Anomalous polarization of elastic waves in transversely isotropic media

TLDR: In this article, the behavior of transversely isotropic elastic media is analyzed from both the kinematic (slowness surface) and dynamic (particle displacement) point of view.

Abstract: The behavior of transversely isotropic elastic media is analyzed from both the kinematic (slowness surface) and dynamic (particle displacement) point of view. The relations for the slowness surfaces and wave front surfaces are derived in polar coordinates. Examination of the eigenvectors of the displacement equations of motion gives the relation for the polarization of the displacement vector associated with any plane wave. It is shown that the polarization of plane quasi‐P and quasi‐SV waves depends strongly on the sign of a particular elastic modulus, call it A, whereas the shape of the slowness surface is independent of the sign of A. When A is positive, which is the usual case, the particle displacement vector rotates in the same sense as the slowness vector. When A is negative, which is the “anomalous” case, the sense of rotation of the particle displacement vector is opposite to that of the slowness vector. Thus there is a direction in the medium for which the displacement vector associated with the...