Description of weak anisotropy and weak attenuation using the first-order perturbation theory

Vaclav Vavrycuk


Velocity anisotropy and attenuation in weakly anisotropic and weakly attenuating structures can be treated uniformly using the weak anisotropy-attenuation (WAA) parameters. The WAA parameters are constructed in a very analogous way to weak anisotropy (WA) parameters designed for weak elastic anisotropy. The WAA parameters generalize the WA parameters by incorporating the attenuation effects. The WAA parameters can be represented alternatively by one set of complex values or by two sets of real values. Assuming high-frequency waves and using the first-order perturbation theory, all basic wave quantities such as the slowness vector, polarization vector, propagation velocity, attenuation and quality factor are linear functions of the WAA parameters.

Numerical modeling shows that the perturbation formulas have different accuracy for different wave quantities. The propagation velocity is usually calculated with high accuracy. However, the attenuation and quality factor may be reproduced with appreciably lower accuracy. This happens mostly when strength of velocity anisotropy is higher than 10% and attenuation is moderate or weak (Q-factor > 20). In this case, the errors of the attenuation or quality factor can attain values comparable with strength of anisotropy or can be even higher. It is shown that a simple modification of the formulas by including some higher-order perturbations improves the accuracy three to four times.


Anisotropy, attenuation, perturbation theory, theory of wave propagation.

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In: Seismic Waves in Complex 3-D Structures, Report 19, pp. 191-218, Dep. Geophys., Charles Univ., Prague, 2009.
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