The Turning Point of Elastodynamic Waves

Abstract

It is demonstrated how a uniform asymptotic expansion can be developed for the elastodynamic wave equations in a spherically symmetric medium. The expansion is valid in the neighbourhood of first order turning points except at discontinuities. Because the dependent variables in the expansion are the displacement and stress, discontinuities are easily included. The extra terms from the Earth‐flattening transformation are included. The optimum transformations for SH and acoustic waves diner significantly. They compensate different terms in the transformed wave equations. In the SH case, the shear stress and strain are corrected for the geometrical differences in the co‐ordinate systems, whereas in the acoustic case, the hydrostatic pressure is maintained unaltered and the transformation compensates for the geometrical change in dilatation. A P wave is a mixture of dilatation and shear, and an optimum transform cannot be found. Copyright © 1974, Wiley Blackwell. All rights reserved