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

Journal Article · Thu Dec 31 23:00:00 EST 1992 · Journal of the Acoustical Society of America; (United States)

DOI:https://doi.org/10.1121/1.405664· OSTI ID:6608939

Schafbuch, P J; Thompson, R B; Rizzo, F J ^[1]

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1. Iowa State Univ., Ames (United States)

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 Newmann series. Terms in this series correspond physically to Nth-order Born approximations of the scatterers interaction. The relative advantage of this hybrid scheme depends on the number of interactions 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. 32 refs., 13 figs., 1 tab.

• OSTI ID: 6608939
• Journal Information: Journal of the Acoustical Society of America; (United States), Journal Name: Journal of the Acoustical Society of America; (United States) Vol. 93:1; ISSN 0001-4966; ISSN JASMAN
• Country of Publication: United States
• Language: English

Related Subjects

661300* -- Other Aspects of Physical Science-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BORN APPROXIMATION
BOUNDARY ELEMENT METHOD
CALCULATION METHODS
DIAGNOSTIC USES
EQUATIONS
FINITE ELEMENT METHOD
HYDROMAGNETIC WAVES
INTEGRAL EQUATIONS
ITERATIVE METHODS
MAGNETOACOUSTIC WAVES
NUMERICAL SOLUTION
SCATTERING
THREE-DIMENSIONAL CALCULATIONS
USES