Site Response, Shallow Shear-Wave Velocity, and Wave Propagation at the San Jose, California, Dense Seismic Array

Transcription

1 Bulletin of the Seismological Society of America, Vol. 93, No. 1, pp , February 2003 Site Response, Shallow Shear-Wave Velocity, and Wave Propagation at the San Jose, California, Dense Seismic Array by Stephen Hartzell, David Carver, Robert A. Williams, Stephen Harmsen, and Aspasia Zerva Abstract Ground-motion records from a 52-element dense seismic array near San Jose, California, are analyzed to obtain site response, shallow shear-wave velocity, and plane-wave propagation characteristics. The array, located on the eastern side of the Santa Clara Valley south of the San Francisco Bay, is sited over the Evergreen basin, a 7-km-deep depression with Miocene and younger deposits. Site response values below 4 Hz are up to a factor of 2 greater when larger, regional records are included in the analysis, due to strong surface-wave development within the Santa Clara Valley. The pattern of site amplification is the same, however, with local or regional events. Site amplification increases away from the eastern edge of the Santa Clara Valley, reaching a maximum over the western edge of the Evergreen basin, where the pre-cenozoic basement shallows rapidly. Amplification then decreases further to the west. This pattern may be caused by lower shallow shear-wave velocities and thicker Quaternary deposits further from the edge of the Santa Clara Valley and generation/trapping of surface waves above the shallowing basement of the western Evergreen basin. Shear-wave velocities from the inversion of site response spectra based on smaller, local earthquakes compare well with those obtained independently from our seismic reflection/refraction measurements. Velocities from the inversion of site spectra that include larger, regional records do not compare well with these measurements. A mix of local and regional events, however, is appropriate for determination of site response to be used in seismic hazard evaluation, since large damaging events would excite both body and surface waves with a wide range in ray parameters. Frequency wavenumber, plane-wave analysis is used to determine the backazimuth and apparent velocity of coherent phases at the array. Conventional, high-resolution, and multiple signal characterization f-k power spectra and stacked slowness power spectra are compared. These spectra show surface waves generated/ scattered at the edges of the Santa Clara Valley and possibly within the valley at the western edge of the Evergreen basin. Introduction In recent years, initial 3D velocity models have been developed for some important urban areas in the western United States that are exposed to significant seismic hazard (Brocher et al., 1997; Magistrale et al., 2000; Frankel and Stephenson, 2000). Each of these regions is characterized by sediment-filled basins. In order to quantify the seismic risk in each of these areas, it is necessary to understand the wave propagation characteristics of these basins. Advances in this area can be made by theoretical modeling and by studying ground-motion records from the basins in question. Each of these lines of investigation complements the other. Better ground-motion data allow the validation and improvement of velocity models and better velocity models allow more accurate prediction of ground motions. In general, alluvial basins can affect ground motion in the following ways: (1) amplification by low-velocity surface sediments, (2) resonances induced by impedance contrasts in the sedimentary layers, (3) surface-wave generation by conversion of shear waves at the basin edges, and (4) focusing and turning of rays by the 3D geometry of the basin. These effects lead to higher-amplitude, longer-duration shaking, particularly at longer periods. Significant early 2D basin modeling includes work by Aki and Larner (1970) and Bard and Bouchon (1980a,b, 1985). These studies showed the generation of surface waves at the edges of basins and the propagation of these waves 443

