Elastic Wave Propagation in Large Composite Media: Models, and Their Analytical and Numerical Analysis

Dr. Xiaobing Feng

Department of Mathematical Sciences
University of Tennessee

November 14, 1997

Abstract

Problems of elastic wave propagation in infinite composite media have long been subjects of both theoretical and practical studies. Important applications of the studies are found in inverse scattering, seismology, underwater acoustics, and geosciences. In this talk, we will present a general model for elastic wave propagation through large or infinite composite media, and will then concentrate on the case of fluid-filled medial (so called borehole environment). The main point is that to avoid the traditional integral equation formulations for infinite domain problems, artificial boundaries are introduced and absorbing (radiation) boundary conditions are imposed on the artificial boundaries to minimize unphysical wave reflections. Another difficulty, which will also be addressed in the talk, for modeling is to find the appropriate interfacial boundary conditions on the interfaces of different media. Finally, we will present the analytical results such as existence, uniqueness, regularity of solutions for the models, and the numerical results such as finite element methods, error estimates and domain decomposition algorithms.