12. Inversion Procedures
In this paper, we address the inversion problem in the scattering of elastic waves from scatterers using a probabilistic approach. This work extends that of previous efforts in that it considers a wider set of input measurements and a wider class of possible defects. For a given transducer arrangement, the input measurements involve the coefficient A2. which characterizes scattering at low frequencies, and a second quantity that is related to the distance from the center of the scatterer to the front face tangent plane perpendicular to the direction of the incident beam. The first property is deducible from low frequency scattering data and the second from low and intermediate frequency scattering data. These properties are determined for a set of transducer configurations. The class of possible scatterers now includes a finite discrete set of possible inclusions as well as a void. The boundary geometry is assumed to be ellipsoidal. In the probabilistic approach we start with a statistical ensemble of scatterer properties and measurement errors and then remove the members inconsistent with the scattering data obtained from the measurements. The best estimates of the geometrical properties and inclusion types (with the void regarded as a special case) are then the average or most probable values of these properties in the resultant reduced ensemble. These estimates are accompanied by several types of confidence measures. The behavior of the inversion algorithm using theoretical test data, both noiseless and noisy, was studied by computer simulation.
Fertig, K. W. and Richardson, John M., "Inverse Scattering at Low and Intermediate Frequencies" (1980). Proceedings of the DARPA/AFML Review of Progress in Quantitative NDE, July 1978–September 1979. 71.