2 444 S. Hartzell, D. Carver, R. A. Williams, S. Harmsen, and A. Zerva back and forth within the shallow deposits, as well as the development of resonance modes in deeper basins. Twodimensional simulations, stressing the significance of surface waves, have been used to explain observed ground motions for the 1971 San Fernando earthquake (Vidale and Helmberger, 1988), the 1985 Mexico City earthquake (Kawase and Aki, 1989), and basin resonances in Garm, Tadjikistan (Bard and Bouchon, 1985). Two-dimensional modeling has also been used to investigate focusing/diffraction effects from basin structure for the 1994 Northridge earthquake (Alex and Olsen, 1998; Graves et al., 1998) and basin edge effects for the 1995 Kobe earthquake (Kawase, 1996). Three-dimensional simulations of ground motion in simple, symmetric basins have been used to illustrate resonant modes (Rial, 1989). Scenario earthquake rupture models in 3D velocity media, including basin structures, have been used to evaluate ground motion in the Santa Clara Valley, California (Frankel and Vidale, 1992; Harmsen and Frankel, 2001), the San Bernardino Valley, California (Frankel, 1993), the Los Angeles basin (Olsen et al., 1995; Graves, 1998; Hartzell et al., 1999; Olsen, 2000), and the Seattle basin, Washington (Frankel and Stephenson, 2000; Hartzell et al., 2002). Basin effects have been attributed for areas of elevated ground motion and damage in 3D modeling of the Kobe earthquake (Pitarka et al., 1998). Previously, Frankel et al. (1991) used a small triangular array to study ground motion in the Santa Clara Valley from aftershocks of the Loma Prieta earthquake. They concluded that the long-duration velocity and displacement records are composed of mainly surface waves formed at the edges of the basin. They also observed backazimuths considerably different from the source, implying scattering from different parts of the basin. Stidham et al. (1999) used a simplified 3D velocity model for the San Francisco Bay region and simulated the 1989 Loma Prieta rupture. They found amplified ground motion within sedimentary basins compared to a 1D velocity model. Harmsen and Frankel (2001) used an improved 3D velocity model for the area (Brocher et al., 1997) and simulated ruptures on the Hayward fault. They found that low-velocity sediments near the surface can significantly amplify ground motion at long wavelengths compared to the thickness of the layer and that standard strongmotion attenuation relationships do not adequately represent ground motion in the alluvial basin environment. Fletcher et al. (2002) analyzed data from 40 stations distributed across the Santa Clara Valley to investigate basin structure and site response. They found travel times to be consistent with the existence of the deeper Cupertino basin to the west and the Evergreen basin to the east within the Santa Clara Valley but slower than those predicted by the Brocher et al. (1997) velocity model. Amplification factors below 2 Hz were found to be a factor of 1.5 to 3 higher over these deeper basins. Hartzell et al. (2001) used aftershocks of the Loma Prieta earthquake to calculate site response in Los Gatos on the western edge of the Santa Clara Valley. They concluded that a complex pattern of alluvial sediment thickness contributed to the variability in site response and the presence of resonance peaks between 2 and 7 Hz. Frankel et al. (2001) analyzed data from the San Jose dense seismic array. Their spectral ratios reveal larger amplitudes for stations further from the edge of the Santa Clara Valley and above the western edge of the Evergreen basin. Late-arriving surface waves from events to the east were found to move from south to north across the array and possibly originate from converted S waves at the southern border of the Santa Clara Valley. In this article, we examine ground-motion records from local and regional events recorded on the San Jose, California, dense seismic array. Our interests lie with the variation in site response across the array and its structural causes, as well as, the wave propagation characteristics of the basin for sources at different azimuths. Because of new data, we are able to use an earthquake data set of over twice as many events as previous studies. A formal source/site spectral inversion is applied to the ground-motion data for the first time. The resulting site response spectra are then inverted for the shear-wave velocity structure using an improved global search algorithm. These shear-wave velocities are compared with independently derived velocities from seismic reflection/refraction. Finally, plane-wave propagation is investigated using f-k power spectra. Array Configuration and Data The San Jose seismic array is located near the eastern edge of the Santa Clara Valley south of the San Francisco Bay (Fig. 1). The Santa Clara Valley is bounded on the west by the San Andreas fault and associated northeast-vergent Berrocal, Shannon, Monte Vista, and Sargent faults. On the east, the Santa Clara Valley is bounded by the Hayward and Calaveras faults. Two main structural basins, identified in gravity data (Brocher et al., 1997), are found within the valley, the Cupertino basin on the west side and the Evergreen basin on the east side. The pre-cenozoic basement depth in these basins is estimated to be 4 7 km. The basins are filled with lower Miocene sandstones of the Temblor Formation, overlain by the Monterey Formation composed of largely siliceous, marine shales of Miocene age. These rocks are overlain by Pleistocene and Holocene alluvial-fan, stream, and basin-fill deposits (McLaughlin et al., 1999). The array was sited over the Evergreen Basin in part to evaluate the effects that this basin may have on wave propagation. Frankel et al. (2001) gave a detailed description of the array configuration. Briefly, the array currently consists of the 52 sites listed in Table 1. Each site has a K2 digital recorder with a sample rate of 100 samples per second and a three-component Episensor force-balance accelerometer. This sensor has a flat response at low frequencies, which allows us to analyze longer-period ground motion (greater than 1 sec). The average station spacing is about 1 km. All of the stations lie on alluvium in the Santa Clara Valley, except for two sites on mapped Mesozoic rock in the hills east of the valley.

3 Site Response, Shallow Shear-Wave Velocity, and Wave Propagation at the San Jose Dense Seismic Array 445 San Francisco Bay CALAVERAS BERROCAL SAN ANDREAS Basement elevation (km) Cupertino MONTEVISTA Basin SILVER CR. Evergreen Basin SJ ARRAY Km Figure 1. Area map of the San Jose array (black dots) with Quaternary deposits and major faults in bold red lines. Contours (0.5-km intervals) to the depth of the pre- Cenozoic basement are indicated by the light red lines and reveal the locations of the Cupertino basin on the western side of the Santa Clara Valley and the Evergreen basin on the eastern side. The black star and dashed line indicate the locations of a synthetic source and line of receivers, respectively, shown in Figure 9. Mesozoic rock is shown in white. Qhf: Holocene alluvial-fan deposits, Qhf1 (younger), Qhf2 (older). Qhff, finegrained Holocene alluvial-fan deposits; Qhbm, Holocene San Francisco Bay mud; Qhl, Holocene alluvial-fan levee deposits; Qf, Latest Pleistocene to Holocene alluvial-fan deposits; Qpf, Latest Pleistocene alluvial-fan deposits; QTsc, Santa Clara Formation, Pleistocene, and Pliocene. Modified from Knudsen et al. (2000). This study uses ground-motion data from the 24 events listed in Table 2. The locations of these sources are shown in Figure 2a and b. The data consist of both local and regional earthquakes ranging in magnitude from 2.5 to 7.1. There are several smaller events (magnitude ) from the Calaveras fault zone east and southeast of the array and the from San Andreas fault zone further to the south. Events to the north include sources around the San Francisco Bay. Larger, regional events are from the Mammoth Lakes area, California, near Scotty s Junction, Nevada, and the Hector Mine earthquake in southern California. Site Response Using the source/site spectral inversion method of Hartzell (1992), we have inverted for site amplification factors at the array stations. After correcting for path effects and taking the logarithm (base 10) to obtain a linear expression, the observed ground-motion spectral amplitudes U(f) may be expressed as the sum of a source term S(f) and a site term R(f), for source i, site j, and frequency k, as log S (f ) log R (f ) log U (f ). i k j k ij k

