Application of Supervised Descent Method for 3-D Gravity Data Focusing Inversion

Three-dimensional gravity inversion is an effective method for extracting underground density distribution from gravity data. However, traditional deterministic gravity inversion methods suffer from problems such as skin effect, low computational accuracy, and poor efficiency. Therefore, we propose a three-dimensional gravity data focusing inversion algorithm based on the supervised descent method. Supervised descent method (SDM) is a non-linear optimization method based on the combination of machine learning and gradient descent method. In the offline phase, we construct a training set based on a priori information and iteratively learn a set of average descent directions between the initial model and the training model. In the online phase, we introduce a focused regularization into the prediction objective function. This addition aims to obtain a sharp boundary density model that conforms to the physical distribution. Additionally, we incorporate property boundary constraints in both the offline and online phases to control the upper and lower bounds of the density values to ensure consistency with reality. Model tests show that the proposed method can effectively overcome skin effect, improve the resolution of gravity inversion. Moreover, the construction of the training set of the proposed method is less affected by prior information, and it has strong generalization ability. Furthermore, the method does not require solving large-scale linear equations, accelerating the inversion computation speed and having strong noise resistance. Field examples demonstrate that this method has good potential for improving the accuracy and efficiency of actual gravity data inversion.