## Boundary attenuation angles for inhomogeneous plane waves
in anisotropic dissipative media

**Vlastislav Cerveny** and
**Ivan Psencik**
### Summary

Attenuation angles *γ* of inhomogeneous plane waves propagating in
isotropic or anisotropic, perfectly elastic or viscoelastic media are
investigated. In isotropic viscoelastic media, the attenuation angle always
varies between *0*^{0} and *90*^{0}. In anisotropic viscoelastic media, however,
the attenuation angle varies in the range <*0*^{0}, *γ*^{*}>, where the boundary
attenuation angle *γ*^{*} may be greater than, equal to, or less than
*90*^{0}. The boundary attenuation angle depends on the viscoelastic moduli of
the medium and on the properties of the plane wave under consideration,
mainly on the direction of propagation of the wave.

In the plane-wave attenuation analysis, the attenuation angle *γ* is often
considered as a parameter of the inhomogeneous plane wave under
consideration, which can be chosen arbitrarily. It is shown in this paper
that such parameterization of the inhomogeneous plane wave may lead to
serious errors and problems, particularly if the attenuation angle is
chosen greater than or close to the boundary attenuation angle. For
*γ* > *γ*^{*}, such approach yields non-physical results (forbidden
directions), for *γ* < *γ*^{*} but close to *γ*, it yields inaccurate,
unstable and even indefinite expressions. As the boundary attenuation angle
is usually not known a priori, the attenuation angle should not be chosen freely.

A simple approach to compute quantities characterizing propagation of
inhomogeneous plane waves, used in this paper is based on the so-called mixed
specification of the slowness vector. The mixed specification does not use
the attenuation angle *γ* as a free parameter of the inhomogeneous plane
wave, and avoids the problems mentioned above. It makes possible to compute
exactly the phase velocity of the wave, the attenuation angle, the boundary
attenuation angle, the propagation and attenuation vectors, etc. The derived
equations may be used quite generally, for isotropic or anisotropic,
perfectly elastic or viscoelastic media, and for homogeneous and
inhomogeneous waves (including evanescent waves).

Numerical examples are presented and discussed.

### Whole paper

The paper is available in
PDF (239 kB).

In: Seismic Waves in Complex 3-D Structures, Report 20,
pp. 169-192, Dep. Geophys., Charles Univ., Prague, 2010.