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GRADIENT METHOD WITH PRECONDITIONER FOR SOLVING NONLINEAR INVERSE GRAVIMETRY PROBLEM
Abstract
The most important geophysical problem is the inverse gravimetry problem. The problem is in finding an interface between two layers with different densities using known gravitational data. This problem is described by a nonlinear integral Fredholm equation of the first kind; so it is ill-posed. After the discretization of the integral operator, the problem is reduced to solving a system of nonlinear equation. For large grids, it is necessary to develop parallel algorithms for multiprocessor computing systems. To solve the inverse gravimetry problem of reconstructing a density interface using known gravitational data, an efficient gradient method with preconditioner is constructed. The parallel algorithm was developed and numerically implemented on the multicore processor incorporated in the Uran parallel computing system. The structural gravimetry problem with model data was solved. The comparison of the conjugate gradient method with preconditioner and the conjugate gradient method without preconditioned in terms of the number of iterations and execution time was carried out.
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