The combined inversion of seismic and geodetic data for the source process of the 16 October,

Transcription

1 1 The combined inversion of seismic and geodetic data for the source process of the October, 1999, Mw7.1 Hector Mine, California, earthquake Asya Kaverina, Douglas Dreger and Evelyn Price Berkeley Seismological Laboratory, UC Berkeley In press, Bull. Seism. Soc. Am. Special Issue on the Hector Mine Earthquake, October 29, 2001 Abstract We investigate the source process of the Mw7.1 Hector Mine earthquake by inverting broadband regional and local seismic displacement waveforms combined with GPS and InSAR geodetic measurements. We find that the three data sets individually produce remarkably similar slip distributions over a multi-segment fault. A simultaneous inversion of the three data sets is presented, and the sensitivity of the combined inversion to the weighting of the three independent data sets is examined. The results indicate that the overall length of the fault that slipped is 42 with a peak slip of 5.50 m and total scalar seismic moment of.8e19 Nm. The majority of slip is located on the western branch of the Lavic Lake fault to the northwest of the hypocenter, although the overall rupture is bilateral with appreciable slip on the Bullion Fault to the southeast. Some slip is located on an eastern branch of the Lavic Lake fault, an apparent sub-parallel bifurcation, which is also evident from aftershock locations. The average slip and stress drops are 2.70, 1.2, 1.0 m, and 78, 3 and 55 bars for the western Lavic Lake, the eastern Lavic Lake, and Bullion faults, respectively. The results also indicate that the overall rupture process is slow, which is characterized by a several second delay before the onset of significant slip, a 1.8 km/s rupture velocity of the primary asperity, and long, spatially variable, dislocation rise times. Introduction The Mw7.1 Hector Mine earthquake occurred on October, 1999 in the Mojave Desert in southeastern California (Figure 1). It ruptured about 48 km along the Lavic Lake and Bullion faults (Treiman et al., 2001), which are located 20 km to the east of the 1992 Mw7.3 Landers earthquake. The closeness of the two events in both space and time suggest that the Landers earthquake may have accelerated the occurrence of the Hector Mine event. The coulomb stress change on the Hector Mine earthquake faults due to the Landers rupture seems to correlate with where slip occurred, however the hypocenter is located in a region that had only a minor, favorable coulomb stress change (Parsons and Dreger, 2000). In fact, the level and sign of the coulomb stress change in the hypocentral region is strongly dependent upon the assumed coefficient of friction and the geometry and slip distribution of the Landers earthquake. Other studies have investigated delayed triggering mechanisms such as poro-elastic response, viscous loading (Freed and Lin, 2000; Wang and Jackson, 2000; Pollitz and Sacks, this issue), and time-dependent changes in frictional strength of the fault surface (Price and Bürgmann, this issue). The visco-elastic studies indicate that ductile loading from the upper mantle response to the Landers earthquake may in fact concentrate stress in the hypocentral region of the Hector Mine earthquake (e.g. Freed and Lin, 2000).

2 2 Dreger and Kaverina (2000) presented a preliminary finite-source model with a simplified spatio-temporal parameterization of the rupture, and found an apparent southward directivity. The source model in that study utilized a single fault plane with constant rupture velocity and constant dislocation rise time. Surface faulting and geodetic data were not used because they were not available in the near-real-time epoch of that study. The shakemap that they calculated from the preliminary slip model was found to agree very well with observed near-fault strong-motions, which were not used in the source inversion. Here, we supplement the original strong-motion data set with seismograms from additional stations to improve azimuthal coverage, and also include geodetic measurements. The addition of the geodetic data sets improves the spatial coverage of the near-field region. As geodetic measurements are static displacements they complement the frequency range provided by the seismic data set and spatially constrain the rupture process allowing the seismic data to better resolve the temporal heterogeneity (Cohee and Beroza, 1994a). In addition, we use geologically mapped surface offsets, which effectively constrain the inferred slip distribution on the shallow portion of the fault model. Surface faulting (Treiman et al., 2002), and aftershock seismicity (Hauksson et al, 2002) indicate a complex fault geometry for the event, with a possible bifurcation of rupture north of the hypocenter. To account for the reported complexity we invert each of the data sets separately using a three-segment fault model. Each fault segment is allowed to slip in a series of staggered time windows to image possible rupture velocity and dislocation rise time variability. Finally, we present a simultaneous inversion of the three data sets, and explore the sensitivity of the results and trade-offs due to the assumed weighting of the individual data sets. Data and Processing The seismic data consist of 21 displacement waveforms recorded at seven local and regional stations. The closest station, HEC, is located about 27 km to the north of the epicenter. Both the data and theoretical Green's functions were bandpass filtered between 0.01 to 5 Hz, retaining the high-frequency content. However, as will be shown, the rupture velocity was relatively slow and the dislocation rise time long. Both result in relatively long period seismograms that are dominated by frequencies less than 1 Hz. A SAR interferogram was formed by combining two radar images taken on September 15, 1999 and October 20, 1999 by the European Space Agency's ERS-2 satellite and span 30 days before to 4 days after the earthquake. A four-pass InSAR method was used to remove the topographic signal in the original interferogram yielding a deformation map whose apparent displacements are a mixture of the actual coseismic displacements caused by the earthquake, noise, and any interseismic or postseismic deformation. The coseismic interferogram is a set of 5743 displacements of the Earth's surface in the direction of the radar s line-of-sight between the two times of imaging. The interferogram shown here is very similar to the ones computed by groups at the Jet Propulsion Laboratory (JPL); the California Institute of Technology (Caltech); Stanford University; and the University of California, San Diego (UCSD) (Peltzer et al., 1999; Simons et al., 1999; Zebker et al., 1999; Sandwell et al., 1999) and is the same one used in Price and Bürgmann (this issue). The GPS data were obtained from the SCIGN network at 170 stations and processed by D. Agnew (personal communication, 2000). No correction was made for pre-seismic or post-seismic motion. Because most of the sites were observed in , before the earthquake, and within 2 weeks after, this should not be a large correction. As will be presented, the scalar moment obtained

