Strains of scattering of near-field of a point source |
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| Authors: | M D Sharma |
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| Institution: | (1) Department of Mathematics, Kurukshetra University, 136 119, India |
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| Abstract: | Three dimensional scattering of near-field is studied for dilatation and rotation in the time domain. The perturbation method
is applied to solve the equation of motion for the first order scattering from a weak inhomogeneity in an otherwise homogeneous
medium. The inhomogeneity is assumed close enough to the point source so that the near-field intermediate wave is dominating
over the far-field sphericalP andS pulses. The integral expressions are derived to relate dilatation and rotation of scattering to the radial fluctuations of
velocities and density in the inhomogeneity. These integrals are solved to calculate the strains of scattering from (a part
of) an inhomogeneous spherical shell of arbitrary curvature. Variable curvature may allow the shape of inhomogeneity volume
element to change uniformly from spherical to rectangular. Rotation of scattering from a spherical shell is independent ofP wave velocity inhomogeneity. Dilatation of scattering does not involveS wave velocity inhomogeneity but its gradient. The back scattering results are obtained as a special case. Strains are computed
numerically, for hypothetical models to study the effects of various parameters viz., velocity inhomogeneity, distance of
source from inhomogeneity and from receiver, and thickness of inhomogeneity. The curvature of the spherical shell is varied
to study the effects of the shape of inhomogeneous volume element on scattering. |
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| Keywords: | Scattering volume inhomogeneity near-field point source strains |
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