The Large Aftershocks of the Northridge Earthquake and Their Relationship to Mainshock Slip and Fault-Zone Complexity

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1 Bulletin of the Seismological Society of America, Vol. 87, No. 5, pp , October 1997 The Large Aftershocks of the Northridge Earthquake and Their Relationship to Mainshock Slip and Fault-Zone Complexity by Douglas Dreger Abstract The distribution of fault slip for the Northridge mainshock and two Mw 6 aftershocks is estimated using an approach that inverts the far-field momentrate functions derived by empirical Green' s function deconvolution. The slip for these events was found to have a strong negative correlation with the locations of small aftershocks, and there is a notable clustering of aftershocks near the edges of slip, suggesting that these events are triggered by a redistribution of stress following the mainshock rupture. The two largest aftershocks ruptured the updip regions adjacent to the leading edge of the mainshock rupture. One aflershock, 11 hr after the main event, initiated 8 km west of the mainshock slip terminus and ruptured east to the western edge of mainshock slip. This event was found to have ruptured the same south-dipping fault as the mainshock. The two events, however, are separated by a lateral offset in the depth of seismicity that serves as a geometrical barrier to throughgoing rupture. An M w 6.2 aftershock approximately 1 min after the main event is inferred to have ruptured an updip region of the mainshock fault that is relatively devoid of small aftershock seismicity. This event was located at the eastern edge of the sequence that overlaps with the north-dipping fault responsible for the 1971 San Fernando earthquake. Although the south-dipping plane is favored for this aftershock, it is not possible to rule out that it occurred on the north-dipping fault structure, or within the hanging block of the mainshock. ntroduction The 17 January 1994 Northridge earthquake (Mw 6.7) has received considerable attention due to its proximity to the dense population of Los Angeles and the level of damage that was inflicted. This earthquake sequence remains one of the best ever recorded due to its location within the dense short-period Southern California Seismic Network (SCSN), the broadband high dynamic range TERRAscope and Berkeley Digital Seismic Network (BDSN), the strong-motion instrumentation operated by both the USGS and CDMG, and geodetic monuments. With this distinction, the data recorded for the Northridge earthquake provide the best opportunity to date for a detailed investigation of the rupture process of an earthquake sequence as a whole. t has become a more or less routine practice to estimate finite fault or distributed slip parameters of large damaging earthquakes. For example, the detailed slip history of the Northridge mainshock was investigated using empirical Green's functions (Dreger, 1994); strong-motion, teleseismic, and geodetic data sets (Wald and Heaton, 1994a; Wald et al., 1996); and a genetic algorithm to invert local strong motions (Zeng and Anderson, 1996). Song and Helmberger (1995) modeled regional broadband waveform data using theoretical Green's functions to estimate the gross directivity properties of the mainshock, while Thio and Kanamori (1996) modeled teleseismic body waves using a time variable point-source approach. Hudnut et al (1996) and Shen et al (1996) modeled the fault slip from the static displacement field. Massonnet et al. (1996) were able to model the mainshock and two moderate aftershocks using radar interferometry data. The scalar seismic moment reported for the Northridge mainshock using seismic data (e.g., Dreger, 1994; Wald et al., 1996; Thio and Kanamori, 1996) ranges from 1.1 X 1026 to 1.6 X 1026 dyne-cm and compares well with the scalar seismic moment estimates from geodetic measurements (e.g., Hudnut et al., 1996; Massonnet et al, 1996; Wald et al., 1996) that range from 1.0 X 1026 to 1.7 x 1026 dyne-cm. There is general agreement between the seismologically derived slip models; however, there is a notable lack of correlation between results derived separately from the geodetic and the seismologic data. For example, the slip distribution obtained from geodetic data (Hudnut et al., 1996; Wald et al, 1996) tends to result in a circular patch of slip centered approximately 10 km updip and 5 km west of the hypocenter with negligible slip located at the hypocenter. Furthermore, there is no heterogeneity in the slip that might lead to the radiation of subevents as is observed in the 1259

