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GEOREF RECORD

Local Fourier transform of the Helmholtz wave equation

Steve T. Hildebrand
Local Fourier transform of the Helmholtz wave equation
Geophysics (September 1987) 52 (9): 1303-1305

Abstract

A local Fourier transform of a wave field is an integral transformation from space-time coordinate space to phase space, i.e., ray parameter, spatial coordinate, and intercept- time space. McMechan (1983) introduced the concept of a local slant-stack/Fourier transform. Using this integral transform, he was able to define a wave field in phase space. By projecting the resulting wave field to the spatial coordinate space, he obtained a representation of the wave field in the ray-parameter and the spatial-coordinate plane. In this paper, the local Fourier method is used to transform the Helmholtz wave equation into a phase-space coordinate system. The resulting wave equation is then written in a state-variable form of coupled first-order differential equations. A propagator solution is then shown.


ISSN: 0016-8033
EISSN: 1942-2156
Coden: GPYSA7
Serial Title: Geophysics
Serial Volume: 52
Serial Issue: 9
Title: Local Fourier transform of the Helmholtz wave equation
Pages: 1303-1305
Published: 198709
Text Language: English
Publisher: Society of Exploration Geophysicists, Tulsa, OK, United States
Accession Number: 2002-076124
Categories: Applied geophysics
Document Type: Serial
Bibliographic Level: Analytic
Country of Publication: United States
Secondary Affiliation: GeoRef, Copyright 2017, American Geosciences Institute. Reference includes data supplied by Society of Exploration Geophysicists, Tulsa, OK, United States
Update Code: 200223
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