  An inverse problem of acoustic sounding is under consideration in a form of
3D inverse coefficient problem for wave equation. Unknown coefficient is the
local propagation velocity of vibrations, which is associated with
inhomogeneities of the medium. We are looking for this coefficient, knowing
special time integrals of the scattered wave field. In the article, a new
linear 3D Fredholm integral equation of the first kind is introduced, of which
it is possible to find the unknown coefficient from these time integrals. We
present and substantiate a numerical algorithm for solving this integral
equation. The algorithm does not require large computational resources and
big-time implementation. It is based on the use of fast Fourier transform under
some a priori assumptions about unknown coefficient and observation region of
the scattered field. Typical results of solving this 3D inverse problem on a
personal computer for simulated data demonstrate the capabilities of the
proposed algorithm.
