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THE SPECTRAL FUNCTION OF A VERTICALLY INHOMOGENEOUS MEDIUM 1
Author(s) -
URSIN B.
Publication year - 1988
Publication title -
geophysical prospecting
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.735
H-Index - 79
eISSN - 1365-2478
pISSN - 0016-8025
DOI - 10.1111/j.1365-2478.1988.tb02147.x
Subject(s) - source function , physics , energy flux , bounded function , discontinuity (linguistics) , reflection (computer programming) , invariant (physics) , wave propagation , optics , computational physics , mathematical analysis , mathematics , quantum mechanics , astrophysics , computer science , programming language
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.