2.7 1027521 2.3 1029263 2.5 1 9 Table 2.2 Continued 1029729 2.3 1031330 2.1 1032007 2.3 1032517 2.3 1033810 2.0 1035304 2.3 1039047 2.0 1041391 2.3 1043969 2.1 1046703 2.0 1047396 2.2 1048764 2.2 1049121 2.2 1049375 2.7 1049455 2.2 1049704 2.4 1049915 2.2 1050066 2.4 1050339 2.1 1050528 2.7 1050973 2.8 1051219 2.1 1051516 2.1 1051890 2.0 1052305 2.0 1052751 2.2 1053250 2.5 1056359 2.1 1056845 2.0 1057091 2.1 1057726 2.1 1057904 2.6 1058344 2.4 1059739 2.2 1060674 2.3 1061386 2.2 141581 2.0 141631 2.2 2000510 2.1 2004990 2.0 1030566 2.0 1031826 2.4 1032273 2.2 1032915 2.0 1034014 2.3 1037059 2.0 1041173 2.0 1041806 2.0 1044764 2.2 1046975 2.3 1047680 2.1 1048930 2.1 1049139 2.2 1049386 2.5 1049546 2.2 1049848 2.0 1050065 2.1 1050328 2.4 1050470 2.8 1050863 2.6 1051004 2.5 1051367 2.1 1051723 2.2 1052011 2.3 1052650 2.0 1053036 2.8 1054656 2.7 1056656 2.1 1056985 2.3 1057444 2.1 1057860 2.5 1058128 2.1 1059500 2.2 1059880 2.2 1061248 2.4 1062973 2.3 141611 2.8 2000388 2.7 2001592 2.1 2005450 2.1 20 Table 2.2 Continued 2006265 2.4 2006902 2.1 2007259 2.3 2007740 2.2 2009640 2.8 2009872 2.4 2010619 2.6 2011918 2.2 2012740 2.1 2013502 2.3 2014974 2.0 2016811 2.3 2018272 2.3 2018367 2.1 2020249 2.3 2021788 2.2 2023423 2.5 2026968 2.2 2027883 2.3 2028990 2.3 2031330 2.4 2031857 2.1 2033805 2.2 2034665 2.2 2034878 2.6 2035761 2.0 2036279 2.0 2036795 2.0 2037371 2.7 2038470 2.3 2039858 2.6 2040890 2.1 2041608 2.3 2043013 2.4 2045331 2.5 2046792 2.4 2047716 2.1 2049223 2.2 2050425 2.0 2006842 2.0 2007066 2.3 2007508 2.8 2008705 2.1 2009716 2.0 2010327 2.8 2011803 2.8 2012511 2.2 2013322 2.5 2014076 2.4 2016600 2.1 2018158 2.2 2018345 2.0 2019758 2.3 2021538 2.2 2022106 2.2 2026299 2.1 2027507 2.0 2028018 2.8 2030706 2.6 2031596 2.2 2032636 2.0 2033881 2.1 2034780 2.1 2035187 2.2 2036040 2.0 2036637 2.2 2036986 2.1 3075339 2.2 2039224 2.2 2042328 2.2 2041206 2.8 2042344 1.8 2043837 2.1 2046007 2.4 2047352 2.3 2048907 2.1 2049678 2.0 2051081 2.2 Table 2.2 Continued 2051486 2.0 2052827 2.1 2053519 2.1 2054705 2.4 2055643 2.2 2055972 2.4 2056971 2.2 3037078 2.0 3041609 2.1 3047134 2.5 3047748 2.1 3051941 2.1 3056399 2.2 3057785 2.3 3058595 2.4 3059370 2.1 3060023 2.1 3061066 2.2 3063918 2.2 3065345 2.0 3066502 2.1 3067797 2.2 3070094 2.1 3070973 2.4 3072510 2.4 3073235 2.4 3073782 2.5 3074430 2.1 3075339 2.2 2051739 2.3 2053387 2.5 2053709 2.3 2054857 2.1 2055711 2.2 2056511 2.1 3034293 2.2 3041584 2.3 3042987 2.4 3047148 2.4 3050850 2.1 3055895 2.2 3057177 2.1 3058206 2.2 3059266 2.1 3059599 2.3 3060290 2.4 3062062 2.2 3064706 2.2 3066110 2.0 3067165 2.1 3069475 2.0 3070591 2.2 3071939 2.4 3072851 2.1 3073545 2.2 3074009 2.4 3074885 2.4 22 Table 2.3 Cusp number and magnitude of the earthquakes used to obtain the value of coda Q_ 1 in region 2 for time w indow of 10-20 sec. Cusp # Magnitude Cusp # Magnitude 1024558 2.2 1036759 2.1 1038404 2.2 1046854 2.6 1059573 2.2 1061239 2.3 2001274 2.3 2001539 2.0 2007256 2.5 2008474 2.1 2009798 2.1 2012715 2.3 2020102 2.2 2028220 2.1 2030732 2.0 2033193 2.4 2036155 2.0 744879 2.1 2039585 2.2 2041139 2.2 2047183 2.2 2048881 2.2 2054783 2.1 3050085 2.2 3058000 2.2 3059669 2.3 3070591 2.2 3081937 2.1 Table 2.4 Cusp number and magnitude of the earthquakes used to obtain the value of coda Q_ 1 in region 3 for time window of 15-40 sec. Cusp # Magnitude Cusp # Magnitude 642001 2.0 691490 2.7 744879 2.1 1007874 2.1 1009900 2.2 1010228 2.0 1017646 2.3 1024558 2.2 1032024 2.1 1035172 2.3 1036759 2.1 1038404 2.2 1046854 2.6 1055964 2.6 2 3 Table 2.4 Continued 1061239 2.3 2001274 2.3 2001539 2.0 2007042 2.1 2007256 2.5 2009563 2.4 2012715 2.3 2013858 2.4 2015624 2.5 2020102 2.2 2028220 2.1 2030732 2.0 2033193 2.4 2036155 2.0 2038740 2.1 2039585 2.2 2041139 2.2 2047183 2.2 2048881 2.2 2054583 2.4 3038197 2.3 3043570 2.3 3081937 2.1 3085201 2.2 3050085 2.2 3055484 2.4 3058000 2.2 3059669 2.3 3062506 2.2 3070591 2.2 3075664 2.1 3078629 2.0 3081937 2.1 3085201 2.2 Table 2.5 Cusp num ber and m agnitude of the earthquakes used to obtain the value of coda Q -l in region 3 for tim e w in d ow of 15-40 sec. Cusp # M agnitude 152794 2.5 621918 2.3 638734 2.4 642082 2.7 642993 2.4 643932 2.2 716062 2.8 716254 2.4 717142 2.2 718902 2.0 Cusp # M agnitude 621879 2.7 622978 2.4 640319 2.2 642542 2.5 643385 2.1 715736 2.1 716133 2.1 716735 2.2 717144 2.2 719111 2.8 24 Table 2.5 Continued 719468 2.8 720320 2.2 721779 2.5 724099 2.7 737413 2.1 741779 2.1 746805 2.3 1007144 2.2 1008467 2.1 1012745 2.1 1014452 2.3 1017349 2.4 1018927 2.1 1022733 2.3 1029426 2.7 1032802 2.3 1036842 2.1 1039817 2.1 1041456 2.8 1044764 2.2 1045891 2.0 1048439 2.2 1051921 2.8 1052686 2.3 1055042 2.1 1058227 2.1 1060648 2.0 2003274 2.1 2005558 2.3 2006265 2.4 2007259 2.3 2009314 2.3 2011593 2.4 2015941 2.6 2017398 2.1 2020258 2.3 2022220 2.7 2026980 2.4 2029471 2.1 2035187 2.2 2036911 2.2 719545 2.1 721075 2.7 722353 2.2 726682 2.6 740351 2.3 743189 2.6 753953 2.1 1007592 2.6 1012431 2.7 1013348 2.8 1015398 2.2 1017492 2.1 1020456 2.7 1026621 2.5 1031949 2.3 1033569 2.1 1039564 2.7 1041130 2.2 1042870 2.4 1045705 2.1 1045971 2.3 1050637 2.9 1052636 2.5 1053091 2.4 1057248 2.5 1060528 2.3 1062209 2.5 2005086 2.8 2006086 2.6 2007158 2.6 2007708 2.2 2010475 2.4 2014422 2.7 2017270 2.3 2018158 2.2 2020716 2.3 2023271 2.1 2028267 2.2 2034775 2.2 2036012 2.5 25 Table 2.6 Cusp number and magnitude of the earthquakes used to obtain the value of coda Q"1 in region 3 for time w indow of 20-45 sec. Cusp # Magnitude Cusp # Magnitude 152794 2.5 621879 2.7 621918 2.3 622978 2.4 638734 2.4 639675 2.1 640319 2.2 642082 2.7 642542 2.5 642993 2.4 643932 2.2 652710 2.4 715384 2.1 715736 2.1 716062 2.8 716133 2.1 716254 2.4 716735 2.2 717142 2.2 717144 2.2 718902 2.0 719111 2.8 719468 2.8 719545 2.1 721075 2.7 721779 2.5 722353 2.2 724099 2.7 726682 2.6 734931 2.3 737413 2.1 740351 2.3 741779 2.1 743189 2.6 746805 2.3 753953 2.1 1007144 2.2 1007592 2.6 1008467 2.1 1012431 2.7 1012745 2.1 1013348 2.8 1014452 2.3 1015398 2.2 1016335 2.3 1017349 2.4 1017492 2.1 1018927 2.1 1020456 2.7 1022527 2.6 1022733 2.3 1024907 2.8 1025577 2.9 1026621 2.5 1029426 2.7 1031949 2.3 1032802 2.3 1033569 2.1 1035364 2.7 1036842 2.1 1039564 2.7 1039817 2.1 1041130 2.2 1041456 2.8 1042870 2.4 1043719 2.0 2 6 Table 2.6 Continued 1044764 2.2 1045891 2.0 1046639 2.2 1048439 2.2 1050637 2.9 1052686 2.3 1055042 2.1 1057248 2.5 1058493 2.5 1060528 2.3 1061602 2.6 2000715 2.7 2003274 2.1 2005196 2.8 2006086 2.6 2007158 2.6 2007708 2.2 2009314 2.3 2010475 2.4 2011593 2.4 2014473 2.2 2017093 2.1 2017398 2.1 2019914 2.5 2020716 2.3 2022220 2.7 2024794 2.2 2028267 2.2 2034775 2.2 2036012 