U.S. Geological Survey, 525 South Wilson Avenue, Pasadena, California 91106
To appear in Journal of Physics of the Earth
Near-source ground motions, teleseismic body waveforms, and geodetic displacements produced by the 1995 Kobe, Japan, earthquake have been used to determine the spatial and temporal dislocation pattern on the faulting surfaces. A linear, least-squares approach was used to invert the data sets both independently and in unison in order to investigate the resolving power of each data set and to determine a model most consistent with all the available data. A two-fault model was used, with a single rupture plane representing faulting beneath Kobe and a second plane representing slip underneath Awaji Island. The total seismic moment is estimated to be 2.4 x 1026 dyne-cm (Mw 6.9), with rupture partitioned such that about 40% of the slip was relatively deep (5-20 km) and northeast of the epicenter toward Kobe, and about 60% was toward the southwest and shallower (mostly 0-10 km) beneath Awaji Island. Analysis of the slip model indicates that the ground motions recorded within the severely damaged region of Kobe originated from the region of relatively low slip (about 1 meter) deep beneath Kobe and not from the shallow, higher slip regions (about 3 meters) beneath Awaji Island. Although the slip was relatively low beneath Kobe, the combined effects of source rupture directivity, a short slip duration, and site amplification conspired to generate very damaging ground motions within the city.
1. Introduction
The extensive damage and loss of life due to the Kobe, Japan, earthquake of January 17, 1995 provided a harsh reminder of the very destructive nature of strong ground motions. Peak ground velocities recorded during this event rival those recorded in any other earthquake. In this report, I have modeled near-source ground motions, teleseismic body waveforms, and geodetic displacements to determine the overall dislocation pattern on the fault surfaces. The fault parameterization involves a variable-slip, multiple-segment, finite-fault model that treats the diverse data sets in a consistent manner, allowing them to be inverted both independently and in unison. The model provided herein is a working model for on-going seismological studies and for an assessment of the relationship between damage and fault slip. Improvements to the results presented here will be made as additional strong-motion data is released, and refined earth structure models for the Kansai region are developed, allowing for more accurate representation of the local and regional wave propagation.
2. Data and Initial Preliminary Analysis
2.1 Strong Motion and Teleseismic Data
Strong motion data from the Kobe earthquake were provided in digital form by the Japan Meteorological Agency (JMA) and by Toki et al. (1995) from the Committee of Earthquake Observation and Research in the Kansai Area (CEORKA). I scanned and digitized additional data provided in a report by Nakamura (1995) from the Japan Railway (JR). The locations of the near-source strong motion stations are shown in Figure 1. Adjacent to selected stations, I also show the low-pass filtered (1 Hz) velocity recordings, rotated into the direction that produces the maximum velocity. This rotation angle is indicated with a line through the station symbol. The largest velocity recording is at Takatori (TAK), which is located in one of the regions of JMA Intensity 7 (shaded regions, (Fig. 1) within the city of Kobe. Unfiltered, the peak ground velocity of the fault normal component at TAK is about 176 cm/sec. For comparison, the highest peak ground velocity recorded during the 1992 Northridge, California, earthquake was about 183 cm/sec at the Rinaldi Receiving Station ( Wald et al., 1996). Note that the largest motions at TAK are nearly normal to the fault strike direction (Fig. 1), consistent with a near-source, SH directivity pulse from strike-slip faulting. Similar observations have been documented for a number of other earthquakes over the last few decades (Somerville and Graves, 1993; Hall et al., 1995).
Although no ground motions were recorded on the northern part of Awaji Island (Fig. 1), ground motions there were probably severe. The percentage of damaged buildings on the northwestern portion of the island is even higher than in all portions of the city of Kobe (Comartin et al., 1995) and the JMA intensity was 7 in several locations (Fig. 1). The one ground motion recording made on Awaji Island, station AWA on the central part of the island (Fig. 1), is quite distant from the fault rupture, and unfortunately, the north component at AWA malfunctioned; this component was not used in the inversion. Similarly, north components at stations AID, AIO, MIN, SAK, and WAC malfunctioned and were not used, but I compute and display the predicted ground motions there from modeling the other data. Further, the east component at station TAZ and the vertical component at KBU are contaminated by long-period noise, so this component was not used.
