Numerical and Theoretical Study of Seismic Wave Diffraction in Complex Geologic Structure.

摘要

This report presents results of a theoretical study on wave propagation and diffraction effects in irregular geologic media. The first objective of the study is to demonstrate and validate some large-scale finite element methods for analyzing linear and nonlinear seismic effects in the surficial geologies relevant to several Air Force missions. The second objective is to solve the hitherto intractable problem of vector edge diffraction, which strongly influences seismic wave interactions at the geologic discontinuities ubiquitous in near-surface structure. The first paper describes a variety of linear and nonlinear, finite element seismic simulations at small- and large-scale, and their performance on minicomputers and supercomputers, particularly the Cray-2. The second paper develops a rigorous theory of vector wave diffraction for the canonical planar wedge problem. The third paper presents a numerical evaluation and verification of the two-dimensional diffraction theory for various types of incident plane-wave polarization. The diffraction solutions described here are used to verify discrete numerical solutions in the neighborhood of sharp edges. Validation is required because basis functions for the discrete solvers do not support the field singularities that actually occur at an edge. In fact, the exact solution evaluated here indicates that edge-diffracted seismic wave fields calculated by discrete numerical methods probably exhibits significant errors. (jhd)