| Heterogeneous 3D velocity structure is manifest in seismograms through a variety of geometric and non-geometric effects, such as phase shifting, amplitude distortion, focusing, diffraction and refraction. Accounting for such complex propagation effects in waveform studies facilitates accurate prediction of waveforms for the purpose of estimation of velocity structure, focal mechanisms and ground motion. To this end, we have developed a number of tools to assist in accounting for the affects of heterogeneous velocity structure: spherical-coordinate finite-difference wave propagation schemes, reciprocal heterogeneous CMT inversion methodology and robust layered absorbing boundary conditions.; We have developed a velocity-stress spherical-coordinate based finite-difference scheme that allows for accurate regional-scale wave propagation in a variety of heterogeneous velocity structures. The scheme includes a planar free-surface, moment tensor source initiation, higher-order interpolation operators and absorbing boundary conditions. An irregular-grid version is shown to decrease numerical dispersion and improve accuracy. The spherical-coordinate finite-difference scheme, along with Green's function reciprocity and a grid-search technique, is used to develop a CMT inversion methodology for use with heterogeneous velocity structure. In solving for a number of Hector Mine's aftershocks, we demonstrate the methodology and its efficiency. Finally, we present on the implementation of the perfectly matched layers absorbing boundary condition in a 3D fourth-order velocity-stress finite-difference scheme. Suppression of boundary artifacts, particularly in the presence of 3D media, is required to distinguish 3D effects from boundary artifacts. The perfectly matched layers condition provides superior absorption in a variety of simulations, including those containing 3D structure. |