3 3 inverting only GPS data is in fact not significantly larger than the value obtained inverting only the seismic data, further confirming that post seismic deformation cannot be large. Some of the closer sites were observed months after the earthquake, but available data from nearby locations suggests that there was not a large amount of post-seismic motion in this region (D. Agnew, personal communication, 2000). The near-fault GPS data provide important constraints on ground displacement between the two branches of the Lavic Lake fault (segments 1 and 2, Fig.1), and complement the SAR data, which provide a more complete coverage at larger distances from the source. A set of surface displacement measurements (Scientists, 2000) was used to constrain the slip along the top of our fault model, and were implemented by averaging the slip values over a subfault dimension (2 km). The surface slip data was found to provide an important constraint on the shallow slip in the inversion, however it has negligible influence on the distribution of slip at depth. Inverse Method To invert the data we use a non-negative, least-square inversion method with simultaneous smoothing and damping, which is presented elsewhere (e.g. Hartzell and Heaton, 1983; Wald and Heaton, 1994; Dreger and Kaverina, 2000). Described briefly, the method we use inverts for fault slip distributed over a grid of point sources that are triggered according to the passage of a circular rupture front. Distortions from the constant rupture velocity and variations in the rise time are accomplished by using the multiple-time-window technique of Hartzell and Heaton (1983), where each point source can rupture in any of a few time windows after the initial rupture trigger time. This temporal rupture model is preserved for the static cases for consistency although there is no time dependence in those inversions. A Laplasian-smoothing operator, slip positivity, and a scalar moment minimization constraint is applied in all of the inversions. In separate inversions of different data types the weight of the smoothing varies, each having an optional value related to model smoothness and level of fit to the given data. We use this fact in choosing the appropriate weights for different data sets in the simultaneous inversion. Green s functions for the Southern California (SoCal; Dreger and Helmberger, 1993) velocity profile, shown to be effective in modeling regional wave propagation (Dreger and Helmberger, 1991), were used to invert the seismic waveforms. The Green's functions were calculated using a frequency-wavenumber integration method (Saikia, 1994) for 5 km intervals in distance and 3 km intervals in depth. For the geodetic data, a half-space representation of SoCal crustal velocities was used to calculate the surface displacements. The fault model includes the fork between the two northern segments of the Lavic Lake fault in order to investigate the hypothesis of a coseismic bifurcated rupture (Figure 1). The three fault segments overlap by only a single column of subfaults. The lengths for segments 1-3 are 2, 38, and 2, respectively. Dreger and Kaverina (2000) reported that the onset of large amplitude P-wave accelerations was delayed by as much as 3 seconds, which was verified by our preliminary multitime-window runs. To reduce the size of the model space we apply a 3 second delay in all of the calculations presented in this study, and limit the total number of time windows to five. We used the hypocenter coordinates (34.59 N, 1.27 W, depth of 5 ± 3 km) reported in Scientists (2000). A hypocentral depth of.0 km depth was used, the same as in Dreger and Kaverina (2000). All segments have a dip of 77 o and rake of -180 o, reported as the optimal moment tensor solution (Scientists, 2000). We performed inversions that allowed variable rake, and found that the rupture is dominated by the strike-slip component, and that the dip-slip component did not produce a

4 4 statistically significant improvement in fit. Considering that there is also evidence of considerable temporal complexity in the rupture, necessitating the use of multiple time windows, we limit the inversions in this study to the pure strike-slip case to reduce the overall number of free parameters. It will be shown that despite this, a very high level of fit to the each data set is obtained. The strikes of the model faults in our study are based on the observed surface rupture, mapped faults, and aftershock locations and are 325 o for segments 1 and 3 and 345 o for segment 2 (Figure 1). All fault segments are discretized by a number of subfaults each with 2 x 2 km area. Given the assumed depth of the hypocenter, dip of the fault, and the subfault dimension, the top of the fault system is at 0.15 km depth. Adjusting the position of the fault to intersect the free-surface would not alter the results of this study. There are 2700 subfaults where slip is determined in the model. The dislocation rise time for each time window is characterized by an isosceles triangle with a duration of 2.4 seconds. Each time window for a given fault segment is staggered by 1.2 sec. Thus our temporal model parameterization allows for a maximum dislocation rise time of 7.2 seconds. Several inversions were performed investigating higher resolution of the rise time in which isosceles triangles with durations of 1.2 and 0. seconds were tested. It was observed in these higher resolution inversions that the overall slip distribution and the fit to the displacement seismograms were the same, although significantly better fits to the velocity waveforms were obtained. A range of rupture velocities was tested and a maximum value of 2.2 km/s was found to result in the best fit to the data. This value for rupture velocity was also found to corroborate the 3 second delay in rupture onset that was observed directly in the accelerograms (Dreger and Kaverina, 2000). Other values of rupture velocity also yielded good levels of fit, and the same overall spatial slip distribution. Smoothing and Weighting Multiple Data Sets The inversion problem for separate data sets can be represented as the following two systems of equations G 1 X = D 1 s 1 L X = 0 G 2 X = D 2 s 2 L X = 0 where G 1 and G 2 are matrices of Green's functions, D 1 and D 2 are data vectors and s 1 and s 2 are smoothing weights for two different types of data, respectively. L is the smoothing operator and X is the fault slip solution vector. By multiplying the second system by s 1 /s 2, we obtain, s 1 G s 2 X = s 1 D 2 s 2 2 s 1 L X = 0 Now that the two systems of equations are related through a smoothing parameter they may be combined into a single system of equations that may be simultaneously solved. G 1 X = D 1 s 1 G s 2 X = s 1 D 2 s 2 2 s 1 L X = 0 Since the smoothing weight is an arbitrary parameter, the actual weights of different data sets are adjusted by inspection of the resulting slip distribution. In practice, we search for the smoothest model that yields a level of fit that is not significantly reduced from the best fitting un-smoothed

