Some Algebraic Aspects of the Lamb Problem.
Abstract
This paper discusses the classical Lamb problem for the elastic wave equation. The motivation, for the authors, is to be able to conveniently construct Green's functions (matrices) for later use in formulating and solving various problems. For example, we will want to be able to solve for perturbations from constant reference densities ad Lamb parameters. Hence, Green's function for the homogeneous isotropic equation is discussed. Due to the scattering taking place in inverse problems it is usually impossible to retain the P-SV and SH decoupling; hence, we do not persue this decoupling in the formation of the Green's functions herein. While nothing conceptually new is presented here, the approach is a bit different and, we believe, is helpful in isolating some important issues. The approach is algebraic in nature and makes heavy use of several simple facts from linear algebra; for example, the spectral decomposition of special matrices. This approach facilitates some helpful decoupling, particularly in solving for reflection coefficients.
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 01, 1986
- Accession Number
- ADA175424
Entities
People
- David S. Gilliam
- Frank G. Hagin
Organizations
- Colorado School of Mines