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The solution of Cagniard's problem for an SH line source in elastic and anelastic media, calculated using — k integrals

SCHOOL OF MATHEMATICAL SCIENCES RAYMOND AND BEVERLY SACKLER FACULTY OF EXACT SCIENCES RAMAT-AVIV, TEL AVIV 69978, Israel
SEISMOLOGY LABORATORY DEPARTMENT OF PHYSICS UNIVERSITY OF ALBERTA, EDMONTON, ALBERTA, Canada, T6G 2J1

Abstract

Computations have been performed using an improper — k double integral representing the response to an SH pulse generated by a line source, acting in a model consisting of two homogeneous isotropic elastic or linear viscoelastic half-spaces separated by a plane boundary. The advantage of this method is its universality: complete seismograms for relevant time and frequency windows are produced by the program. The calculated synthetic seismograms are accurate enough even for a small number of frequencies and compare well with exact results for elastic models obtained using Cagniard's method.

For the simple models of two anelastic or one elastic and one anelastic half-space in welded contact considered here, all the arrivals that are predicted by elasticity theory, including the incident, reflected, head, transmitted, and evanescent waves, are present. It seems that attenuation does not radically change the physical picture seen in the elastic case but rather modifies it: there is continuous variation with dispersion and attenuation. For viscoelastic media, the seismograms present features due to the nonplanar wavefronts propagating from a line source. Such features cannot be explained by the inhomogeneous plane wave theory.

This article has been cited by other articles:

				G. E. Quiroga-Goode, E. S. Krebes, and L. H. T. Le Modeling viscoelastic waves: a comparison of ray theory and the finite-difference method Bulletin of the Seismological Society of America, December 1, 1994; 84(6): 1882 - 1888. [Abstract] [PDF]

				L. H. T. LE On Cagniard's problem for a qSH line source in transversely isotropic media Bulletin of the Seismological Society of America, April 1, 1993; 83(2): 529 - 541. [Abstract] [PDF]