Investigation of the Rupture Process of the 28 June 1992 Landers Earthquake Utilizing TERRAscope

Bulletin of the Seismological Society of America, Vol. 84, No. 3, pp. 713-724, June 1994 nvestigation of the Rupture Process of the 28 June 1992 Landers Earthquake Utilizing TERRAscope by Douglas S. Dreger Abstract Displacement seismograms recorded by TERRAscope for the 28 June 1992 Landers earthquake (Mw 7.3) are deterministically modeled using a forward, point-source summation technique. Although the data set is sparse, it was possible to robustly determine important rupture parameters such as gross slip distribution, rupture velocity, rise time, and total source duration. The relatively simple approach lends itself to rapid application following large earthquakes, provided that a catalog of Green's functions appropriate for the region is available. The fault used in the modeling of the Landers mainshock has a length of 70 km along strike and a width of 15 km along dip. A model was found in which the distribution and amplitude of slip at the surface matches the observed surface slip and provides a very good level of fit to the seismic data. Seismically, the Landers earthquake is characterized as two subevents. The peak slip of the first subevent is 10 km north of the epicenter and the second is 40 km northwest along strike from the epicenter. The seismic moment is distributed as 2 10 26 dyne-cm to the first and 6 10 26 to the second subevent, respectively. t was assumed in our modeling that the distribution of seismic moment along strike was the same at all depths. This assumption implies that slip at depth is 69% of that at the surface as a result of differences in the material properties in the velocity model. The sensitivities of the source model to rupture velocity and dislocation rise time were examined. A rupture velocity of 2.9 km/sec (80% of the shear-wave velocity) and a rise time of 1 to 3 sec were found to satisfy the data. The rise time is only a fraction of the total source process time of 24 sec, and implies that slip on the fault occurred within a narrow band (3 to 10 kin), at any instant during the rupture. ntroduction The 28 June 1992, 11:57:34 UTC Landers earthquake (Mw 7.3) was the largest event to strike California in the last 40 yr. t was located in the eastern Mojave desert approximately 160 km east-northeast of Pasadena, California, and was well recorded by the broadband, high dynamic range TERRAscope network. The combination of the location of the event within the TERRAscope network and the near-real time access to the data afforded the opportunity to analyze the motions of this earthquake rapidly following the event, as well as to assess the type of information that may be robustly determined in nearreal time following future large earthquakes. Events of this size typically clip regional short-period arrays at the arrival of the first P-wave motions. The relatively shortperiod strong-motion networks remain onscale, but the retrieval and processing of the records often create delays in the distribution of the data. Thus, TERRAscope provided the first observations of the Landers earthquake rupture process. There are several reasons why the data set has been limited to only TERRAscope seismograms. First and foremost, a major portion of the analysis presented herein was completed in the weeks immediately following the event, when the strong-motion data was not generally available. Second, while the addition of strong-motion recordings would improve the coverage surrounding the fault, these are typically surface sites located on varied materials, and site corrections could be quite large. n comparison, the TERRAscope stations are relatively quiet vault installations in regions of hard rock. Third, considerable effort has been expended in the modeling of broadband waveforms at these stations for several recent moderate sized earthquakes (e.g., Dreger and Hehnberger, 1990; Helmberger et al., 1993). n addition, at the 713

714 D.S. Dreger time of this event, a precomputed catalog of Green's functions existed (e.g., Dreger, 1992; Dreger and Helmberger, 1993), such that analysis began immediately using this instrumentation. Therefore, the goal of this article is to quantify some aspects of the rupture process, such as the rupture velocity, rise time, overall duration, and gross slip distribution, using the emplaced catalog of Green's functions, and to demonstrate that it should be possible to retrieve these parameters relatively quickly following large earthquakes. Since the number of stations used is small, no attempt is made to try to map the detailed slip on the fault plane. Rather, the primary interest is to develop a model that explains the azimuthal variations in peak amplitude and the relative timing and amplitudes of major source phases, as well as to examine the sensitivities of the various model parameters to determine which could be robustly determined rapidly following large earthquakes. Observations of surface slip revealed peak values of 6.5 m and showed that several faults, namely the Johnson Valley, Landers, Homestead Valley, Emerson, and Camprock faults, were involved during the event (Sieh et al., 1993). These faults form an arcuate trace approximately 70-km long, north of the epicenter. At the southern end the strike is nearly due north, while at the northern end the trace rotates to 322. The inversion of teleseismic body waves showed that there were two periods of significant moment release during the mainshock, and that the strikes of the two subevents agree with the surface observations (Kanamori et al., 199~2). This was further substantiated by the teleseismic, empirical Green's function deconvolution results of Ammon et al. (1993), which indicate that there were two periods of significant moment