4 446 S. Hartzell, D. Carver, R. A. Williams, S. Harmsen, and A. Zerva Table 1 Array Station Locations Table 2 Earthquakes Recorded by the San Jose Array Used in This Study Station Latitude (N) Longitude (W) Elevation (m) Ch. 1 Ch. 2 Ch. 3 Event No. Origin Time (Yr.Day.Hr.Min) Lat. (N) Long. (W) Mag. Location Back Azimuth COM Z N E FAI Z N E LAC Z RCK Z N E ROC Z N E WAL Z N E N Z N E N Z N Z N E N Z N E N Z N E N Z O Z N E O Z N E O Z N E O Z N E O Z N E O Z O Z N E P Z N E P Z N E P Z N E P Z N E P Z N E P Z N E P5E Z N E P5S Z N E P5W Z N E P5X Z N E P Z N E P Z N E Q Z N E Q Z N E Q Z N E Q Z N E Q Z N E Q Z N E Q Z N E R Z N E R Z N E R Z N E R Z N E R Z N E R Z N E R Z N E S Z N E S Z N E S Z N E S Z S Z N E S Z S Z This equation can be written in matrix form as the leastsquares inverse problem G x kf d kc Mammoth Lakes Mammoth Lakes Calaveras Fault Calaveras Fault Calaveras Fault Scotty s Junction Scotty s Junction Scotty s Junction Bolinas Rohnert Park San Andreas Fault Calaveras Fault Hector Mine Calaveras Fault Calaveras Fault Calaveras Fault Concord San Andreas Fault Calaveras Fault Kenwood Alameda San Andreas Fault San Andreas Fault Calaveras Fault In this expression, x is the solution vector of source and site response spectra, d is the vector of observed ground-motion spectra, G is a sparse matrix of ones and zeroes indicating the sources and sites for which there are data. The appended equations, kfx kc, are a constraint needed to remove the undetermined degree of freedom from the problem. k is a relative weighting factor that balances fitting the constraint against fitting the data. The constraint we use sets the average response at the two Mesozoic rock (Franciscan tuff) sites, ROC and RCK, equal to 1.0 with a j value (Anderson and Hough, 1984) of This value of j was suggested by Boore (1996) for coastal California rock. The previous matrix equation is solved using the Chebyshev accelerated tomographic method of Olson (1987). The source/site spectral inversion uses the root mean square (rms) of the two horizontal components of ground motion. The record sections used start at the direct S-wave arrival and are variable in length. Lengths are chosen to include most of the shearwave energy. For the local events, these lengths are about 15 to 20 sec. Records from the Mammoth Lakes, Scotty s Junction, and Hector Mine earthquakes have longer duration because of their greater magnitude and distance and significant surface wave content. Record lengths for these events range from 30 to 40 sec. Implications of the surface waves in these records are discussed subsequently. Inversions were run using two different sets of the data in Table 2. The first inversion uses all the events in Table 2 (referred to as the all data inversion). The second inversion includes events on the Calaveras fault, as well as event num-

5 Site Response, Shallow Shear-Wave Velocity, and Wave Propagation at the San Jose Dense Seismic Array 447 Figure 2. Locations of earthquakes recorded by the San Jose array and used in this study: (a) all earthquakes, (b) detail of earthquakes in San Francisco Bay area. Size of circles scales with magnitude. The numbering of the events is keyed to Table 2. Star indicates the location of the San Jose array. bers 11, 21, and 23; in other words, all the closer sources (referred to as the local inversion). Calculations were done in the frequency band from 0.2 to 10 Hz. All the records used were first carefully scanned to ensure good signal-tonoise ratio. Figure 3 compares site amplification factors for these two inversions and two lines of stations, P00 to P70 and S00 to S60, extending from the eastern edge of the Santa Clara Valley to the west over the Evergreen basin. (Station locations are shown in Fig. 4.) A clear pattern of amplification is seen in Figure 3. Lower-frequency amplification factors are greater when all the data are used. The difference between the two inversions increases moving further from the edge of the Santa Clara Valley, with the exception of stations P00 and S00, which do not fit this pattern because they were installed later and recorded only two local events. At higher frequencies, above about 4 Hz, the two solutions converge. These observations can be explained by surfacewave generation in the Santa Clara Valley by the regional earthquakes. Surface waves not only increase the duration of shaking, but also the longer-period amplitude levels. The two inversions produce slightly different curves at P00 and S00 because a least-squares criterion is used, and although the data are the same at these two stations for both inversions, the data are different at the other stations. This difference in the total data set affects the least-squares fitting process. Also, the rock site constraint is given a weight in the inversion, which is also affected by the makeup of the data matrix. We do not consider the difference between the two curves for stations P00 and S00 to be significant. The results in Figure 3 point out the importance of understanding the composition of the records used to calculate site response and choosing record lengths appropriately. Field et al. (1992) recognized this fact and recommended using a generous record length if the objective is earthquake hazard assessment. Using longer record lengths averages over different wave types and includes phases that would presumably be important in a damaging earthquake. Related results were obtained by Joyner et al. (1981) and Williams et al. (1994), among others. In these earlier studies, observed soil-to-rock amplification factors were underpredicted by simple, plane-layered velocity models. In particular, the observed and predicted site amplification curves of Williams et al. (1994) show the same character as the all data and local inversion curves in Figure 3, with higher observed values at lower frequencies and convergence with the predicted values above 5 Hz. These earlier studies attributed the discrepancies to nonplanar velocity structures and to scattered and converted phases not included in their simple models. Shallow Shear-Wave Velocity Because shallow shear-wave velocity is an important site characterization parameter, we wish to clarify the relationship between shear-wave velocity and the local and all data inversion results. We use the hybrid global search algorithm of Liu et al. (1995) and Hartzell and Liu (1995) to

