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.

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.

Aagaard, B. T., T. M. Brocher, D. Dolenc, D. Dreger, R. W. Graves, S. Harmsen, S. Hartzell, S. Larsen, and M.L. Zoback, Ground-Motion Modeling of the 1906 San Francisco Earthquake, Part I: Validation Using the 1989 Loma Prieta Earthquake, *Bull. Seism. Soc. Am.*, 98, 989-1011, doi: 10.1785/0120060409,2008a.

Aagaard, B. T. M. Brocher, D. Dolenc, D. Dreger, R. W. Graves, S. Harmsen, S. Hartzell, S. Larsen, K. McCandless, S. Nilsson, N. A. Petersson, A. Rodgers, B. Sjogreen, and M. L. Zoback, Ground-Motion Modeling of the 1906 San Francisco Earthquake, Part II: Ground-Motion Estimates for the 1906 Earthquake and Scenario Events, *Bull. Seism. Soc. Am.*, 98, 1012-1046, doi: 10.1785/0120060410,2008b.

Boore, D. M. and G. M. Atkinson, Ground-motion prediction equations for the average horizontal component of PGA, PGV, and 5%-damped PSA at spectral periods between 0.01 s and 10.0 s, *Earthquake Spectra* 24, 99-138,2008.

Brocher, T. M., Emprical relations between elastic wave speeds and density in the Earth's crust, *Bull. Seism. Soc. Am.*, 95 No. 6, 2081-2092,2005.

Dreger D. and B. Romanowicz, Source Characteristics of Events in the San Francisco Bay Region, USGS open-file report, 94-176, 301-309, 1994.

Brocher, T., Compressional and Shear-wave velocity versus depth relations for common rock types in Northern California, *Bull. Seism. Soc. Am.*, 98 No. 2, 950 - 968, 2008.

Campbell, K. and Y. Bozorgnia, NGA Ground Motion Model for the Geometric Mean Horizontal Component of PGA, PGV, PGD and 5% Damped Linear Elastic Response Spectra for Periods Ranging from 0.01 to 10 s, *Earthquake Spectra* 24, 139-171,2008.

Jachens, R., R. Simpson, R. Graymer, C. Wentworth, T. Brocher, Three-dimensional geologic map of northern and central California: A basic model for supporting ground motion simulation and other predictive modeling, 2006 SSA meeting abstract, *Seism. Res. Lett.*, 77, No.2, p 270, 2006.

Larsen, S. and C. A. Shultz, ELAS3D: 2D/3D elastic finite-difference wave propagation code, Technical Report No. UCRL-MA-121792, 1995.

Rodgers A., N., A. Petersson, S. Nilsson, B. Sjogreen, and K. McCandless, Broadband waveform modeling of moderate earthquakes in the San Francisco Bay Area and preliminary assessment of the USGS 3D Seismic velocity model, *Bull. Seism. Soc. Am.*, 98 no. 2, 969-988, 2008.

Berkeley Seismological Laboratory

215 McCone Hall, UC Berkeley, Berkeley, CA 94720-4760

Questions or comments? Send e-mail: www@seismo.berkeley.edu

© 2007, The Regents of the University of California