5 5 results. The amount of smoothing can affect the peak value of slip, but does not tend to result in large differences in the overall extent of the slip, nor the average level. In the combined inversions the smoothing weight is scaled to preserve smoothness of the solution, and to maximize the fit to each of the data sets. This is accomplished using a tradeoff plot, which is illustrated later. Inversion Results Inversion of the seismic data The slip distribution obtained from the seismic data is shown in Figure 2a. Most of the slip, covering an area of approximately by km, was found on the segment 1 representing the western strand of the Lavic Lake fault. The slip reaches 5.00 m on this segment. As much as 5.00 m of slip is observed on segment 2. Segment 2 has slip as much as km north of the hypocenter, and 15 km south to the edge of the segment. Up to 2.00 m of slip is mapped onto segment 2 to the north of the hypocenter. A sensitivity study was conducted to compare synthetic waveforms, computed with and without the slip on the northern part of segment 2. A variance reduction of 87 percent was obtained with the slip, and 83 percent without it. However, an inversion for a model that does not allow segment 2 to extend north of the hypocenter fits the data as well as the full degree of freedom inversion, and accomplishes this by adjusting the distribution of slip on segment 1. Therefore we cannot prove that slip on the northern part of segment 2 is required from the seismic data alone. The scalar seismic moment of the seismic inversion is.e19 Nm. The range in scalar moment from other finite-source studies is.0e19 -.3e19 (e.g. Yagi and Kikuchi, written communication, 1999; Ji et al., 2000; Ji et al., 2002). As we looked at the scalar moment sensitivity for our different finite-fault models, we found that the total recovered scalar moment does depend on the total source duration and the fault geometry. For this study, the model has five time windows with a total duration of 7.2 sec that are preceded by the rupture delay of 3 seconds. Inversions that we performed without the initial delay, and a greater number of time windows were found to result in greater scalar seismic moment. Second, the addition of the northern extension of segment 2 (Figure 1) tends to reduce the scalar seismic moment. The strike of segment 2 (345 o ) is very close to the azimuth to station HEC (348 o ), and slip on this segment produces near-maximum SH radiation in that direction, and the solution therefore requires less slip to explain a given amplitude. In comparison, the various point-source scalar moment estimates are significantly less (e.g. Harvard, 5.98e19; TriNet, 3.93e19 Nm; and Berkeley, 4.2e19 Nm), which is likely due to the limitations of the assumed point-source approximation. The fit of the synthetic, three-component, displacement waveforms is shown in Figure 3a. The total data variance reduction for this solution, calculated as a normalized squared misfit, is 87 percent indicating a very good level of fit. Inversion of the geodetic data Results of the separate inversions of the GPS and SAR data are presented in Figures 2b and 2c. Both solutions are smoothed, and have the surface slip constraint applied. The fit to the GPS and InSAR data is shown in Figure 3b and 3c and is quite good. The InSAR solution reproduces the shape and amplitude of the image well particularly to the NW and SE of the epicenter. The misfit is worse at points further from the fault. The GPS velocity vectors are very well fit in terms of both the direction and the amplitude. Quantitatively, the data are fit with 85 and 95 percent variance reductions, respectively. The GPS and InSAR data sets are seen to be complimentary to each other

