Moderate earthquake ground motion validation in the San Francisco Bay Area

Ahyi Kim, Douglas Dreger, and Shawn Larsen


We performed 3D ground motion simulations for 10 recent moderate earthquakes in the San Francisco Bay Area to evaluate the two versions of the USGS 3D velocity models. Comparisions were made in terms of modeling phase arrival timing, peak ground motion amplitudes, and general seismic waveforms. One model, version 5.1.0 was released in 2005 (Brocher et al., 2005; Jachens et al., 2006) and it was used by Rodgers at al. (2007)to simulate waveforms of moderate earthquakes in the San Francisco Bay Area in the low frequency band (f $<$ 0.25Hz). Rodgers found that version 5.1.0 predicted the peak amplitude well but that energy arrived earlier than observed. The other model, version 8.3.0, was released in May 2008 (Brocher 2008), was used to simulate the ground motions for the 1906 San Francisco earthquake (Aagaard et al., 2008b), and was validated by modeling the 1989 Loma Prieta earthquake strong ground motions (Aagaard et al., 2008a). This model reduced both P- and S-wave velocities in granite, Franciscan, gabbro, lower crust, and upper mantle to correct the earlier phase arrival timing mismatch reported by Rodgers et al. (2007). We directly compared the two models in each 200m grid layer and found that the mean velocity of each layer was reduced by approximately 5% in the depth range from 5 to 30km in model 8.3.0.

Computational set up and 3D model used in the simulations

For the 3D waveform modeling, we used the elastic finite-difference code, E3D developed by Larsen and Schultz (1995). With the BSL cluster we can simulate ground motions throughout the greater San Francisco Bay Region to a maximum frequency of 0.5 Hz for models with a minimum wave speed of 500m/s. We have performed simulations of 9 Mw4.1-5.0 events using source parameters obtained from the BSL Moment Tensor Catalog (Table 2.1). Broadband seismic data was obtained from the Berkeley Digital Seismic Network (BDSN), and strong motion data was obtained from the USGS strong Motion Instrumentation Program (SMIP) and the California Geologic Survey (CGS) California Strong Motion Instrumentation Program (CSMIP). The data was corrected to absolute ground velocity (cm/s). We compare synthetic and observed ground velocity in three passbands, namely 0.03-0.15Hz, 0.1-0.25Hz, and 0.1-0.5Hz.

Figure 2.74: Top shows the relative time shift between synthetic and observed P-waves for model 5.1.0. Positive time shift means the synthetics is early and the model is fast. The color scale shows the level of cross-correlation of the synthetic and observed P waveforms. The bottom shows the same for model 8.3.0.
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Figure 2.75: Top row shows the comparison between observed and synthetic PGV in three passbands, 0.03-0.15, 0.1-0.25, and 0.1-0.5 Hz for model 5.1.0. The bottom row shows the same for model 8.3.0. The symbols are for different simulated events. The corresponding legends are to the right.
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Table 2.1: Earthquakes simulated in this study. Event ID and the source parameters are obtained from BSL Moment Tensor Catalog.
ID Date lon lat Strike Dip Rake Depth Moment Mw
gilr93016 01/16/1993 -121.46 37.03 331 83 166 7 2.40E+23 4.9
boli99230 08/18/1999 -122.69 37.91 115 49 69 8 7.25E+22 4.5
napa00247 09/03/2000 -122.41 38.38 60 75 18 11 3.74E+23 5
gilr02134 05/14/2002 -121.6 36.97 212 87 -6 8 2.86E+23 4.9
dubl03033 02/02/2003 -121.94 37.74 67 88 -19 14 1.36E+22 4.1
smar06166 06/15/2006 -121.49 37.1 360 78 -152 5 4.18E+22 4.4
glen06215 08/03/2006 -122.59 38.36 256 86 19 5 5.64E+22 4.4
lafe07061 03/02/2007 -122.1 37.9 82 89 -1 14 2.77E+22 4.2
oakl07202 07/20/2007 -122.18 37.8 321 89 168 5 2.52E+22 4.2
alum07251 10/31/2007 -121.78 37.43 323 87 180 11 1.85E+24 5.4

