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Geometric Elastodynamics: Rays and Generalized Rays

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Seismic Waves and Sources

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Abstract

The separation of dependent and independent variables is of fundamental importance in the analytic determination of the fields associated with the partial differential equations of mathematical physics. In particular, the determination of the displacement field at any point of a heterogeneous elastic medium is greatly simplified if the vector wave equation of elasticity can be split into three equations; corresponding to the P, SV, and SH waves of seismology. Although the SH motion can be separated from the P and SV motions for all radially heterogeneous isotropic media, the P and SV motions, in general, can at most be reduced to a system of two coupled scalar equations. The vector wave equation is called decoupled if these two scalar equations can be transformed into two uncoupled equations, one corresponding to P waves and the other to SV waves.

Everything should be made as simple as possible, but not simpler.

(Albert Einstein)

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Authors and Affiliations

  1. Weizmann Institute of Science, Rehovot, 76100, Israel

    Ari Ben-Menahem (Professor of Geophysics)

  2. Maharshi Dayanand University, Rohtak, 124001, India

    Sarva Jit Singh (Professor of Mathematics)

Authors
  1. Ari Ben-Menahem
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  2. Sarva Jit Singh
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© 1981 Springer-Verlag New York Inc.

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Ben-Menahem, A., Singh, S.J. (1981). Geometric Elastodynamics: Rays and Generalized Rays. In: Seismic Waves and Sources. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-5856-8_7

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  • DOI: https://doi.org/10.1007/978-1-4612-5856-8_7

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-5858-2

  • Online ISBN: 978-1-4612-5856-8

  • eBook Packages: Springer Book Archive

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