Some relationships between reflection and transmission coefficients for stratified elastic media

Document Type

Article

Publication Date

12-1-1989

Abstract

The longitudinal and shear speeds for stratified elastic media at depth are deduced from reflection coefficient data and from speeds commonly known in applications. In particular a matrix involving the known reflection coefficient matrix, as a function of incidence and angles and known speeds, has two non-negative eigenvalues. These eigenvalues have the following property: both are zero near grazing incidence and remain zero for angles less than the nearest critical angle. Between the two critical angles one eigenvalue is zero and the second is non-zero. For larger angles both are non-zero. Thus the eigenvalues determine the critical angles and therefore the speeds. Specifically, if the interface reflection coefficient matrix is known as a function of incidence angle, between two constant-coefficient half-spaces, then the speeds of the reflecting layer are determined by these eigenvalues.

Identifier

0024913057 (Scopus)

Publication Title

Inverse Problems

External Full Text Location

https://doi.org/10.1088/0266-5611/5/6/021

ISSN

02665611

First Page

1163

Last Page

1172

Issue

6

Volume

5

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