## SH plane-wave reflection/transmission coefficients
in isotropic, attenuating media

**Ivan Psencik** **,**
**Milosz Wcislo** **&**
**Patrick F. Daley**
### Summary

An attempt is made to extend the applicability of the weak-attenuation
concept (WAC) to ray-theory computations. WAC allows an approximate
evaluation of effects of attenuation on seismic-wave propagation in
smoothly varying laterally inhomogeneous media encountered in most
seismological studies. The goal is to find under which conditions WAC
could be applicable to layered media. Specifically, if the use of WAC
is necessary, under which conditions it can be used for the approximate
evaluation of the reflection and transmission coefficients at interfaces
separating attenuating media. It turns out that outside critical
incidence regions, where the ray theory is not applicable, the effects
of attenuation on the reflection and transmission are negligible in
comparison with effects of attenuation on wave propagation inside layers.
Despite of it, the approximate formulae for reflection and transmission
coefficients including effects of attenuation are derived and presented.
For better insight and simplicity, effects of attenuation on SH plane-wave
coefficients at interfaces separating homogeneous, attenuating isotropic
half-spaces are studied. The coefficients are expressed in the form of
the sum of coefficients in a reference elastic medium plus a perturbation
due to weak attenuation. The study is based on the assumption of the
validity of the correspondence principle despite indications of its
inapplicability in some situations. A fixed frequency is considered.
A basic role in the evaluation of coefficients is played by slowness
vectors of incident and transmitted waves. They are required to satisfy
constraints resulting from the corresponding equation of motion, Snell's
law and radiation condition. The resulting formulae for coefficients are
singular for the angles corresponding to critical incidence in the
reference elastic medium. It is shown that the approximate formulae work
well in the subcritical region. Problems arise in the overcritical region
of reference elastic media. The problems are related to the inapplicability
of the commonly used correspondence principle. An artificial modification
of formulae is proposed, which resolves the problem. However, it leads to
the violation of the equation of motion and Snell's law constraints.

### Keywords

Attenuation, weak-attenuation concept, correspondence principle,
SH-wave displacement reflection/transmission coefficients.

*Journal of Seismology*, in press.