Strains of scattering of near-field of a point source

Three dimensional scattering of near-field is studied for dilatation and rotation in the tune 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 spherical P and S 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 of P wave velocity inhomogeneity. Dilatation of scattering does not involve S 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.