2.5 2038538 2.5 2040377 2.2 2042315 2.6 2043013 2.4 2044941 2.3 2045886 2.3 2047035 2.5 2052392 2.2 2054962 2.6 1045705 2.1 1045971 2.3 1047905 2.7 1049175 2.2 1051921 2.8 1053091 2.4 1056308 2.2 1058227 2.1 1058868 2.3 1060648 2.0 1062209 2.5 2003212 2.4 2005086 2.8 2005558 2.3 2006265 2.4 2007259 2.3 2009147 2.2 2010173 2.6 2010893 2.2 2014422 2.7 2015941 2.6 2017270 2.3 2018158 2.2 2020258 2.3 2021444 2.6 2023271 2.1 2026980 2.4 2029471 2.1 2035187 2.2 2036911 2.2 2038846 2.4 2041272 2.2 2042809 2.3 2044526 2.1 2045289 2.4 2046413 2.7 2047085 2.2 2052860 3.0 2056189 2.3 27 Table 2.6 Continued 3018225 2.3 3060620 2.7 3066623 2.7 3072357 2.3 3076014 2.3 3080090 2.1 3084231 2.1 3043054 2.2 3063702 2.4 3067878 2.5 3074776 2.4 3077103 2.8 3083716 2.2 28 2 0 ' 10 ' 50' 40l 20 ' 117° 50* 40' 20 30 Figure 1. Map showing the epicenters of small earthquakes (open circles) used in Su's coda Q_ 1 analysis. The region inside of the rectangular box sandwiched between longitudes 116° 25’ and 116° 52’ , and latitudes 33° 51' and 34° 10' is defined as the mainshock area, and the region outside of this box is the surrounding area, courtesy of Feng Su. 29 20km Big Beag Lake0 a 0 „ Lenders Yucca Joshua Tree j5<3iW6.1 117*0' 116*0' Figure 2. Map showing the epicenters of Joshua Tree, Landers, and Big bear earthquakes, courtesy of Yong Gong Li. 30 i 3- F M 2 . 0 H Z , T M 0 - 2 0 S i . t_______ O 5 O 2 4 * 2 3L fe 10 < 8 Ui F » 6 ,0 H z , T > 1 0 - E O S I j j — - 1 ^ "-T— £ _ T F * 3 .0 H z , F « 3 .0 H x , T « 1 0 - 2 0 S 6 * - 16 1 4 [ - • • T _ t j t F - _ I .5 H x , T « 1 5 - 3 0 S _ 12 10 I— x t _______x . ' 1 - * 4 _ H - 1 1981 1982 1983 1984 1985 1986 1987 1988 (TIME) Figure 3. Coda Q_ 1 m ean value vs. time obtained by Su for the mainshock region. The time window for 1.5 Hz is 15 to 30 sec. and that for 3.0, 6.0, 12.0 Hz is 10 to 20 sec. Each point on the curve represents the mean of 30 measurements of coda Q '1 with 15 overlapping points. The vertical bar indicates the range of standard error of the mean. The arrow indicates the origin time of the main shock, reproduced from Su's paper, 1991, courtesy of Feng Su. 3 1 2 - I L - 5 r O 4 O 0 3 * 1 I u. 8 ° 7 < 6 U 5 2 4 14 r 12 10 8 1981 £----- T ------------- 1 ------------- 1 ---------- F *12.0 Hz, T > 15 - 40S i ■ F * 6.0 Hz, T > 15 - 40S F« 3.0 Hz, T ■ I 5 -4 0 S - F - 1.5 Hz, T > I 5 -4 0 S £ 1982 1983 1984 1985 1986 1987 1988 (TIME) Figure 4. Same as figure 3, but for the time window of 15 to 40 sec. for all frequencies. 32 12.0Hz, T * 10 - 20S i 85 86 88 89 90 92 93 O O o * o li_ o z < U J 8 7 6 5 4 - 3 85 6.0H z, T -I 0 -2 0 S I I 85 86 86 87 87 88 89 90 91 88 89 90 91 92 92 93 3.0 H z, T* 10- 20S I 93 1.5 Hz, T • 15 - 30S 87 85 86 89 90 92 TIME Figure 5. Mean value of Coda Q"1 vs. time obtained by us for region 1 (115° 55' to 117° 30' longitude, 33° 30' to 34° 30' latitude). The time window for 1.5 Hz is 15 to 30 sec. and that for 3.0, 6.0, 12.0 Hz is 10 to 20 sec. Each point on the curve represents the mean of 20 measurem ents of coda Q'1 w ith 10 overlapping points. The vertical bar indicates the range of standard error of the mean. 33 o o o * o U u o z < 1 1 1 z 85 86 12.0Hz, T-I5-40S 1 — 85 .-l.. . 86 ----- 1-----------1-----------1 ______ l _______u. 87 88 89 90 91 ---------1 _ , i 92 93 5 r 6.0 H z, T > 15 - 40S 4- - 3 - i i r i i i i i 85 86 87 88 89 90 91 92 93 3 r 3 - 3.0 H z, T > I5-40S 7 - > - i r I I I 1 1 i i 85 86 87 88 89 90 91 92 93 Vr 1.5Hz, T> I5 -4 0 S 5 - - ) - i - - i i i i i i ____i_ I 87 88 89 time 90 91 92 93 Figure 6. Mean value of Coda Q '1 vs. time obtained by us for region 1. The time window is 15 to 40 sec. for all frequencies. Each point on the curve represents the mean of 30 measurements of coda Q'1 with -15 overlapping points. The vertical bar indicates the range of standard error of the mean. 34 12.0Hz, T 1 10 - 20S 85 86 87 88 89 90 91 92 93 O O o * a 8 7 6 5 4 3 85 86 6 .0 Hi, T '(0 -2 0 S 87 68 89 90 91 92 93 < bJ 14 13 12 11 h 10 9 8 7 85 ! f- 3.0 Hi, T 110- 20S 86 87 88 89 TIME 90 91 92 93 Figure 7. Mean value of Coda Q-1 vs. time obtained by us for region 2 (116° 25* to 116° 52' longitude, 33° 51' to 34° 10' latitude). The time w indow is 10 to 20 sec. for 3.0, 6.0, and 12.0 Hz. Each point on the curve rep resen ts the m ean of 10 m easurem ents of coda Q _ 1 w ith 5 overlapping points. The vertical bar. indicates the range of standard error of the mean. 3 5 o o o * o < UJ 85 8 r - 7 - 6 - 5 - 4 - 3 85 14 13 - 12 11 10 9 8 7 85 86 86 86 87 F *(2.0Hi, T-I5-40S 89 90 91 92 6.0 Hi, T < (5 - 40S 89 90 91 92 3.0 Hr, T* 1 5 -4 0 5 87 88 - i 90 - i 91 I- - - - - i 89 1.5 Hr, T* I5 -4 0 S P " ' 1 _ _ L _ 92 - - i 87 88 69 time 90 91 92 93 93 _I 93 Figure 8. Mean value of Coda Q_ 1 vs. time obtained by us for region 2. The time window is 15 to 40 sec. for all frequencies. Each point on the curve represents the m ean of 20 m easurem ents of coda Q*1 w ith 10 overlapping points. The vertical bar indicates the range of standard error of the mean. 3 6 o a) w o o I i K m - , | s [ j i i —i — i —i t i i i i i i i i i i ...................... O O p j o * " o o A r* O + 1937 1945 1953 1961 YEAR 1009 1977 1985 Figure 9. Mean value of coda Q_ 1 vs. time by Jin. The vertical bar indicates the standard error of the mean. The value of is computed according to b=7tfQ'1 at f=1.61 Hz, reproduced from the paper by Jin and Aki, 1989. 3 7 12.0Hz, T: 15-40 see o O O * o c o 0 ) 2 1 85 5 4 3 86 87 88 89 90 91 92 6.0 Hz, 15-40 sec 90 91 92 93 _i 93 9 8 7 6 5 4 3.0Hz, T : 15-40 sec 93 91 92 90 89 B7 88 86 85 Time Figure 10. Mean value of Coda Q 'l vs. time obtained by us for region 3 (116 10’ to 116° 50’ longitude, 33* 10’ and 33° 50' latitude). The time window is 15 to 40 sec. for 3.0, 6.0, and 12.0 Hz, Each point on the curve represents the mean of 30 measurements of coda Q-1 w ith 15 overlapping points. The vertical bar indicates the range of standard error of the mean. 3 8 3 r 12.0Hz, T: 20-45 sec r* "* — j— J ________ L -T * -* 85 86 87 88 89 90 91 92 93 O O O O c a a > 4 3 2 85 8 7 6 5 4 3 2 85 86 86 87 6.0 Hz, 20-45 sec 88 89 90 91 92 3.0Hz, T: 20-45 sec 87 88 89 93 90 91 92 93 14 13 12 1 1 10 9 8 7 1.5Hz, T: 20 -45 sec 86 87 85 88 89 90 93 Time Figure 11. Mean value of Coda Q*1 vs. time obtained by us for region 3. The time window is 20 to 45 sec. for 1.5, 3.0, 6.0, and 12.0 Hz. Each point on the curve represents the mean of 30 measurements of coda Q '1 with 15 overlapping points. The vertical bar indicates the range of standard error of the mean. 39 Quarry *BTL Landers Big Bear 10' Joshua Tree : o K U B O * 30' S O ’ 117 Figure 12. Map showing quarry site (square), stations used (triangles) and earthquakes (stars) used by Ouyang, courtesy of Ouyang. 