一种重力数据快速聚焦反演方法

A fast method for focusing inversion of gravity data

本文研究提出一套重力数据快速聚焦反演方法,以用于高效清晰刻画地下目标地质体.所提出反演方法利用随机广义奇异值分解算法来求解矩阵的近似广义奇异值分解,能够有效地降低原始反演问题的维度.与常规奇异值分解算法相比,能够在占用较少的内存的情况下快速得出反演结果.同时在反演目标函数中融入聚焦约束矩阵以实现反演结果的聚焦性,利用广义交叉验证方法进行正则化参数选取.文章给出了所提出的反演方法的详细计算步骤,并通过两个理论模型试验和一组实测数据的反演试算佐证了所提出快速聚焦反演方法的有效性与高效性.

In this paper,a fast and focusing inversion method for gravity data is proposed for describing the target geological body efficiently and clearly.The proposed method uses the Randomized Generalized Singular Value Decomposition(RGSVD)algorithm to solve the approximate Generalized Singular Value Decomposition(GSVD)of the inversion matrix,which can effectively reduce the dimension of the original inverse problem and can obtain inversion results quickly with less memory compared with the conventional SVD algorithm.Meanwhile,a focus constraint matrix is integrated into the total objective function to achieve a focusing of inversion result,and the regularization parameters are selected by generalized cross validation method.In this paper,the detailed calculation steps of the proposed fast and focusing inversion method are given,and the effectiveness and efficiency of the proposed inversion method are verified by two theoretical model tests and a real field data test.