Abstract
The paper is devoted to construction of the stable regularized algorithms for solving the structural inverse gravimetry problem for the case of multiple surfaces. The problem is in finding the surfaces that divide the layers of different constant densities using the known gravitational field. The problem is described by the nonlinear integral equation of the first kind; thus, it is an ill-posed one. After discretization, the problem is reduced to solving the system of nonlinear algebraic equations. To solve it, we propose the regularized variant of the discretized equation and construct stable algorithms based on the steepest descent and conjugate gradients methods. The algorithms are tested on the model problem with quasi-real disturbed data. We show that the proposed algorithms provides better accuracy than the classic ones.