## Velocity, attenuation, and quality factor in anisotropic
viscoelastic media: A perturbation approach

**Vaclav Vavrycuk**
### Summary

Velocity, attenuation, and the quality (Q-) factor of waves propagating in
homogeneous media of arbitrary anisotropy and attenuation strength
are calculated in high-frequency asymptotics using a stationary slowness
vector, the vector evaluated at the stationary point of the slowness surface.
This vector is generally complex-valued and inhomogeneous, meaning that
the real and imaginary parts of the vector have different directions.
The slowness vector can be determined by solving three coupled polynomial
equations of the sixth order or by a nonlinear inversion. The procedure is
simplified if perturbation theory is applied. The elastic medium is viewed
as a background medium, and the attenuation effects are incorporated as
perturbations. In the first-order approximation, the phase and ray velocities
and their directions remain unchanged, being the same as those in
the background elastic medium. The perturbation of the slowness vector is
calculated by solving a system of three linear equations. The phase attenuation
and phase Q-factor are linear functions of the perturbation of the slowness
vector. Calculating the ray attenuation and ray Q-factor is even simpler
than calculating the phase quantities because they are expressed in terms of
perturbations of the medium without the need to evaluate the perturbation of
the slowness vector. Numerical modeling indicates that the perturbations
are highly accurate; the errors are less than 0.3% for a medium with a Q-factor
of 20 or higher. The accuracy can be enhanced further by a simple modification
of the first-order perturbation formulas.

### Whole paper

The reprint is available in
PDF (660 kB).

*Geophysics*, **73** (2008), No.5, D63-D73.

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