The contrast-source stress-velocity integral-equation formulation of three-dimensional time-domain elastodynamic scattering problems: A structured approach using tensor partitioning

The contrast-source stress-velocity integral-equation formulation of three-dimensional time-domain elastodynamic scattering problems is discussed. A novel feature of the formulation is a tensor partitioning of the relevant dynamic stress and the contrast source volume density of deformation rate. The partitioning highlights several features about the structure of the formulation. These can advantageously be incorporated in a computational implementation of the method. An application to the case of a scatterer composed of isotropic material and embedded in an isotropic elastic background medium shows that the corresponding newly introduced constitutive coefficients are more natural as a characterization of the media than the traditional Lame coefficients.