Numerical Methods for Mathematical Modeling of 3D Forward and Inverse Gravity Problem for Variable Density Model

The problems of potential theory are closely related to the mathematical apparatus necessary for the subsequent study of the gravitational field and internal structure of the Earth, geodynamic processes of various nature occurring in its bowels. In this regard, it is important to emphasize the universality of mathematical foundations and methods for various problems of geophysics. In the theory of potential geophysical fields, there are two most important classes of problems – forward and inverse. Numerical calculation methods, which are a logical continuation of the discretization of geophysical problems on the grid, also remain an important aspect. The paper considers the possibilities of using analytically and approximate methods for solving a three- dimensional forward gravimetry problem as an aid to solving a more complex inverse problem. The model linear inverse problem of density recovery is considered, the classical approach to regularization is applied, the question of regularization of the simplex method as another possible method for solving this type of problems is raised.