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An inverse problem of acoustic sounding is under consideration in a form of3D inverse coefficient problem for wave equation. Unknown coefficient is thelocal propagation velocity of vibrations, which is associated withinhomogeneities of the medium. We are looking for this coefficient, knowingspecial time integrals of the scattered wave field. In the article, a newlinear 3D Fredholm integral equation of the first kind is introduced, of whichit is possible to find the unknown coefficient from these time integrals. Wepresent and substantiate a numerical algorithm for solving this integralequation. The algorithm does not require large computational resources andbig-time implementation. It is based on the use of fast Fourier transform undersome a priori assumptions about unknown coefficient and observation region ofthe scattered field. Typical results of solving this 3D inverse problem on apersonal computer for simulated data demonstrate the capabilities of theproposed algorithm.

Economic numerical method of solving coefficient inverse problem for 3D wave equation