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The application of rational approximations to the solution of problems in theoretical seismology

DEPARTMENT OF APPLIED MATHEMATICS THE WEIZMANN INSTITUTE OF SCIENCE, REHOVOT, Israel

Abstract

The method of approximate Laplace transform inversion, by analytically inverting suitable rational approximations to a function of the operator p is applied to the problem of propagation from a quadratic pulse point source in a uniform liquid sphere.

Apart from this main problem, the relation between the efficiency of the method and the sharpness of the pulse is illustrated in a general way by considering three simple examples (in descending order of sharpness), namely the approximate inversion of the Laplace transforms of a delayed Heaviside unit function, a simple function having a gradient discontinuity, and a quadratic pulse.

In order to suggest how the technique can be extended to more difficult theoretical seismic problems, the method is applied to a simple function having branch points on the imaginary axis in the p-plane.