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Book Chapter

On the Reflection and Transmission of Seismic Waves at Surfaces of Discontinuity

By
Karl Zoeppritz
Karl Zoeppritz
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Published:
January 01, 2007

Abstract

In a recently published paper (E. Wiechert and K. Zoeppritz, “On Earthquake Waves”), Professor E. Wiechert has treated the reflection of seismic waves at the surface of the earth. Effects caused by an air or water layer were neglected in view of their negligible influence, and the reflection was treated as if it occurred at a free surface. Given today’s unavoidable uncertainty in seismic measurement methods, as can be seen from a rough estimate, this is a very good approximation. However, it seems of interest to find the formulas for the reflection and transmission of elastic waves at a boundary formed by two elastic media of arbitrary constitution. This is of interest not only with regard to the behavior at the surface of the earth but even more so with respect to interfaces in the earth’s interior. Following a suggestion by Professor Wiechert, I have treated this more general case and will present some results in the following.

I consider the planar intersection between two media, 1 and 2, with densities ρ1 and ρ2 and elastic constants a1, b1 and a2, b2. Here, a and b denote the propagation velocities of the pure dilatational and the dilatation-free shear waves. For ease of comparison, I briefly present the formulas giving the relation of these variables with Lamé’s constants λ and μ as well as with Poisson’s constant σ:

Regarding the equations of motion for isotropic, elastic media, I refer to the relevant discussion in the above-cited work by E. Wiechert. To

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Contents

Society of Exploration Geophysicists Geophysics Reprint Series

Classics of Elastic Wave Theory

Michael A. Pelissier
Michael A. Pelissier
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Henning Hoeber
Henning Hoeber
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Norbert van de Coevering
Norbert van de Coevering
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Ian F. Jones
Ian F. Jones
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Society of Exploration Geophysicists
Volume
24
ISBN electronic:
9781560801931
Publication date:
January 01, 2007

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