Memory efficient algorithm for solving the inverse gravimetry problem of finding several boundary surfaces in multilayered medium

For solving the inverse gravimetry problem of finding several boundary surfaces in a multilayered medium, the parallel algorithm was constructed and implemented for multicore CPU using OpenMP technology. The algorithm is based on the modified nonlinear conjugate gradient method with weighting factors previously proposed by authors. To reduce the memory requirements and computation time, the modification was constructed on the basis of utilizing the Toeplitz-block-Toeplitz structure of the Jacobian matrix of the integral operator. The model problem of reconstructing three surfaces using the quasi-real gravitational data was solved on a large grid. It was shown that the proposed implementation reduces the computation time by 80% in comparison with the earlier algorithm based on calculating the entire matrix. The parallel algorithm shows good scaling of 94% on 8-core processor.