6 448 S. Hartzell, D. Carver, R. A. Williams, S. Harmsen, and A. Zerva Figure 3. Site amplification factors for the P and S lines of stations in the San Jose array. See Figure 4 for locations. Solid curve uses all the earthquakes in Table 2, including regional ones. Dashed curve is based on smaller, local events only, those near the Calaveras fault plus event numbers 11, 21, and 23 in Table 2. Sites P00 and S00 were installed most recently and recorded only two local earthquakes. invert the site response spectra for shallow shear-wave velocity. This method uses a combination of simulated annealing and the downhill simplex algorithm to efficiently search nonlinear model space. This hybrid algorithm shares the advantages of both local search methods that perform well if the local model is suitable and global methods that are able to explore the full model space. The simulated annealing algorithm initially searches widely to find an appropriate model that is not far from the global minimum. Then the simplex algorithm moves the model quickly to the global minimum. Throughout the process the nonzero probability of long jumps allows the method to escape from local minima. Also throughout the search, N 1 possible solutions are stored, where N is the number of model parameters. Therefore, at any given time, the algorithm has a stored experience of N 1 models. This scheme allows for a far more complex and capacious memory of accumulated experience and more efficient searches. The inversion only requires a way of calculating the forward problem and an objective function. The forward problem in this case is calculated by the linear response of a damped, vertically propagating S wave through a stack of flat layers using the code NRATTLE (R. Herrmann, personal comm., 2000). This code is based on the formulation of Kramer (1996) and modified from an earlier code by C. Mueller (written comm., U.S. Geological Survey [USGS], 1997). The objective function is the L 2 norm fit to the site amplification curves obtained from our previous inversion of the array ground motion. The unknowns in our problem are the layer shear-wave velocities, shear-wave Q values, and thicknesses. We assume a 10-layer problem with layer densities that vary smoothly from 1.9 g/cm 3 at the surface to 2.2 g/cm 3 in the tenth layer. This sequence overlies a half-space with a reference velocity and density of 1000 m/sec and 2.3 g/cm 3,

7 Site Response, Shallow Shear-Wave Velocity, and Wave Propagation at the San Jose Dense Seismic Array 449 N10 O10 O O60 N40 O50 P60 P N30 P P5E O40 P5W P5S Q60 N20 P40 P5X O30 R60 P30 Q50 O R50 P20 Q S60 R40 Q30 S50 P10 Q31 R Q20 S40 R P Q11 R10 S30 Q10 Q00 S S10 N N60 RCK ROC S00 LAC WAL FAI COM 5km Figure 4. Detail of the San Jose array with surficial geologic units. Numbers in red are the average shear-wave velocities in the top 30 m we obtained from seismic reflection/refraction. Pre-Cenozoic basement depth contours (500-m intervals) in blue. H2O, water; Af, artificial fill; Qhc, modern stream channel deposits; Qhb, Holocene basin deposits; Qhf, Holocene alluvial-fan deposits; Qhl, Holocene alluvial-fan levee deposits; Qht, Holocene stream terrace deposits; Qf, latest Pleistocene to Holocene alluvial-fan deposits; Qa, latest Pleistocene to Holocene alluvium; Qoa, early to late Pleistocene alluvium; Br, Mesozoic bedrock. Geology modified from Knudsen et al. (2000).

8 450 S. Hartzell, D. Carver, R. A. Williams, S. Harmsen, and A. Zerva respectively. The total thickness of the layered stack is constrained to not exceed 800 m. This value is selected because the solution represented by the global minimum is always significantly less than 800 m. In addition, liberal upper and lower search bounds are set for the shear-wave velocity and Q of each layer. Figure 5a and b shows inversion results for two stations, P50 and S40. In order to match the greater amplitudes at lower frequencies for the site response spectra based on all the ground-motion data, it is necessary to have shallow shear-wave velocities up to a factor of 2 lower. Are these low shear-wave velocities reasonable? Using the seismic reflection/refraction method of Williams et al. (1999a, b), we measured shear-wave velocities at 10 sites in the San Jose array. The measured average shear-wave velocities in the top 30 m, V S30, are given in red in Figure 4. Figure 6 compares the velocity inversion results (dashed lines) with those obtained from seismic reflection/refraction (solid lines) for six sites. Velocities obtained from the inversion of site response spectra obtained from the local ground-motion data compare quite favorably with the seismic reflection/refraction values. Velocities based on the all-data ground-motion set are consistently low. The inversion results in Figure 6, however, depend on the half-space reference velocity. We argue that the reference velocity of 1000 m/sec is reasonable. Because the site response spectra we invert are calculated relative to the rock sites ROC and RCK, the half-space reference velocity should be representative of the velocity under these two sites. Both of these sites are on rock outcrops, but because of the limited exposure of the rock, the seismic reflection/refraction measurements had to be taken on nearby road-cut fill. The profile near ROC reaches a depth of 35 m Figure 5. Results of global-search inversion of site response spectra for shear-wave velocity and Q: (a) station P50, (b) station S40. Inversions are done using two different spectra, one based on the ground-motion records for all the events in Table 2, the other based on only local events on the Calaveras fault plus event numbers 11, 21, and 23 in Table 2. Top frames show the site response spectra obtained from the ground-motion records (solid lines) and the site response spectra calculated from the inversion velocity model (dashed lines). The shear-wave velocity and Q obtained from the inversion are shown in the middle and bottom frames, respectively. The upper and lower bounds on shear-wave velocity and Q used in the inversions are indicated by dashed lines.

