The Propagation of Surface Waves in an Elastic Medium with Orthorhombic Symmetry

A medium with orthorhombic symmetry is characterized by nine elastic constants. The geophysical interest of a discussion of the surface waves on such a medium is that olivine crystallizes in this system, and any considerable departure from isotropy in the material of the upper mantle might be detected by a study of surface elastic waves of long-period in various azimuths. Equally, anisotropy might show up in a study of body waves. An earlier investigation for a medium with cubic symmetry shows that surface waves of Rayleigh and Love types are associated only with principal planes of symmetry; the present work, accordingly, deals with the six possible Rayleigh waves propagated in principal directions on free surfaces that are principal planes. The corresponding wave velocities have been calculated for a sample of olivine, the constants of which were measured by R. K. Verma. Some representative examples, too, have been computed to show the variation of the three types of body wave with direction. The particular crystal used by Verma was of rather extreme composition, mainly forsterite, and experimental work on a wider range of composition is desirable. The range of variation in the velocity of both body waves and surface waves in this specimen is much greater than is met with in seismological investigations, and in the absence of further evidence suggests that the upper mantle behaves like an aggregate of crystals in randóm orientation.