Implementation and Application of 3-D Numerical and Analytical (Modal) Modeling Methods for the Prediction and Analysis of Discriminatory Seismic Signals.

Abstract : The generalization of the Fourier pseudospectral method developed in this study involved supplementing a Fourier trigonometric basis set with discontinuity functions and using the weak Galerkin form of weighted residuals to approximate the governing equations for momentum conservation for wave propagation in heterogeneous media. Using the sawtooth and quadratic discontinuity functions, accurate simulations were obtained for problems with a traction free surface and general 3-D velocity variations. It is shown how a general coordinate transformation can be used to incorporate surface topography and irregular material interfaces into models of strongly heterogeneous earth structure and to improve the resolution of small scale wavefield features. Comparisons of modeling results with analytic and other numerical solutions for both elastic and anelastic media with discontinuities shows an exceptional level of accuracy without significantly increasing the computational requirements compared to the standard Fourier method. An analytical approach, using modes defined on subregions of the medium, was also developed to model seismic wave propagation in media with vertically and horizontally variable elastic and anelastic properties. The restriction on the medium variability is that it can be represented by step function variations in its properties in both the vertical and horizontal directions. The theory is exact when the lateral variations are actually discontinuous step changes in properties. Consequently, when the actual changes can be well approximated as a sequence of steps, the method should be superior in computational accuracy and speed to numerical methods.