9 Site Response, Shallow Shear-Wave Velocity, and Wave Propagation at the San Jose Dense Seismic Array 451 Figure 6. Comparison between shear-wave velocity obtained from seismic reflection (solid line) and shear-wave velocity obtained from inversion of site response spectra for (a) all the events in Table 2, including regional ones, and (b) only local events on Calaveras fault plus event numbers 11, 21, and 23 in Table 2. and a maximum shear-wave velocity of 787 m/sec at a depth of 27 m. This profile probably underestimates the velocities at ROC because it was taken on fill. More representative values can be obtained from the same type of survey conducted on the west side of the Santa Clara Valley (Hartzell et al., 2001) on similar rock. Here velocities reach 1000 m/ sec at a depth of 4 m. A reference velocity of approximately 2000 m/sec would be required for the site response spectra based on the all data inversion to yield velocities similar to the measured ones. Use of the site response curves based on the local inversion, or alternatively the all-data inversion, depends on the application. If the interest is estimating shear-wave velocity under the site, then local ground-motion records, uncontaminated by surface waves, should be used. Shear waves from these events arrive at the surface with nearly vertical incidence, consistent with the theory usually applied to calculate the response of a stack of plane layers. If the objective is earthquake hazard assessment, then an average response calculated from sources at different azimuths and distances is needed. For a sedimentary basin site, these records would include surface waves and possible basin-edge effects similar to the observations in Mexico City, Los Angeles, and Kobe (Kawase and Aki, 1989; Kawase, 1996; Alex and Olsen, 1998; Graves et al., 1998; Pitarka et al., 1998). Thus, site response spectra derived from the all-data inversion is appropriate for earthquake hazard assessment, but the shallow shear-wave velocities calculated from it are not. In this study surface waves are excited by regional events, but it should be made clear that we do not expect a significant seismic hazard to the Santa Clara Valley from regional sources. These events are used only as surrogates for large, damaging, local events that we would expect to excite similar surface waves. Figure 7 shows the spatial distribution of site amplification in three different frequency bands ( Hz, Hz, Hz) for the local and all-data ground-motion sets. The pattern of amplification is similar for both data sets, but with larger values at lower frequencies for the all-data set solution, as we have seen before. Both solutions, however, give maximum values above the western edge of the Evergreen basin, where the basin rapidly shallows. Similar observations were made by Frankel et al. (2001) and Fletcher et al. (2001). There are probably several factors that cause this pattern. From Figure 4 we see about a factor of 2 decrease in the V S30 values moving southwest away from the edge of the Santa Clara Valley. This decrease may be due to the natural sorting of alluvium from coarser near the bounding hills to finer and siltier near the center of the valley. Grain size has also been used as part of a site classification scheme (Wills et al., 2000). We do not have sufficient V S30 values to the west to completely define this pattern, but the available measurements are suggestive. Another factor is the thickening of Quaternary deposits moving away from the edge of the Santa Clara Valley (Brocher et al., 1997). Also, the shallowing of the Evergreen basin together with the fact that most of our sources lie to the east provide for a generation/trapping of surface waves above this section of the valley. Figure 8 shows bandpass-filtered velocities from to 0.5 Hz for an event near Scotty s Junction, Nevada. Significantly larger surface waves are seen near 20 sec on the western side of the array. This pattern is different than the one obtained from available ground-motion records for the Los Angeles basin, where the largest, long-period motions are over the deepest parts of the basin (Wald and Graves, 1998). However, the Los Angeles data are not as dense as the San Jose array and are not concentrated over a dramatic shallowing of the basin. Also, the Los Angeles basin has a much different size and geometry from the Evergreen basin. The Los Angeles basin is about 40 km wide and 9 km deep, compared to 8 km wide and 7 km deep for the Evergreen basin. This difference in geometry is expected to have a large effect on the amplitude and period of surface waves. To test our hypothesis that surface waves contribute to the larger ground motions above the western edge of the Evergreen basin, we have run a synthetic earthquake model.

10 452 S. Hartzell, D. Carver, R. A. Williams, S. Harmsen, and A. Zerva All Events 0.2 to 0.5 Hz Local Events 0.2 to 0.5 Hz 1to2Hz 1to2Hz 6to8Hz 6to8Hz Figure 7. Contour maps of site amplification values in the area of the San Jose array for three different frequency ranges ( Hz, 1 2 Hz, 6 8 Hz) and two different data sets (all the events in Table 2, including regional ones, and only local events on the Calaveras fault plus event numbers 11, 21, and 23 in Table 2). Station locations are indicated by plus signs. Contours in bold black lines give the depth to the pre-cenozoic basement of the Evergreen basin (Brocher et al., 1997). Depth contours are in 0.5-km intervals and reach a maximum depth of about 7.5 km near the P5 triangular subarray of stations (refer to Fig. 4).

11 Site Response, Shallow Shear-Wave Velocity, and Wave Propagation at the San Jose Dense Seismic Array 453 Range (km) Figure 8. Observed velocity records across the San Jose array, arranged by increasing epicentral distance, for a magnitude 5.6 earthquake near Scotty s Junction, Nevada. Records are bandpass filtered from to 0.5 Hz. The radial component of motion is east west. Figure 9 shows finite-difference synthetics for a magnitude 5.7 earthquake on the southern end of the Hayward fault, where it truncates with the Calaveras fault (epicenter N, W), using the Brocher et al. (1997) 3Dvelocity model. (See Fig. 1 for the location of the source and the line of stations.) Although this source is much closer than our data example in Figure 8, the Hayward fault is a more likely source of a damaging earthquake for the Santa Clara Valley. Large surface waves are again seen in the same location above the western edge of the Evergreen basin. It is important to remember that the 00 stations (on the far western edge of the array) were installed most recently and only recorded two local events. Therefore, source sampling at these sites does not include surface-wave generation, and their ground motion amplification factors are erroneously low. Frequency Wavenumber Analysis and Wave Propagation across the Array Frequency wavenumber (f-k) analysis is used to analyze plane-wave propagation across the San Jose array. Our interest is in identifying the direction of approach and apparent velocity of waves as they move over the array and thereby distinguish body waves from surface waves and possibly identify their origin. A good review of the commonly used methods of evaluating f-k spectra is given by Zerva and Hayward Finite Source, M 5.7, Fault Normal Component L East ArrayLocation West Figure 9. Finite-difference, velocity time histories for a magnitude 5.7 earthquake on the southern end of the Hayward fault (epicenter N, W). Calculations use the 3D velocity model of Brocher et al. (1997). Stations are arranged along a line across the Santa Clara Valley over the Evergreen and Cupertino basins (see Fig. 1 for location). The fault normal component is approximately east west. Records are bandpass filtered from 0 to 0.46 Hz. Zhang (1996). Briefly, we consider the four methods: conventional (CV) (Lacoss et al., 1969), high resolution (HR) (Capon, 1969, 1973), multiple signal characterization (MU- SIC) (Schmidt, 1986), and stacked slowness spectra (SS) (Spudich and Oppenheimer, 1986). Let W(r,t) be the ground motion at point r and time t for an array of sensors, and W(j,x) be the spatial and temporal domain Fourier transform. Then, the f-k power spectrum is given by (Burg, 1964); 2 P(j,x) W(j,x), where j x/c and c is apparent velocity. The cross spectral matrix, S(x), has the elements S (x) W(r,x)W*(r,x), jl j l and the beamsteering vector, U(j), has the elements, Time (sec)