release with substantially different strikes and a strong northward directivity. t is interesting to consider the effects of the chang- Preliminary Observations Before presenting the results of the distributed pointsource summations, there are several interesting observations regarding the directivity and nucleation of the event. Following the acquisition of the low gain data (within 2 hr, Kanamori et al., 1992), integration of the accelerograms to velocity and displacement revealed a very strong signature of northward directivity. The azimuthal variation of peak displacement amplitudes recorded at the four closest TERRAscope stations clearly shows the effect of the propagating rupture front. The level of ground motions recorded at GSC are 7.5 times greater than those recorded at PFO, despite the fact that GSC has nearly twice the epicentral distance and that the closest edge of the fault to both stations is nearly the same (Fig. 1). n addition to the amplitude disparity, the duration of signals recorded at GSC are shorter than at PFO and form a relatively simple, two-sided pulse. At PFO the arrivals are spread out in time, resolving two relatively long-period pulses of motion. Waveforms recorded at SVD and PAS, located to the west of the fault, show two distinct pulses of motion separated in time by approximately 10 sec. n addition, the peak amplitudes and durations at these stations are intermediate to those at GSC and PFO. These observations are consistent with what would be expected for a northward propagating rupture. The double pulse waveforms at SVD, PAS, and PFO are indicative of at least two large subevents during the rupture of the mainshock. n fact, the comparison of north-south component displacement seismograms of the 23 April 1992 Joshua Tree mainshock (Mw 6.1) and foreshock (Mw 4.3) with the Landers mainshock clearly show that the initial subevent was followed approximately 10 sec later by a larger more extended (greater duration) subevent (Fig. 2). 35 34 June 28, 1992 Landers EQ \, -'-, -, h/ -118-117 -116 West Lon#tude Figure 1. Map showing the locations of the TERRAscope stations used in this study. The stars show the locations of the Landers mainshock, and Joshua Tree foreshock and mainshock. The terms SE1 and SE2 refer to fault plane solutions for the two primary subevents of the Landers mainshock determined from teleseismic body waves (Kanamori et al., 1992). The solutions for the Joshua Tree events were obtained from regional surface waves (H. Thio, personal comm., 1992). The surface trace of faulting determined by Sieh et al. (1993) is shown in bold. Also plotted are the predominantly tangential direction displacement seismograms written at GSC (EW), PAS (NS), PFO (EW), and SVD (NS). The peak-to-peak amplitude in centimeters is also plotted, and the relative amplitudes of the waveforms are correct.

nvestigation of the Rupture Process of the 28 June 1992 Landers Earthquake Utilizing TERRAscope 715 ing strike and geometrical spreading terms during the earthquake on predicted relative amplitudes at the four stations. Table 1 shows that even when these factors are taken into account, the predicted relative amplitudes of the four stations differ significantly from the observed. For the epicentral location, the observed amplitudes are 6.8, 2.9, and 0.4 times the predicted values at GSC, PAS, and PFO, respectively. When the centroid of the second subevent and corresponding strike are used, the observed amplitudes are found to be 3.5, 2.3, and 0.7 times the predicted values for the same stations, respectively. Summarizing, these calculations show that the observed level of motions at PFO are consistently lower and GSC and PAS are consistently greater than what is predicted from the differences in distance and changes in focal parameters alone. The motions at all of the stations are dominated by the A4, vertical strike-slip term (see Helmberger, 1982, for details) throughout the duration of the earthquake. Thus, the changing strike is very important for the excitation of Love waves at all of the stations, but is not sufficient in itself to account for the anomalous amplitude pattern. As will become evident in the modeling section, a north propagating rupture front is necessary to explain the relative amplitudes of the four stations. Finally, an interesting observation that concerns the 7 0 X -0.5 ' ' ' ' 1992 M~aslaoek At~ 2a, 1992~ April 23, 1992 F ~ 10 20 3O 40 Figure 2. Comparison of the north-south displacement records for the Landers mainshock (28 June 1992) and the Joshua Tree mainshock and foreshock (23 April 1992). Note the large second pulse of motion evident on the Landers record beginning at approximately 32.5 sec. 50 nucleation of the mainshock was made by R. Abercrombie (personal comm., 1992). By examining the records of the mainshock recorded downhole at Cajon Pass with those of aftershocks, she found that a relatively small foreshock preceded the mainshock by 2.5 to 3 sec. Figure 3a shows the vertical component accelerations recorded at GSC, PAS, PFO, and SVD. Note that, several following the arrival of the initial P wave, a group of relatively large amplitude P waves arrive nearly at the same time at each of the stations. Abercrombie and Mori (1994) extended their analysis to include both a relocation of these arrivals relative to the epicenter, and an empirical Green's function deconvolution of the first 3 sec of the P wave. The results of their analysis indicate that the Landers mainshock began as a Mw 4.4 event followed 0.5 sec later by a Mw 5.6 event. The locations of these two events are within 1 to 4 km north of the epicenter, indicating that either they are either individual earthquakes not associated with a propagating rupture' front or perhaps the rupture front was propagating at a slow 0.3 to 