Affiliation:
1. Department of Applied Mathematics The Weizmann Institute of Science Rehovot , Israel
Abstract
Abstract
The method of approximate Laplace transform inversion, by analytically inverting suitable rational approximations to a function f¯(p) 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 f¯(p) having branch points on the imaginary axis in the p-plane.
Publisher
Seismological Society of America (SSA)
Subject
Geochemistry and Petrology,Geophysics
Cited by
7 articles.
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1. Computation of the padé table;International Journal of Computer Mathematics;1972-01
2. Laplace Transform Inversion of Rational Functions;Geophysical Journal International;1971-12-01
3. Computation of Theoretical Seismograms;Geophysical Journal International;1970-12
4. Bibliography;Mathematics in Science and Engineering;1969
5. Bibliography;Mathematics in Science and Engineering;1969