Backscattering from spherical elastic inclusions and accuracy of the Kirchhoff approximation for curved interfaces

Details Backscattering from spherical elastic inclusions and accuracy of the Kirchhoff approximation for curved interfaces Backscattering from spherical elastic inclusions and accuracy of the Kirchhoff approximation for curved interfaces

Sep 2006

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006geoji.166.1249e&link_type=abstract

Geophysical Journal International, Volume 166, Issue 3, pp. 1249-1258.

Astronomy and Astrophysics

Astronomy

2

Elastic-Wave Scattering, Kirchhoff Approximation, Spherical Inclusions

Scientific paper

The Kirchhoff (or tangent plane) approximation, derived from the theoretically complete Kirchhoff-Helmholtz integral representation for the seismic wavefield, has been used extensively for the analysis of seismic-wave scattering from irregular interfaces; however, the accuracy of this method for curved interfaces has not been rigorously established. This paper describes an efficient Kirchhoff algorithm to simulate scattered waves from an arbitrarily curved interface in an elastic medium. Synthetic seismograms computed using this algorithm are compared with exact synthetics computed using analytical formulae for scattering of plane P waves by a spherical elastic inclusion. A windowing technique is used to remove strong internal reverberations from the analytical solution. Although the Kirchhoff method tends to underestimate the total scattering intensity, the accuracy of the approximation improves with increasing value of the wavenumber-radius product, kR. The arrival times and pulse shapes of primary reflections from the sphere are well approximated using the Kirchhoff approach regardless of curvature of the scattering surface, but the amplitudes are significantly underestimated for kR <= 5. The results of this work provide some new guidelines to assess the accuracy of Kirchhoff-synthetic seismograms for curved interfaces.

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