1.4 km/sec. n addition, they find that the mainshock reruptured the patches of the fault that slipped during the foreshocks. The long-period excitation resulting from these foreshocks is evident in the velocity records of TERRAscope. Examination of the horizontal velocity records at GSC, PAS, PFO, and SVD (Fig. 3b) show that there are substantial near-field phases evident in the data. The P-wave portions of the seismograms were recorded by both the Streckeisen and FBA-23 instrumentation; the former records ground velocity. Figure 3b compares ground velocity recorded by the Streckeisen instrumentation with that derived by integrating the acceleration data. There appear to be some drift problems with the integrated accelerations, but there are clearly near-field phases present in the velocity data. Near-field phases are typically ramps in displacement and therefore steps in velocity. The fact that the shape of the near-field are ramps in velocity indicate that the event is growing in size. Further examination of the near-field records show that at all of the stations, approximately 2.5 see after the initial onset, there is a marked change in the slope of the nearfield phases, indicating that the rate at which the earthquake was growing increased significantly at this time. When the displacement records are examined (Fig. 3c), only the post 2.5-sec near-field phases are significant. t is therefore necessary to compensate for the apparent delay in the displacement records in the point-source summation modeling. Methodology The forward methodology employed in this study is similar to that used by Heaton and Helmberger (1979) to study the 1971 San Fernando earthquake. The primary difference is that we do not limit ourselves to halfspace

716 D.S. Dreger Table 1 Radiation Pattern Sensitivity* Location Radiation Pattern Coefficients Amplitude Ratio Station Reference Distance (R) Azimuth A A2 A3 A4 A5 Predicted Observed GSC epicenter 126.7 344.6 0.48-0.12 0-0.87-0.01 0.45 3.04 first subevent 116 343.6 0.51-0.12 0-0.85-0.02 0.59 second subevent 87.2 345.1-0.41-0.04 0-0.91-0.05 0.87 PAS epicenter 159.8 268.4-0.02-0.02 0 0.99-0.12 0.40 1.15 first subevent 159.6 264.5-0.16-0.01 0 0.98-0.12 0.49 second subevent 153.8 254.1-0.38-0.04 0 0.93-0.05 0.51 PFO epicenter 65.6 181.2-0.07 0.12 0 --0.99-0.02 0.98 0.4 first subevent 76.3 180-0.03 0.12 0-0.99-0.02 1.04 second subevent 103.7 174.2-0.67 0.04 0-0.74-0.05 0.6 SVD epicenter 61.6 260.2-0.3 0 0 0.95-0.12 1 1 first subevent 63.5 250.5-0.6 0.02 0 0.79-0.12 1 second subevent 68.5 225.5-0.58-0.02 0 0.82-0.05 1 *The distance and asimuth values are calculated for the epicentral coordinates and the centroids of the first and second subevents. The A coefficients are as defined in Helmberger (1982), in which A1, A2, and A3 are multipliers to the radial and vertical component, vertical strike slip, vertical dip-slip, and 45 dip-slip Green's functions, respectively. The A4 and A5 coefficients are multipliers to the tangential component vertical strike slip and vertical dip-slip Green's functions, respectively. A strike of 359, rake of 180, and dip of 85 were used for the epicentral and first subevent locations. The strike was changed to 322 for the second subfault calculations. The 15redicted amplitude ratio is computed from (A4) 1/R for each station, normalized to SVD. The observed amplitude ratio is computed from the peak-to-peak amplitudes on the tangential component (relative to the epicentral location) relative to SVD. Vertical Acceleration Horizontal Velocity Horizontal )isploeement -lc P"ve ',r,i-0e-,,.- sw SVD -NS '. 'i :h NS n /~^ -0.~-, :~ ~ ~'' i-'c P,0,,... l _j 10 12 14 16 18 20 10 12 14 16 18 20 10 20 30 i 40 A) Seconds B) Seconds C) S~,onds Figure 3. (a) Vertical component of acceleration. The onset of the P wave is marked by a solid line. All of the traces are aligned at the P-wave arrival time and plotted on the same time scale. Note the steady growth of the P-wave coda. (b) Horizontal velocity. The velocity recorded by the clipped STS-1 Streckeisen sensors are plotted dashed. Velocity derived by integrating FBA-23 accelerograms are plotted solid. Note the clear nearfield ramps. (c) Displacement obtained by doubly integrating acceleration. The arrival of the far-field S wave is marked with the dashed line, and the P-wave onset determined from the acceleration records is labeled with the solid line. Note that only the near-field following a 2.5 to 3-sec delay is significant on the displacement records. Green's functions, and the Green's functions are not interpolated between the individual subfanlts. With this method, it is assumed that the motions resulting from the mainshock may be approximated by summing the motions resulting from point sources distributed along a plane with the dimensions and orientation of mainshock. The timing of the individual point sources is controlled by the passage of a propagating, circular rupture front (constant rupture velocity). Each point source is allowed to slip only once. Changes in radiation pattern as a result of a propagating rupture front are taken into account. Complications in the source process are introduced by varying the seismic moment of each of the subfaults (point sources). Alternatively, one could vary the slip across the fault plane. To simplify the modeling procedure, we chose to vary the seismic moment and require that the distribution of seismic moment along strike be the same for all depths on the fault. This simplification implies that slip at depth is necessarily less than at the surface, as a result of the change in material properties in the velocity model. This method requires two primary assumptions. The first is that the Green's functions adequately describe wave propagation in the bandwidth used. The second is that the geometry of the fault plane must be defined, although it is possible to test various geometries. The Green's functions that were used were computed with a velocity model that has been found to be appropriate for a number of paths throughout southern California (Dreger and Helmberger, 1993). Table 2 lists the velocity model parameters used to compute the Green's functions. An F-K integration code that computes corn-