I also include strong motion data from more distant stations (Fig. 1, inset) to improve the azimuthal coverage of the source. In the Osaka area, numerous recordings were made in addition to those shown, so I chose representative sites. The stations used in the inversion are listed in Table 1. Between 30 and 35 seconds of all three components of ground velocity (bandpass filtered from .05 to 0.5 Hz) are modeled at each site. Several near-fault stations (AWA, KBU, KOB, NIS, TAZ, and TAK) are doubly weighted in the inversion with respect to other stations since the wave propagation to the closer stations is more adequately modeled with a simplified velocity model, and several of these sites represent heavily damaged regions.
The teleseismic stations used in this study, recorded by the Incorporated Research Institutions for Seismology (IRIS) network, are listed in Table 2. Their distribution also provides a distributed azimuthal coverage of the source (Fig. 2). Fifty seconds of the broadband P and SH velocity records, low-pass filtered at 0.5 Hz, are modeled.
2.2 Geodetic Data
The geodetic data consist of GPS (Global Positioning System) and leveling-line resurvey data (Fig. 3) made available by Hashimoto et al. (1995). The GPS data is a combined set of data from both continuous recording and campaign-type surveys. As with the strong motion data, the station coverage on Awaji Island is not particularly dense, but station G5 (Fig. 3) indicates about one meter of right-lateral displacement to the southeast, which places an important constraint on the amount of shallow slip along the northeast portion of the Nojima fault. Overall, the pattern of geodetic movement (Fig. 3) indicates that the largest horizontal displacements are on Awaji Island, suggesting either greater and/or shallower slip beneath Awaji Island than under the city of Kobe. Further, the fault location within the area of southernmost Kobe is well constrained by the leveling data. The vertical projection of the fault surface must be very near leveling station number 30 (Fig. 3) and certainly between station numbers 29 and 31.
Even though the faulting during the Kobe earthquake was primarily right-lateral strike slip, the leveling uplift data (Fig. 3, inset) along thttp://www.scecdc.scec.orgire uplift of the northwest side of the fault relative to the southeast. Although this is opposite in the sense of uplift along the fault surface trace on Awaji Island where, on average, the southeast side moved up relative to the northwest side (Sugiyama et al., 1995), the uplift along both faults reflects the long term pattern seen in the local geomorphology. Hence, the vertical component of the rake vectors along the fault northeast and southwest of the epicenter may be expected to differ.
3. Inversion Methodology
The fault parameterization and inversion procedure is after Hartzell and Heaton (1983). The multiple finite fault, combined data set inversion procedure I employ is more fully described in ( Wald and Heaton (1994). In this study, faulting during the Kobe earthquake is represented with two nearly vertical fault planes (Fig. 1), abutting each other at depth and dipping in opposite directions. The southwestern plane is 20 km long, strikes 45 degrees, dips 80 degrees toward the southeast, and represents slip along the Nojima fault. The northeastern plane is 40 km long, strikes 50 degrees and dips 85 degrees to the northwest, representing slip on the Suma and Suwayama faults. Both faults extend from the surface to a depth of about 20 km.
These planes were chosen based on the location of surface faulting on Awaji Island, the location of mapped faults in Kobe (Fig. 4), aftershock seismicity (Fig. 3) and consideration of the static displacements (Fig. 3) discussed above. Note that the width of aftershock zone in map view is narrower on the Kobe side than the Awaji Island side, consistent with a steeper dip to the northeast fault segment. Rupture begins at a depth of 17 km, approximately where the fault planes intersect at depth, and propagates bilaterally outward at an assumed rupture velocity of 2.8 km/sec (about 80% of the local shear velocity). The faults are discretized into 96 subfaults for the Kobe segment and 48 subfaults for the Nojima segment.
Each subfault's motion is obtained by summing the responses of 25 point sources uniformly distributed over each subfault. Each point source is lagged appropriately in time to include the travel-time difference due to the varying source-to-station positions and to simulate the propagation of the rupture front across each subfault. Thus, all subfaults separately include the correct effects of directivity. Complete local synthetic seismograms are generated using a frequency-wavenumber algorithm (Saikia, 1994) for two one-dimensional velocity structures (Table 3) which were based on the work of Pitarka et al. (1995). In practice, I calculate a master set of synthetics for 1 km increments in depth from 0.2 to 22.0 km and for ranges between 0 and 160 km, to allow for the closest and farthest possible subfault-station combinations. Then for each point-source station pair, the required response is derived by a linear interpolation of the closest Green's functions available in the master set. The linear interpolation of adjacent Green's functions performed by aligning the waveforms according to their shear-wave travel times.
