Given the scarcity of near-source recordings for large earthquakes, numerical simulations play an important roll in the prediction of possible ground motion from future events. Simulations also give insight to physical processes of fault rupture that are difficult or impossible to empirically measure. In this dissertation I develop a numerical method to simulate spontaneous shear crack propagation within a heterogeneous, three- dimensional, viscoelastic medium. The implementation is highly scalable, enabling large scale, multi-processor calculations. Wave motions are computed on a logically rectangular hexahedral mesh, using the generalized finite difference method of Support Operators. This approach enables the modeling on nonplanar boundaries, as well as nonplanar ruptures. Computations are second-order in space and time. Stiffness and viscous hourglass corrections are employed to suppress suppress zero-energy grid oscillation modes. Model boundaries may be reflective or absorbing, where absorbing boundaries are handled using the method of perfectly matched layers (PML). Three well known test problems are used to verify various aspects of the numerical method: wave propagation in a layered medium; surface amplification due to a semi-cylindrical canyon; and spontaneous rupture of a rectangular fault. Tests are repeated with varying amounts of simple shear deformation of the mesh. Sufficient accuracy is preserved under high- angle mesh shearing to permit modeling of thrust- earthquake geometries. The method is used to simulate a large (M[omega]7.6) earthquake scenarios along the southern San Andreas fault, using a piecewise planar fault representation and true topography of the ground surface. The crustal velocity structure is taken from the Southern California Earthquake Center Community Velocity Model (SCEC-CVM), which is currently the most complete three- dimensional model available for the region. Heterogeneous initial traction conditions are derived from an inversion of the M7.3 1992 Landers strong ground motion records. Heterogeneity in the traction model leads to focusing of the rupture front, in many cases producing super-shear rupture velocity in areas of high initial traction (asperities). Focusing sometimes occurs between the asperities, with the notable result that highest peak slip rates occur in areas of low initial traction. The overall distribution of simulated peak ground velocities is consistent with those derived from the current empirical models, with some important deviations associated with basin wave-guide and directivity effects

We present a new, 3D description of crust and upper mantle velocity structure in southern California implemented as a Unified Structural Representation (USR). The USR is comprised of detailed basin velocity descriptions that are based on tens of thousands of direct velocity (Vp, Vs) measurements and incorporates the locations and displacement of major fault zones that influence basin structure. These basin descriptions were used to developed tomographic models of crust and upper mantle velocity and density structure, which were subsequently iterated and improved using 3D waveform adjoint tomography. A geotechnical layer (GTL) based on Vs30 measurements and consistent with the underlying velocity descriptions was also developed as an optional model component. The resulting model provides a detailed description of the structure of the southern California crust and upper mantle that reflects the complex tectonic history of the region. The crust thickens eastward as Moho depth varies from 10 to 40 km reflecting the transition from oceanic to continental crust. Deep sedimentary basins and underlying areas of thin crust reflect Neogene extensional tectonics overprinted by transpressional deformation and rapid sediment deposition since the late Pliocene. To illustrate the impact of this complex structure on strong ground motion forecasting, we simulate rupture of a proposed M 7.9 earthquake source in the Western Transverse Ranges. The results show distinct basin amplification and focusing of energy that reflects crustal structure described by the USR that is not captured by simpler velocity descriptions. We anticipate that the USR will be useful for a broad range of simulation and modeling efforts, including strong ground motion forecasting, dynamic rupture simulations, and fault system modeling. The USR is available through the Southern California Earthquake Center (SCEC) website (http://www.scec.org).