Abstract
The problem of a scalar wave propagation from the point impulsive source in the layer of a nonstationary multidimensional medium is considered. The boundary problem for the wave equation is reformulated in the problem with the initial condition using the invariant imbedding method. The integral-differential inverse procedures of the various orders were obtained from the imbedding equations using the singularities method. The order of inverse procedure is defined by the degree of a polynomial in the analytical representation of the medium characteristic near the layer boundary. It was shown that the coefficients of the polynomial are calculated with the help of the differential characteristics of the point impulsive source in the inhomogeneous medium. The cause and character of the multidimensional inverse problem overdefiniteness are considered. The application of the proposed procedure for a statistical problem is discussed.
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