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.

中文翻译：

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一种求解圆柱区域标量声学三维逆多频问题的快速算法

提出了一种求解圆柱区域内非均匀介质声波三维标量逆问题的稳定算法。问题的数据是在圆柱层的声不均匀性区域之外测得的波场的复振幅。使用傅立叶变换和傅立叶级数，将反问题简化为求解一组第一类一维Fredholm积分方程，随后计算非均匀性区域中波场的复振幅，然后得出在该区域中找到所需的声速场。该算法允许在数十秒内针对具有足够精细的三维网格的平均性能的个人计算机上解决反问题。