Original scientific paper
Stable parallel algorithms for solving the inverse gravimetry and magnetometry problems
Elena N. Akimova
; Institute of Mathematics and Mechanics, Ural Branch of Russian Academy of Sciences, S. Kovalevskaya str.,16, Ekaterinburg, 620219, RUSSIA
Vladimir V. Vasin
; Institute of Mathematics and Mechanics, Ural Branch of Russian Academy of Sciences, S. Kovalevskaya str.,16, Ekaterinburg, 620219, RUSSIA
Abstract
The three-dimensional inverse problems of gravimetry and magnetometry for finding the interfaces between mediums from the gravitational and magnetic data are investigated. We assume that a model of the lower halfspace consists of three mediums with constant densities which are separated by the surfaces S1 and S2 to be determined. The inverse problems are reduced to nonlinear integral equations of the first kind, hence these problems are illposed. After discretization of the integral equation we obtain a system of nonlinear equations of large dimension. To solve this system, we use the iteratively regularized Gauss-Newton method. To realize one step of this method, we have to solve a system of linear algebraic equations with full matrix. For this aim, parallel variants of the Gauss, Gauss-Jordan and the conjugate gradient method are applied. Their realization has been implemented on the Massively Parallel Computing System MVS-1000. The analysis of the efficiency of parallelization of the iterative algorithms with different numbers of processors is carried out. Parallelization of the algorithms decreases significantly the time of solving the problems. The interfaces S1 and S2 obtained by the Gauss-Newton method correspond to the real geological perceptions about the Ural region under investigation.
Keywords
parallel algorithms, gravimetry, magnetometry, parallelization
Hrčak ID:
313903
URI
Publication date:
21.12.2003.
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