A new algorithm for the stable solution of a three-dimensional scalar inverse problem of acoustic sounding of an inhomogeneous medium in a cylindrical region is proposed. The data of the problem is the complex amplitude of the wave field, measured outside the region of acoustic inhomogeneities in a cylindrical layer. Using the Fourier transform and Fourier series, the inverse problem is reduced to solving a set of one-dimensional Fredholm integral equations of the first kind, to the subsequent calculation of the complex amplitude of the wave field in the region of inhomogeneity, and then to finding the required sound velocity field in this region. The algorithm allows solving the inverse problem on a personal computer of average performance for sufficiently fine three-dimensional grids in tens of seconds. A numerical study of the accuracy of the proposed algorithm for solving model inverse problems at various frequencies is carried out, and the issues of stability of the algorithm with respect to data perturbations are investigated.

翻译：提出了在圆柱形区域对不相容的介质进行声学探测的三维二次反向问题稳定解析的新算法。 问题的数据是,在圆柱形层声学不均匀区域以外测量的波场的复杂振幅。 使用 Fourier 变形和 Fourier 序列, 反向问题被归结为解决第一种单维Fredholm 集成方程式, 以及随后计算出不均匀区域波场的复杂振幅, 然后寻找该区域所需的声速场。 算法使个人计算机平均性能的反向问题能够在数秒内为足够精细的三维电网解决。 对解决不同频率模型反向问题的拟议算法的准确性进行了数字研究, 并调查了在数据扰动方面算法的稳定性问题。