Acceleration of near-field scattering from an inhomogeneous spherical shell |
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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: | 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. |
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Keywords: | Scattering near-field acceleration inhomogeneity |
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