# PRAGUE CENTRE OF
MATHEMATICAL
GEOPHYSICS,
METEOROLOGY, AND THEIR
APPLICATIONS

(MAGMA)

### Anomalous polarization in anisotropic media

Klaus Helbig, Hannover, Germany

Prague, Dec 1, 2004
In “standard” anisotropic media with {C_11, C_22, C_33} > {C_44, C_55, C_66}, the angle between
polarization vector of the fastest wave and propagation direction as a rule is less than pi/4, i.e.,
the fastest wave is “quasi-longitudinal”. There are a few exceptions to this rule, as pointed out
by Helbig and Schoenberg (1987) for transversely isotropic media and by Carcione and
Helbig (2000) for orthotropic media. In these “anomalously polarized” media the polarization
vector can make any angle with the propagation direction, and in particular there are
propagation directions where the fastest wave is transversely polarized. Such media have a
“normal” companion medium. The two companion media have identical slowness surfaces
(and thus identical ray-wavefront systems) but different polarization patterns.

Here the general conditions for the occurrence of anomalous polarization in any
anisotropic medium are investigated. It turns out that anomalous polarization can occur in
transversely isotropic, orthotropic and monoclinic media: an isotropic medium can have one
anomalous companion medium, an orthotropic medium three, and a monoclinic medium can
have one anomalous companion.

It was shown by Carcione and Helbig that there are orthotropic companion pairs where
both members satisfy the stability. It is shown here that to any stable orthotropic companion
pair there exists a class of “monoclinic extensions” obtained by adding to the stiffness matrix
either C_14<>0, C_25<>0, or C_36<>0, depending on the nature of the orthotropic pair.

No claim is made that such media occur in geological settings, only that they are allowed
by the laws of physics.

Last edited Dec 6, 2004