6 in which the GPS data provides essential coverage in the near-fault region, where there is a lack of coherency in the SAR interferogram. The two geodetic based slip distributions are remarkably similar, however the respective scalar moments (7.0e19 Nm and 8.1e19 Nm) are and 20 percent larger than the scalar moment for the seismic inversion. In the case of the GPS inversion the difference in scalar moment compared to the seismic value is not significant considering the uncertainties due to assumed velocity structure. Wald and Graves (2001) examined, numerically, the effect of half-space, layered 1D, and 3D velocity models on static displacements, and found that in the case studied the static displacements for the layered and 3D velocity models were consistently larger than those for the half-space. In fact, the difference was found to be as large as a factor of two. The difference between the scalar moments for the seismic and GPS inversions, in this study, is relatively small indicating that the possible bias introduced by assuming a half-space velocity model is small. Furthermore, the closeness of the values suggests that contamination of the GPS data by post-seismic deformation is also likely to be small. This is as expected from examination of postseismic GPS time-series of displacements that indicate that less than half a centimeter of horizontal displacement occurred at representative GPS sites within the 4 days following the earthquake (e.g. Pollitz et al, 2001): this amount is less than the allowable error in the InSAR displacement map. In the case of the SAR inversion, the scalar moment discrepancy is large. Most of the extra moment is introduced as non-physical slip along the bottom edge of the model. This may be due to the assumption of a half-space structure, but it may also be due to the attempt to fit the relatively small line-of-sight change at large distance from the fault. The maximum slip is.8m and 4.7 m in the GPS and SAR cases, respectively, and is located above the hypocenter in both models. With the exception of the non-physical slip at the bottom of the SAR model, and the deeper slip on segment 1 in the GPS model, the slip in both geodetic inversions tends to be shallower than in the seismic inversion. In common with the seismic inversion the most significant asperity is located on segment 1 representing the western branch of the Lavic Lake Fault. The GPS model, and to a degree the SAR model, agree with the seismic result in terms of a low point in slip immediately to the southeast of the hypocenter. The three models are also similar in terms of the along strike dimension of the slip, though the SAR model tends to place slip a little further southeast. In contrast to the seismic inversion, both geodetic inversions produce more slip on the two northern segments of the Lavic Lake Fault (segment 1 and segment 2 north of the hypocenter). The SAR model has this slip in equal proportion, while the GPS model tends to have larger amplitude slip on segment 1. It is noteworthy that the GPS data provides the only observation of displacement between the two northern branches of the fault, and therefore provides an important constraint on the partitioning of slip on the two fault branches. All of the models presented in Figure 2 have been smoothed. The smoothing weight was determined by finding the smoothest model that does not significantly worsen the fit to the data. Interestingly, we found that the GPS data requires half the smoothing of the SAR data in order to produce slip maps that have a similar level of smoothness that is also consistent with the seismic results. To arrive at a single value of the smoothing weight for a combined inversion of the GPS and SAR data, we scale the smoothing with a relative weight for each data set (Figure 4a). The appearance of the slip distribution changes gradually from the InSAR solution to the GPS solution with increasing weight of the GPS data set. The level of smoothing and the peak slip remains very similar over the range of weights. We chose the relative weighting of the GPS and SAR data to be 0. and 0.4, respectively. With these values the fit to each data set is reduced by less than 2 percent, and the resulting slip distribution reveals features that are similar to the slip distributions

7 7 shown in Figures 2b and 2c. In the following section we examine the weights needed for the combined inversion and explore their sensitivity with respect to the fit to all of the data sets. Combined inversion of the seismic and geodetic data Combining the seismic and geodetic data we use the same approach as in the case of the joint inversion of the SAR and GPS data. To maintain a similar level of smoothness for each data set, and recognizing that the seismic data requires a smoothing parameter about 300 times less than the geodetic data, the ratio of the weights of the geodetic and seismic data also has to be of the order of 300. Figure 4b is a tradeoff curve relating the relative weighting of each data set for a series of combined inversions. As expected, the fit of the seismic data decreases and the fit of the geodetic data increases with the weight. However, changes in variance reduction are small, indicating that the data sets are consistent, reflecting the fact that the individually derived solutions are quite similar (see Figure 2). For the combined inversion, we settled on intermediate values of smoothing and relative weighting, which minimizes the reduction of fit to each data set (identified by the arrow on Figure 4b). The fit to the three data sets for the combined inversion are shown in Figure 5. The combined model fits the GPS, InSAR and seismic data with data variance reductions of 92.8, 83.5, and 8.2 percent, respectively, which is only 2-3 percent lower than the data fits in the individual cases. The preferred combined model (Figure ) inherits higher slip values updip and to the north of the hypocenter from the geodetic models, and has a scalar seismic of.8e19 Nm. The peak slip is 5.5 m. Segment 1 has the greatest amount of slip, and the seismic data tends to require that some of this slip is relatively deep. The mapping of the deeper slip may be due to the relative depth of the hypocenter (e.g. Ji et al., 2000; 2002). They found that increasing the depth of the hypocenter resulted in a shallowing of slip in their seismic only inversions. We chose to use the hypocentral depth used in Dreger and Kaverina, which is within the range reported by Scientists (2000). The non-physical, deep slip in the geodetic model (Figure 2b and 2c) is not seen in the combined inversion. The northern part of segment 2 has slip extending 8 km north of the hypocenter indicating that there was a bifurcated rupture of the forked fault system. There is a large area of low amplitude slip below the hypocenter, as in the seismic and GPS models (Figure 2a and 2b). Moderate levels of slip are mapped on to segment 3. The overall, along strike dimension of the slip model is 14 km north and 28 km south of the hypocenter for a total length of 42 km. The static stress drop was calculated for the three fault segments by averaging the slip above 10 percent of the maximum slip level for each segment, and determining an equivalent circular fault area. The results of this calculation give average slip levels of 2.70m, 1.2m, and 1.0m, corresponding to static stress drop values of 7.8, 3. and 5.5 MPa for segments 1-3, respectively. While the spatial complexity of the Hector Mine earthquake is very interesting, the required temporal complexity is perhaps the most interesting. In Figure 7 snapshots of the rupture evolution for the combined inversion are shown. This figure shows the rupture history beginning after the initial 3 second delay discussed previously. Each time window represents 2 seconds of rupture time. This figure illustrates both spatial variations in the rupture velocity and the dislocation rise time. The best maximum rupture velocity was found to be 2.2 km/s, but as Figure 7 shows lower values are more typical of the initial rupture. The northern extent of the rupture is attained by the 7-9 second snapshot indicating a rupture velocity of approximately 1.8 km/s. After this time the western branch of the Lavic Lake Fault (segment 1) continues to slip resulting in a very long dislocation rise time for some of the subfaults. The slip on the northern part of segment 2 is seen to

