## Attenuation vector in heterogeneous, weakly dissipative,
anisotropic media

**Vlastislav Cerveny**,
**Ludek Klimes** and
**Ivan Psencik**
### Summary

Attenuation vector **A** plays an important role
in the investigation of waves propagating in
dissipative, isotropic or anisotropic media. It is defined
as the imaginary part of the
complex-valued slowness vector
**p**=**P**+i**A**. In this paper,
simple expressions for the attenuation vector
**A** are derived for seismic body waves propagating
in heterogeneous, weakly dissipative, anisotropic
media. Ray-theory
perturbation method is used, in which the dissipative medium
is considered to be a small
perturbation of perfectly elastic medium. The general perturbation
procedure proposed by Klimes (2002)
is very suitable for this purpose, as it does not require
to perform ray tracing in dissipative media;
the computation of rays in the background perfectly elastic medium,
followed by quadratures along them, is quite sufficient. It is shown
that the waves propagating in a heterogeneous, weakly dissipative,
anisotropic or isotropic medium are,
in general, inhomogeneous.
This means that their attenuation vector **A** is not
parallel to the propagation
vector **P**. This holds also for waves generated by
a point source, propagating in homogeneous
anisotropic dissipative media. Exception is a wave generated by
a point source in a homogeneous isotropic
dissipative medium, where the generated wave is homogeneous.
Thus, the commonly used concept of homogeneous waves,
used often in isotropic dissipative media, cannot be used
in anisotropic dissipative media. The situation is
different for plane waves propagating in homogeneous dissipative
isotropic or anisotropic media. In this case,
the homogeneity or inhomogeneity of the plane wave depends on
initial conditions, which may be chosen freely.
It is also shown that the intrinsic attenuation factor
*A*^{in}, defined as twice the projection
of **A** into the direction of the reference ray,
does not depend on the weak inhomogeneity of the wave, and
represents a convenient measure of material dissipation.
The intrinsic attenuation factor is used to determine
the position and direction dependent quality factor *Q*
for heterogeneous anisotropic weakly dissipative media.

### Keywords

Anisotropy, attenuation, attenuation vector, inhomogeneous waves,
perturbation ray theory, viscoelasticity.

### Whole paper

The
image of the paper in GIF 150dpi (846 kB)
is designed for an instant screen preview.

The paper is available in
PostScript (225 kB)
and GZIPped PostScript (87 kB).

In: Seismic Waves in Complex 3-D Structures, Report 17,
pp. 195-212, Dep. Geophys., Charles Univ., Prague, 2007.

SW3D
- main page of consortium ** Seismic Waves in Complex 3-D Structures **.