A FAST COMPONENTWISE GRADIENT METHOD FOR SOLVING STRUCTURAL INVERSE GRAVITY PROBLEM

References: 15th International Multidisciplinary Scientific GeoConference SGEM 2015, www.sgem.org, SGEM2015 Conference Proceedings, ISBN 978-619-7105-33-9 / ISSN 1314-2704, June 18-24, 2015, Book1 Vol. 3, 775-782 pp

ABSTRACT
One of the most important geophysical problems is reconstructing a density interface using known gravitational data. This problem is described by a nonlinear integral Fredholm equation of the first kind. After the discretization the problem is reduced to solving a system of nonlinear equations.
The real gravity measurements are carried out over a large area producing large-scale grids. Processing of gravity data is time consuming and requires a lot of memory. So it is necessary to develop parallel algorithms for parallel computing systems.
In this paper, for solving the inverse gravity problem, a new efficient componentwise gradient method with damping factor is constructed. The parallel algorithm was developed and numerically implemented on the multicore processor incorporated in the Uran parallel computing system at the Institute of Mathematics and Mechanics of the Ural Branch of RAS, Yekaterinburg. The structural gravity problem with real data was solved. The comparison of the new method with the linearized conjugate gradient and local corrections methods in terms of the number of iterations and execution time was carried out.

Keywords: structural inverse gravity problem, gradient methods, parallel algorithms, multicore processors.