2 1260 D. Dreger seismic data. The seismic slip models show significant slip in the depth range preferred by the geodetic data, slip near the hypocenter, and a greater level of complexity. This difference in the derived slip distributions can be due to the inability of geodetic data to resolve the temporal distribution of fault slip, the poorer resolution of geodetic modeling of dislocation at greater depth, and perhaps more importantly the possibility that large aftershocks contributed to the observed static displacement field. These points are not meant to diminish the utility of geodetic observations, which is obvious, but they are important in the context of how geodetic data are routinely incorporated into joint inversions for distributed slip parameters (e.g., Wald and Heaton, 1994b; Wald et al., 1996). There has yet to be a detailed seismological study of the slip distribution of the Northridge sequence that includes the mainshock and the two largest M w >= 6 aftershocks. The purpose of this article is to report on my continued study of the Northridge rupture process and specifically on the relationship of the two largest aftershocks to the malnshock rupture area. n this report, the far-field moment-rate functions derived for a 23:33 UTC (Mw 6.0) aftershock are inverted to estimate the spatio-temporal distribution of fault slip. A 12:31 UTC (Mw 6.2) aftershock, 62 sec after the mainshock, will be considered in the context of the slip distribution map, the distribution of smaller aftershocks, and in terms of fault complexity inferred from seismicity. Overview The Northridge earthquake occurred on a south-dipping fault plane (Fig. 1) adjacent to the north-dipping fault that ruptured during the M w San Fernando event. The Northridge and San Fernando events overlap at the eastern edge of the Northridge aftershock zone (Mori et al., 1995). Aftershock seismicity reveals the presence of lateral ramps or vertical deflections of the fault plane along the strike direction, and Hauksson et al. (1995) has suggested that these lateral ramp structures might have controlled the extent of the mainshock rupture. The Northridge earthquake sequence included over 10,000 aftershocks (Hauksson et al., 1995), two of which had M w >= 6.0 (Dreger, 1994; Thio and Kanamori, 1996). These two events, one just over a minute after the mainshock (12:31 UTC), and the other 11 hr later (23:33 UTC), herein referred to as AS 1 and AS2, have scalar seismic moments that indicate that these events have considerable fault dimension. These aftershocks were capable of producing damaging ground motions and contributing to the static displacement field. Figure 2 compares the north-south component of ground velocity recorded at PAS for the three events studied. Considering the complex fault structure evident by the proximity of the Northridge and San Fernando sequences, the goals of this study are to determine the fault plane, the spatial relationships of the large Northridge aftershocks relative to the mainshock, and the relationships of the events to 34 24' iii -- 34* 12' -r" ~119" 00' ' ' ' A) LONGTUDE ~o.~o _. i~ ~ oooo " ~ ~ ~ ~ o ~o o o B) DSTANCE (KM) Figure 1. (a) Magnitude 2.5 and larger aftershocks from 17 January 1994 to 31 December The event locations were obtained from the SCEC data center. Fault-plane solutions of the mainshock, AS2 (23:33 UTC), and their respective empirical Green's functions were computed by moment-tensor inversion of long-period waves. (b) Cross-section BB'. The filled symbols are those aftershocks that are located within 3 km of the fault plane defined by the mainshock hypocenter and the south-dipping nodal plane of the moment-tensor inversion results. complex fault structure imaged from aftershock locations (e.g., Hauksson et al., 1995). Empirical Green's Function Method The method that is used to determine the slip distribution of the large aftershocks involves the inversion of farfield moment-rate functions (MRF) derived from empirical Green's function (egf) deconvolution of broadband waveforms. The deconvolution process removes the shared propagation terms leaving the MRF of the target event. n this article, the target events are the mainshock, AS1, and AS2. The egfs are smaller aftershocks. Data from both TERRAscope and BDSN are essential for this type of study for two primary reasons. First, the dynamic range (nominally 200 db) of these networks enables the on-

