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EXACT SOLUTION OF THE REFLECTION AND REFRACTION OF ARBITRARY SPHERICAL COMPRESSIONAL WAVES AT LIQUID‐LIQUID INTERFACES AND AT SOLID‐SOLID INTERFACES WITH EQUAL SHEAR VELOCITIES AND EQUAL DENSITIES*
- Source: Geophysical Prospecting, Volume 10, Issue 1, Jan 1962, p. 35 - 67
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- 27 Apr 2006
Abstract
A new method of treating three‐dimensional elastic wave problems is described by applying it to the most simple case of the reflection and transmission of arbitrary homogeneous spherical compressional waves at plane liquid‐liquid interfaces. The case of plane solid‐solid interfaces with equal shear velocities and equal densities can be treated under the same heading.
The step‐response is obtained from the expressions for sinusoidal source excitation by a simple direct integration. The solutions for arbitrary source excitations are given in the usual way by the superposition integral. The solutions are proved by inserting them into the differential equations, followed by an application of the uniqueness theorem. The method is simple; all stages of establishing the solution (with the exception of the proof) are carried through in detail.