### ASA 124th Meeting New Orleans 1992 October

## 1aPA6. On the propagation of plane waves in dissipative anisotropic media.

**Jose M. Carcione
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*Osservatorio Geofisico Sperimentale, P.O. Box 2011 Opicina, 34016 Trieste,
Italy
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Hamburg Univ., Germany
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**Fabio Cavallini
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*Osservatorio Geofisico Sperimenale, Trieste, Italy
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A theory for propagation of time-harmonic fields in dissipative
anisotropic media is not a simple extension of the elastic theory. Firstly, one
has to decide for an appropriate constitutive equation that reduces to Hooke's
law in the elastic limit. In this work, one relaxation function is assigned to
the mean stress and three relaxation functions are assigned to the deviatoric
stresses in order to model the quality factors along preferred directions.
Secondly, in dissipative media there are two additional variables compared to
elastic media: the magnitude of the attenuation vector and its angle with
respect to the wave-number vector. When these vectors are colinear (homogeneous
waves), phase velocity, slowness, and attenuation surfaces are simply derived
from the complex velocity, although even in this case many of the elastic
properties are lost. The wave fronts, defined by the energy velocities, are
obtained from the energy balance equation. The attenuation factors are directly
derived from the complex velocities, but the quality factors require the
calculation of the potential and loss energy densities, yet resulting in a
simple function of the complex velocities. [Work supported by EEC.]