nvestigation of the Rupture Process of the 28 June 1992 Landers Earthquake Utilizing TERRAscope 717 plete waveforms including near-field terms was used to generate the Green's functions. At the time of this event, a precomputed catalog of these Green's functions existed for use in routine source analysis of moderate sized earthquakes (Dreger, 1992). This catalog was initially computed for receiver distances from 30 to 400 km and source depths of 8, 11, and 14 km. While the preliminary analysis in the days following the earthquake used only these Green's functions, additional Green's functions were computed with source depths of 2 and 5 km to augment the catalog for the near-surface rupture. The Green's functions were sampled at 5-km intervals laterally and 3-km vertically. There is little ambiguity of the orientation of the fault plane responsible for the Landers earthquake. As discussed previously, surface offsets were observed north of the epicenter, along a 70-km multi-fault trace which is seen to change strike from due north at the southern end to the northwest at the northern end (Sieh et al., 1993). n addition, slip was observed to the south of the epicenter, but the amplitude of the southern slip is a factor of 30 smaller than that observed to the north. As will become evident in the modeling section, there is no compelling evidence in the TERRAscope waveforms suggesting that there was appreciable slip at depth south of the epicenter, at least in the time required to rupture the fault to the north. Hough et al. (1993) find evidence that the southern slip may be attributable to a large aftershock that occurred 3 min after the mainshock. Through the course of the modeling effort, multiple fault geometries were tested as more detailed information regarding the actual dimensions and attitudes of the fault became available. nitially, a straight fault (80 km in length) with the strike of the Harvard Centroid Moment Tensor (CMT) solution was tested (Fig. 4, model A). Next, a model approximating the mechanisms of the two subevents determined by the inversion of teleseismic body waves was tested (Fig. 4, model B). The final model was comprised of three segments, designed to better fit the trace of the surface slip. A rake of 180 and dip of 85 (average of the dips of the teleseismic body wave results, Kanamori et al., 1992) were assumed. The results of this analysis would not change if a dip of 90 was used instead. The total length of models B and C was 70 km, and the width of the fault was set at 15 km since the aftershock zone extends from 0 to 14 km in depth (Hauksson et al., 1994). A focal depth of 6.2 km Table 2 vp (km/sec) V~ (on/see) p (kg/m 3) Z (kin) Q~ Qt~ 5.5 3.18 2400 0 600 300 6.3 3.64 2670 5.5 600 300 6.7 3.87 2800 16 600 300 7.8 4.5 3000 35 600 300 was assumed and is within the range reported by Hauksson and co-workers. nitially, a rupture velocity of 2.9 km/sec (80% of the shear-wave velocity), a rise time of 2.4 sec, and a total seismic moment of 1.0 1027 dyne-cm were assumed. After the initial computations were performed, the sensitivities of the synthetics to variations in both the rupture velocity and the rise time were examined. Modeling Straight Fault, Model A To begin, a number of uniform seismic moment (slip) models were tested. Figure 5a compares the predominant tangential direction displacement data with synthetics computed for a straight fault with the strike of the CMT solution and a uniform seismic moment distribution. This model produces the anomalous amplitude pattern, especially in terms of the relative peak amplitudes at GSC and PFO, but fails to model the complexity in the PAS and SVD waveforms. Such a model, although oversimplified, could be rapidly implemented and provide useful i ~.4 34.6 34.2 34 L i \A' Model Location B.-,~.~~,~ \ \~N~ e'' ~ \ B" \ ~, C' ~-~ B.C! -116.75-116.5-116.25 Longitude Figure 4. Locations of assumed fault planes used in the distributed slip modeling (dashed lines). The term AA' is a straight fault with a strike of 340 and a total length of 80 km, BB" is a twosegment fault model (strikes, 359 and 323 ), and CC" is a three-segment fault model (strikes, 359, 333, and 323 ). The dip and rake of all of the models are 85 and 180, respectively. The total length of models B and C is 70 kin. The star marks the location of the epicenter and the solid line shows the position of mapped surface faulting (Sieh et al., 1993). B'

718 D.S. Dreger preliminary information regarding fault dimension and rupture direction. Fault Model B Next, the fault was broken into two segments with the strikes determined from the teleseismic body waves (Kanamori et al., 1992) (Fig. 4, model B), although the strike of the second subevent was changed from 333 to 323 to better fit the trend of the surface offsets. The seismic moment is uniformly distributed on each segment. Figure 5b compares the data and the synthetics. This model improves the fit at SVD and PAS, because the change in the radiation pattern of the fault B"B" relative to BB' increases the level of excitation of the A4 Green's functions at these stations, and produces a secondary S arrival. There is still a problem with the duration of the synthetic pulses, however. To try to better model the relative amplitudes and timing of the two large Fo,Jt ilodd ^ Uniform Sllp Fmlt Mo~ B ~lorm Slip Foull Mo~ B H~m-tmifolm Slip 20 40 60 80 100 20 40 60 B0 100 20 4,0 ~ 80 100 -,,,,, - -2 20 ~ 60 80 100 20 40 60 80 00 20 40 60 80 100 2f.