12 454 S. Hartzell, D. Carver, R. A. Williams, S. Harmsen, and A. Zerva U j(j) exp(ij r j). Then, the CV f-k power spectrum is given by, CV 1 T P (j,x) 2 U (j)s(x)u*(j), N where N is the number of stations in the array, T indicates transpose, and the asterisk indicates complex conjugate. The HR f-k power spectrum is given by HR 1 P (j,x) T 1. U (j)s (x)u*(j) The HR method suppresses, in a least-squares sense, all waves with wavenumber different from the one considered and thus gives higher resolution than the conventional method (Capon, 1969). Because of the singular nature of S(x), prewhitening is usually required. For array time histories composed of M N plane waves with amplitudes A j, let R be the covariance matrix of the motions or the time domain equivalent of the cross spectral matrix. Then, Before we analyze data from the San Jose array, it is important to consider the array beam pattern. Knowledge of the beam pattern will help eliminate misidentification of power spectral peaks. Figure 10a and b shows the theoretical beam pattern for the San Jose array, calculated by the 2D Fourier transform of the spatial distribution of stations. The first ring of secondary peaks consists of six maxima at a radial distance of 1.15 cy/km (Fig. 10a). The central peak of the beam pattern has a half width of cy/km at the 12dB level (Fig. 10b). Another important factor is the frequency range to consider. Figure 11 shows SH-velocity waveforms for a magnitude 2.1 earthquake near the Calaveras fault (epicenter N, W). This event was considered too small for our site response calculations, but it illustrates the limits of the coherency of the waveforms. The velocity records are bandpass filtered between 1 T 2 R(j) U*(j)QU (j) r I, where Q diag[ A 1 2, A 2 2,..., A M 2 ], r 2 is the variance of the noise, and I is the identity matrix. Let E n be the eigenvector matrix of R associated with the N-M small-noise eigenvalues. Then, MUSIC searches for the plane-wave vectors, a(j), that have minimum projection in the noise subspace by finding peaks in the directional function (Schmidt, 1986; Goldstein and Archuleta, 1991), 1 D(j). a(j) E n 2 Because body waves are nondispersive, they have the same slowness vector, s j/x, at all frequencies. Slowness spectra can therefore be stacked to yield the stacked slowness power spectrum, SS, (Spudich and Oppenheimer, 1986), SS P (s) P(s,x l). l Zerva and Zhang (1996, 1997) found that the MUSIC method gave the highest resolution, followed by the HR and then the CV methods. They preferred, however, the CV method used in conjunction with slowness stacking for the identification of broadband body waves. Slowness stacking utilizes all the information contained in a broadband signal. Furthermore, slowness stacking reduces the effect of spatial aliasing, because spatially aliased peaks have wavenumber shifts that depend inversely on the frequency and are thus smoothed out. Figure 10. Theoretical beam pattern for the San Jose array: (a) wide view and (b) detail of central maximum. Units are in cycles/km.