40 Mean of 1/Q * 1 0 0 0 i 12.0 8.0 3.0 1.5 M N O - O - O 87 8 8 89 t i m e ( y e a r ) Figure 13. Plot of mean of coda Q-l vs. time at 1.5, 3.0, 6.0, and 12.0 Hz for lapse time 15-40 sec. by Ouyang. For the 1.5 and 3.0 Hz, each point is obtained by averaging over 20 mearsurements. For the 6.0 and 12.0 Hz, each point is obtained by averaging over 10 m easurem ent, courtesy of Ouyang. Chapter III Scaling law of seismic spectrum for the Landers earthquake sequence of 1992 3.1 Introduction The widely accepted empirical laws governing the occurrence of earthquakes, such as the frequency-magnitude relation by Gutenberg and Ritcher, the w-square model of seismic spectral scaling are scale independent. The observation that the source parameters of major earthquakes deviate systematically from the self-similarity, however, supports the presence of characteristic length scale in earthquake phenom ena. Scale dependence manifests itself as the existence of a unique length influencing earthquakes in a given region. For example, the repeated breaking of a fixed fault segment determines the maximum earthquake. Schwartz and Coppersm ith (1984) define such an earthquake as a "charateristic earthquake". The interrelation between seismogenic structures and earthquake processes at various scale lengths can help us understand the various aspects of earthquake source. Corners and kinks of plate boundaries define the largest scale length. The relative plate motion controls the kinematics of earthquake faults. The width and depth of the brittle zone may be another length scale affecting earthquakes. The concept of the charateristic earthquake has made long term earthquake prediction hopeful. However, we need to look for clues from higher order or smaller scale irregularities for short to interm ediate term earthquake prediction. Geometric and material irregularities are thought to play an important role in controlling the nucleation and propagation of the earthquake. Others may influence precursory phenomena such as coda Q"1 before the occurence of a major earthquake (Aki, 1992). 4 2 Seismic scaling law study can reveal information on fault zone structure and seismic source parameters. The idealized far field displacement spectrum (fig. 14) can be described by, Q(f) = Q(o){l+(f/f0)P}-l (4) where f0 = the comer frequency Q(o) = the value of the flat part of the displacement spectrum which is proportional to the seismic moment M0 ( 3 = the absolute value of the slope of the high-frequency asymptote. The co-square model ({3=2 in equation 4), initially proposed by Aki (1967), has been reaffirmed by Hanks (1979) to support observations such as M b-M s relations, peak accelerations near the source (clOkm) and strong ground motion spectra (Papageorgiou and Aki, 1983). However, tremors in a deep gold mine in South Africa do not seem to obey w-square model (Spottiswoode and McGarr, 1975). They found that the spectra of the seismograms can best be modeled by the w-cube model (b=3 in equation 4). Near the sources of tremors, a series of widely separated fractures were found on mine walls with unaffected regions of rock mass among them. These observations suggest that discontinuous segments were created in different directions and the rupture did not occur along a simple smooth plane. One of the most important parameters in earthquakes engineering is the cutoff frequency fmax of the acceleration spectrum (fig. 14). The origin of fmax has generated many controversies among seismologists. Whether it is due to source, path or site effect or a combination of the three still remains a m ystery today. Ida attributed fmax to the source effect and found that the critical slip is on the order of 10 cm in his slip-weakening model. H ank’s initial interpretation (1979) of the cutoff frequency as anelastic attenuation suggests strong attenuation of high frequencies, small Qb, independent of frequency. It fails to accommodate for the observation that Qb is strongly frequency dependent. Later Hanks (1982) interpreted it as local site effect. Papageorgiou and Aki (1983) suggested that fmax of large earthquakes is related to the w idth of a fault zone in their slip-weakening model. They estimate the critical slip to be on the order of a few tenths of meters and the size of cohesive zone ranges from a few hundred meters to a few kilometers. The cohesive zone is assumed to be of the same order of m agnitude as w idth of the fault zone. By analyzing the seismic radiation, one m ay infer param eters that describe the size and distribution of heterogeneities of the fault plane as well as the breakdow n process at the rupture front. The radiation of high frequency waves can be attributed to the interaction of the rupture front with the heterogeneities. In the specific barrier model by Papageogiou and Aki (1983a,b), the scale-length of heterogeneities is described by the barrier interval, and the break down process at the crack tip occurs in the cohesive zone. The controversial cutoff frequency fm ax is interpreted in terms of a slip weakening model (Aki, 1973; Papageogiou and Aki, 1983). fm a x = v /d , where v is the spreading velocity of the rupture front, d the size of the cohesive zone. An extremely interesting observation is that fmax for large earthquakes is almost the same as the corner frequency of small earthquakes w hen it 44 becomes constant below a certain magnitude, about 3 for San Fernando, California (Chouet 1978, Rautian and Khaltarin 1978). This suggest that the corner frequency of small earthquakes with the fault length less than the fault width may be controlled by the fault zone width. This is confirmed by the observation of a kink in the magnitude-frequency relation obtained in the L A basin at magnitude around 3 (Aki, 1989), reflecting a departure from self similarity due to the effect of fault zone width. The creep model of Jin and Aki (1989) suggests aseismic slip in the brittle-ductile transition taking place over cracks w ith a predom inant size characteristic to a region. The characteristic size corresponds to 3.0<M<3.5 for southern California. 