~ ~ 21 pulses observed at SVD and PAS, nonuniform seismic moment models were tested. The gross distribution of observed surface slip was used as an additional constraint. Approximately 0 iterations were performed before the preferred slip distribution was found. Tapering seismic moment at the edges of the faults produced the desired effect in terms of modeling the durations of the pulses (Fig. 5c). Figure 6 compares the surface slip of the model with the observed. To model the absolute amplitudes, we found that it was necessary to reduce the total seismic moment from 1 x 1027 to 8 X 1026 dynecm. The preferred model has the seismic moment partitioned between the two fault planes as 2 x 1026 dynecm on plane BB' and 6 x 1026 dyne-cm on plane B"B". The total seismic moment is less than that determined from long-period surface waves (1.1 x 1027 dyne-cm), but is consistent with the value of 8 1026 determined from teleseismic body waves and empirical Green's function deconvolution of TERRAscope data (Kanamori et al., 1992). Cohee and Beroza (1994) and Wald and Heaton (1994) also find lower values consistent with the value determined in this study (6 1026 and 7 to 8 x 1026 dyne-cm, respectively). Figure 7 compares the three-component displacement data for each of the stations with synthetics computed with model B and the nonuniform slip distribution (Fig. 6). A single horizontal component dominates the motions at GSC, PAS, and PFO. n contrast, SVD is clearly affected by the finiteness of the fault since comparable amplitude waves are observed on both horizontal components. Surface Slip Profile!!!,,,,, 20 40 60 80 100 20 40 60 80 100 20 40 60 80 100 2G 2( PFO EW f~ o ~....r,,~*,~-.,,-:--... "....... -20-2 -,,,,,,,,,, 20 40 60 80 100 20 40 60 80 100 20 40 60 80 100 A) B) C) Figure 5. (a) Comparison of displacement data and synthetics computed with fault model A and a uniform distribution of seismic moment along strike. (b) Comparison of displacement data and synthetics computed with fault model B and a uniform distribution of seismic moment along strike. (c) Comparison of displacement data and synthetics computed with fault model B and a nonuniform distribution of seismic moment along strike. A common amplitude scale was used for the entire plot. The synthetics were delayed 2.5 sec to account for the slow onset of the earthquake. ~5 0 - - Me.asur~ Slip... u. stip _ S%,-X..., /,-\ L.-, ~ \~ -- -- NU. Slip r / A..J &.t '7,, \-, " U--: }:) 20 40 60 Di~n_.,.~ Along Strike (kin) Figure 6. The predicted surface slip of the uniform and the preferred nonuniform seismic moment models are compared with the mapped surface slip (K. Hudnut, personal comm., 1992). The slip has been projected onto the line striking 340 (model A, Figure 4). The assumption that the distribution of seismic moment along strike is the same at all depths necessarily implies that below 5.5 km the slip is 69% of the surface values.

nvestigation of the Rupture Process of the 28 June 1992 Landers Earthquake Utilizing TERRAscope 719 As a check of the influence of the changing strike on the synthetics, fault model A was parameterized with the nonuniform slip distribution. The fits were generally found to be better than for the uniform distribution, but the relative amplitudes of the two horizontal components at SVD and of the specific phases resulting from the two subfaults at all of the stations were poorly modeled. Fault Model C To evaluate a possible bias in our results as a result of the rather coarse parameterization of the fault planes, model C (Fig. 4) was tested. n this model the planes were more precisely fit to the surface trace of the fault. Three planes were used with a total length of 70 km. The only difference between model B and C is that the strike of the fault in the C'C" region is accounted for. The nonuniform seismic moment distribution in model B was used. There was no need for further refinement of the moment distribution. The seismic moment was partitioned as 1.95 1026 dyne-cm on CC', 0.9 10 z6 on C'C", and 5 1026 on C"C". Figure 8 compares the three-component displacement data and synthetics computed for this model. There is a slight improvement of the fit to the east-west component of motion recorded at PFO in terms of the relative amplitude and timing of the phase resulting from the second subevent, and the absolute amplitude of the east-west component of motion at GSC agrees better with the data. Thus, accounting for the fault strike in the region of C'C" only provides a slight improvement over the coarser parameterization of model B. The data do not require significant moment release from this portion of the fault, and resolution of the strike in this area is low. Rise Time Sensitivity Parameter Sensitivities Since it was possible to model the displacement records fairly easily with the simplifying assumptions that we made, we were curious to see how well the velocity and acceleration motions could be predicted. Figure 9 compares the PAS displacement, velocity, and acceleration data with synthetics computed with model C and several different rise times. The model C synthetics were convolved with triangular rise-time functions with du- Model B - Three Component Comparison North-South Eost-West Up-Down GSC -20.... ~ ' 1~ -, 1 /, _,,, 60, 80 100. ", 20 40 60 80 100 20 40 60 80 100 20 40 60 80 100 ~0.... 0 -..., 20 40 60 80 100 20 40 60 80 100 20,,, ~ i 40 60 80 100 20 40 60 80 100 20 40 60 80 100 20 40 60 80 100 Figure 7. Comparison of three-component displacement data and synthetics computed with fault model B and the nonuniform seismic moment distribution. The relative amplitudes of the three components at a given station are correct, but the amplitude scale changes for each station.

