When upward-propagating rays transporting seismic energy are recorded at the earth's surface, the vertical and horizontal components of displacement are not the vector decomposition of the associated amplitude vector. Rather, a more involved interaction of the incident ray, either P or Sv, and two related reflected arrivals at this interface, the PP and PSv in the first case and the SvP and SvSv in the second, are incorporated. Although the earth's atmosphere is a fluid, it is usually assumed to be a vacuum so that no disturbance exists above the interface.
In the analogous situation at a liquid/solid interface, where the receivers are located on, and are assumed to be coupled to, the solid, the effect of the fluid becomes significant and must be included in the problem, as a compressional (P) ray of seismic interest propagates in the liquid. This results in a marginally more complex problem than the vacuum/solid interface. Also, this is a highly idealized statement of the problem, as in most realistic situations, a transition zone between the liquid and the solid exists which is quite different from the sharp discontinuity referred to above. However, it is thought to be instructive to first consider the simpler case before proceeding to the more difficult transition layer problem.
As reflection coefficients at a liquid/solid boundary are required in the derivation of these conversion coefficients, the formulae for the case of the solid being a transversely isotropic medium are presented which allows additional flexibility. For completeness, all reflection and transmission coefficients for a transversely isotropic medium in contact with a fluid are presented.
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