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Book Chapter

Multifold Phase Space Path Integral Synthetic Seismograms

By
Mrinal K. Sen
Mrinal K. Sen
1
Institute for Geophysics, The University of Texas at Austin, Austin, Texas 78759, USA
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L. Neil Frazer
L. Neil Frazer
2
Hawaii Institute of Geophysics, Honolulu, Hawaii 96822, USA
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Published:
January 01, 2016

Summary

We consider a medium consisting of homogeneous layers separated by curved interfaces. In order to evaluate the response of a single generalized ray, the source and receiver wavefields are expanded in a series of plane waves. The coupling of these plane waves at each point of the surfaces of material discontinuity is determined by means of a Kirchhoff integral using generalized reflection and transmission coefficients. The resulting integral, called the multifold phase space path integral (PSPI) consists of a series of integrals over ray parameters and over interfaces touched by the generalized ray on its way from the source to the receiver. This approach is a generalization of the multifold configuration space path integral (CSPI) to which it reduces by successive application of the stationary phase point method over the ray-parameter integrals.

The PSPI like the CSPI automatically includes diffractions from corners. In addition classical head waves are included, although for curved interfaces the head waves are only approximate. 2-D synthetic seismograms are converted to equivalent approximate point-source responses by assuming cylindrical symmetry about source and/or receiver. The waveforms and amplitude of PSPI synthetic seismograms compare well with those computed by generalized ray theory for a 1-D model, and with finite difference synthetics for a 2-D model.

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Contents

Society of Exploration Geophysicists Geophysics Reprint Series

Seismic Diffraction

Kamil Klem-Musatov
Kamil Klem-Musatov
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Henning Hoeber
Henning Hoeber
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Michael Pelissier
Michael Pelissier
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Tijmen Jan Moser
Tijmen Jan Moser
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Society of Exploration Geophysicists
Volume
30
ISBN electronic:
9781560803188
Publication date:
January 01, 2016

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