720 D.S. Dreger rations of 0.8, 1.4, 2.4, and 4.4 sec. All of the modeling up to this point assumed a rise time of 2.4 sec and a rupture velocity of 2.9 km/sec. For PAS we found that the synthetics computed with the 2.4-sec rise time fit the displacement data well, but underpredicted the velocity and acceleration amplitudes. A shorter duration of 1.4 sec seemed to work better. A value of 0.8 sec clearly overpredicts the acceleration amplitudes. Both the velocity and the acceleration records appear to be dominated by arrivals owing to the subevents. Although the accelerograms reveal some additional complexity, the predicted duration agrees well with the data. An interesting observation is that using the displacement records alone, the rise time is not resolvable. Short-period information is needed. Figure 10 compares the amplitude spectra observed at the four stations with the spectra of the synthetics computed with the four different dislocation rise times. Clearly, a rise time of 4.4 sec fails to fit the data. At PAS, PFO, and SVD a rise time of 1.4 to 2.4 sec seems to agree very well with the data. However, GSC seems to require a larger value, between 2.4 to 4.4 sec, which could be a result of differences in wave propagation and attenuation along this path. Nevertheless, a value less than 4 sec is substantially smaller than the overall duration of the source. A measure of the lower limit of the rise time is difficult because other path-dependent factors such as attenuation, scattering, and complex wave propagation can affect the pulse widths of the arrivals, but it seems that a rise time between 1 to 3 sec is favored by the data. t is possible that the dislocation rise time is variable throughout the rupture, but this analysis suggests that the average value is between 1 to 3 sec. Both models B and C do not require a delay associated with the transfer of slip from one fault to the other, indicating that the earthquake may be modeled as a throughgoing pulse of slip traveling at a constant rupture velocity of 2.9 km/sec. The total source process time is 24.1 sec. The rise-time sensitivity analysis indicates that the dislocation rise time is less than 4 sec in duration, implying that each point of the fault slips in a fraction of the time of the total rupture (< 15%), and within a band less than 12-km wide (4 sec 2.9 km/sec). Heaton (1990) compiled the fault dislocation rise times for Model C - Three-component Comparison North-~ooth Eost-West Up-Down.-..:.. _,ilpjl,,,, 1, _TS-, ;,,,, _,,, '" 20 40 60 80 100 ~ 2040 60 80 100 80, 1oo " SVD 20 40 60 80 100 20 40 60 80 100 20 40 60 80 100 -fol"-,, i ~,, - t,,,, -,,,, j 20 40 60 80 180 20 40 60 80 100 20 40 60 80 100 - l-,,,,, ~;" ":\ 20 40 60 80 100 20 40 60 80 100 20 40 60 80 180 Figure 8. Comparison of three-component displacement data and synthetics computed with fault model C and the nonuniform seismic moment distribution. The relative amplitudes of the three components at a given station are correct, but the amplitude scale changes for each station.

nvestigation of the Rupture Process of the 28 June 1992 Landers Earthquake Utilizing TERRAscope 721 a number of earthquakes ranging in size from M, 5.7 to 8.1 and found that in each case the dislocation rise times required to model the waveform data were substantially less (approximately 10%) than the total duration of the earthquake, and proposed a model of a self-healing slip pulse for earthquake rupture. The results of this study are consistent with the earlier findings and Heaton's selfhealing slip pulse model. Rupture Velocity Sensitivity nitially, the rupture velocity was assumed to be 2.9 km/sec (80% of the shear-wave velocity). A slower rupture velocity of 2.5 km/sec has been proposed by Cohee and Beroza (1994), while Wald and Heaton (1994) find evidence of a variable rupture velocity with values ranging from 1 to 4 km/sec with an average value of 2.7 km/sec. Campillo and Archuleta (1993) found a value of 3 km/sec using a simpler parameterization of the source. To test the sensitivity of the model C solution to rupture velocity, values ranging from 2.3 to 3.3 km/sec were tested. Figure 11 shows that the time separations of the various phases and the durations are strongly affected by the rupture velocity. The slower rupture ve- Displacement Dislocation Rise Time Sensitivity Velocity 10- ~ o~ foe-. O 0 _1oL---<b- 10- ~ase "rim= l O t " 0 _~---~ TM 0~-~ ~_.- -10_-- -10~ ' lo-... jc-.:---'v'w-- -10 "" 21C- 10. 1C- 2'' c - l o b -c - 1 0 ~ - lc - OL-~~ 4s C a/b'~- -1011,1,1,1,1-1C,,1,1,1 20 40 60 80 100 20 40 60 80100 lo- -10- O- Acceleration -lo:t,, ~, i, J 20 40 60 80100 Figure 9. Dislocation rise-time sensitivity. The north-south component displacement, velocity, and acceleration data recorded at PAS are compared to synthetics computed with model C, the nonuniform seismic moment distribution and rise times of 0.8, 1.4, 2.4, and 4.4 sec. The rise time is introduced by convolving the Green's functions with triangles with the appropriate durations. Both data and synthetics were bandpass-filtered from 0.02 to 2 Hz. A rise time of 1.4 sec appears to fit the displacement, velocity, and acceleration records quite well. Note that the displacement waveforms are relatively insensitive to the tested dislocation rise-time