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