A problem of reconstruction of inhomogeneity parameters of a two-dimension body by the measurement results of acoustic field

Background. The inverse problems arise in many areas science and technology such as medicine, manufacturing and etс. The main purposes of this work are to formulate and to solve the inverse problem, to analyze solutions depending for the introduced noise and the frequency of the source, to develop an algorithm of filtering of solutions. Materials and methods. We obtain an integral equation of the first kind based on the results of measurements at observation points. We can calculate the function of the wave number in the body using a formula and result of solving of integral equation. Results. A two-step method of restoring inhomogeneities of the body was applied. The Solution of the problem depending on introduced errors was investigated. The algorithm of filtering noisy data was considered. Conclusions. Solving the problem by this method allows restoring the internal structure of the body, and the filtration method helps to recognize true inhomogeneities.