3.2 Data The Lander's earthquake of June 28, 1992 and its aftershocks provide an excellent data set to test the above observations and hypotheses. A mobile seismic array of seven stations was deployed by Li et al. (1994) at eleven sites along the fault trace of the Landers earthquake from mid July to mid August in 1992. The array consists of five six-channel REFTEK instruments and seven L4-c 1 Hz three-component sensors (Li et al., 1993). The array is deployed in such a way that the maximum offset is 1 km from the trace (fig. 15). Li et al. (1994) found a distinct wavetrain following S waves, which is interpreted as seismic guided waves trapped in the low velocity fault zone. The trapped wave energy only show up when both epicenters and stations are close to the fault trace. Thus for a station close to the fault trace, it is reasonable to assume that those earthquakes showing the trapped mode energy occur inside the fault zone, while the earthquakes without the trapped mode energy occur outside the fault zone. From these two group of earthquakes, we can study the influence of the fault zone structure on earthquake source. We expect to see a departure from self similarity for earthquakes occuring inside the fault zone for magnitude smaller than 3. Earthquakes occuring outside the fault zone are expected to obey self-similarity. Hopefully, this will help to confirm the physical basis of the source-controlled fmax- The aftershocks of Joshua Tree earthquake of April 23, 1992 recorded by station EDCY are also studied. Figure 17 shows the locations of three Joshua Tree stations. We select three stations 0500, 0503, 0489 at site 9 (fig. 15) for the Landers aftershocks. Figure 16 shows the distribution of stations at site 8. This configuration of stations with respect to the Landers fault is applicable to site 9. Station 0500 and station 0503 can be represented by G3 and G4. They are either in the fault zone or very close to the fault zone. Station 0489 can be represented by Gl. It is off the fault zone (fig. 16). Two distinctive sets of data, one consisted of seismograms with trapped mode energy, the other one without trapped modes are provided by Li et al.. Only the vertical component is used in this study. For the Joshua Tree data, no assumption of locations of epicenters of earthquakes with respect to the fault is involved. Earthquakes used in the three Landers's stations and one Joshua Tree station are listed in table 3.1 through table 3.4. 3.3 Method of analysis We intend to study the characteristic scale length of southern Califonia earthquakes by finding the critical magnitude at which the earthquakes depart from self similarity. First, we shall establish an accurate procedure to estimate 4 6 the seismic moment of small earthquakes. We cannot rely on the magnitude reported by standard catalogs because they are based on an extrapolation of some empirical formula towards smaller magnitude and may be biased (Aki, 1987). We estimate moment magnitude based on the amplitude of coda spectrum following Aki (1987). Since the corner frequency is higher than 1.5 Hz for earthquakes studied in the chapter, the coda spectrum at 1.5 Hz is proportional to its seismic moment, we can write, logM0 = logA(1.5) + b (6) where A(1.5) is the amplitude of coda spectrum at 1.5 Hz, M0 is the seismic moment, b is a constant. To find the value of b, we use the formula by Hanks and Kanamori (1979), lo g M o = 1.5MW + 16.1 (7) where Mw is equated to local magnitude reported routinely by Caltech. The magnitude based on the above coda method is more accurate than that reported by catalogs for small earthquakes (Aki, 1987). We apply the fundamental separability of source, path and site effects of coda waves to two sets of earthquakes described above at site 9. The ratio of A(f)/A(1.5) is obtained for each earthquake, where A(1.5) is the amplitude of the displacement spectrum of an earthquake at 1.5 Hz, and A(f) is amplitude of the same spectrum at frequencies that we are interested. First, two sets of earthquakes recorded by a single station (0500) are chosen. The ratio 47 A(f)/A(1.5) are obtained for the coda window of 10 to 15 sec. for f= 24hz, 12hz, 6hz, and 3hz. We plot the log(A(f)/A(1.5)) against the seismic m om ent M0. The observed relation log(A(f)/A(1.5)) vs M0 depends on the station site effect at the frequency f. Since this effect is common to all the points in this plot, the site am plication only affect the absolute level of the relation log(A (f)/A (1.5)) vs. M 0. The observed shape of this relation, w hich is independent of site effect, will be com pared w ith prediction for source models. We applied the same analysis to data obtained by station (0503 and 0489). In addition, the ratio of A(f)/A(1.5) of S waves are also obtained for the time w indow of the 5 sec. interval starting at the S wave arrival time at the above three stations. Joshua Tree aftershock data recorded by station EDCY is also analysed in the same way. The mean value of log(A(f)/A(1.5)) is plotted against the mean value of log of moment over subgroup of earthquakes w ith similar moments in figure 18 through figure 31. We consider two source m odels based on two distinctive relations between the corner frequency f0 and seismic moment. Model 1 assumes self sim ilarity for all earthquakes. fD can be calculated by extrapolation from Hanks' relation, logf0=(logM0-22.45) /-3.0 (8) M odel 2 uses equation 8 for earthquakes with m agnitude greater than 3. For earthquakes w ith m agnitude less than 3, it assum es the following empirical relation found by Li (personal communications) for the Joshua Tree area, logf0=(logM0-31.98) /-13.7, Mc < 1Q 20 dynecm (9) 48 M odel 2 represents a departure from self-sim ilarity. Rewriting equation 4, we have, A (f)=A (o)/( l + ( f / f0)P) (10) where A(o) is a constant proportional to seismic moment (3 — 2. The normalized spectrum can be written following equation 10, loS(A (f)/A (1.5))=log((l+(l.S/f0)2 )/(l+(f/f0)2)) - a (11) where a, reflecting site effect, can be determined by fitting equation 10 to the observations in the least square sense. A l and a2 are the two constants needed for the two models proposed above to fit the observations in the least square sense. The sum of square of residuals between two models and the observations (rl and r2) are calculated. A l, a2, rl, r2, and the ratio of rl and r2 are listed in table 3.5 for the landers stations and the Joshua tree station respectively. 