The strong motion stations were grouped into either the "rock" or deep "soil" category, (Table 3) to differentiate the shallow conditions at the sites. I considered stations ABN, KAK, KOB, SHI, SKI, TAK, TAZ, and TDO to be deep soil sites. Since there is clear evidence for soil non-linearity at some sites that recorded the mainshock (e.g., Aguirre and Irikura, 1995), I low-pass filtered the data at 2 seconds to minimize this problem. Even so, due to concern over possible (unmodeled) contamination due to nonlinear soil behavior at stations KOB and TAK, their contribution to the solution was examined by removing these stations from the inversion. There was little change in the overall solution, indicating that these individual stations do not strongly controls the solution. The recorded strong motions in the Osaka region indicate waveform complexity introduced from wave propagation through the deep Osaka basin; more realistic Green's functions will be needed to refine the modeling at these stations.
The subfault slip time history is modeled using six time windows, each 0.4 sec apart. The displacement in each window is represented by the integral of a 0.7 sec isosceles triangle. Hence, the time windows partially overlap. As discussed above, preliminary analysis of the surface offset and geodetic data indicates a significant difference in the slip direction northeast and southwest of the epicenter. Variable rake is permitted by solving for the relative amounts of 135 degrees and 225 degrees components of slip on each subfault. I use a constrained, damped, linear least-squares inversion to determine the amount of slip on each subfault and in each time window that minimizes the difference between the observed and synthetic observations. The fault parameterization is identical for the strong motion, teleseismic, and geodetic inversions; only the Green's functions change.
4. Inversion Results
In this section, I first present the results of the source inversions of the individual data sets (strong motion, teleseismic, and geodetic) followed by a discussion of a joint inversion of the three data sets combined. The resulting dislocation models are presented in Figures 5a, 5b, 5c, and 5d, respectively.
4.1 Strong Motion Inversion
The results of the strong motion inversion is shown in Figure 5a, a summary of the slip parameters is given in Table 4, and the corresponding observed and synthetic velocity waveforms are presented in Figure 6. The dislocation pattern can be characterized by two main regions of relatively deep slip beneath Kobe reaching a maximum slip of over one meter, and a more complicated pattern of slip beneath Awaji Island, including a substantial amount of shallow slip with a peak slip value approaching 3 meters. The pattern of rake vectors (Fig. 5a) indicates that the slip direction differs slightly from the Nojima segment to the Suma/Suwayama segment. The average rake on the Nojima fault indicates slight uplift of the southeast side with respect to the northwest, consistent with both the observed surface offset and the local long-term uplift pattern. In contrast, the rake vectors beneath Kobe indicate uplift of the northwest side with respect to the southeast, again consistent with the local topography.
The overall fit to the waveforms is reasonable, though exceptions are notable. The vertical components at KOB and TAZ are not fit, suggesting a sensitivity to the exact location of the true P wave node at the surface. In order to resolve this, any non-planar nature of the fault surface must be considered in addition to variations in the take-off angles due to velocity structure complexities.
4.2 Teleseismic Inversion
The slip pattern resulting from the inversion of the teleseismic data is shown in Figure 5b; the corresponding velocity waveforms are shown in Figure 7. The overall slip pattern is similar to the strong motion model, though the average and peak slip is slightly greater (Table 4), and the ratio of slip on the Awaji side relative to the Kobe side is larger. The models have in common three subevents beneath Kobe and a high slip area along the shallow portion of the Nojima fault. Again, the average direction of slip is northwest down on the Nojima fault, and northwest up on the Kobe side (Fig. 5b).
4.3 Geodetic Inversion
The result of the inversion of the geodetic data alone is shown in Fig. 5c, and the corresponding comparison of the observed and predicted static displacements is displayed in Figure 3. In general, the horizontal and vertical displacements are recovered by the model, though there is a mismatch at station G11. It is likely that shallow ground disruption in this vicinity is responsible for this mismatch.
The overall pattern of slip direction and the depth extent of the faulting determined from the geodetic data are similar to both the strong motion and teleseismic models. Even in detail, the pattern of slip along the Nojima fault is in agreement with the strong motion model. However, on the Kobe side, since the geodetic data cannot resolve detailed slip variations at depth, and the overall average amount of slip is relatively small and deep, a fairly smooth pattern is sufficient to match the geodetic observations. In contrast, a more heterogeneous slip is necessary to fit the waveform data as seen in Figures 5a and 5b.
