Anisotropic elastic materials that have one or two sheets of spherical slowness surface

Abstract

It is shown that certain anisotropic elastic materials can have one or two sheets of spherical slowness surface. The waves associated with a spherical slowness sheet can be longitudinal, transverse or neither. However, a longitudinal wave can propagate in any direction if and only if the slowness sheet is a sphere . The same cannot be said of transverse waves. A transverse wave can propagate in any direction without having a spherical slowness sheet. If a spherical slowness sheet exists, the waves need not be transverse. The existence of a spherical slowness sheet means that the associated velocity surface and the wave surface also have a sphere. Thus, one sheet of the wave front due to a point source is a sphere, a rather unusual phenomenon for anisotropic elastic materials. Particularly interesting anisotropic elastic materials are the ones in which one longitudinal and two transverse waves can propagate in any direction. They have one spherical slowness sheet for the longitudinal waves. In the special case, they have a second spherical slowness sheet which is disjoint from the spherical slowness sheet . The third slowness sheet is a spheroid.