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Bulletin of the Seismological Society of America; December 1974; v. 64; no. 6; p. 1733-1742
© 1974 Seismological Society of America
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Phase shift and pulse distortion in body waves due to internal caustics

DAVID P. HILL

NATIONAL CENTER FOR EARTHQUAKE RESEARCH U.S. GEOLOGICAL SURVEY, MENLO PARK, CALIFORNIA

Abstract

Body waves that form an internal caustic attain a±{pi}/2 phase shift in the vicinity of the point where the ray touches the caustic. This phase shift distorts a pulse propagating along the ray into its allied function. Asymptotic and numerically exact solutions for a particular model illustrate this property for waves on the back branch of a travel-time curve and the class of multiply reflected waves analogous to PdP waves in the Earth. Numerically exact solutions show that the {pi}/2 phase shift is a high-frequency effect and that the phase shift tends toward zero for very low frequencies. The frequency dependence of the phase shift acts to maintain causality for broad-band pulses. Properties of the phase shift associated with internal caustics can be used to predict wave forms in a variety of applications; multiply reflected waves in a sphere (pP, PP, PPP) provide a simple example.




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