Time domain scattering of elastic waves by a cavity, represented by radiation from equivalent body forces

A method of representing scattering in the time domain by a cavity in an elastic body of infinite extent by radiation from equivalent body forces is presented. It is shown that the equivalent body forces are a combination of double and single forces. The equivalent forces are determined in terms of properties of the incident wave, the solid's elastic constants and the volume of the scatterer, which may be of arbitrary shape. Once the equivalent forces have been determined, the scattered field is determined by the use of a Green's function. Scattering by cavities of 2D and 3D general shape is considered and analyzed. Two special cases, namely, a circular cavity and a spherical cavity, are used to illustrate the method. The results are valid for large measurement distances and waves that are long relative to a characteristic length of the cavity. The method can easily be extended to scattering by cavities in waveguides.