The time domain elastodynamic Kirchhoff approximation for cracks: The inverse problem
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.
classical two-dimensional Radon transform
scientific article; zbMATH DE number 3913798
scientific article