3 The Large Aftershocks of the Northridge Earthquake and Their Relationship to Mainshock Slip and Fault-Zone Complexity 1261 Location Map - Aftershoek 2 N 3~ :if ~,,,,,,,, seconds Figure 2. (a) North-south component of velocity recorded at PAS (distance of 34 krn). AS 1 occurred 62 sec after the mainshock and is distinct from mainshock coda at high frequencies. The relative amplitudes of both events indicate that AS 1 is M w 6.2. (b) North-south component of velocity recorded at PAS for AS2 (17 January :33 UTC) approximately 11 hr after the mainshock. Moment-tensor analysis revealed that this event was M w 6.0. scale recording of the mainshock and aftershocks. Second, the data have the bandwidth necessary to compute momenttensor solutions that are used to search for egfs with source radiation characteristics similar to the target events using long-period data and to capture the details of complicated fault slip using broadband information. High gain and strong-motion networks fail to meet these two requirements because high gain instruments clip during the main events and strong-motion recorders fail to record the smaller aftershocks used as egfs. Figure 3 shows the TERRAscope and BDSN stations used in the egf analysis. Unfortunately, AS 1 is affected by high levels of mainshock coda, and consequently, detailed waveform analysis is not possible (Fig. 2). nstead, the extent of slip for AS1 is inferred from the mainshock and AS2 slip results, and the distribution of smaller aftershocks. For both the mainshock and AS2, a time-domain moment-tensor inverse method (Romanowicz et al, 1993; Dreger and Romanowicz, 1994; Pasyanos et al., 1996) was used to determine their focal mechanisms and to search for potential egf events. Figure la shows the fault plane solutions for the mainshock, AS2, and their respective egfs. Table 1 lists the event parameters. Generally, a suitable egf (1) is an earthquake smaller than the mainshock by more than one order of magnitude (i.e., represents a point source in a relative sense), (2) is 80 84" 32* -122" -120" -18" longitude Figure 3. Location map. Circles show the broadband TERRAscope and BDSN stations used in the directivity analysis. The stars denote the location of the three events that were studied. -116" nearly collocated, and (3) has a similar focal mechanism. As Table 1 shows, the egf used for each event meets the relative size requirement and has both a similar mechanism and location compared to the respective target events. t is worthwhile to note that the optimal egf location is near the slip centroid (Dreger, 1995). Therefore, when dealing with large earthquakes, it is not always advantageous to have mainshock-egf pairs with identical high-frequency hypocentral locations. n the two cases examined in this article, the egf events are within 8 km of the respective target event hypocenters. Moreover, the performance of a given egf is more strongly correlated to the relative depths of the mainshock and egf rather than the lateral location. As Table 1 shows, the centroid depths obtained for the target events and their respective egf events are the same. Although the egf method for determining fault slip from local (e.g., Hartzell, 1978; Moil and Hartzell, 1990; Moil, 1993), regional (e.g., Dreger, 1994; Hough and Dreger, 1995; Li etal, 1995; Kanamori et al, 1992), and teleseismic (e.g., Antolik et al, 1996; Velasco et al, 1994) data is adequately presented elsewhere, it is useful to define the model that will be used to invert the MRF data. A rather simple finite fault model is fit to the MRF data. This model consists of a discretized fault plane with the orientation of one of the possible fault planes determined from the moment-tensor analysis. n practice, both planes are tested to find the plane that best fits the data and to provide

4 1262 D. Dreger Table 1 Event nformation Event MW Date time (UTC) Lat.( N) Lon.( W) z* Z]" Str. Rake Dip M0* Mainshock ,017,12: Main egf ,17: AS ,23: , AS2-eGf ,04: *Hypocentral depths (kin) from the SCEC data center. t Centroid depths (kin) from moment-tensor analysis. :) Scalar seismic moment (dyne-cm). an independent estimate of the actual fault plane. n this way, it is possible to determine the causative fault planes for small events or aftershocks that do not have their own aftershock distributions (Mori and Hartzell, 1990), or in areas where event locations are poor and well-defined fault planes cannot be deduced from locations alone. The overall fault-plane model dimensions used for both the mainshock and AS2 were larger than the expected fault lengths, and the slip in each inversion tapers to zero well away from the edge of the model, indicating that the finite edge constraints are not limiting or biasing the slip distribution results. Synthetic MRF are constructed by summing subfault MRF with constant rise time and taking into account the propagation delay of a radially expanding rupture front and the relative subfault-station distances. n particular, MRFi(t) = ~j. ~Mo B(t - zij), where i is the station index, j is the subfault index,/z is the rigidity, U is the subfanlt slip that is solved for, A is the subfault area, M 0 is the total scalar seismic moment derived from moment-tensor analysis, B is the subfault MRF, and r is the delay due to rupture propagation and the relative station-subfault distance. A linear non-negative least-squares inversion is performed to find the slip amplitudes. A variety