## Velocity and attenuation of wavefields generated by point sources
in anisotropic viscoelastic media: asymptotic approach

**Vaclav Vavrycuk**
### Summary

Asymptotic wave quantities in anisotropic viscoelastic media such as
ray velocity and ray attenuation are calculated using a stationary
slowness vector defined as the slowness vector that predicts the
complex energy velocity parallel to a ray. The stationary slowness
vector is, in general, complex-valued and inhomogeneous. Its
computation involves finding two independent unit vectors, which
specify the directions of its real and imaginary parts. The wave
inhomogeneity affects the asymptotic quantities and complicates their
computation. The critical quantities are attenuation and the
*Q*-factor, which can significantly vary with the slowness vector
inhomogeneity. If the inhomogeneity is neglected, the directional
variation of attenuation and the *Q*-factor can distinctly be
distorted. The errors can attain values commensurate to strength of
velocity anisotropy, so up to tens of percent for sedimentary rocks.
This applies to strongly as well as weakly attenuative media. On the
contrary, the ray velocity, which defines the wavefronts and physically
corresponds to the energy velocity of a high-frequency signal
propagating along a ray, is almost insensitive to the slowness vector
inhomogeneity and thus can be calculated in a simplified way except for
media with extremely strong anisotropy and attenuation.

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In: Seismic Waves in Complex 3-D Structures, Report 17,
pp. 243-265, Dep. Geophys., Charles Univ., Prague, 2007.

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