4 9 Table 3.1 E arthquakes recorded at station 0500 are divided into two groups. These aftershocks all occurred on July 31, 1994. The first six digits of the reftek num ber indicate the trigger time ( hour, m inute and second) of the recording instrum ent. in the fault off the fault Reftek # Reftek # 04.12.20.0500 06.25.14.0500 04.24.20.0500 06.28.37.0500 05.08.09.0500 06.57.09.0500 05.16.42.0500 08.05.05.0500 06.20.10.0500 08.56.57.0500 06.24.01.0500 09.07.44.0500 07.52.55.0500 09.24.51.0500 08.03.12.0500 09.31.28.0500 08.06.52.0500 09.38.53.0500 09.22.02.0500 10.12.07.0500 10.47.58.0500 10.22.18.0500 10.57.48.0500 10.45.24.0500 11.38.23.0500 11.29.47.0500 12.20.32.0500 13.41.13.0500 14.14.43.0500 15.35.36.0500 16.55.05.0500 15.56.43.0500 17.22.04.0500 17.32.07.0500 18.03.05.0500 5 0 Table 3.2 Earthquakes recorded at station 0503 are d ivid ed into tw o groups. T hese aftershocks all occurred on July 31, 1994. The first six d igits o f the reftek num ber indicate the trigger tim e (hour, m inute and second) o f the recording in strum ent. in the fault off the fault Reftek # 04.24.20.0503 05.08.09.0503 05.16.42.0503 06.20.10.0503 06.24.02.0503 07.52.55.0503 08.03.11.0503 08.06.57.0503 09.22.02.0503 10.48.02.0503 10.57.48.0503 11.38.23.0503 16.55.07.0503 17.32.07.0503 Reftek # 06.25.14.0503 06.28.37.0503 06.57.09.0503 08.05.05.0503 08.56.57.0503 09.08.06.0503 09.24.51.0503 09.31.29.0503 09.38.53.0503 10.12.07.0503 10.22.18.0503 10.45.25.0503 11.29.47.0503 13.41.13.0503 15.35.36.0503 15.57.03.0503 5 1 Table 3.3 Earthquakes recorded at station 0489 are divided into two groups. These aftershocks all occurred on July 31, 1994. The first six digits of the reftek num ber indicate the trigger time (hour, minute, and secord) of the recording instrum ent. in the fault off the fault Reftek # Reftek# 04.24.20.0489 06.25.14.0489 05.08.09.0489 06.28.37.0489 05.16.42.0489 07.53.21.0489 06.12.09.0489 08.05.04.0489 06.20.10.0489 08.56.58.0489 07.53.21.0489 09.07.44.0489 08.03.11.0489 09.24.51.0489 08.06.57.0489 09.31.30.0489 09.22.02.0489 09.38.53.0489 10.27.55.0489 10.12.06.0489 10.47.58.0489 10.51.20.0489 10.57.47.0489 11.29.47.0489 11.27.49.0489 15.35.36.0489 11.38.23.0489 16.42.34.0489 12.20.32.0489 16.55.04.0489 17.22.04.0489 17.32.07.0489 17.39.12.0489 Table 3.4 Earthquakes recorded at station EDCY used in the study are listed below. Each earthqauke can be identified by the reftek number and its corresponding cusp number. The first six digits of the reftek number indicate the trigger time of the instrument. Reftek number Cusp number 00.22.30.0505 x2052663 01.36.47.0505 x2052311 5 2 Table 3.4 Continued Reftek number 02.26.23.0505 02.29.20.0505 02.32.37.0505 02.34.51.0505 03.20.04.0505 05.10.40.0505 05.15.26.0505 07.54.17.0505 08.41.41.0505 09.06.44.0505 09.24.00.0505 09.43.28.0505 11.33.38.0505 12.23.41.0505 12.26.00.0505 12.37.45.0505 12.55.15.0505 13.32.49.0505 14.01.52.0505 15.10.57.0505 16.31.39.0505 16.54.07.0505 17.00.15.0505 17.12.29.0505 17.25.44.0505 17.51.01.0505 18.28.39.0505 18.37.15.0505 19.32.43.0505 19.36.28.0505 20.36.54.0505 20.40.14.0505 21.49.15.0505 21.54.53.0505 23.50.16.0505 Cusp number X2051558 X2050935 X3024923 X2051110 X2050942 X2050956 x2052324 X2050772 X2051911 x2051855 X2052340 x2050784 X2051928 X2050804 X2052353 x2050808 X2050810 X2050811 x2052866 X2051341 x2051024 X2051652 X2052743 X2053022 X2051037 X2051659 X3024365 X2051210 x2051520 X2051217 X2052768 X2051229 x2050510 X2050699 x2052792 Table 3.5a Least square fitting results of earthquakes recorded at Joshua Tree station EDCY for coda time w indow of 10-15 sec.. A l and a2 are constants needed for the data to fit two m odels in the least squre sense. R l and r2 are the sum of square of residuals. frequency al a2 rl r2 r l/r2 3 Hz -0.5633 -0.5700 1.8117 1.8613 0.9733 6 Hz -0.1934 -0.2212 1.9181 1.9494 0.9839 12 Hz 0.2057 0.1362 2.5469 1.9093 1.3339 24 Hz 0.4196 0.3125 3.1815 2.7693 1.1488 Table 3.5b Sam e as Table 3.5a, but for S wave. frequency al a2 rl r2 r l/r2 3 Hz -0.7266 -0.7354 1.2329 1.2384 0.9956 6 Hz -0.5854 -0.6218 2.3080 2.2796 1.0125 12 Hz -0.5044 -0.5983 3.0283 2.5309 1.1909 24 Hz -0.0061 -0.1630 5.2347 4.0868 1.2809 54 Table 3.5c Least square fitting results of earthquakes occuring in sid e the fault zone recorded at Landers station 0500 for coda tim e w in d ow of 10-15 sec.. A l and a2 are constants needed for the data to fit tw o m odels in the least squre sense. R l and r2 are the sum of square of residuals. frequency al a2 rl r2 r l/r 2 3 H z 0.3204 0.3031 0.9894 0.9655 1.0248 6 Hz 0.9772 0.9199 1.0392 1.1866 0.8736 12 Hz 1.2724 1.1140 1.3110 1.3367 0.9808 24 Hz 1.6740 1.3833 2.3439 3.1591 0.7420 Table 3.5d Sam e as 3.5c, but for S w ave. frequency al a2 rl r2 r l/r 2 3 Hz 0.7187 0.7334 1.2868 1.2758 1.0086 6 Hz 0.9005 0.8386 2.7841 2.9644 0.9392 12 Hz 1.4839 1.3195 3.1412 3.6850 0.8524 24 Hz 1.8316 1.5468 1.8082 2.4296 0.7442 5 5 Table 3.5e Least square fitting results of earthquakes occuring off the fault zone recorded at Landers station 0500 for coda time w ind ow of 10-15 sec.. A l and a2 are constants needed for the data to fit two m odels in the least squre sense. R l and r2 are the sum of square of residuals. frequency a l a2 rl r2 rl/r2 3 Hz 0.7246 0.7084 4.5724 4.5097 1.0140 6 Hz 1.0150 0.9438 3.4901 3.2092 1.0875 12 Hz 1.5508 1.3667 2.8180 2.3035 1.2236 24 Hz 2.0932 1.7667 1.9256 0.9944 1.9364 Table 3.5f Same as 3.5e, but for S wave. frequency al a2 rl r2 rl/r2 3 Hz 0.3204 0.3031 0.9894 0.9655 1.0248 6 Hz 0.6160 0.5409 1.4398 1.3020 1.1058 12 Hz 1.1287 0.9149 1.4447 1.4446 1.0000 24 Hz 1.9801 1.5712 2.7422 1.7439 3.6862 Table 3.5g Least square fitting results of earthquakes occuring inside the fault zone recorded at Landers station 0503 for coda time w indow of 10-15 sec.. A l and a2 are constants needed for the data to fit two m odels in the least squre sense. R l and r2 are the sum of square of residuals. frequency al a2 rl r2 rl/r2 3 Hz 0.3238 0.3102 0.5504 0.5534 0.9946 6 Hz 1.3397 1.2829 1.1155 1.1502 0.9698 12 Hz 1.4458 1.2978 1.1940 1.3152 0.9078 24 Hz 1.9918 1.7620 7.0900 6.7800 1.0460 Table 3.5h Same as Table 3.5g, but for S wave. frequency al a2 rl r2 rl/r2 3 Hz 0.2371 0.2232 0.9453 0.9282 1.0184 6 Hz 1.0773 1.0187 1.9367 1.9366 1.0005 12 Hz 1.4620 1.3066 2.7780 2.9501 0.9417 24 Hz 1.7954 1.5282 1.5527 1.6353 0.9497 57 Table 3.5i Least square fitting results of earthquakes occuring off the fault zone recorded at Landers station 0503 for coda time window of 10-15 sec.. A l and a2 are constants needed for the data to fit two models in the least squre sense. Rl and r2 are the sum of square of residuals. frequency al a2 rl r2 rl/r2 3 Hz 0.3227 0.3063 0.7968 0.7802 1.0213 6 Hz 1.2051 1.1356 2.1987 1.9470 1.1190 12 Hz 1.2741 1.0840 1.4289 1.0392 1.3750 24 Hz 1.6124 1.2689 1.9150 1.0410 1.8395 Table 3.5j Same as 3.5i, but for S wave. frequency al a2 rl r2 rl/r2 3 Hz 0.1566 0.1400 1.3521 1.3487 1.0025 6 Hz 0.8552 0.7816 1.2781 1.2290 1.0400 12 Hz 1.1947 0.9770 2.9522 2.1022 1.4040 24 Hz 1.5992 1.1700 1.9528 0.8052 2.4250 5 8 Table 3.5k Least square fitting results of earthquakes occuring inside the fault zone recorded at