Gravity and Magnetic Data Inversion With Random Projection

Three-dimensional inversion of gravity and magnetic data can determine the geometric location of anomalous subsurface bodies and quantitatively calculate the size and spatial distribution of the target body's physical parameters, providing a foundation for subsequent geological interpretation. The Tikhonov regularization method typically controls the model space in gravity and magnetic data processing to reduce the nonuniqueness of inversion problems. However, various regularization forms and the change in weighting coefficient yield generally different inversion results, and the depth resolution of the potential field data is insufficient. This article proposes an inversion method with random projection to obtain accurate distribution results for physical property parameters. This method can derive physical property parameters by solving inversion problems involving well-posed equations without Tikhonov regularization constraints or constraint terms of the depth weighting function. The original ill-posed equations are transformed into stably solvable low-dimensional well-posed equations by random projection many times, and the high-dimensional inversion solutions are obtained by averaging the solutions of multiple low-dimensional equations. The inversion accuracy and the proposed method resolution are evaluated using theoretical model tests. In addition, this method can constrain the prior geological information such as horizon, tilt Angle, and block into the projection process, and realize the joint inversion of gravity and magnetic data and prior geological information, so as to obtain more reliable physical property inversion results. The random projection inversion method is then applied to the magnetic data in Gonghe Basin, Qinghai Province, and the spatial distribution range of deep hot dry rocks is delineated, providing direction for the continued exploration of geothermal resources in this area.