Scattering of a spherical pulse from a small inhomogeneity: Dilatation and rotation
Perturbations in elastic constants and density distinguish a volume inhomogeneity from its homogeneous surroundings. The equation of motion for the first order scattering is studied in the perturbed medium. The scattered waves are generated by the interaction between the primary waves and the inhomogeneity. First order scattering theory is modified to include the source term generating the primary waves. The body force equivalent to the scattering source is presented in a convenient form involving the perturbations in wave velocities and gradient of density perturbation.
A procedure is presented to study the scattering of a spherical pulse from a small inhomogeneity, in time domain. The size of inhomogeneity is assumed small as compared to its distance from source and receiver. No restrictions are placed on the positions of source, receiver and inhomogeneity. The dilatation and rotations are calculated for a pulse scattered from an arbitrary point in a spherical volume. The aggregate of the scattered phases from all the points of the inhomogeneity, reaching at a fixed receiver, gives the amount of scattering from the inhomogeneity. The interaction of bothP andS waves with inhomogeneity are considered. Dilatation and rotations for scattering are obtained as integral expressions over the solid angle of inhomogeneity. These expressions are computed numerically, for hypothetical models. The effects of source (unit force) orientations, velocity and density perturbations, and size of inhomogeneity, on the scattered phases, are discussed.
Volume 129, 2020
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