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Book Chapter

Self-Consistent Analysis of Waves in Rocks Containing Arrays of Cracks

By
F. J. Sabina
F. J. Sabina
Proyecto Universitario de Fenomenos Nolineales y Mecanica (FENOMEC) Instituto de lnvestigadones en Matematicas Aplicadas y en Sistemas Universidad Nacional Autonoma de Mexico Apdo. Postal 20-726, Admon. No. 20 Delegadon de Alvaro Obregon 01000 Mexico D.F, Mexico
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J. R. Willis
J. R. Willis
Department of Applied Mathematics and Theoretical Physics University of Cambridge Silver Street Cambridge CB3 9EW, United Kingdom
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Published:
January 01, 1996

Abstract

A self-consistent scheme has recently been implemented to study wave propagation through a variety of materials with microstructure such as, for example, anisotropic matrix containing a random array of aligned spheroidal inclusions, and its limiting case of penny-shaped cracks. Dispersion and attenuation curves calculated using this method show a characteristic resonance behaviour as a function of frequency that is independent of the wave type and the angle of incidence in almost all cases. Also, there is a frequency dependence of the azimuthal behaviour of the speed and attenuation coefficients in some cases. At low frequencies, very similar results may be found by employing the method of smoothing or the quasicrystalline approximation. But only the self-consistent method has been developed to yield wave speeds and attenuation for finite frequencies.

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Seismic Anisotropy

Erling Fjær
Erling Fjær
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Rune M. Holt
Rune M. Holt
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Jaswant S. Rathore
Jaswant S. Rathore
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Society of Exploration Geophysicists
ISBN electronic:
9781560802693
Publication date:
January 01, 1996

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