On a New Approach to Solving Gravimetry Problems within the Framework of the Discrete Potential Theory

The paper deals with the possibility of finding solutions to direct and inverse gravimetry problems by means of the apparatus of eigenfunctions of the Laplace operator. Data acquired through remote sensing of the Earth’s physical fields are of a discrete character (often in the form of bit chains). The discrete gravitational potential theory allows restoring, with a relatively high degree of reliability, grid mass distributions that are equivalent with respect to an external field complicated by random noise, as well as solving various direct and inverse gravimetry problems. Construction of eigenfunctions of a discrete analogue of the Laplace operator in three-dimensional domains with complex structure eliminates the need for multiple solutions of ill-conditioned systems of linear algebraic equations (SLAE).