Low-Cost Numerical Method for Solving a Coefficient Inverse Problem for the Wave Equation in Three-Dimensional Space

For the acoustic-sensing problem of determining the characteristics of a local inhomogeneity scattering a wave field in three-dimensional space, a numerical algorithm is proposed and justified that is efficient in terms of computational resources and CPU time. The algorithm is based on the fast Fourier transform, which is used under certain a priori assumptions on the character of the inhomogeneity and the observation domain of the scattered field. Typical numerical results obtained by solving this inverse problem with simulated data on a personal computer are presented, which demonstrate the capabilities of the algorithm.