of smoothing constraints can also be applied to provide stability in the inversion. n this study, a spatial first derivative minimization constraint is employed. While this approach adequately takes multi-dimensional directivity into account, it fails to consider complexities such as geometrical bends, multiple rupture planes, variable rupture velocity, and variable dislocation rise time. Nevertheless, the comparison of Northridge mainshock results using this approach (Dreger, 1994) with the strong-motion results of Wald and Heaton (1994a), Wald et al. (1996), and Zeng and Anderson (1996) indicates that this simple methodology is capable of recovering the gross slip distribution quite well. Figure 4a shows the MRF obtained for the mainshock, which clearly shows evidence of northward directivity and two subevents as discussed in Dreger (1994). Figure 5 shows the MRF obtained for AS2. AS2's MRF are simpler than those obtained for the mainshock; however, it is interesting ` ~ SBC-283 t 15 PKD L- ', a9 150~-^^ ~ 5 3 _dfx,,-'v 1) VTV L A svo.0. A~ PFO r,, t L A 150E-^. i /\11 BAR' F-/\ " A) seconds B)seconds Figure 4. (a) Mainshock far-field moment-rate functions derived by empirical Green's function deconvolution. MRF amplitudes arc dyne-crrdsec and must be multiplied by the M0 of the egf (xm0[egf]). Note the thinning of the MRF toward stations CMB and PKD1 and the evidence of subevents at GSC, PFO, and BAR. (b) Synthetic MRF (dashed) are compared to data from (a). Both are normalized to unit area. to note that the duration is of the same order. The AS2 MRF show that pulse widths narrow at stations GSC and VTV (east-northeast), indicating rupture directivity to the east. This differs from the mainshock in which the rupture was observed to propagate to the north. While the mainshock ruptured primarily updip and to the north, AS2 ruptured east

5 The Large Aftershocks of the Northridge Earthquake and Their Relationship to Mainshock Slip and Fault-Zone Complexity ~ ',h, PKD 301-,/~,,! _30 c_ -v~;,,~ (Ju~- 3oL- :A ; CMB ',f/; 601-,(~, GSC 3o~,/,. oe v.j VT~ 3060~ -3oi- ;v " } o o -30 W ~ 30 o SVD 60L-- : A: PFO '1\,. 0 ', ' 60, P--- ',A BAR ~{0 - i d,.2 t -30b-,M ~-j, ~l A) seconds o2fa o%, B) seconds Figure 5. (a) AS2 (23:33 UTC aftershock) far-field moment-rate functions derived by empirical Green's function deconvolution. MRF amplitudes are dynecm/sec and must be multiplied by the M0 of the egf (xmo[egf]). Note the thinning of the MRF toward stations GSC, PFO, and VTV. (b) Synthetic MRF (dashed) are compared to data from (a). Both are normalized to unit area. with a small component of updip rupture. The fit of synthetic MRF to the data for both events is very good (Figs. 4b and 5b) and results in the combined slip map shown in Figure 6. Note that the slip of both events is located in regions with relatively few small aftershocks. This has been observed for other earthquakes (Mendoza and Hartzell, 1988) and may indicate that much of the stress in the high slip regions was relieved or that the clustering of aftershocks near the edges of slip may simply reflect the loading of adjacent areas of the fault. The seismicity that bounds the bottom edge of AS2 (Fig. 6b) suggests a northward fault dip; however, the spatial extent of these aftershocks is insufficient to unambiguously define the fault plane. When the slip obtained for AS2 for a north-dipping fault is correlated with these aftershocks, it is found that the aftershocks tend to be located in the regions of greatest slip in stark contrast to the mainshock and other recent earthquakes. Mori and Hartzell (1990) demonstrated that it is possible to use this method to test both possible nodal planes of the moment-tensor solution to independently determine the actual fault plane. This is done by performing a number of inversions testing different rupture velocities, for each of the two possible nodal planes, to find the combination that gives the best fit to the data determined by a minimum variance. Figure 7a shows that, for the mainshock, the south-dipping plane provides a significantly better fit to the data. Of course, the aftershock distribution can be used to directly map the fault plane of the mainshock. Both data sets for the Northridge mainshock yield the south-dipping plane. Figure 7b compares the same plot for AS2. Although the difference between the two planes is not large, the south-dipping plane gives consistently better fits to the data for all of the rupture velocities that were tried. The difference in the variance/rupture-velocity plots for the two events is probably due to different levels of source complexity. Since the smaller event (AS2) is not as complex, there is less information that can be used to determine the fault plane. n other words, the subevents provide the information necessary