Even though the coverage of geodetic stations over the Kobe region is fairly dense, it is difficult to constrain the exact up-dip projection of the rupture surface. This is likely due to failure of the assumption that the plane that ruptured at depth can be continued to the surface when, in fact, the fault surface need not be perfectly planar. Fortunately, tests of minor changes in the exact location of the surface projection that I have performed for each of the data sets indicated that the overall slip pattern is robust with respect to such changes. I attribute this to the fact that most of the slip is deep beneath Kobe, and the number of stations insensitive to the exact surface location is large enough to provide stability to the overall solution.
4.4 Combined Inversion
For the combined inversion, we determined the relative weighting of the three data sets by a trial-and-error process. Initially the data sets were equally weighted, and I then varied the weights such that the increased misfit to each data set was comparable.
The combined waveform and geodetic model (Fig. 5d) shares features of all three models, preserving the very shallow concentration of slip on the Nojima fault found in the geodetic model, yet keeping the more detailed features of the waveform models on the Suma/Suwayama faults, as constrained by the near-source strong motion recordings. The total seismic moment of the combined model is 2.4 x 1026 dyne-cm and the peak slip is over 3 meters (Table 4). In general, the matches to the observed strong motion and teleseismic waveforms (Fig. 8 and (Fig. 9, respectively) and static displacements (Fig. 10) are only slightly degraded when compared with the separate inversions when a compromise solution is obtained. Since the combined solution is compatible with the most data, further analysis is based on this model.
5. Discussion
As a check on the model assumptions used above, I tested inversions with a number of variations to the assumed parameters. A three segment model was tried by dividing up the Kobe fault segment into two separate planes with a right step toward the northeast between the them. The resulting slip patterns were nearly identical to the two segment model used here, so the added complexity of the third fault was not deemed necessary. Further complexity of the faulting geometry was not further pursued. I also tested rupture velocities ranging from 2.5 to 3.2 km/sec. Although rupture velocities higher than 2.8 km/sec give a marginally better fit to the strong motion waveforms, the resulting slip patterns from both waveform data sets were less compatible with the independent geodetic slip pattern.
In order to examine the relative importance of slip on different portions of the rupture planes for contributing to the ground motions at different station locations, I decomposed the subfault contributions to the synthetic strong motions. Figure 11 shows comparisons of the observed strong motions with synthetic waveform contributions from both faults combined, the rupture beneath Kobe (Suma/Suwayama faults), the Nojima fault, and the shallowest row of subfaults along the Nojima fault. Nearly all of the simulated ground motion at KOB is due to the rupture beneath Kobe; only a small contribution comes from rupture along the Nojima fault. This is true at all the stations within Kobe as well as TDO. In contrast, at AWA on Awaji Island, the contribution from the Nojima fault is dominant over the northeastern portion of the rupture. Similarly, OKA is comprised of energy contributed almost entirely from the Nojima fault. Station NIS is at a location equally sensitive to slip on the two fault segments and the total synthetic waveform there is made up of a complex interference of arrivals contributed from both the northeast and southwest portions of the rupture. The last column of Figure 11 indicates the contribution to the synthetics from the shallow Nojima fault. At most stations this contribution is relatively small in amplitude, suggesting that while it certainly contributes to the final solution, it does not represent a major portion of the final synthetic seismograms.
Figure 12 depicts the slipping portion of the fault for the combined model and the amount of slip during 1-sec "slices" in time; hence, the images can be thought of as slip velocity. For regions of deep slip, the local slip duration is less than about 1.5 sec, whereas the total rupture duration is over 10 sec. However, the slip along the shallow portion of the Nojima fault had a substantially longer duration (at least 3 sec) as seen during the rupture times between about 5-9 sec ((Fig. 12). It is not clear whether this actually represents a slower rupture velocity, a longer slip duration, or both and as discussed above, this feature may not be particularly well resolved since the overall contribution to the ground motions is not great. However, this long duration for shallow slip is a consistent feature in all inversion runs and a similar relationship among slip duration, rupture velocity, and depth was noted by Wald et al., 1994) for the 1992 Landers earthquake. A comparison of the Kobe slip distribution with other recent earthquakes in California is shown in Figure 13. By displaying the dislocation patterns on the same scale it becomes easy to visualize how slip and rupture dimensions scale with magnitude, and to examine the relative degree of heterogeneity for different events. The Kobe rupture is slightly larger than the comparable-sized Loma Prieta earthquake but has smaller average slip amplitudes. Surprisingly, the region of the fault that generated the damaging ground motions in Kobe has only about 1 meter of slip, substantially less than the source of damaging ground motions for the Northridge or Loma Prieta earthquakes.