Modeling results

We performed an analysis of P-wave arrival times by using cross-correlation to determine arrival time differences. For this analysis we low pass filtered the velocity records using an acausal Butterworth filter with corners of 0.1 and 0.5Hz, and then used waveform cross-correlation to find the relative arrival times. We limited the synthetic to shift in time by plus or minus two seconds (for f $<$ 0.5Hz) to avoid possible cycle skipping. As Figure 2.74 shows, consistent with Rodgers et al. (2007) for S-e arrival times, the P-wave arrival times for model 5.1.0 are systematically early. The arrival time difference increase with distance suggests it is a systematic error in the seismic wave speed, where P-wave velocity is too high. A recalculation using model 8.3.0 shows that the simulated arrivals are still a little early, but that most of the disagreement with the observations has been accounted for.

The comparison of Peak Ground Velocity (PGV) for both models 5.1.0 and 8.3.0 reveals that both 3D models predict the observed PGV well (Figure 2.75). The comparison shown is for over 4 orders of magnitude values exceeding 1 cm/s where damage begins to manifest in weak unreinforced structures. In the low frequency band (0.03 - 0.15Hz), all of the small events are essentially point-sources, and we see that there is very good one-to-one correspondence between observed and simulated PGV. Both models perform well, but model 8.3.0 seems to reduce the dispersion slightly. This is also true of the intermediate passband (0.1-0.25 Hz). At higher frequencies, the correlation remains good; however, unaccounted for source effects for the larger events, and 3D wave propagation and site conditions become more important, leading to higher dispersion in the predicted amplitudes. Since PGV seems to scale approximately linearly in large events (e.g. Boore and Atkinson, 2008; Campbell and Bozorgnia, 2008), and PGV in large events is carried by waves of 1 to several seconds period, well within the ranges of the passband of our simulations, the comparison strongly suggests that both 3D velocity models, and particularly model 8.3.0, are suitable for simulating strong ground motion scenarios for the region's high risk faults. It is noted however that the comparison in Figure 2.75 is log-scale, and that the dispersion represents a factor of 2 to 4 in simulated motions. This fact should be considered in the interpretation of predictive maps of scenario earthquake simulations (e.g. Aagaard et al., 2008b). Finally, for the largest event that we considered, the 2007 Mw 5.4 Alum Rock earthquake, there can be significant differences in simulated PGV depending upon the assumed duration of the source. For this event, at most stations synthetic PGV is overestimated, which is due to the strong southwestward rupture directivity and the fact that most stations are located to the northwest of the epicenter. For this event, we also simulated the ground motions by including a uniform slip finite-source model with southeastward rupture. Using this simple finite-source model reduced the amplitude at stations located to the northwest of the epicenter and improved the overall PGV fit (Figure 2.75).

Although the PGV is relatively well explained, and in many cases the three component waveforms match that data well, there remain paths that could benefit from model refinement. In Figure 2.76a three component waveforms for the Bolinas earthquake are compared, and in all cases, except the paths to BDM and POTR, the fit is good. The paths to BDM and POTR are in the same general eastward direction, yet while the fit to the BDM record is much improved with the model 8.3.0, there remains significant misfit at POTR indicating unmodeled structure north of delta, and possibly in the San Pablo Bay. In Figure 2.76b for the 2002 Gilroy earthquake, the two closest stations have good agreement with the primary S waveform amplitudes, but the model fails to explain the large secondary surface wave train at station 1404 due to sediments in the Hollister and Salinas valleys. While the synthetics explain PGV at sites 1404 and 1854 within a factor of less than two (190% and 130%, respectively), they significantly under predict the duration of strong shaking.

Figure 2.76: Three-component velocity waveforms (black) for 1999 Bolinas earthquake (a) and 2002 Gilroy earthquake (b) are compared to synthetics for models 5.1.0 (cyan) and 8.3.0 (blue). The data and synthetics have been bandpass filtered between 0.10 to 0.25Hz.
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