8 8 rupture simultaneously with segment 1 with a slower apparent rupture velocity, however most of the slip on this part of the model is accumulated in the 9-15 second snapshots. On segment 2 there is some southward directivity, which has a slip pulse appearance. However, it is on segment 3 where the most pronounced directivity effect is observed. At the 7-9 second snapshot segment 3 (Bullion Fault) begins to rupture with an apparent rupture velocity of 2.2 km/s. In fact the southward rupture propagation begins on segment 2 in the 5-7 second snapshot and is seen to continue through the fault bend between segments 2 and 3 in a more or less continuous rupture. Furthermore, the dislocation rise time of segment 3 is generally shorter than for both segments 1 and 2. This southward slip pulse style of rupture is consistent with the strong southward directivity signature observed in the preliminary finite-fault inversion of Dreger and Kaverina (2000). Discussion of Results The inversion results for the individual data sets (Figure 2) are very similar indicating that the data are consistent; a fact supported by the ability to simultaneously fit all of the data individually above 83 percent variance reduction and the rather small reduction in overall fit to each data set in the combined inversion. The inclusion of the geodetic data in the combined inversion provides improved constraint on the spatial slip distribution and allows the seismic data to be used to investigate the temporal characteristics of the rupture (Cohee and Beroza, 1994a). The complicated fault geometry indicated by aftershocks and surface faulting (Figure 1) seems to be necessary to model the data. The multi-segmented, multi-time-window inversion of the seismic data resulted in a high level of fit (87 percent variance reduction). Using the same seven seismic stations and the single fault plane model of Dreger and Kaverina (2000) a variance reduction of only 8 percent was obtained. The value of the geodetic data is seen when comparing a combined inversion (without surface slip constraint) for the single fault model of Dreger and Kaverina (2000). In this case the total variance reduction is a mere 48 percent. Similarly a combined inversion using the threesegment geometry, but with only one time window for each segment yielded a variance reduction of only 8 percent. These sensitivity tests reveal that to fit the entire data set well, the multisegmented, multi-time-window model is required. The Hector Mine earthquake was located only 20 km from the earlier and larger rupture of the 1992, Mw7.3 Landers earthquake, and differs significantly from the 1992, Mw7.3 Landers earthquake in terms of its rupture kinematics. First, the Landers event was found to be a unilateral rupture from south to north with a relatively large average rupture velocity 2.5 km/s (Cohee and Beroza, 1994b), 2.9 km/s (Dreger, 1994) and 2.7 km/s (Wald and Heaton, 1994), although Wald and Heaton s (1994) model does have slow rupture velocity (1-1.4 km/s) in the region of slip transfer between the Johnson Valley and Homestead Valley Faults, as well as between the Homestead Valley and Emerson Faults. The Hector Mine earthquake is best described as bilateral, however there are some interesting complications. Segment 3 was found to have a rupture velocity that while on the slow side (2.2. km/s), was consistent with the values observed in the Landers earthquake. Segments 1 and 2, on the other hand, have much slower rupture speeds on the order of 1.8 km/s, which is only 50 percent of the shear wave velocity at seismogenic depth in the SoCal velocity model (Dreger and Helmberger, 1993). Second, in the Landers earthquake the dislocation rise time was found to be relatively short, between 1-4 seconds (Dreger, 1994), but variable over the rupture (Cohee and Beroza, 1994b; Wald and Heaton, 1994). The Hector Mine earthquake in contrast had a spatially variable dislocation rise time that varied from 2.4 to 7.2 seconds in our model. From Figure 7 it is clear that the overall dimension of segment 1 was established within 9