13 Site Response, Shallow Shear-Wave Velocity, and Wave Propagation at the San Jose Dense Seismic Array 455 Figure 11. Example of a small, high-frequency earthquake recorded on the San Jose array. Records are velocities bandpass filtered from 1 to 15 Hz and arranged in increasing distance from the epicenter. and 15 Hz and arranged in order of increasing distance from the epicenter. It is clear from this plot that the SH-arrival times are not consistent with distance due to velocity variations along the ray paths. Frequency wavenumber analysis of the direct SH phase in this frequency band yields azimuths inconsistent with the known backazimuth of the source. We therefore perform f-k analysis below 0.5 Hz where consistent backazimuth results are obtained. Because few studies compare the range of f-k methods discussed previously on actual ground-motion records, we first compare the four different approaches (CV, HR, MUSIC, SS) using the vertical ground motion from the M 7.1 southern California Hector Mine earthquake. Power spectra are compared in Figure 12a and b for the 4-sec time windows displayed in Figure 13a. All spectra are oriented north south (vertical) and east west (horizontal). The time series in Figure 13a is the vertical acceleration, bandpass filtered from to 0.5 Hz, for site Q40, a representative station near the center of the array. The CV, HR, and MUSIC spectra are computed at a frequency of 0.39 Hz (2.56 sec). This frequency is used because it lies within the range where we found coherency of the waveforms, and it is a convenient choice based on the sample interval of the data (0.01 sec). The spectra are sampled within the wavenumber range cy/km. The limit of cy/km corresponds to a maximum slowness of 2.0 sec/km or a minimum apparent velocity of 0.5 km/sec. The SS spectra are based on the CV method and stack spectra over the frequency range to 0.5 Hz. The maximum slowness considered is 2.0 km/sec, so SS spectral plots may be compared directly with the individual frequency power spectra. Whitening of the slowness power spectra before stacking, suggested by Spudich and Oppenheimer (1986), was not performed. This process boosts the power of weak frequencies to equal the power of the strongest, but was found to obscure spectral peaks for our data set. All the time windows are 4 sec long with Hanning window weights. In general, the four methods give similar spectra and we conclude from this comparison that the results of this study are not dependent on the power spectral method selected. We would arrive at similar values for backazimuth and apparent velocity regardless of the approach used. However, we have selected the MUSIC method for the rest of this article based on its somewhat better resolution, as measured by the narrower power spectral peaks in windows A, B, and C of Figure 12a. The advantages of the SS method are not realized in this study because we are looking at primarily narrowband surface waves. Dispersion is the main cause of the broader peaks for the SS method in Figure 12a and b. The spectral peak in the northwestern corner of window H in Figure 12b is part of the secondary beam pattern and should be ignored. The lower plot in Figure 13a, which is used elsewhere in this article, shows the backazimuth and apparent velocity obtained for individual time windows using the MUSIC method, superimposed on the generalized geology of the Santa Clara Valley. To facilitate our interpretations, we also indicate the theoretical arrival times for P n, P g, S n, S g, and R (Rayleigh wave) on the time domain record. The P n and S n times are taken from Gutenberg (1951). The P g and S g times are based on the near earthquake phases table of Jeffreys and Bullen (1958). The Rayleigh wave times are calculated using a velocity of 0.92V s for a Poisson soil, which gives values similar to the suggested crustal Rayleigh wave velocity of 3.1 km/sec by Bullen (1963). These arrival times are included only as general guidelines. Waves initially arrive from the direction of the source at higher apparent velocities, indicating body waves. However, for time windows I through L, arrivals with surface-wave velocities coming from the northeast dominate the records. Most of the windows between J and K give similar backazimuths and velocities. These waves come from the direction of the closest edge of the Santa Clara Valley and are likely Rayleigh waves generated at this boundary. These waves arrive too early to be direct Rayleigh waves from the source region and indicate a local origin from converted shear waves. Figure 13b shows moving-window, backazimuths and apparent velocities for the same record. The interpreted basin surface waves can be seen arriving during several different time intervals, intermixed with body waves and other surface waves from the source. This complex pattern of arrivals illustrates the complexity of ground motion within the basin. In this study we do not attempt to identify the particular body waves responsible for the basin surface waves but simply to identify likely basin surface waves on the basis of apparent velocity and

14 456 Figure 12. Comparison of CV (conventional), HR (high-resolution), and MUSIC (multiple signal characterization) frequency wavenumber power spectra and stacked slowness power spectra (SS) for selected four-second time windows of the vertical ground motion from the magnitude 7.1 Hector Mine earthquake. The frequency wavenumber power spectra are for a frequency of 0.39 Hz and a wavenumber range cy/km. The stacked slowness power spectra have a range of slowness 2.0 sec/km and a frequency range from to 0.5 Hz. The time windows are indicated in Figure 13 for the Q40 record. (a) time windows a f, (b) time windows g l.

15 Figure 12. Continued. 457

16 458 S. Hartzell, D. Carver, R. A. Williams, S. Harmsen, and A. Zerva (a) Event Vertical Q40 P n P g S n S g R ab c d e f gh i j k l mn ' ' ' 20 sec ' l d ji k ab c f ng h m e BAZ ' Figure 13a. Vertical acceleration record, bandpass filtered from to 0.5 Hz, for station Q40 from the southern California Hector Mine earthquake. Time windows a-n shown on the Q40 record form the basis of the frequency wavenumber and stacked slowness power spectra in Figure 12. The results of the planewave analysis are given in a map view centered on the San Jose array. The corresponding letter for each time window is plotted on a radial grid of backazimuth and apparent velocity. Apparent velocities range from 0.5 km/sec on the outer ring to infinite (vertical incidence) at the center of the plot. The backazimuth of the Hector Mine earthquake is labeled BAZ. Figure 13b. Moving-window apparent velocities and backazimuths calculated for the vertical component of ground motion at the San Jose array for the southern California Hector Mine earthquake. Results are compared with the vertical component at station Q40. All estimates are based on 4-sec time windows. A horizontal line at 121 degrees indicates the backazimuth to the source. backazimuth. The Hector Mine record exemplifies the importance that basin geometry plays in ground motion that will be reinforced by the other sources we consider subsequently. In analyzing the f-k power spectra we have taken a cautious approach in our interpretation, by considering only the larger spectral peaks and discounting any peak at a spacing equal to the theoretical beam pattern spacing. Figure 14 shows results for the vertical component of ground motion from a Mammoth Lakes earthquake, (event 1 in Table 2). Initial arrivals are close to the backazimuth to the source. It is not always possible to analyze the first arrival because of late triggers at some stations. Between windows D and E, backazimuths are in the direction of the source, and apparent velocities decrease from 9 km/sec to 0.6 km/sec, indicating a shift from body-wave arrivals to surface waves. The low apparent velocities correspond with the theoretical Rayleighwave arrival time. Windows B, C, and E show a complex pattern of body-wave and surface-wave arrivals, including body and surface waves from the source region as well as an arrival tentatively identified as a basin surface wave from Figure 14. MUSIC power spectra and the backazimuth and apparent velocity of f-k spectral peaks for the vertical component of ground motion from a magnitude 5.6 earthquake near Mammoth Lakes, California. The Q40 acceleration record is shown, bandpass filtered from to 0.5 Hz, with the 4-sec time windows used in the analysis labeled a f. The frequency of the power spectra is 0.39 Hz, and the wavenumber range is cy/km. Each arrow on the map views indicates the direction of approach of a plane-wave source and is plotted at a radial distance appropriate for its apparent velocity. Apparent velocities range from a minimum of 0.5 km/sec on the outer ring to infinite (vertical incidence) at the center of the plot. The backazimuth of the earthquake is labeled BAZ. The surficial geology in the map views is simplified to three units: lightest gray, Quaternary alluvium, medium gray, San Francisco Bay mud; darkest gray, Mesozoic rock.

