Equation for wave processes in inhomogeneous moving media and functional solution of the acoustic tomography problem based on it

Abstract

The paper considers the derivation of the wave equation and Helmholtz equation for solving the tomographic problem of reconstruction combined scalar-vector inhomogeneities describing perturbations of the sound velocity and absorption, the vector field of flows, and perturbations of the density of the medium. Restrictive conditions under which the obtained equations are meaningful are analyzed. Results of numerical simulation of the two-dimensional functional-analytical Novikov–Agaltsov algorithm for reconstructing the flow velocity using the the obtained Helmholtz equation are presented.