CONDITIONS UNDER WHICH THE SLOWNESS SURFACE OF AN ANISOTROPIC ELASTIC-MATERIAL IS THE UNION OF ALIGNED ELLIPSOIDS

The slowness surface of an anisotropic elastic material is described as consisting of aligned ellipsoids when it is the union of three coaxial ellipsoids each common principal axis of which is a specific direction for a longitudinal plane wave. It is shown that the slowness surface has this property only when the material has orthorhombic symmetry. Five sets of conditions are obtained, one of them necessary and each sufficient, for the slowness surface of an orthorhombic elastic material to be formed from aligned ellipsoids. A complete characterization of the conditions referred to in the title of the paper is thus provided. © 1990 Oxford University Press.