## Energy flux in viscoelastic anisotropic media

**Vlastislav Cerveny** ** & **
**Ivan Psencik**
### Summary

We study properties of the energy-flux vector
and other related energy quantities of homogeneous
and inhomogeneous time-harmonic P and S plane waves,
propagating in unbounded
viscoelastic anisotropic media, both analytically
and numerically. We propose an algorithm
for the computation of the energy-flux vector,
which can be used for media of unrestricted
anisotropy and viscoelasticity, and for arbitrary
homogeneous or inhomogeneous plane waves.
Basic part of the algorithm is determination of the
slowness vector of a homogeneous or inhomogeneous
wave, which satisfies certain constraints following
from the equation of motion.
Approaches for determination of a slowness vector
commonly used in viscoelastic isotropic
media are usually difficult to use in viscoelastic
anisotropic media. Sometimes they may even
lead to non-physical solutions. To avoid these
problems, we use the so-called mixed specification
of the slowness vector, which requires,
in a general case, solution of a complex-valued
algebraic equation of the sixth degree.
For simpler cases, as for SH waves propagating in
symmetry planes, the algorithm yields simple
analytic solutions. Once the slowness vector is
known, determination of energy flux and of other
energy quantities is easy.We present numerical
examples illustrating the behaviour of the
energy-flux vector and other energy quantities,
for homogeneous and inhomogeneous plane P, SV
and SH waves.

### Keywords

Attenuation vector, energy flux, energy-velocity vector, inhomogeneous plane
waves, propagation vector, viscoelastic anisotropic media.

### Whole paper

The reprint is available in
PostScript (7138 kB !, colour figures),
GZIPped PostScript
(1148 kB !, colour figures),
and PDF (2072 kB !, colour figures).

*Geophys. J. int.*, **166** (2006), 1299-1317.

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