Scattering of a spherical pulse from a small inhomogeneity: Dilatation and rotation |
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| Authors: | M D Sharma |
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| Institution: | (1) Department of Mathematics, Kurukshetra University, 136 119 Kurukshetra, India |
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| Abstract: | 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. |
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| Keywords: | Scattering inhomogeneity spherical pulse perturbations dilatation rotation |
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