Landers station 0489 for coda time window of 10-15 sec.. A l and a2 are constants needed for the data to fit two models in the least squre sense. R l and r2 are the sum of square of residuals. frequency al a2 rl r2 rl/r2 3 Hz 0.4763 0.4627 0.6062 0.6077 0.9975 6 Hz 0.8994 0.8425 0.8634 0.8367 1.0319 12 Hz 1.0862 0.9463 1.2864 1.5891 0.8095 24 Hz 1.5192 1.2792 1.9804 2.3961 0.8265 Table 3.51 Same as 3.5k, but for S wave. frequency al a2 rl r2 rl/r2 3 Hz 0.3140 0.2991 1.2780 1.2570 1.0167 6 Hz 0.6461 0.5839 2.1417 1.9332 1.1078 12 Hz 1.1774 1.0154 2.1621 2.1999 0.9828 24 Hz 1.4278 1.1548 1.9868 1.8214 1.0908 5 9 Table 3.5m Least square fitting results of earthquakes occuring off the fault zone recorded at Landers station 0489 for coda time w indow of 10-15 sec.. A l and a2 are constants needed for the data to fit two m odels in the least squre sense. R l and r2 are the sum of square of residuals. frequency al a2 rl r2 rl/r2 3 Hz 0.6116 0.5964 1.5994 1.5952 1.0026 6 Hz 0.9895 0.9252 6.3595 6.0207 1.0563 12 Hz 1.2417 1.0799 3.1939 2.4084 1.3262 24 Hz 1.5184 1.2176 2.6766 2.0249 1.3218 Table 3.5n Same as Table 3.5m, but for S wave. frequency al a2 rl r2 rl/r2 3 Hz 0.3872 0.3713 1.0992 1.1206 0.9809 6 Hz 0.6072 0.5390 0.6752 0.6465 1.0440 12 Hz 0.9394 0.7508 0.7136 0.5650 1.2630 24 Hz 1.3646 1.0194 1.5164 1.0383 1.4605 60 * » u c o v ! • a a I 3 o * o « u e o M a (2) ■ O o > o O ) log frequency ( Hz ) (a) (b ) Figure 14. (a) Displacement and (b) acceleration amplitude spectra of the "co-square" source model for two constant stress drop earthquakes observed at the same distance in an elastic, homogeneous, isotropic, unbounded medium, reproduced from the paper by Papageorgiou and Aki, 1983. 61 20km Barstow 87-Nl sn A SB ' S4 S5 SB Big Bear Lake ‘ -£jM6.5 Landers M7.4 Yucca Valley Joshua Tree j 1 0 ' 3 0 ' 2 C f 50' 117*0' 4 0 Figure 15. Map showing the location of 10 sites for the Landers aftershocks, courtesy of Yong Gong Li. 34° I 9 G A Linn Rd. 'G1 G 2G 3 G4G5 G6 □ □ i« GB E ncantado Rd. Site 8 G7 GC 1 km Figure 16. Map showing the distribution of stations at site 8, courtesy of Yong Gong Li. 10’ - 34* — Pinto Mountain Fault! Joshua Tree 5 0 ’ Yucca Valiev B. AQUA A ^ Ot 0 l '°'h s 20 KM I t I I t I ■ I ■ I I I J I I I I I I l_J DEPTHS 10.0+ 15.0+ MAGNITUDES 0.0 + 5 .0 + — I — '— < ~ 10 ' 1 — r ' Figure 17. Map showing the location of station EDCY used in the study of Joshua Tree aftershocks. 64 f=3hz f=6hz -0 .2 -0.8 20 22 24 -0.5 -1.5 -2.5 20 22 24 f-12hz f»24hz '£*'-1.5 S’-2.5 \ \ 22 20 log(moment) 24 20 log(moment) 22 24 Figure 18. M ean valu e o f norm alized coda spectrum vs. m ean of m om ent from Landers aftershocks occurring in the fault zone recorded at station 0500 for the frequency of 3, 6, 12, and 24 H z. The tim e w in d o w is 10-15sec.. Each point is obtained b y averaging over three points. The verticle and horizontal bar indicate the range of standard error of the m ean. The dash line incorporates Hanks' relation. The dash dot line uses Li's em pirical relation for m om ent <10E20 dynecm and Hanks' relation for m om ent > 10E20 dynecm . 65 f»3hz f-6hz 1 0 -o.a -20 22 f«12hz -0.5 N 22 log(moment) 0 -0.5 -1 -1.5 18 20 22 •2.5 -3.5 20 22 log(moment) Figure 19. Same as figure 18, but for earthquakes occurring off the fault zone. 6 6 f=3hz i n -0.5 -1.5 22 f«6hz -0.5 -1.5 20 22 f-12hz -0.5 in - *1.5 16 18 log(moment) 20 22 f*24hz -1.5 -2.5 -3.5 16 18 20 log(moment) 22 Figure 20. Mean value of normalized S wave spectrum vs. mean of moment from Landers aftershocks occurring in the fault zone recorded at station 0500 for the frequency of 3, 6, 12, and 24 Hz. The time window is the 5 sec interval starting at the S wave arrival time. Each point is obtained by averaging over three points. The verticle and horizontal bar indicate the range of standard error of the mean. The dash line incorporates Hanks' relation. The dash dot line uses Li’ s empirical relation for moment <10E20 dynecm and Hanks' relation for moment >10E20 dynecm. 67 f=3hz in - 0.8 22 20 18 f-12hz -0.5 -1 2 20 22 18 log(moment) f=6hz -0.5 N\ 20 18 22 f«24hz -1.5 2 -2.5 -3 -3.5 -4 20 22 16 18 log(moment) Figure 21. Same as figure 20, but for aftershocks occurring off the fault zone. 6 8 f “3hz f=6hz $ -0.4 S ’-0.6 0.8 17 20 1.5 ■ s 20 C N -2.5 17 20 17 20 log(moment) log(momertt) Figure 22. M ean value of norm alized coda spectrum vs. m ean of m om ent from Landers aftershocks occurring in the fault zone recorded at station 0503 for the frequency of 3, 6, 12, and 24 Hz. The time w indow is 10-15sec.. Each point is obtained by averaging over three points. The verticle and horizontal bar indicate the range of standard error of the mean. The dash line incorporates Hanks' relation. The dash dot line uses Li's empirical relation for m om ent <10E20 dynecm and Hanks' relation for moment > 10E20 dynecm. f=3hz f=6hz 0.2 N JZ |- ° - 4 § . 0.6 0.8 16 18 20 22 2.5 20 22 f«12hz n'-I.5 8*-2.5 16 20 22 log(moment) 20 22 log(moment) Figure 23. Same as figure 22, but for earthquakes occurring off the fault zone. 7 0 fe3hz f=6hz | g^o-s 17 19 20 f-12hz N X Z in $ f - 1 .5 S 17 20 log(moment) -0.5 -1.5 20 f=24hz -2.5 -3.5 20 19 log(moment) Figure 24. Mean value of normalized S wave spectrum vs. mean of moment from Landers aftershocks occurring in the fault zone recorded at station 0503 for the frequency of 3, 6, 12, and 24 Hz. The time- window is the 5 sec interval starting at the S wave arrival time. Each point is obtained by averaging over three points. The verticle and horizontal bar indicate the range of standard error of the mean. The dash line incorporates H anks’ relation. The dash dot line uses Li’ s empirical relation for moment <10E20 dynecm and Hanks' relation for moment >10E20 dynecm. 7 1 f=3hz f=6hz 0.5 kh S .-0.5 18 20 22 -0.5 $ - 1 .5 -2.5 16 22 log(moment) Figure 25. Same as figure 24, but zone. -0.5 1.5 20 22 f»24hz -1.5 -2.5 -3.5 16 18 20 log(moment) 22 earthquakes occurring off the fault 72 f«3hz f=6hz « - 0.2 N S Z to _ ^ -0.4 - -0.8 18 19 20 -0.4 -0.6 - 0.8 -1.2 -1.4 18 19 20 f»12hz f»24hz -0.5 19 log(moment) 20 -1.5 -2.5 19 log(moment) 20 Figure 26. M ean value of norm alized coda spectrum vs. m ean of m om ent from Landers aftershocks occurring in the fault zone recorded at station 0489 for the frequency of 3, 6, 12, and 24 Hz. The time w indow is 10-15sec.. Each point is obtained by averaging over three points. The verticle and horizontal bar indicate the range of standard error of the m ean. The dash line incorporates H anks' relation. The dash dot line uses Li's em pirical relation for m om ent <10E20 dynecm and Hanks' relation for m om ent > 10E20 dynecm. 