## Componental specification of plane waves
in isotropic and anisotropic viscoelastic media

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

Time-harmonic, homogeneous and inhomogeneous plane waves propagating in
isotropic and anisotropic viscoelastic media are investigated.
The componental specification of the slowness vector **p** is used, in which
the slowness vector **p** is computed from its known projection
**p**^{Σ} to an arbitrarily chosen plane Σ. The vectors
**p** and **p**^{Σ} are, in general, complex-valued. The most
important step in the procedure consists in the determination of the
component σ of the slowness vector **p** to the normal
**n**^{Σ}
to Σ.
For general anisotropic viscoelastic media, the component σ
is a root of an algebraic equation of the sixth
degree, with complex-valued coefficients. For isotropic viscoelastic media,
the algebraic equation of the sixth degree factorizes to simple quadratic equations.
For SH plane waves propagating in the plane of symmetry of a monoclinic
(orthorhombic, hexagonal) viscoelastic medium it also factorizes providing
a quadratic equation for SH waves. The componental specification of
the slowness vector plays an important role in the solution
of the problem of the reflection/transmission of plane waves at a plane interface
between two viscoelastic anisotropic media.

### Whole paper

The paper is available in
PDF (209 kB).

In: Seismic Waves in Complex 3-D Structures, Report 21,
pp. 185-207, Dep. Geophys., Charles Univ., Prague, 2011.