for determining the timing and position of fault slip. nterestingly, the rupture velocity for the mainshock was 3.0 km/sec, while AS2 yields a minimum variance for a rupture velocity of 1.6 km/sec. This substantial difference in rupture velocity can only be partially explained by the shallow depth of the event within the sediments of the San Feruando basin, which are approximately 10 to 15 l~n thick in this region (Huftile and Yeats, 1996; Haase et al, 1996). t is possible that the slower rupture velocity represents a difference in the materials involved in the faulting process or in the frictional properties of the fault. The shallow depth suggested by the slip inversion results for AS2 is corroborated by the shallow depths obtained from the moment-tensor analyses. For example, Thio and Kanamori (1996) find a depth of 3 krn, and a depth of 5 km was obtained in this study (Table 1). Furthermore, the greater relative excitation of surface waves of AS2 (Fig. 2b) compared to either the mainshock or the AS 1 (Fig. 2a) suggests, qualitatively, a relatively shallow source depth for this event. The radially expanding rupture model with constant rupture velocity is certainly an oversimplification of the actual rupture history. Recent studies using local strong-motion data (e.g., Wald and Heaton, 1994b; Cohee and Beroza, 1994a) indicate that there may be substantial acceleration and deceleration of fault rupture near regions that experience substantial slip or have geometrical complexities. Wald et al. (1996) examined the possibility of variable rupture velocity in the Northridge earthquake by allowing slip to occur in multiple time windows. Their results indicate that most slip occurs in the first window that lends support to the constant rupture velocity assumed in this article. Although the model used in this article does not take into account these additional complexities, the favorable comparison of the mainshock results (Dreger, 1994) with the strong-motion results of Wald and Heaton (1994a) and Zeng and Anderson (1996) demonstrates that the approach is capable of resolving the gross distribution of fault slip.

6 1264 D. Dreger O 34 24' Q 34 ~ 12' L Gilibrand Canyon Lateral Ramp J -119 ~ 00' A) ± Aftemt" ; 23:33U 7-118" 48" l -118" 36' Longitude ' ~" 10 c~ 20 25! ~Gilibrar i Lateral Distance (krn) B) 35O "~ 150 CO 100 5O Figure 6. (a) Map view of in-plane M >- 2.5 aftershocks (red symbols; the filled symbols in Fig. lb) and fault slip for the mainshock and AS2. The color bar shows the slip scaling. The peak mainshock slip is 330 cm. (b) West-east (AA' Fig. 2a) crosssectional view of in-plane aftershocks and mainshock and AS2 fault slip. The location and dimension of AS1 (light blue ellipse) is inferred from the relocation of the hypocenter 6 kin north to the mainshock plane where there are locally relatively fewer small aftershocks. n both the map view and cross-sectional images, the approximate boundaries of the Gilibrand Canyon lateral ramp inferred from Hanksson et al.'s (1995) Figure 10b are shown as orange dashed lines. The eastern line marks the location of a westside 2-km downward deflection of the bottom of the Northridge aftershock zone. Geodetic Slip Maps The results of this study have important implications for the modeling of geodetic displacements for fault slip. Hudnut et al. (1996) report that large aftershocks could indeed affect static displacement calculations, and Shen et al. (1996) demonstrate that the geodetic data are better fit by a model with two planes, one of which is constrained to lie within the south-dipping aftershock distribution and the second within the hanging block. Massonnet et al. (1996) con- clude that radar interferometry data show static displacements of aftershocks and that a single fault model fails to explain the geodetic data, particularly along the western edge of the sequence. Both the geodetic (Shen et al, 1996) and radar interferometry data (Massonnet et al., 1996) require shallow slip at the western edge of the sequence with scalar seismic moments of 1.9 X 1025 and dyne-cm, respectively. The seismic moment obtained in this study for AS2 is 1.0 X 1025 dyne-cm and agrees to within a factor of 2 of the values obtained by both Massonnet et al. (1996)

