Acceleration of near-field scattering from an inhomogeneous spherical shell

Abstract

The three dimensional scattering of near-field, from a point source, is studied for acceleration in the time domain. The perturbation method is applied to define the acceleration for the first order scattering from a weak inhomogeneity in a homogeneous surrounding. A body force, arising from the interaction between the primary waves and the inhomogeneity, acts as the source generating the scattered motion. The acceleration of scattered waves is related to the velocity and density fluctuations of the inhomogeneity. No restrictions are placed on the inhomogeneity size or locations of the source and receiver. Decoupling of scattered motion enables the identification of different phases. Integral expressions are derived for the scattering acceleration due to the incidence of near-field wave (from an impulsive point force) at a radially inhomogeneous volume element. These integrals are solved further for scattering from an inhomogeneous spherical shell. The accelerations for back scattering are obtained as a special case. These accelerations are simple analytically solvable expressions in closed form.

Only spherical asymmetry ofP wave velocity inhomogeneity can affect the scatteredS acceleration. ScatteredP acceleration is affected by the gradient ofS wave velocity inhomogeneity. The back scattering of near-field from a spherical shell, is independent of radial inhomogeneity ofP wave velocity. Inhomogeneity with smoothly perturbedS wave velocity does not back-scatter any acceleration. Accelerations are computed numerically for scattering from a part of inhomogeneous spherical shell. Hypothetical models are considered to study the effects of the distances of spherical shell from source, receiver, its thickness and its position relative to the direction of impulsive force.