Supercomputer modeling in coefficient inverse problems of wave tomography with attenuation

Abstract

 Efficient methods are proposed for solving inverse problems of wave computer tomography. Inverse problem is viewed as a coefficient inverse problem for the wave equation for unknown functions that characterize both the velocity and attenuation in the diagnosed region. Mathematical model has to deal with diffraction, refraction, attenuation effects. Algorithms are based on direct computation of the gradient of the residual functional. We used data over the entire boundary of the computational domain (full-range tomography scheme) to solve the inverse problem. Mathematical modeling methods investigated the effects of the attenuation to the possibility of reconstruction. The problem of the large amount of computation for solving the inverse problem is overcome by using a supercomputer cluster-type. Used explicit finite difference scheme is ideally suited for parallelization. Computations of model problems show that it is possible to reconstruct not only the velocity, but also the attenuation in the diagnosed medium. The algorithms that we developed can be used in the design of ultrasound tomographs, electromagnetic diagnostics, seismic exploration, and earthquake engineering.