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The effect of focal depth on the spectra of P waves I. Theoretical formulation

DEPARTMENT OF EARTH AND ATMOSPHERIC SCIENCES ST. LOUIS UNIVERSITY, St. Louis, Missouri 63156

Abstract

Since the Earth's free surface acts as a reflector, one may except the spectra of seismic body waves to be influenced by the focal depth of an earthquake. In order to investigate this effect, a boundary value problem has been formulated involving (n – 1) homogeneous, isotropic, perfectly elastic plane layers overlying a homogeneous half-space. The sources of the elastic waves are represented as discontinuities of stress across a conceptual interface inside the medium. Certain functions of the wave potentials which govern the solution of the boundary value problem are denoted as the source functions in the mathematical formulation of the problem. Expressions for the source functions for P and SV waves are derived for different kinds of point sources, including a double couple point source oriented in an arbitrary manner inside the medium.

Footnotes

^* Now with Mathematics Department, Texas Southern University, Houston, Texas 77004.

This article has been cited by other articles:

				S. J. SINGH Deformation of a multilayered half-space by stress dislocations and concentrated forces Bulletin of the Seismological Society of America, December 1, 1971; 61(6): 1625 - 1637. [Abstract] [PDF]

				S. K. GUHA and W. STAUDER The effect of focal depth on the spectra of P waves II. Observational studies Bulletin of the Seismological Society of America, October 1, 1970; 60(5): 1457 - 1477. [Abstract] [PDF]