Inversion for the Velocity Structure of the Santa Clara Valley, California

David Dolenc, Doug Dreger, and Shawn Larsen (Lawrence Livermore National Laboratory)


In our previous work, we have found strong correlations between basin depth reported in the USGS 3D seismic velocity model (ver. 2) (Jachens et al., 1997) and different relative measures of ground motion parameters, such as teleseismic arrival delays, P-wave amplitudes, wave energy, local earthquake S-wave amplitudes, and periods of microseism horizontal to vertical spectral ratio peaks (Dolenc et al., 2005; Dolenc and Dreger, 2005). The teleseismic, local earthquake, and microseism observations were also found to be strongly correlated with one another. The results suggested that all three datasets are sensitive to the basin structure and could, therefore, be used together to improve the 3D velocity model.

We started to develop a simultaneous inversion of the observations from the three datasets to refine the velocity model within the SCV basins. To reduce the extremely large model space, we invert for the velocity structure within the basins while the basin geometry, as defined in the USGS ver. 2 velocity model, is held fixed. Basin geometry in the USGS model was mainly constrained by the inversion of the gravity data and is one of the better known parameters in the model.

We use the 3D elastic finite-difference code E3D to simulate the teleseismic, local, and microseism wavefields for the models with increasing levels of complexity in the basins. To model the plane wave from the teleseismic events, we used a disc of point sources in the deepest homogeneous layer of the model, representing the upper mantle. To simulate the microseisms, we used a localized source of isotropic Rayleigh waves located offshore.

In the next step, we use the simulated wavefields to do the inversion following the approach developed by Aoi [2002]. In his study, Aoi [2002] used the inversion scheme to estimate the 3D basin shape from the long-period strong ground motions. In this work we keep the basin geometry fixed and invert for the velocity structure within the basins.


In the test inversions, we used the synthetic waveforms obtained with a selected target model instead of true observations. This was to test the inversion method while the target 3D velocity structure was known and based on the USGS ver. 2 model. We also used teleseismic data from a set of 38 stations. The structure within the basins was laterally uniform with a single velocity gradient. An example of the test inversion is presented below. The velocities and density of the target and of the starting model are listed in Figure 24.1. The velocity and density gradients in the SCV basins in the target model were the same as in the USGS model. The velocity and density gradients in the starting model were 50% smaller than the USGS gradients in the SCV basins. The perturbation steps used for all six model parameters (P- and S-wave velocity and density at the surface and their gradients with depth) were 15% of their starting values.

The computations were performed on the BSL Linux cluster. Because of the computational limitations, the slowest velocities in the model were increased to a minimum S-wave velocity of 1 km/s. The slowest P-wave velocity was 1.75 km/s. The computation time for a single forward simulation was $\sim\!\!70$ minutes when 16 cluster nodes and 2 processors per node were used. Each forward computation required $\sim\!\!4.5$ GB of memory.

Results for a subset of four stations are presented in Figure 24.1. Stations 120 and 238 are located over the basins; station 186 is south of the Cupertino basin, and station PG2 is between the basins. Waveforms for the starting model and for a model from iteration steps 2 and 4 are shown (solid lines) as well as the waveforms obtained with a target model (dotted). Waveforms were bandpass filtered between 0.1 and 0.5 Hz as the waveforms from the recorded teleseisms had most of the energy in this frequency band. Only the first 20 s of the waveforms were used in the inversion. This time period includes the P-wave arrival as well as the P- to S-wave converted arrivals. The waveforms shown in Figure 24.1 include the arrival of the pP-wave that was also modeled, but not included in the inversion, as it arrives after the first 20 s. Results from the test inversions performed so far showed that the method is stable, and that four or less iteration steps were needed to reach the target model (Dolenc, 2006).

The presented inversion example used only teleseismic waveforms. Future inversions will use additional parameters obtained from the local earthquake and microseisms data. For the local earthquakes, these parameters will include energy estimates and peak ground velocity values. For the microseisms data, the parameter that will be included in the inversion will be the value of the horizontal to vertical spectral ratio peak. Additional parameters that would characterize the teleseismic waves coda could also be added.

Figure 24.1: Top left: Closer look at the SCV region. Contours of the SCV basins from the USGS ver. 2 model at 1 km, 3 km, 5 km, and 6 km are shown in gray. Top right: The velocities and density in the SCV basins. Bottom: Results from a test inversion. Waveforms for the four SCV station are shown for the starting model (solid, top row) and for a model as it was modified after iteration 2 and 4 (solid, bottom rows). Waveforms obtained with the target model are shown for comparison (dotted).
\epsfig{file=dolenc06_1_1.eps, width=16cm}\end{center}\end{figure*}


Part of this work was supported by the USGS grants 99HQGR0057 and 00HQGR0048. The Hellman Faculty Fund is acknowledged for partial support.


Aoi, S., Boundary shape waveform inversion for estimating the depth of three-dimensional basin structures, Bull. Seism. Soc. Am., 92, 2410-2418, 2002.

Dolenc, D., D. Dreger, and S. Larsen, Basin structure influences on the propagation of teleseismic waves in the Santa Clara Valley, California, Bull. Seism. Soc. Am., 95, 1120-1136, 2005a.

Dolenc, D. and D. Dreger, Microseisms observations in the Santa Clara Valley, California, Bull. Seism. Soc. Am., 95, 1137-1149, 2005.

Dolenc, D., Results From Two Studies in Seismology: I. Seismic Observations and Modeling in the Santa Clara Valley, California II. Observations and Removal of the Long-Period Noise at the Monterey Ocean Bottom Broadband Station (MOBB), Ph.D. Thesis, University of California, Berkeley, 2006.

Jachens, R. C., R. F. Sikora, E. E. Brabb, C. M. Wentworth, T. M. Brocher, M. S. Marlow, and C. W. Roberts, The basement interface: San Francisco Bay area, California, 3-D seismic velocity model, EOS Trans. AGU., 78, F436, 1997.

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