Application of Multiple Scattering Theory to Sub-Surface Defects

Domany, Eytan; Entin‐Wohlman, O.

doi:10.1007/978-1-4684-1194-2_9

Review of Progress in Quantitative Nondestructive Evaluation 1984

DOI: 10.1007/978-1-4684-1194-2_9

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Application of Multiple Scattering Theory to Sub-Surface Defects

Eytan Domany

O. Entin‐Wohlman

Abstract: A recently developed multiple scattering formalism is applied to treat scattering of elastic waves by subsurface defects. In particular, the problem of a spherical cavity near a stress free surface is treated.

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1993

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Elastic scatterer interaction via generalized Born series and far-field approximations

Schafbuch

Thompson

Rizzo

1993

The Journal of the Acoustical Society of America

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Methods for solving elastic wave scattering problems in three dimensions (3D) with multiple inhomogeneities are discussed. A problem of homogeneous, isotropic elastic defects in an otherwise homogeneous, isotropic elastic full-space is formulated as a boundary integral equation. This equation is solved by discretizing the surface of each scatterer in a fashion known as the boundary element method. The resulting matrix equation may be solved in a fully implicit manner, but an implicit-iterative method is more efficient. With this hybrid method, a portion of the nonsingular integral operator is expanded in a Neumann series. Terms in this series correspond physically to N th-order Born approximations of the scatterers' interaction. The relative advantage of this hybrid scheme depends on the number of iterations required. Except for closely situated strong scatterers, terms beyond the first few orders are not significant and thus the method can be quite advantageous. When the separation is large, another approximate method which ignores the evanescent portion of the near scattered field and further neglects the curvature of scattered waves is appropriate. Results from the converged, implicit-iterative approach are compared with this far-field approximation for many situations involving spheroidal voids. The validity of this approximation is explored in the near field.

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Elastic scatterer interaction via generalized Born series and far-field approximations

Schafbuch

Thompson

Rizzo

1993

The Journal of the Acoustical Society of America

View full text Add to dashboard Cite

show abstract

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Application of Multiple Scattering Theory to Sub-Surface Defects

Abstract: A recently developed multiple scattering formalism is applied to treat scattering of elastic waves by subsurface defects. In particular, the problem of a spherical cavity near a stress free surface is treated.

Cited by 1 publication

References 3 publications

Elastic scatterer interaction via generalized Born series and far-field approximations

Elastic scatterer interaction via generalized Born series and far-field approximations

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