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The efficient iterative methods for solving inverse problems of wave tomography were developed. The computation of the Fréchet derivative includes solving both the direct and the conjugate problems with the Neumann boundary condition. The efficient methods for numerical computations where the solution is found using the detector measurements of the wave field and its normal derivative were developed. The wave field normal derivative values at detector locations are found by solving the exterior boundary value problem with the Dirichlet boundary conditions. The efficiency of this approach by applying it to model problems was illustrated. The algorithms developed are designed to be run on supercomputers.