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MODIFIED CONJUGATE GRADIENT METHOD FOR SOLVING THE NONLINEAR INVERSE GRAVIMETRY PROBLEM IN THE CASE OF MULTILAYERED MEDIUM
Abstract
The paper is devoted to construction of the time efficient algorithm for solving the structural inverse gravimetry problem. The problem is in finding by known gravitational data multiple interfaces between layers with different constant densities. This problem is described by a nonlinear integral equation of the first kind; so, it is ill-posed. After discretization of the area and approximation of the integral operator, the problem is reduced to solving a system of nonlinear equations. An efficient method was constructed on the basis of the nonlinear conjugate gradient method. The approximation method based on dropping out the lesser elements of Jacobian matrix was proposed. The parallel algorithm was developed and numerically implemented for the multicore processor. The structural gravimetry problem of reconstructing three surfaces using quasi-real data was solved. Comparison of the proposed matrix approximation approach with the exact calculation in terms of the execution time was carried out. The scaling of the parallel algorithm was studied.
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References8
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