The models presented here share similar features with rupture models determined by other investigators from subsets of the data used in this analysis. Sekiguchi et al. (1995), recovered many similar features in their slip model determined from strong motion data; similarly, Ide and Takeo (1995) modeled mostly distant strong motions and also found over two meters of shallow slip on the Nojima fault, and predominantly deep slip on the fault rupture beneath Kobe. Two notable features common in these two models and this study are the small amount of slip directly beneath the city of Kobe and the relatively long duration of slip in the shallow portion of the Nojima fault. Kikuchi (1995), using teleseismic body waves, found a bilateral subevent at the hypocenter with two subevents to the northeast, corresponding to the first two subevents on the Suma Fault in my waveform models. Finally, the geodetic modeling of Hashimoto et al. (1996) indicates similar relative slip directions northeast and southwest of the epicenter and comparable relative slip depths. As does this study, Yoshida et al. (1996) present results of a joint inversion of near- and far-field waveforms, in addition to the geodetic data. Although the faulting geometry used in both studies is quite similar, the inversion methodologies used are quite different. Nonetheless, the resulting slip models from the individual data sets and the combined data set share many similarities. One notable difference, however, is in the total amount of slip found beneath Kobe: I find just over a meter of slip whereas Yoshida et al. (1996) require a peak slip near 2.5 meters. This may be in part due to the larger amplification within the shallow velocity structure I used, relative to the (faster) shallow velocity structure used by Yoshida et al. (1996).
6. Conclusions
A relatively simple, two-fault model was used to represent faulting under Kobe and Awaji Island. The total seismic moment is estimated to be 2.4 x 1026 dyne-cm (Mw 6.9) and the peak slip reached over 3 meters. Rupture is partitioned such that about 40% the slip was relatively deep (mostly 5-20 km) and northeast of the epicenter toward Kobe, and more than half the slip was to the southwest and shallower (mostly 0-10 km) beneath Awaji Island. There are strong similarities among the strong motion, teleseismic, and geodetic models, though they are derived from independent data sets. Each model requires predominantly deep (5-20 km) slip on the Suma fault beneath Kobe, where no surface trace was found and shallow slip on the Nojima fault, where the surface offset reached almost two meters.
Many of the largest velocity recordings made during the Kobe earthquake are within the densely populated regions of the city. In contrast, the largest velocity recordings in the 1994 Northridge, California, earthquake were made well north of the more densely populated areas of the San Fernando Valley ( Wald et al., 1996). Likewise, the largest ground velocities produced during the 1989 Loma Prieta, California, earthquake were only experienced in remote areas northwest of the epicenter and not in the urban areas of San Francisco (Wald et al., 1990; Wald et al. (1991). This difference in the location of the largest peak ground velocities with respect to the heavily urbanized areas is one primary reason for the much greater damage that occurred in Kobe compared with the damage from the Loma Prieta and Northridge earthquakes.
Examination of the simulated ground motion reveals that the source contribution to the most damaging ground motion in Kobe is from the relatively low slip beneath Kobe and not from regions of greater slip on Awaji Island. This can be attributed to the additional distance to the large slip regions on Awaji Island, shorter slip durations on slip beneath Kobe (relative to the Nojima fault slip), and the direction of rupture with respect to Kobe. Rupture on Awaji was directed away from Kobe, radiating more energy away from the city; rupture beneath Kobe was both upward and toward the city, concentrating shear arrivals in time and resulting in larger velocity pulses. These pulses were, of course, further amplified within the soft sediments beneath the heavily damaged portion of the city (e.g., Iwata et al., 1995).
ACKNOWLEDGMENTS
The data used in this study were provided by K. Toki, K. Irikura, and Y. Iwasaki of CEORKA, S. Mori of JMA, and Y. Nakamura of JR. M. Hashimoto kindly provided the geodetic data used in this analysis. Aftershock data was provide by A. Pitarka from H. Nemoto. I benefited greatly from conversations with W. Ellsworth, T. Heaton, S. Ide, K. Irikura, Y. Kinugasa, A. Pitarka, T. Sato, H. Sekiguchi, P. Somerville, and M. Takeo. Preprints provided by M. Hashimoto, S. Ide, A. Pitarka, and H. Sekiguchi were particularly helpful.
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