Solving some inverse problems of gravimetry and magnetometry using an algorithm that improves matrix conditioning

For inverse problems of gravimetry and magnetometry, a possible problem formulation is considered, which consists in finding hypothetical point sources at a given depth that correspond to potential fields measured on the Earth’s surface. The uniqueness of solutions to these inverse problems is proved. Their discretized variants are solved numerically using a new algorithm based on improving the condition number of the problem’s matrix with the help of the minimal pseudoinverse matrix method (MPMI algorithm). The algorithm is tested on model problems of gravimetry and magnetometry, which are solved separately. A variant of the MPMI algorithm for the joint solution of these inverse problems is also proposed and tested. Finally, the algorithm is used for separate and joint processing of some well-known gravity and magnetic exploration data, namely, for the Kursk Magnetic Anomaly.