Elastic waves in anisotropic media

The displacements due to a radiating point source in an infinite anisotropic elastic medium are found in terms of Fourier integrals. The integrals are evaluated asymptotically, yielding explicit expressions for displacements at points far from the source. The relative amplitudes of waves from a point source are thus determined, and it is found that although in general the decay of wave amplitudes is proportional to the distance from the source, it is possible that in certain directions the decay is less than this. The method used in this paper is also shown to be an alternative way of deriving known results concerning the geometry of the propagation of disturbances. As an example, the radiation in a transversely isotropic medium from an isolated force varying harmonically with time is discussed.