## Weakly inhomogeneous plane waves in
anisotropic, weakly dissipative media

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

Weakly inhomogeneous time-harmonic plane waves
propagating in homogeneous
anisotropic, weakly dissipative media are studied
using the perturbation method. Only
dissipation mechanisms, which can be described within
the framework of a linear viscoelasticity, are
considered. As a reference (non-perturbed) case,
plane waves with a real-valued slowness
vector propagating in perfectly elastic
anisotropic media are used. Simple approximate
expressions for the complex-valued slowness
and polarization vectors of weakly
inhomogeneous plane waves propagating in anisotropic,
weakly dissipative media are derived.
Special attention is devoted to the imaginary
part of the slowness vector, known as the
attenuation vector, which is responsible for
the amplitude attenuation of a plane wave.
The derived approximate expression for the
attenuation vector depends on the material
(intrinsic) dissipation parameters as well
as on the inhomogeneity of the plane wave. Its
scalar product with the energy-velocity
vector yields, however, the intrinsic
attenuation factor, which does not depend
on the inhomogeneity of the wave, and which
thus represents a very suitable measure of
the material dissipation. The derived
expression for the intrinsic attenuation factor
is valid for media of unrestricted anisotropy and
weak dissipation and for homogeneous as well
as weakly inhomogeneous plane waves.
The intrinsic attenuation factor is inversely
proportional to the scalar quantity, which, in
isotropic viscoelastic media, corresponds
to the well-known quality factor *Q*. Its
generalization to anisotropic weakly viscoelastic
media is directionally dependent. Numerical
examples are presented, in which the accuracy
of the approximate formulae based on the
perturbation method is studied. The results
indicate that the presented perturbation
results are sufficiently accurate to be used
in practical applications. Strong directivity
of the intrinsic attenuation factor shows its
great potential for the solution of inverse
problems.

### Keywords

Anisotropy, attenuation, inhomogeneous plane waves, perturbation methods,
viscoelasticity.

### Whole paper

The reprint is available in
PDF (1519 kB !).

*Geophys. J. int.*, **172** (2008), 663-673.

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