Conjugate Gradient Method for Solving the Inverse Gravimetry Problem in Multilayered Medium: Parallel Implementation

The paper is devoted to construction of the time efficient algorithm for solving the structural inverse gravimetry problem in the case of multilayered medium. The problem is in finding multiple interfaces between layers with different constant densities using known gravitational data. This problem is described by a nonlinear integral equation of the first kind; 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 algorithm uses the approximation of the Jacobian matrix of the integral operator based on dropping out the lesser elements and utilizing the Toeplitz-block-Toeplitz structure of the matrix. The parallel algorithm was implemented for the multicore processors and graphics processors using OpenMP and CUDA technologies. The structural gravimetry problem of reconstructing three surfaces using quasi-real data was solved.