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An earth-flattening transformation for waves from a point source

Hill, David P. (1972) An earth-flattening transformation for waves from a point source. Bulletin of the Seismological Society of America, 62 (5). pp. 1195-1210. ISSN 0037-1106. http://resolver.caltech.edu/CaltechAUTHORS:20140826-131547771

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Abstract

An earth-flattening transformation is developed for wave-propagation problems that can be formulated in terms of uncoupled scalar Helmholtz equations. Through the transformation, wave problems in isotropic, spherically symmetric media with a specified radial heterogeneity can be expressed in terms of a flat geometry with a suitably vertical heterogeneity. The transformation is exact for homogeneous (no source) problems and is useful for normal mode studies. When a point source of waves is present, the earth-flattening transformation together with the Watson transform converts the reflected wave field from a sum over discrete, spherical eigenfunctions to an integral over continuous wave numbers in a flat geometry. The far-field form of this integral shares many properties with the Weyl integral and is useful for body-wave studies in a spherical earth.


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http://bssa.geoscienceworld.org/content/62/5/1195.abstractPublisherArticle
Additional Information:Copyright © 1972, by the Seismological Society of America. Manuscript received February 24, 1972. I would like to thank C. B. Archambeau for his advice and encouragement and D. L. Anderson and P. G. Richards for many helpful discussions during this study. Some of the results presented in this paper are contained in a thesis submitted in partial satisfaction of requirements for a Ph.D. degree at the California Institute of Technology. This research was supported in part by the Air Force Office of Scientific, Research under contract AFOSR F44620-69-C-0067.
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Air Force Office of Scientific Research (AFOSR)F44620-69-C-0067
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Caltech Division of Geological and Planetary Sciences2137
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Deposited By: George Porter
Deposited On:26 Aug 2014 20:21
Last Modified:13 Feb 2019 18:06

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