73 f*=3hz f«=6hz in -0.5 1.5 22 18 20 f-12hz ■ -1.5 18 20 22 log(moment) 20 22 f-24hz 18 20 log(momerrt) Figure 27. Same as figure 26, but for earthquakes occurring off the fault zone. 7 4 W3hz f=6hz 0.2 m - -0.2 -0.4 -0.8 20 « -0.5 -1.5 f“12hz f«24hz -0.5 -2.5 17 20 log(moment) -1.5 -2.5 log(momerrt) Figure 28. Mean value of normalized S wave spectrum vs. mean of moment from Landers aftershocks occurring in the fault zone recorded at station 0489 for the frequency of 3, 6, 12, and 24 Hz. The time window is the 5 sec interval starting at the S wave arrival time. Each - point is obtained by averaging over three points. The verticle and horizontal bar indicate the range of standard error of the mean. The dash line incorporates Hanks' relation. The dash dot line uses Li’ s empirical relation for moment <10E20 dynecm and Hanks' relation for moment >10E20 dynecm. 7 5 log(A(f)/A(1.5hz» log(A(f)/A(1.5hz)) f*3hz f=6hz 0.5 22 ■0.5 -2.5 22 log(moment) f»24hz 18 20 log(moment) Figure 29. Same as figure 28, but for earthquakes occurring off the zone. f=3hz f=6hz -0.5 0.5 -0.5 S 1 log(moment) -0.5 -1.5 -2.5 log(moment) Figure 30. Mean value of normalized coda spectrum vs. mean of moment from Joshua Tree aftershocks recorded at station EDCY (0505) for the frequency of 3, 6,12, and 24 Hz. The time window is 10-15sec.. Each point is obtained by averaging over four points. The verticle and horizontal bar indicate the range of standard error of the mean. The dash line incorporates Hanks' relation. The dash dot line uses Li's empirical relation for moment <10E20 dynecm and Hanks' relation for moment >10E20 dynecm. 77 f=3hz f**6hz 1.2 0.2 18 19 20 22 f«12hz 0.5 to 18 19 20 22 log(moment) 1 0.5 0 18 19 20 21 22 f=24hz 0.5 -1.5 20 22 log(moment) Figure 31. Mean value of norm alized S wave spectrum vs. mean of m om ent from Joshua Tree aftershocks recorded at station edcy (0505) for 3, 6, 12, and 24 Hz. The time window is the 5 sec interval starting at the S wave arrival time. Each point is obtained by averaging over five points. The verticle and horizontal bar indicate the range of standard error of the mean. The dash line incorporates Hanks' relation. The dash dot line uses Li’ s empirical relation for moment <10E20 dynecm and Hanks' relaion for moment >10E20 dynecm. 78 3.4 Results For the Landers aftershocks, contrary to our expectation, those earthquakes occurring outside the fault zone generally fit model 2 better for both coda and S waves for all frequencies at all stations (table 3.5, figure 19, figure 21, figure 23, figure 25, figure 27, figure 29). Model 2 fits the data significantly better at 24 Hz. For 3, 6, and 12 Hz, model 2 fits slightly better or there is no significant difference between two models. For those earthquakes occurring inside the fault, a more complex pattern emerges. In general, model 1 fits slightly better for both S and coda waves at station 0500 and station 0503 (table 3.5, figure 18, figure 20, figure 22, figure 24). At station 0489, model 1 fits better for coda waves and there is no major difference between two models for S wave (table 3.5, figure 26, figure 28). The results from coda wave at three stations are consistent. This further confirms the common path for coda waves. Station 0500 and 0503 are located on the fault zone, while station 0489 is located outside the fault zone. For the Joshua Tree data, we found model 2 fits the data better for both S and coda waves. This gives an independent support for Li's observation of departure from self-similarity at m agnitude around 3 for the Joshua Tree aftershocks. The above results suggest that earthquakes inside the main fault zone of Landers earthquake follow self-similarity, while those outside the fault zone show departure from self-similarity for magnitude below 3. 79 3.5 Sum m ary We found a departure from self-similarity below magnitude 3 needed to account for the Joshua Tree aftershock data at station EDCY. This is further confirmed by the Conner frequency and magnitude relation found by Li and Beltas (personal communications) for the Joshua Tree aftershocks using three stations. For the Landers event, an opposite pattern from what we expected was found. We expected to see those earthquakes occurring outside the fault zone to follow self-similarity. Earthquakes occuring inside the fault zone are thought to depart from self-similarity because of the existence of the finite fault zone w idth which is presumed to control fmax- fmax is believed to be related to the constant corner frequencies for earthquakes sm aller than m agnitude 3 (Aki, 1992). The discrepencies can come from following sources: (1) The division of two data sets for the Landers aftershocks may not be accurate. We do not know exactly where the locations of those earthquakes are. Maybe they are all on the fault zone. (2) We only have a limited am ount of data available. A larger data set is needed to make sure the results are statistically significant. Results of the Landers aftershocks, however, raise some doubts about whether departure from self-similarity for magnitude below 3 is universal in southern California. Analysis of data from a bolehole station at depth by 8 0 Abercrombie (1994) demonstrates that earthquakes follow self-similarity relation down to M= -1. Observations of departure from self-similarity at surface station are attributed to the attenuation in the surface layer. Li, however, obtained his results from stations located on granite with little attenuation. To doublecheck, an attenuation factor like the one introduced by Anderson can be used to remove the attenuation effect in the observed spectrum of Joshua Tree and Landers data. The remaining spectrum should show departure from self-similarity if fmax is due to source effect. References Aki, K. (1969). Analysis of seismic coda of local earthquakes as scattered waves, J. Geophys. Res. 74, 615-631. Aki, K. (1979). Characterization of barriers on an earthquake fault , J. Geophys. Res., 84, 6140-6148. Aki, K. (1980a). Attenuation of shear-waves in the lithosphere for frequencies from 0.05 to 25 Hz, Phys. Earth Planet. Inter., 21, 50-60. Aki, K. (1980b). Scattering and attenuation of shear waves in the lithosphere, J. Geophys. Res., 85, 6496-6504. Aki, K. (1984). Asperities, barriers,characteristic earthquakes and strong motion prediction, J. Geophys. Res., 89, 5867-5872. Aki, K. (1987). Magnitude -frequency relation for small earthquakes: A clue to the origin of fmax of large earthquakes, J. Geophys. Res., 92, 1349-1355. Aki, K. (1992). Higher-order interrelations between seismogenic structures and earthquake processes, Tectonophysics, 211, 1-12. Aki, K. (1992). Scattering conversions P To S versus S to P, Bull. Seism. Soc. A m , 82,1969-1972. Aki, K. Earthquake Sources and Strong Motion Prediction, SCEC Publication No. 7,1-15. Aki, K. and B. Chouet (1975). Origin of coda waves : source, attenuation and scattering effects, J. Geophys. Res., 80, 3322-3342. Chouet, B. (1979). Temporal variation in the attenuation of earthquake coda near Stone Canyon, California, Geophys. Res. Lett., 6, 143-146. 