Energy Partitions among Elastic Waves for Dynamic Surface Loads in a Semi-Infinite Solid
Abstract
We examine the energy partitions among elastic waves due to dynamic normal and tangential surface loads in a semi-infinite elastic solid. While the results for a dynamic normal load on the surface of a half-space with Poisson ratio of 1/4 is a well-known result by Miller and Pursey (1955), the corresponding results for a dynamic tangential load are almost unknown. The partitions for the normal and tangential loads were computed independently by Weaver (1985) versus Poisson ratio (0≤ν≤1/2), using diffuse-field concepts within the context of ultrasonic measurements. The connection with the surface load point was not explicit, which partially explains why these results did not reach the seismological and engineering literature. The characteristics of the elastic radiation of these two cases are quite different. For a normal load, about 2/3 of the energy leaves the loaded point as Rayleigh surface waves. On the other hand, the tangential load induces a similar amount in the form of body shear waves. It is established that the energies injected into the elastic half-space by concentrated normal and tangential harmonic surface loads are proportional to the imaginary part of the corresponding components of the Green's tensor when both source and receiver coincide. The relationship between the Green's function and average correlations of motions within a diffuse field is clearly established.