Inverse Problems of Ultrasonic Tomography in Nondestructive Testing: Mathematical Methods and Experiment

Abstract

The article is devoted to developing methods of ultrasonic tomography for nondestructive testing. The inverse problem of reconstructing velocity sections is treated as a nonlinear coefficient inverse problem for a scalar wave equation. Effective iterative methods for solving this problem using supercomputers have been developed. These methods use direct formulas for computing the gradient of a residual functional between the computed wave field and the field experimentally measured on detectors. The effectiveness of the algorithms was tested on real experimental data. The first experiments were carried out on dedicated solid-state samples in the simplest arrangement, with the signals recorded by standard ultrasonic antenna arrays at a frequency of 5 MHz. It is shown that using the developed tomographic methods with reflection and transmission schemes in a real experiment, it is possible not only to detect the boundaries of reflectors, but also to determine the velocity sections inside the reflectors.