82 Chouet, B., Aki, K. and Tsujiura, M. (1978). Regional variations of the scaling law of earthquake source spectra, Bull. Seism. Soc. Am., 68, 49-79. Gao, L. S., L. C. Lee, N. N. Biswas and K. Aki (1983a). Comparison of the effects between single and multiple scattering on coda waves for local earthquakes, Bull. Seism. Soc. Am., 73, 377-389. Gao, L. S., L. C. Lee, N. N. Biswas , and K. Aki (1983b). Effects of multiple scattering on coda waves in three-dim ensional m edium , Pure Appl. Geophys., 121, 3-15. Gusev, A. and V. K. Lemzikov (1980). Preliminary results of studying the coda envelope shape variations of the near earthquakes before the 1971 Ust- Kamchatsk earthquake, Volcanol. Seismol. (in Russian), 6, 82-95. Gusev, A. and V.K. Lemzikov (1984). The anomalies of small earthquake coda wave characteristics before the three large earthquakes in the Kuril- Kamchatka zone,Volcanol Seismol. (in Russian), 4, 76-90. Gusev, A. A. and V. K. Lemzikov (1985). Properties of scattered elastic waves in the lithosphere of Kamchatka: Parameters and tem poral variation, Tectonophysics, 112,137-153. H anks, T. C. (1974). The faulting mechanism of the San Fernando earthquake, J. G. R. 79,1215-1229. Hanks, T. C. (1982). fmax, Bull. Seis. Soc. Am., 72, 1867-1879. Jin, A., and K. Aki (1988). Spatial and temporal correlation between coda Q'^ and seismicity in China, Bull. Seismol. Soc. Am., 78, 741-769. Jin, A., and K. Aki (1989). Spatial and temporal correlation between coda Q"1 and seismicity and its physical mechanism, J. Geophys. Res., 94, 14041-14059. 83 Koyanagi, S., K. Mayeda and K. Aki (1991). Site - effect corrected T-phase amplitudes and infered attenuation in the Kilauea volcano region, Island of Hawaii, EOS 72 ,198. Y. Li, P. Leary, K. Aki and P. Malin (1990). Seismic trapped modes in the Oroville and San Andreas fault zones, Science, 249 763-766. Y. Li, K. Aki, D. Adams and A. Hasemi (1994). Seismic guided waves trapped in the fault zone of the Landers, California, earthquake of 1992, J. G. R, 99, 11705-11722. M eyeda (1991). High frequency scattered S-waves in the lithosphere: Application of the coda method to the study of source, site and path effect, USC PhD thesis. Mayeda, K., S. Koyanagi and K. Aki (1991). Site amplification from S-wave coda in the Long Valley Caldera region, California, Bull. Seism. Soc. Am. Novelo-Casanova, D. A., E. Berg, V. Hsu, and C. E. Helsley (1985). Time-space variation in seismic S-wave coda attenuation (Q"l) and m agnitude distribution (b-values) for the Petatlan earthquake, Geophys. Res. Lett., 12, 789-792. Papageorgiou, A., and K. Aki (1983a). A specific barrier model for the quantative description of inhomogeneous faulting and the prediction of strong ground motion. I. Description of the model, Bull. Seism. Soc.Am , 73, 693-722. Papageorgiou, A., and K. Aki (1983b). A specific barrier model for the quantative description of inhomogeneous faulting and the prediction of strong ground motion. II. Applications of the model, Bull. Seism. Soc.Am, 73, 953-978. Peng, J. Y., K. Aki, B. Chouet, P. Johnson, W.H. Lee, S. Marks, J. T. Newberry, A.S. Ryall, S. W. Stewart, and D. M.Tottongham (1987). Temporal change in 84 coda Q associated with the Round Valley , California, earthquake of November23,1984, J. Geophys. Res., 92, 3507-3526. Peng (1989). Spatial and temporal variation of coda Q-l in California, USC PhD thesis. Phillips, W. S. (1985). The separation of source, path and site effects on high frequency seismic waves: an analysis using coda wave techniques, Ph.D. thesis, Massachusetts Institute of Technology, Cambridge, Massachusetts. Rautian, T. G., and V. I. Khalturin (1978). The use of the coda for determination of the earthquakes source spectrum, Bull. Seism. Soc. Am., 68, 923-943. Robinson, R.(1987). Temporal variation in coda during of local earthquakes in the Wellington region, New Zealand, Pure Appl. Geophys., 125, 579-596. Sato, H.(1986). Temporal change in attenuatuin intensity before and after the eastern Yamanashi earthquake of 1983, in central Japan, J. Geophys. Res., 91, 2049-2061. S. M. Spottiswoode and A. McGarr (1975). Source parameters of tremors in a deep-level gold mine, Bull. Seis. Soc. Am, 65, 93-112. Su, F., and K. Aki (1990). Temporal and spatial variation on coda Q-l associated with the North Palm Springs earthquake of July 8, 1986, Pageoph, 133,23-52. Su (1992). Study of earthquake source, propagation medium attenuation and recording site amplification using coda waves, USC PhD thesis. Tsujiura; M. (1978). Spectral analysis of the coda waves from local earthquakes, Bull. Earthq. Res. Inst., Tokyo Univ., 53, 1-48. 8 5 Wu, R. S. (1985). Multiple scattering and energy transfer of seismic waves - separation of scattering effect from intrinsic attenuation, I. Theoretical modeling, Geophys. J. R. Astr. Soc., 82, 57-80. Wu, R. S. and K. Aki (1988). M ultiple scattering and energy transfer of seismic waves - separation of scattering effect for intrinsic attenuation, II. Application of the theory to Hindu Kush region, Pageoph, 128, 49-80. Wyss, M. (1985). Precursory phenomena before large earthquakes, Earthq. Predict. Res., 3, 519-543. Zeng, Y., F. Su, and K. Aki, (1991). Scattering wave energy propagation in a random isotropic scattering medium, I. Theory, J. Geophys. Res. ,96, 607-620. Zoback, M.D. et al. (1987). New evidence on the state of stress of the San Andreas fault system , Science, 238, 1105-1111. 8 6 INFORMATION TO USERS This manuscript has been reproduced from the microfilm master. UMI films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type of computer printer. 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 afreet reproduction. In the unlikely event that the author did not send UMI 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. 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Liu, Xiaoling
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The study of temporal variation of coda Q⁻¹ and scaling law of seismic spectrum associated with the 1992 Landers Earthquake sequence
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