The time domain elastodynamic Kirchhoff approximation for cracks: The inverse problem
type: Item
instance of: scholarly article
title: The time domain elastodynamic Kirchhoff approximation for cracks: The inverse problem
zbMATH Open document ID: 0572.73034
DOI: 10.1016/0165-2125(86)90003-X
author: Lester W. jun. Schmerr
author: Andrey Ivanovic Sedov
published in: Wave Motion
publication date: 1986-01-01T00:00:00Z
review text: Obtaining the size, shape, and orientation of a crack from ultrasonic elastic wave scattering information is one example of the solution of an inverse problem. Here we obtain the formal solution to this inverse problem for ideal, flat cracks using the Kirchhoff approximation for the scattered elastodynamic wavefield. Time and frequency domain versions of the solution will be given, both in the general case and, in reduced form, for circular cracks. The time domain inverse formulation, in particular, will be shown to be equivalent to the method of projections, leading to a classical two-dimensional Radon transform. A method is also demonstrated for performing a constrained inversion to obtain the parameters of a flat crack that is assumed a priori to be of elliptical shape.
Mathematics Subject Classification ID: 74J25
Mathematics Subject Classification ID: 74R05
Mathematics Subject Classification ID: 74J10
Mathematics Subject Classification ID: 74J20
zbMATH DE Number: 3913798
zbMATH Keywords: nonlinear least squares formulation
zbMATH Keywords: characteristic function
zbMATH Keywords: size
zbMATH Keywords: shape
zbMATH Keywords: orientation of a crack
zbMATH Keywords: ultrasonic elastic wave scattering
zbMATH Keywords: formal solution
zbMATH Keywords: ideal, flat cracks
zbMATH Keywords: Kirchhoff approximation
zbMATH Keywords: scattered elastodynamic wavefield
zbMATH Keywords: Time and frequency domain versions
zbMATH Keywords: general case
zbMATH Keywords: circular cracks
zbMATH Keywords: classical two-dimensional Radon transform
zbMATH Keywords: constrained inversion
zbMATH Keywords: elliptical shape
MaRDI profile type: Publication
cites work: Exterior reconstruction of a three dimensional scatterer
cites work: Q3964084
cites work: Q5186149
cites work: Computerized Tomography: The New Medical X-Ray Technology
cites work: On the derivation of point source responses from line source solutions
full work available at URL: 0165-2125(86)90003-x
OpenAlex ID: W1969693583
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description: scientific article; zbMATH DE number 3913798