An Efficient Numerical Technique for Solving the Inverse Gravity Problem of Finding a Lateral Density

The main goal of our paper is to construct a technique for the gravity inversion problem of finding a variable density in a horizontal layer on the basis of gravitational data. This technique consists of two steps: extracting the gravitational field and solving the linear integral equation of the density. After discretization and approximation of integral operator, this problem is reduced to solving large systems of linear algebraic equations. To solve these systems, we proposed a memory-efficient algorithm based on the iterative method of minimal residuals. The idea of memory optimization is based on exploiting the block-Toeplitz structure of coefficients matrix. The algorithms were parallelized and implemented using the Uran and UrFU supercomputers. A model problem with synthetic gravitational data was solved