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Volume 36 Number 1
  • E-ISSN: 1365-2478

Abstract

ABSTRACT

Elastic, acoustic and electromagnetic waves in media consisting of vertically inhomogeneous layers are considered in a common formulation. The spectral function of a vertically inhomogeneous medium is the downward energy flux due to an impulsive source at the top of the first layer. A propagation‐invariant form is used to derive several identities for the reflection and transmission matrices. When the top layer is bounded by a free surface, one of the expressions reduces to a formula derived by Kunetz for the one‐dimensional wave equation.

A source radiating upwards and downwards gives a discontinuity in the propagation‐invariant form which is equal to the source energy. A new formula is derived for when the source is located just beneath the top interface of the layers.

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2006-04-27
2024-04-27

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  • Article Type: Research Article

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