To understand well the propagation of high-frequency seismic body waves
in *dissipative*, 3-D laterally varying isotropic and anisotropic
structures, containing curved structural interfaces, it is useful to
study first the behavior of plane waves in relevant homogeneous media
with planar interfaces. The ray methods represent, in fact, a local
application of plane waves in more complex structures. For example, the
reflection/transmission coefficients of plane waves at plane interfaces
between two homogeneous halfspaces may be locally applied even to
high-frequency seismic body waves incident at a curved interface between
two inhomogeneous media. This is the reason why this contribution is
devoted to plane waves in *dissipative* homogeneous media with
planar interfaces.

Inhomogeneous, time-harmonic, plane waves, propagating in
dissipative, isotropic and anisotropic media are investigated. The
elastodynamic equation for the dissipative homogeneous media is
solved in terms of eigenvalues and eigenvectors of the 3x3
Christoffel matrix Γ, with complex-valued elements
Γ* _{ik} = a_{ijkl}p_{j}p_{l}*,
where

As *p _{i}* are complex-valued,

A computer routine COEF52 is described, designed to compute arbitrary
frequency-dependent R/T coefficients on a plane interface between two
dissipative isotropic halfspaces, with a constant-*Q* dispersion
relations, assuming an incident plane wave with an arbitrary attenuation
angle γ. Routine COEF52 is a generalization of routine COEF51,
described by Brokesova and Cerveny (1997), where a special
choice of the attenuation angle γ of the incident wave was used.
The routine COEF52 may be also used to compute R/T coefficients from
transition layers.

Results of extensive computations of "reference R/T coefficients" on a
plane interface between two dissipative isotropic halfspaces are
presented and discussed. In all cases,
they are also compared with those
for non-dissipative media. Under reference R/T coefficients, we
understand the R/T coefficients for dissipative media, computed for the
fixed frequency, equal to the reference frequency *f _{r}*,
for which the complex-valued elastic moduli in the model are specified.
The dependence
of R/T coefficients on the attenuation angle γ of the incident
wave is studied in detail. For the computations of R/T coefficients, see
Section 6, and for the conclusions Section 7. In general, the
differences between the moduli of the R/T coefficients for dissipative and
non-dissipative models are usually small for realistic

The paper is available in PostScript (10140 kB !!, colour figures) and GZIPped PostScript (1285 kB !, colour figures).

In: Seismic Waves in Complex 3-D Structures, Report 7, pp. 57-146, Dep. Geophys., Charles Univ., Prague, 1998.