Spectral-element simulations of three-dimensional seismic wave propagation and applications to source and structural inversions

This thesis presents a concise introduction to the spectral-element method and its applications to the simulation of seismic wave propagation in 3-D earth models. The spectral-element method is implemented in the regional scale for a 3-D integrated southern California velocity model. Significantly better waveform fits are achieved for the 3-D synthetics calculated compare to the 1-D synthetics generated from the 1-D standard southern California model, especially for many basin stations where strong amplifications are observed due to the very low wave-speed sediments. A hypothetical earthquake rupturing from northeast to southwest at the southern end of the San Andreas fault is simulated to improve our understanding of the seismic hazards in the Salton Trough region.; With the improved 3-D Green's function, we perform source inversions for both the source mechanisms and event depths of Mw ≥ 3.5 earthquakes in southern California. The inversion results generally agree well with the results obtained by other traditional methods, but with significantly more stations used in the inversions. Time shifts are generally required to align the data and the synthetics, which provides a great dataset for the improvement of the 3-D velocity models in southern California.; We use the adjoint method to formulate the tomographic inverse problem based upon a 3-D initial model. We calculate the sensitivity kernels, a key component of the tomographic inversion, that relate the perturbations of observations to the perturbations of the model parameters. These kernels are constructed by the interaction of the regular forward wavefield and the adjoint wavefield generated by putting the time-reversed signals at the receivers as simultaneous adjoint sources. We compute the travel-time sensitivity kernels for typical phases in both regional and global problems for educational purposes, and outline the procedures of applying the conjugate-gradient method to solve both source and structural inversion problems.