9 9 seconds of the onset of significant rupture, however subfaults on this segment are observed to continue slipping into the second snapshot. It is possible that on some places of the fault the dislocation rise time was shorter than 2.4 seconds, but it is inescapable that a relatively long rise time is needed in many areas of large slip amplitude on the fault. Third, the Hector Mine earthquake nucleated near the juncture of two strands of the Lavic Lake fault, which have a 20 o difference in strike, and the kinematic model indicates a simultaneous rupture of both segments. Earthquake nucleation in an area of geometric fault complexity has been observed in other moderate to large earthquakes (King and Nabelek (1985). Interestingly, both events were observed to have a slow onset to significant rupture (e.g. Abercrombie and Mori, 1994; Dreger, 1994, and Dreger and Kaverina, 2000). The slow rupture velocity of segment 1 that suggests a relatively larger strength parameter, S=(σ y -σ o )/( σ o -σ f ) (e.g. Scholtz, 1990). Strength excess can result from a high yield stress (σ y ), low initial stress (σ o ), high frictional stress (σ f ), a combination of these, or a large slip weakening distance (Guatteri and Spudich, 2000). Variations in the strength parameter can yield variations in the rupture velocity, and for a rupture propagating into a high strength parameter region the rupture velocity would tend to be slower than normal (e.g. Day 1982). The fact that much of segment 1 continues to slip following the passage of the initial rupture front suggests that the frictional stress was not unusually high. If we assume that the frictional stress level is the same over the entire fault surface then the implication is that the yield and initial stresses varied over the length of the fault. This hypothesis is corroborated by the significantly different rupture velocity, and also the differences in the static stress drop on each of the segments. It thus appears that segment 1 represents failure of relatively strong region of the Lavic Lake Fault, an asperity (Lay and Kanamori, 1981) that once failed accumulated relatively large levels of slip. In Dreger and Kaverina (2000) the simulation of near-fault strong ground motions using a finite-source model derived from regional distance data was investigated. In that application, because of realtime computational considerations, a greatly simplified fault model was assumed. This model consisted of a single fault plane with the orientation from a regional distance seismic moment tensor solution, and constant dislocation rise time and rupture velocity. Nevertheless, Dreger and Kaverina (2000) demonstrated that it was indeed possible to simulate reasonable estimates of near-fault strong-ground motion, which were found to agree well with available nearfault observations that were not used to obtain the source model. Given what we now know about the considerable spatial and temporal complexity of the Hector Mine earthquake it is instructive to simulate the near-fault strong ground motions to compare with the results of the earlier study. Figure 8 compares the peak horizontal ground velocity (PGV) map in Dreger and Kaverina (2000) with a PGV map derived from the combined inversion results. The two simulations yield a comparable level of near-fault PGV. Both PGV models correlate well with the peak value observed at station HEC (37 cm/s; Figure 8), and also the station that registered 19.8 cm/s. Both models tend to under-predict the large values to the east (27.3 cm/s) and to the south (32. cm/s). These misfits are likely due to unaccounted for site amplification, or basin structure. Interestingly, the southward directivity on the Bullion Fault (segment 3; Figure 7) seems to elevate the PGV further to the south than in the preliminary model. Although the PGV maps differ in the near-fault details, the overall area that apparently experienced greater than 20 cm/s PGV is similar in the two simulations indicating that the preliminary map (Figure 8a), if rapidly determined, would have value in emergency response applications. Conclusions

10 10 A finite-fault source model for the 1999 Hector Mine earthquake has been obtained from the simultaneous inversion of seismic, GPS, SAR, and fault surface slip data. The preferred fault model consists of three fault segments to account for the reported geometric complexity of the faulting (Hauksson et al., 2002; Treiman et al., 2002). The overall length of the rupture on the three fault segments is approximately 42 km. Peak slip varies from 5.50 m in the seismic model to.84 m in the GPS-based solution, and the scalar moment of the geodetic solutions (7.0e19 8.1e19 Nm) is higher than the seismically derived estimate (.e19 Nm). The preferred scalar moment of.8e19nm was obtained from the combined inversion. We find that including the geometric complexity and allowing for temporal heterogeneity results in significant improvement, fitting an additional 38 percent of the data compared to a previously published fault model. Additionally, the inclusion of the multiple time windows to account for dislocation rise time and rupture velocity heterogeneity results in an additional 18 percent variance reduction over the case with the threesegment fault geometry and a single time window. The addition of geodetic data in the inversion provides a very important constraint on the spatial slip distribution, which allows the seismic data to resolve the temporal evolution of slip. The preferred model indicates that the Hector Mine earthquake had an anomalously low rupture velocity (1.8 km/s) on the Lavic Lake Fault (segments 1 and 2). Additionally, the western branch of the Lavic Lake Fault (segment 1) is seen to accumulate slip for several seconds following the passage of the initial rupture front, and dislocation rise times on this part of the rupture model range between 2.4 to 7.2 seconds. A southward rupture on the Bullion Fault (segment 3) initiates 9.8 seconds after the event origin time, has a higher rupture velocity (2.2 km/s), and the slip accumulates over a shorter interval of time displaying slip pulse behavior. This component of the rupture may explain the predominantly southward directivity obtained in the preliminary model of Dreger and Kaverina (2000). The differences in rupture velocity on the various fault segments suggest that the dynamic conditions of faulting varied over the fault surface. Finally, we find that the area of near-fault PGV greater than 20 cm/s simulated in Dreger and Kaverina (2000) is consistent with simulated PGV using the additional fault model complexity of the combined inversion. This illustrates that although greatly simplified, the near-realtime application of a coupled finite-source inversion and near-fault strong ground motion simulation, as proposed by Dreger and Kaverina (2000), is capable of providing near-fault strong shaking information under relatively sparse monitoring conditions that is of value in an emergency response context. Acknowledgements We thank Katherine Kendrick for providing the surface fault displacement data, Duncan Agnew for the GPS data, and the USGS, CDMG and Caltech for the TriNet and TERRAscope seismic waveform data used in this study. Drs. Susan Hough, Joan Gomberg and Michael Rymer provided helpful criticisms and comments that improved the final version of this paper. Some of the figures were made using Generic Mapping Tools (GMT) software (Wessel and Smith, 1991). This work was partially funded by a PGE/PEER Phase II contract (PGE-0095). This is a contribution number of Berkeley Seismological Laboratory. References

