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

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

We study behavior of attenuation (inhomogeneity) angles γ,
i.e., angles between real and imaginary parts of the slowness
vectors of inhomogeneous plane waves propagating in isotropic
or anisotropic, perfectly elastic or viscoelastic, unbounded
media. The angle γ never exceeds the boundary attenuation
angle γ^{*}. In isotropic viscoelastic media γ^{*}=90°;
in anisotropic viscoelastic media γ^{*} may be greater than,
equal to, or less than 90°. Plane waves with γ > γ^{*}
do not exist. Because γ^{*} in anisotropic viscoelastic media
is usually not known a priori, the commonly used specification of
an inhomogeneous plane wave by the attenuation angle γ may
lead to serious problems. If γ is chosen close to γ^{*}
or even larger, indeterminate, unstable or even nonphysical results
are obtained. We study properties of γ^{*} and show that the
approach based on the mixed specification of the slowness vector
fully avoids the problems mentioned above. The approach allows
exact determination of γ^{*} and removes instabilities known
from the use of the specification of the slowness vector by γ.
For γ - γ^{*}, the approach yields zero phase velocity,
i.e., the corresponding wave is a nonpropagating wave mode. The use
of the mixed specification leads to the explanation of the deviation
of γ^{*} from 90° as a consequence of different orientations of
energy-flux and propagation vectors in anisotropic media. The approach
is universal; it may be used for isotropic or anisotropic, perfectly
elastic or viscoelastic media, and for homogeneous and inhomogeneous
waves, including strongly inhomogeneous waves, like evanescent waves.

### Whole paper

The reprint is available in
PDF (2126 kB !).

*Geophysics*, **76** (2011), WA51-WA62.