values. locities significantly worsened the fit to the GSC data, in that the arrivals resulting from the two subevents became separated in time, producing a significantly more complicated waveform, with lower amplitudes. Similarly, the relative timing and duration of the pulse resuiting from the second subevent at the other stations are adversely affected by slower rupture velocities. Velocities greater than 2.9 km/sec tend to produce synthetics which underpredict the subevent time separations and overpredict the amplitudes. t is possible, however, that the simplification regarding the distribution of seismic moment with depth is biasing the estimate of rupture velocity to higher values, and that using a more complicated slip model coupled with slower rupture velocities could better fit the data. t is conceivable that the rupture velocity is depth dependent, and possibly variable along strike. These possibilities were not explored, in the interest of keeping the number of parameters manageable for a forward modeling approach, and it is unlikely that it would be resolvable using only TERRAscope data. Green's Function Sensitivity An important question that remains is the adequacy of the SoCal model in explaining wave propagation along the specific paths to each of the stations. Dreger and Helmberger (1991; 1.993) showed that for several paths throughout southern California, these Green's functions were sufficient for the recovery of seismic moment and PAS 'i- %"", -2 '<,!, 2 4 68 2 46 10-2 10-1 ~ ~0 0 6SC 102 ~ ~..,%,.,o, V...,o-' t-!:, %...,... Ampfimde Spectra 5V0 101 ~ - - ~ ~ ~.~., ooo o lo i...... i,,;,,, 2 468 2 46-2 l0-1 l-lz ~00 PF0 10t ~, o... 0-2 2 4 68 1 2 4 6800.1 10- l'z Figure 10. Comparison of amplitude spectra computed from the predominantly tangential component displacement data (GSC-EW, PAS-NS, PFO- EW, and SVD-NS) and synthetics computed with model C, the nonuniform seismic moment distribution, and rise times of 0.8, 1.4, 2.4, and 4.4 sec. Both the data and synthetics were bandpassfiltered from 0.02 to 2 Hz. The thick solid line shows the data, and the various dashed patterns show the synthetic spectra.

722 D.S. Dreger fault plane parameters for moderate sized earthquakes at relatively long-periods, and there was good agreement with broadband (0.01 to 1 Hz) displacement waveforms. t is possible, however, that for the specific paths to each of the four TERRAscope stations, there could be significant departures from the SoCal model. Campillo and Archuleta (1993) point out that slower, near-surface shearwave velocities along the path to GSC produce a dispersed Love wave and can account for the complexity observed at GSC. For example, they explain the unmodeled phase at 55 sec on Figure 5c as being due to a dispersed Love wave. Jones and Helmberger (1992) modeled a profile of aftershocks of the Landers earthquake recorded at GSC and found that the near-surface velocities for this path are indeed slower than those used to compute the synthetics used in this analysis. n addition, Hauksson et al. (1994) inverted P-wave arrival times for two calibration explosions and 276 earthquakes in the Landers area to obtain improved hypocenter locations and velocity models. They used essentially the SoCal model (Table 2) as a starting reference and found that the nearsurface velocities needed to be reduced. Middle and lower crustal velocities remained relatively unchanged in comparison. The question then, is, what are the potential effects on the derived source parameters as a result of the assumed velocity model? To address this, Figure 12a compares the north-south displacement records of the 23 April 1992 Joshua Tree foreshock (Mw 4.3) with synthetics computed with the SoCal model (Table 2) and the same model with the S-wave velocity of the top layer reduced by 12%. The synthetics in Figure 12a are aligned in absolute travel time. t is evident that both of these models fit the body waves very well, although Sn appears to be more developed in the data. The reduction in S-wave velocity produces a more dispersed Love wave, which results in better agreement with the observed surface waves. The modified Green's functions were computed for the same distance and depth ranges used in the point-source summations using model C, and it was found that the effect on the results was rather small. Figure 12b compares the north-south displacement data recorded at PAS for the Landers earthquake with model C synthetics computed with the SoCal and modified velocity models. The modified model better fits the duration of the first subevent phase; however, the amplitude of the second subevent phase is slightly overpredicted and there are some unobserved arrivals introduced into the synthetics at times greater than 70 sec. Overall, the waveforms computed with the two velocity models are very similar. A more significant difference is in the time shift needed GSCB/ P~NS ~0~ S'V) ~ 3.? s... -,,, -'~--,, ~,, 20 40 80 80 180 20 40 60 80 100 20 40 60 80 180 20 40 80 80 11~ seconcls Figure 11. Rupture velocity sensitivity. The predominantly tangential component displacement data and synthetics computed with model C, the nonuniform seismic moment distribution, a rise time of 2.4 sec, and rupture velocities ranging from 2.3 to 3.3 km/sec are compared.

