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Exact Time-Domain Solutions for Acoustic Diffraction by a Half Plane

By
David R. Dalton
David R. Dalton
Department of Geophysics and Astronomy, University of British Columbia, Vancouver, V6TIWS, Canada
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Matthew J. Yedlin
Matthew J. Yedlin
Department of Geophysics and Astronomy, University of British Columbia, Vancouver, V6TIWS, Canada
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Published:
January 01, 2016

Abstract

We derive exact time-domain solutions for scattering of acoustic waves by a half plane by inverse Fourier transforming the frequency-domainintegral solutions. The solutions consist of a direct term, a reflected term and two diffraction terms. The diffracting edge induces step functiondiscontinuities in the direct and reflected terms at two shadow boundrics. At each boundary, the associated diffraction term reaches a maximumamplitude of half the geometrical optics term and has a signum function discontinuity so that the total field remains continuous. Wc evaluatesolutions for practical point source configurations by numerically convolving the impulse diffraction responses with a wavelet. We solve theassociated problems of convolution with a singular, truncated diffraction operator by analytically derived correction techniques, Wc produce a zerooffset section and compare it to a Kirchhoff integral solution. Our exact diffraction hyperbola exhibits noticeable asymmetry, with higheramplitudes on the reflector side of the edge. Near the apex of the hyperbola (he Kirchhoff solution approximates the exact diffraction termsymmetric in amplitude about the reflection shadow boundary, bui omits the other low amplitude term necessary to ensure continuity at the directshadow boundary.

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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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