## Slowness vectors of harmonic plane waves
in viscoelastic anisotropic media

**Vlastislav Cerveny** and
**Ivan Psencik**
### Summary

Properties of inhomogeneous plane waves propagating in a viscoelastic
anisotropic medium are investigated. The slowness vector **p** is described
by the so-called mixed specification. In it, the vector **p** is
expressed in terms of two given real-valued, mutually perpendicular
vectors (one of them specifying the direction of propagation), and of
a free complex-valued parameter *sigma*. The parameter
*sigma* must be determined so that the slowness vector **p** satisfies
a constraint relation following from an equation of motion for viscoelastic
media. In this contribution, *sigma* is determined by solving a
complex-valued polynomial equation of the sixth degree. The used algorithm
is quite general. It can be used for homogeneous as well as inhomogeneous
plane waves propagating in elastic or viscoelastic, isotropic or anisotropic
media. It is shown that the inhomogeneous plane waves propagating in
anisotropic viscoelastic media exhibit certain phenomena, not known from
elastic anisotropic or viscoelastic isotropic media. For example,
the inhomogeneous plane qP wave may propagate with the same phase velocity
as one of inhomogeneous plane qS wave. It is also shown that the attenuation
angles of inhomogeneous plane waves can attain values greater than *pi/2*
even for very weakly inhomogeneous plane waves.

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In: Seismic Waves in Complex 3-D Structures, Report 13,
pp. 189-197, Dep. Geophys., Charles Univ., Prague, 2003.

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