17 Figure 14.

18 460 S. Hartzell, D. Carver, R. A. Williams, S. Harmsen, and A. Zerva the west. This surface wave may be generated at the western edge of the Evergreen basin or the high in basement topography between the Evergreen and Cupertino basins. Window F shows a surface wave from the south, most likely formed at the southern end of the Santa Clara Valley. The region labeled G is a period of complex interference with no coherent phases. The region labeled H again shows arrivals from the backazimuth to the source with apparent velocities between 2.5 and 5.0 km/sec. Figure 15 shows results for the radial component (east-west) of ground motion from an earthquake near Scotty s Junction, Nevada, (event 6 in Table 2). After initial arrivals from the source, clear southwesterly arrivals are seen at surface-wave apparent velocities. This same observation was made by Frankel et al. (2001) for this event and can be explained by surface waves either formed at or scattered from the southern end of the Santa Clara Valley. Between windows B and C backazimuths are in the direction of the source with apparent velocities form 1.0 to 2.0 km/sec. Figure 16 shows the results of the analysis of vertical ground motion from a northern San Francisco Bay earthquake, (event 20 in Table 2). This event again shows surface-wave energy from the west, northeast, and southeast. Windows between B and C are similar to window B. Windows between C and D are similar to windows C and D. We can summarize these observations by noting the importance of the boundaries of the Santa Clara Valley and the Evergreen and Cupertino basins in the generation of surface waves. For the location of the San Jose array, the closest boundaries are the most important: the eastern and southern edges of the Santa Clara Valley and possibly the western edge of the Evergreen Basin or the basement high between the Evergreen and Cupertino basins. Conclusions Analysis of the San Jose array data shows a significant difference at frequencies below 3 4 Hz between site amplification factors calculated from small local earthquakes and larger regional events for the Santa Clara Valley. Amplification is up to a factor of 2 greater when regional earthquakes are included. This result is caused by strong surface wave excitation within the Santa Clara Valley for the regional events. Body waves from small, local earthquakes, with steep angles of incidence, experience amplification in the valley due to low near-surface shear-waves velocities, but are not efficient producers of surface waves. Despite these differences, the pattern of amplification is similar for both local and regional earthquakes. Amplification factors increase to the west away from the eastern edge of the Santa Clara Valley. Shallow shear-wave velocity measurements decrease by about a factor of 2 moving away from the edge of the valley, perhaps related to grain-size sorting in the alluvium. Both observed records and finite-difference synthetics show large surface-wave amplitudes above the western edge of the Evergreen basin. In this region, the pre- Cenozoic basement of the Evergreen basin shallows rapidly and may trap surface waves or act as a zone of generation for surface waves. Further to the west, amplification factors are seen to decrease, but this trend is not fully delineated due to the limited extent of the array. The National Earthquake Hazard Reduction Program (NEHRP, 1997) recommendation for site amplification at 1.0 Hz for site class D (180 km/sec V S km/sec) under linear ground-motion conditions is a factor of 2.4. The corresponding factor for site class B (760 km/sec V S km/sec) is 1.0. The reference site in this study is site class B and is also constrained to have an amplification of 1.0. The slower parts of the San Jose array are site class D. Our calculated site amplification factors using predominately body waves from small local earthquakes are consistent with the NEHRP value of 2.4, excluding a few sites with stronger resonances. However, when surface-wave excitation is included, average amplification near 1.0 Hz reaches for linear soil conditions. We have demonstrated that site response spectra for the San Jose array, based on local earthquakes, can be inverted to obtain shallow shear-wave velocities that agree well with measured values from seismic reflection/refraction. The method utilizes a global search algorithm and vertically-incident shear waves in a layered half space. If the objective is seismic hazard evaluation, however, site response should be based on a mix of sources with different ranges, ray parameters, and phases. Frequency-wavenumber power spectra show a significant amount of coherent plane-wave propagation across the San Jose array at frequencies below 0.5 Hz for regional events. Various power spectra are compared: conventional, high resolution, multiple signal characterization, and stacked slowness. We use mainly the multiple signal characterization f-k method because it yields somewhat better resolution for the narrowband surface waves of our primary interest. The plane-wave analysis shows surface waves originating from the closest margins of the Santa Clara Valley to the San Jose array. These margins included the edge of the valley directly to the east of the array and to the south. Surface waves are also seen propagating from the west, possibly originating at the western edge of the Evergreen basin or the ridge between the Evergreen and Cupertino basins. This conclusion is consistent with the large surface waves seen in data and synthetic ground-motion records above the western edge of the Evergreen basin. This study points out the importance of having a good 3D model of the geologic structure in a seismic hazard evaluation of an alluvial basin such as the Santa Clara Valley. Acknowledgments Funds for the purchase of the recording systems used in the San Jose array were provided by Pacific Gas and Electric Company. The authors had useful discussions on site response with Edward Cranswick. Ken Rukstales provided geographic information systems support. The article was improved by reviews from Paul Spudich, Edward Cranswick, Fabian Bonilla, and Lee Steck.

19 Site Response, Shallow Shear-Wave Velocity, and Wave Propagation at the San Jose Dense Seismic Array 461 Figure 15. MUSIC power spectra and the backazimuth and apparent velocity of f-k spectral peaks for the radial (east west) component of ground motion from a magnitude 5.6 earthquake near Scotty s Junction, Nevada. Other details of the figure are the same as Figure 14.

20 462 S. Hartzell, D. Carver, R. A. Williams, S. Harmsen, and A. Zerva Figure 16. MUSIC power spectra and the backazimuth and apparent velocity of f-k spectral peaks for the vertical component of ground motion from a magnitude 5.2 earthquake just north of the San Francisco Bay. Other details of the figure are the same as Figure 14.