nvestigation of the Rupture Process of the 28 June 1992 Landers Earthquake Utilizing TERRAscope 723 to align the synthetics to the data. The shift required with the SoCal model is 3.2 sec, which is slightly more than the 2.5-sec shift needed to compensate for the foreshock. The modified model, on the other hand, requires only a 1.3-sec shift, which is less than required. So it seems that some refinement of the slip model would be needed to better explain the absolute timing. For example, the 1.2-sec difference could be recovered by shifting the slip to the north by 3.5 km. Of course, this would need to be evaluated at all of the stations, and each path might require a different refined velocity model. t would also be prudent to evaluate the trade-offs of slip location and variable rupture velocity as well as variable dislocation rise time. Considering the simple approach taken in this study and the sparse data set, it is unlikely that details in the slip distribution are resolvable. t does not appear, however, that the results of this analysis would change significantly with the use of different Green's functions. Discussion n conclusion, it has been shown that relatively rapid analysis of the earthquake source process is possible, provided a catalog of calibrated Green's functions is available on-line. nformation regarding fault dimension, large-scale slip distribution, rupture velocity, and dislocation rise time can be robustly determined from a relatively sparse network of broadband stations. t has been shown that empirical Green's function deconvolution methods can rapidly identify source directivity and gross slip distribution (Kanamori et al., 1992; Ammon et al., 1993). While the empirical methodology relies on the availability of co-located aftershocks and foreshocks with nearly identical focal mechanisms and sufficient signal-to-noise ratios to allow stable deconvolutions, the technique employed in this article utilized theoretical Green's functions which can simulate earthquakes with arbitrary orientation and source dimension. A drawback to this methodology is the potential for bias in the results as a result of oversimplification of velocity structure used to compute the Green's functions. f the goal of the study was to map the detailed slip distribution by inverting the entire waveforms, then the adequacy of the assumed velocity model becomes a critical issue. Since the goal of this study was to only determine the large-scale features of the slip distribution using a simple parameterization, the limitations of the velocity model are not as important. However, to address this issue, two velocity models that produce substantially different Love wave dispersion were tested with the PAS recordings of the Landers mainshock. t was found that the source results would not change significantly. t appears that the source term dominates the motions recorded at the four closest TER- RAscope stations, which is probably a result of the fact that the stations are all located within two fault dimensions of the earthquake. The results of this analysis indicate that the Landers mainshock was composed of principally two large subevents on a fault 70-kin long. The peak in slip of the first was located 10 km north of the epicentral location and had a seismic moment of 2 1026 dyne-cm. The second was located approximately 40 km north-northwest of the epicenter and had a seismic moment of 6 10 26 dyne-cm. The combination of the changing fault strike, localized high slip subevents, and the northward directivity is needed to explain the anomalous azimuthal dependence of peak ground displacements, as well as the three-component waveforms recorded by TERRAscope. The model predicts slip at the surface that matches the large-scale features of the observed ground displacement. Because of the change in material properties in the velocity model at 5.5-km depth, slip below this level is approximately 69% of the surface values. nterpretation of this result should be made with caution since it is obviously velocity model dependent, and no attempt was made to model small-scale variations in slip at depth 0 '7 - O -- X 2O A) Joshuo Tree Foreshock Recorded ot PAS tta... jtforton -- scb175dll t ; = 40 60 80 100 120 Londers Moinshock Recorded ot PAS. i'~. ~ posn disp.soc - t... sc syn.... scb syn 20 t ~ t i 40 60 ~ 80 100 1 120 B) Figure 12. Green's function sensitivity. (a) The north-south displacement seismogram recorded at PAS for the 23 April 1992 Joshua Tree foreshock (Mw 4.3) is compared with synthetics computed with the SoCal velocity model (sc175dll t, Table 2) and a modified model (scb175dll t) in which the S-wave velocity of the top layer is reduced by 12%. The synthetics and data are aligned in absoluted time. (b) The north-south displacement seismogram recorded at PAS for the Landers mainshock is compared with synthetics computed with model C, the nonuniform seismic moment distribution, a rise time of 2.4 sec, and the two velocity models.

724 D.S. Dreger nor along strike. A rupture velocity of 2.9 km/sec was found to fit the data, and there is no need for a slowing of the rupture front as it crossed the fault segmentations evident in the surface displacements. The total source process time of the earthquake was approximately 24 sec. The broadband waveforms (0.01 to 2.0 Hz) were examined both in the time and frequency domains, and it was found that a dislocation rise time of 1 to 3 sec satisfied the data. The rupture velocity of 2.9 km/sec and a dislocation rise time less than 4 sec implies that the rupture propagated as a band of slip less than approximately 12-kin wide. Generally, the results of this simple approach agree fairly well with the distributed slip inversion results of Cohee and Beroza (1994) and Wald and Heaton (1994) in terms of the gross distribution of slip along the fault plane, source duration, average rise time, and the total seismic moment. There are discrepancies in the estimated rupture velocities among these models. The results of Wald and Heaton (1994) suggest that both the rupture velocity and the rise time were varying during the evolution of the earthquake. Nevertheless, the procedure outlined here is advantageous in that it can be rapidly applied to relatively sparse, but near-real time telemetered networks, and can robustly determine important earthquake slip parameters. Acknowledgments would like to acknowledge Chandan Saikia for providing the F-K integration program used to compute the synthetic seismograms. This article benefited greatly from discussions with Brian Cohee and David Wald. A portion of this work was completed while was at the California nstitute of Technology and was partially funded by USGS contract number 14-08-0001-G1872. References Abercrombie, R. E. and J. Moil (1994). Local observations of the onset of a large earthquake: 28 June 1992 Landers, California, Bull. Seism. Soc. 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Spatial and temporal distribution of slip for the 1992 Landers, California earthquake, Bull. Seism. Soc. Am. 84, no. 3, 668-691. Berkeley Seismographic Station University of California Berkeley, California 94720 Manuscript received 16 April 1993.