7 The Large Afiershocks of the Northridge Earthquake and Their Relationship to Mainshock Slip and Fault-Zone Complexity signal is part of the signal that was observed and interpreted as the mainshock. ~" 2 g == ~t ~, 2.25 g ~4 " ~ o r t south dipping fault B) [ j h fault 2 3 Rupture Velocity (km/s) /111' / 1" - -lff i! \m. ".// sou}h dipping fault north dipping fault 2 3 Rupture Velocity (km/s) Figure 7. (a) Rupture-velocity/variance plots comparing the north- and south-dipping fault planes for the rnainshock. (b) Rupture-velocity/variance plots comparing the north- and south-dipping fault planes for AS2. and Shen et al (1996). The location of AS2 slip relative to mainshock slip in map view is also in agreement with both studies. Although Shen et al (1996) and Massonnet et al. (1996) both favor north-dipping planes, the dip of the secondary fault plane is poorly constrained, and what is required by the geodetic data is shallow slip at the western margin of the sequence. The preferred interpretation of this study is that AS2 ruptured an adjacent segment of the south-dipping mainshock fault plane. t is interesting to note that there is no evidence of AS 1 in the radar interferometry images of Massonnet et al. (1996). Their images (Massonnet et al, 1996; Fig. 2) are either too noisy to see an anomaly or perhaps the lack of an anomaly suggests that this aftershock ruptured the southdipping mainshock plane and that its radar intefferometric Discussion and Conclusions This article documents the distribution of fault slip of the 1994 Northridge earthquake sequence. Two Mw > aftershocks are located along the updip terminus of the mainshock rupture. The first of these, AS 1, is somewhat of an enigma. t was not possible to analyze the waveforms for this event because of high noise levels due to mainshock coda. t is possible, however, to consider this event in the context of the slip distribution for both the mainshock and AS2 and their relationship to small aftershocks. f the hypocenter of AS 1 is well constrained, then this event occurred in the hanging block. f the location of AS1 is poorly constrained, then relocating this event 6 km to the north places it on the mainshock plane in a region where there are fewer small aftershocks (Fig. 6b). This is the location preferred by this study; however, in this position, it is also possible that AS 1 occurred on the adjacent north-dipping Sierra Madre fault responsible for the 1971 San Femando earthquake. Both the mainshock and AS2 appear to have been limited in extent by the Gilibrand Canyon lateral ramp (Figs. 6a and 6b). AS2 initiated at the westeru edge of the Gilibrand Canyon lateral ramp (e.g., Hauksson et al, 1995) approximately 8 km west of the mainshock rupture terminus and ruptured east, stopping at the westward edge of the mainshock rupture. The approximate boundaries of the Gilibrand Canyon lateral ramp on Figures 6a and 6b mark the boundary of a 2-km deflection of the bottom surface of the Northridge aftershock zone (e.g., Hanksson et al, 1995). The clustering of small aftershocks and the locations of the two large aftershocks at the terminus of mainshock slip suggest that these events were triggered by changes in stress due to the mainshock rupture. Stein et al. (1994) illustrate that the Coulomb stress changes on optimally oriented thrust faults of the order of 0.5 to 1.0 bar would be expected in the vicinity of AS2. n fact, their Figure 3c shows that these positive Coulomb stress changes extend in the updip direction toward the north, which is in agreement with the determination of the south-dipping fault plane determined by this study. These stress changes are quite small, approximately 1% of the static stress drop of AS2, and suggest that these adjacent regions were already close to failure at the time of the earthquake. The seismological results of this study and the geodetic results of Shen et al (1996) and Massonnet et al (1996) have important implications regarding the use of geodetic data jointly with seismic data in distributed slip inversions. Geodetic data can clearly be affected by the static displacements of moderate-sized aftershocks, particularly if they are shallow. The static displacement field is the cumulative displacement of all of the events in the sequence, while strongmotion data sets are only sensitive to the mainshock dislocations. This poses a problem because, as Cohee and Beroza

8 1266 D. Dreger (1994b) discuss, the temporal details of rupture propagation cannot be recovered unless the distribution of slip amplitude is constrained by other independent data. n practice, these data have been geodetic from either GPS or leveling. Therefore, when incorporating diverse data sets such as seismic waveforms and geodetic displacements to recover the distribution of fault slip, tremendous care is required to ensure that each data set is representative of the same physical process. Acknowledgments The event locations and TERRAscope data used in this study were obtained from the SCEC Data Center. would like to thank the associate editor and an anonymous reviewer for very helpful comments. This research was supported in part by NSF Grant Number EAR and USD HQ-96-GR This is Contribution Number 96-7 of the UC Berkeley Seismological Laboratory. References Antolik, M., D. Dreger, and B. Romanowiez (1996). 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