Criteria for elastic waves in anisotropic media — a consolidation

The geometry relating to the tangent plane at a stationary point on a surface has been used to re-examine various criteria for the existence of parabolic points (inflexions in 2D-sections) on the outermost sheet of the slowness surface for elastic waves in anisotropic media.Previous results obtained by the authors, exact [4,5], and approximate [6], are related in detail. Further approximations, based on geometrical properties, are derived; one of these proves equivalent to a sufficient condition first applied by McCurdy [8].Numerical investigation shows that, over a wide range of anisotropy, the simply applied approximate criterion of [6] is sufficient and within the accuracy of observation of the elastic stiffnesses.