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A new algorithm is proposed for solving the three-dimensional scalar inverseproblem of acoustic sounding in an inhomogeneous medium. The data for thealgorithm are the complex amplitudes of the wave field measured outside theinhomogeneity region. For the data recording scheme in a flat layer, theinverse problem is reduced using the Fourier transform to solving a set ofone-dimensional Fredholm integral equations of the first kind. Solving theseequations by the use of regularizing methods, we calculate the complexamplitude of the wave field in the inhomogeneity region and then we find thedesired field of sound velocities in this domain. The proposed algorithm allowsus to solve the inverse problem on a personal computer of average performance(without parallelization) for sufficiently fine three-dimensional grids in afew minutes. We demonstrate the results of solving model inverse problems atone frequency and several frequencies simultaneously along with a study of theaccuracy of the proposed algorithm. We also investigate the issues of numericalstability of the algorithm with respect to data perturbations.

To the numerical solution of the inverse multi-frequency scalar acoustics problem