We started to develop a simultaneous inversion of the teleseismic, local, and microseism observations to refine the seismic velocity model within the SCV basins. To reduce the extremely large model space, we only invert for the velocity structure within the basins while the basin geometry, as defined in the USGS velocity model, is held fixed. The inversion is based on the approach described in Aoi (2002). We parameterize the velocity model in the basins and invert it by using teleseismic P-wave waveforms as well as additional relative parameters, such as teleseismic wave energy, local earthquake S-wave amplitude, and periods of microseism horizontal to vertical spectral ratio peaks. The model parameters are determined by the inversion with the constraint that the observation equation, which is nonlinear in the model parameters, is best satisfied in the sense of least squares. The observation equation is linearized by omitting higher order terms and solved iteratively by singular value decomposition. To solve the observation equation, synthetic waveforms as well as sensitivity functions (differential seismograms) are required. The 3D elastic finite-difference code (Larsen and Schultz, 1995) is used to calculate waveforms, and the sensitivity functions are obtained numerically by taking the difference of waveforms from perturbed and unperturbed models. The inversion is performed in the 0.1 to 1 Hz passband in which the SCV seismic experiment observations had a good signal to noise ratio.
We prepared four variations of the USGS model in the basins: (1) laterally uniform velocity with a single vertical velocity gradient, (2) three regions of vertical velocity gradient distributed vertically, (3) six 1-km thick horizontal layers with constant velocities, and (4) multi-layered constant velocity slices draped over the basin geometry.
Because of the computational limitations, the slowest velocities in the models were increased to a minimum S-wave velocity of 1 km/s. The slowest P-wave velocity was 1.75 km/s. To model the plane wave from the teleseismic events, we used a disc of point sources in the deepest homogeneous layer of the velocity model, representing the upper mantle. To simulate the microseisms, we used a localized source of isotropic Rayleigh waves located offshore. The preliminary results of the f-k analysis of the observed and simulated microseisms display strong directionality in their propagation and localization of the source, which supports the use of the point source for microseisms.
Preliminary results show that the model parameters are iteratively modified and that the residuals between the data and synthetic seismograms are converging.
Berkeley Seismological Laboratory
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