11 Abercrombie, R., and J. Mori (1994). Local observations of the onset of a large earthquake: 28 June 1992 Landers, California, Bull. Seism. Soc. Am., 84, Cohee, B. P, and G. C. Beroza (1994a). A comparison of two methods for earthquake source inversion using strong motion seismograms, Annali di Geofisica, vol.37, no., pp Cohee, B. P., and G. C. Beroza (1994b). Slip distribution of the 1992 Landers earthquake and its implications for earthquake source mechanics, Bull. Seism. Soc. Am., 84, Day, S. M. (1982). Three-dimensional simulation of spontaneous rupture: the effect of nonuniform prestress, Bull. Seism. Soc. Am., 72, Dreger, D. S., and D. V. Helmberger (1991). Source parameters of the Sierra Madre earthquake from regional and local body waves, Geophys. Res. Lett., Dreger, D. S., and D. V. Helmberger (1993). Determination of source parameters at regional distances with three-component sparse network data, J. Geophys. Res., 98, Dreger, D. S. (1994). Investigation of the rupture process of the 28 June 1992 Landers earthquake utilizing TERRAscope, Bull. Seism. Soc. Am., 84, Dreger, D. S. and A. Kaverina (2000). Seismic remote sensing for the earthquake source process and near-source strong shaking: a case study of the October, 1999 Hector Mine earthquake, Geophys. Res. Lett., 27, Freed, A.M, and J. Lin (2001). Delayed triggering of the 1999 Hector Mine earthquake by viscoelastic stress transfer, Nature, 411, Guatteri, M., and P. Spudich (2000). What can strong-motion data tell us about slip-weakening fault-friction laws?, Bull. Seism. Soc. Am., 90, Ji, C., Wald, D.J., and D. V. Helmberger (2000). Slip history of 1999 Hector Mine, California earthquake, Seism. Res. Lett., 71, 224. Ji, C., D. J. Wald, and D. V. Helmberger (2002). Source description of the 1999 Hector Mine, California earthquake. Part II: Complexity of slip history, Bull. Seism. Soc. Am., this issue. King, G. C. P., and J. L. Nabelek (1985). The role of bends in faults in the initiation and termination of earthquake rupture, Science, 228, Lay. T., and H. Kanamori (1981). An asperity model of large earthquake sequences, Maurice Ewing, Ser., 4, Hartzell, S. H., and T. H. Heaton (1983). Inversion of strong ground motion and teleseismic waveform data for the fault rupture history of the 1979 Imperial Valley, California, earthquake, Bull. Seism. Soc. Am., 73, Hauksson, E., L. M. Jones, K. Hutton (2002). The 1999 Mw7.1 Hector Mine, California earthquake sequence: Complex conjugate strike-slip faulting, Bull. Seism. Soc. Am., this issue. Parsons, T., and D. S. Dreger (2000). Static-stress impact of the 1992 Landers earthquake sequence on nucleation and slip at the site of the 1999 M=7.1 Hector Mine earthquake, southern California, Geophys. Res. Lett., 27, Peltzer, G., F. Crampe, and P. Rosen (1999). The Mw7.1, Hector Mine, California earthquake: surface rupture, surface displacement field, and fault slip solution from ERS SAR data, Eos Trans. AGU Fall Meet. Suppl., 80, 25. Pollitz, F.F., and I.S. Sacks (2002). Stress triggering of the 1999 Hector Mine earthquake by transient deformation following the 1992 Landers earthquake, Bull. Seism. Soc. Am., this issue. Pollitz, F.F., C. Wicks, and W. Thatcher (2001). Mantle flow beneath a continental strike-slip fault: Postseismic deformation after the 1999 Hector Mine earthquake, Science, 293,

12 12 Price, E. J., and R. Burgmann (2002). Interactions between the Landers and Hector Mine, California, earthquakes from space geodesy, boundary element modeling, and time-dependent friction, Bull. Seism. Soc. Am., this issue. Saikia, C. K. (1994). Modified frequency-wave-number algorithm for regional seismograms using Filon s quadrature - modeling of L(g) waves in eastern North America, Geophys. J. Int., 118, Sandwell, D.T., L. Sichoix, D. Agnew, and J. Minster (1999). Near-real-time radar interferometry of the Mw 7.1 Hector Mine Earthquake, Eos Trans. AGU Fall Meet. Suppl, 80, 257. Scholtz, C. H. (1990). The mechanics of earthquakes and faulting, Cambridge University Press, pp 439. Scientists from USGS, SCEC, CDMG (2000). Preliminary report on the October 1999 M7.1 Hector Mine, California, earthquake, Seism. Res. Lett., 71, Simons, M., Y. Fialko, C. Ji, M. Pritchard, P. Rosen (1999). Analysis of surface deformation from the M7.1 Hector Mine, CA earthquake of 10//99, Eos Trans. AGU Fall Meet. Suppl., 80, 258. Somerville, P.G., N.F. Smith, R.W. Graves, and N.A. Abrahamson (1997). Modification of empirical strong ground motion attenuation relations to include the amplitude and duration effects of rupture directivity, Seism. Res. Lett., 8, Treiman, J. A., K. J. Kendrick, W. A. Bryant, T. K. Rockwell, and S. F. McGill (2002). Primary surface rupture associated with the Mw7.1, October, 1999 Hector Mine earthquake, San Bernardino County, California, Bull. Seism. Soc. Am., this issue. Wald, D. J. and T. H. Heaton (1994). Spatial and temporal distribution of slip for the 1992 Landers, California, earthquake, Bull. Seism. Soc. Am., 84, Wald, D. J., and R. W. Graves (2001). Resolution analysis of finite fault source inversion using 1D and 3D Green's functions, Part II: Combining seismic and geodetic data, J. Geophys. Res., 10, pp Wang, H. and D.D. Jackson (2001). Stresses on the Hector Mine fault from tectonics, co-seismic stress, and viscoelastic relaxation, Eos Trans. AGU Fall Meet. Suppl., 81, 149. Wessel, P., and W. H. F. Smith (1991). Free software helps map and display data, EOS, Yagi, Y. and M. Kikuchi (1999). Preliminary results of rupture process for the October, 1999 Hector Mine earthquake, Zebker, H.A., P. Segall, F. Amelung, and S. Jonsson (1999). Slip distribution of the Hector Mine earthquake inferred from interferometric radar, Eos Trans. AGU Fall Meet. Suppl., 80, 258. Figure captions Figure 1. A) General location map showing the area of study B) Location map showing the hypocenter (unfilled star) and fault trace of the 1992 Landers earthquake, the hypocenter (filled star) and fault trace of the 1999 Hector Mine earthquake, and the seven broadband stations (filled triangles) used in this study. C) Expanded view of the Hector Mine source region showing, the epicentral region, aftershocks reported in the CNSS catalog, which occurred in the first 3 months after the event, and the location of surface faulting (thick gray line) (K.Kendrick, personal communication, 2000; Treiman et al., 2002). The surface projection of our three-segment fault model is shown. The top edges of segment 1, the southern part of segment 2 and segment 3 were aligned to the surface faulting. The three fault segments have the same eastward dip.

13 13 Figure 2. Slip distribution obtained by separate inversions of seismic (A), GPS (B), and SAR (C) data. Hypocenter is marked with a star. The gray scale shows the range in slip in centimeters. The size of the symbols represent the subfault dimension of 2 km. Figure 3. Data fits for the individual seismic, GPS and SAR inversions. A) Comparison of three-component, broadband displacement waveform data (black) and synthetics (red) at seven stations; B) Comparison of observed (black) and predicted (red) GPS displacement vectors. A 1 meter displacement is shown in red for reference; C) Comparison of observed (left) and predicted (right) interferometric images. The color scale gives line of sight change in millimeters. Figure 4. A) Tradeoff curves of relative GPS to SAR weighting and smoothing weight for a simultaneous inversion of geodetic data. B) Tradeoff curves for the combined seismic geodetic data inversions. The arrow indicates the preferred weighting. Variance reduction is given on the left axis and smoothing weight on the right axis. The legend for both plots is shown on the left. Figure 5. Combined inversion data fits. A) Comparison of three-component, broadband displacement waveform data (black) and synthetics (red) at seven stations; B) Comparison of observed (black) and predicted (red) GPS displacement vectors. A 1 meter displacement is shown in red for reference; C) Comparison of observed (left) and predicted (right) interferometric images. The color scale gives line of sight change in millimeters. Figure. Preferred inversion results for the combined inversion. The hypocenter is marked with a star. The individual subfault slip is shown according to the grayscale bar. A) 3D representation of the slip model. The bold numbers refer to the fault segments discussed in the text. B) A 2D representation of the slip model. Figure 7. Snapshots of the rupture evolution for the combined inversion. The hypocenter is shown in each panel as a star. The arrows show the lateral extent of each of the fault segments. The time period after the origin time is given inside the segment 1 panels. For windows that display the characteristics of a propagating rupture the apparent rupture velocity is shown. Figure 8. Comparison of peak horizontal ground velocity (PGV) from A) Dreger and Kaverina, (2000), and B) from the combined slip model of this study. The epicenter (star) and surface trace of faulting (bold line) are shown in each plot. The numbers indicate observed PGV in units of cm/s from unfiltered TriNet data. Predicted PGV are shown as contours, where the first is 20 cm/s and subsequent contours are for increasing intervals of 20 cm/s. The maximum frequency of the synthetic seismograms used to construct these maps was 5 Hz.

14 35.0 California A) Lavic Lake Flt. km GSC HM Epicenter PAS SVD HEC DAN 34.5 DGR LN BC3 Bullion Flt. B) km Figure 1

15 Depth (km) Depth (km) B) A) ' 34 3' Seismic Data Only GPS Data Only SAR Data Only Depth (km) C) 34 3' Slip, cm

16 GSC E PAS N DAN V GSC N PAS V HEC V GSC V DGR E HEC E SVD E DGR N HEC N SVD N DGR V BC3 N SVD V DAN E BC3 E amplitude (cm) PAS E A) Seconds DAN N Seconds BC3 V Seconds Figure 3a

17 m B) Observed Simulated Line of Sight Change (mm) C) Figure 3bc

18 Data Var.Red Smoothing A) GPS weight SAR weight Legend SAR GPS Seismic Smoothing Weight Data Var.Red Smoothing *E B) Weight of (SAR + GPS) relative to seismic Figure 4

19 GSC E PAS N DAN V GSC N PAS V HEC V GSC V DGR E HEC E SVD E DGR N HEC N SVD N DGR V BC3 N SVD V DAN E BC3 E amplitude (cm) PAS E A) Seconds DAN N Seconds BC3 V Seconds Figure 5a

20 m B) Observed Simulated Line of Sight Change (mm) C) Figure 5bc

21 Depth (km) A) ' North Segment Slip, cm Segment 2 Depth (km) Segment 3 South B) Distance along strike (km) Figure

22 Depth (km) Segment 1 Segment 2 Segment km/s 3-5 sec 5-7 sec 7-9 sec 9-11 sec sec sec sec sec sec sec Distance along strike (km) 2.0 km/s 2.2 km/s Slip, cm Figure 7

23 A) B) Figure 8