基于柯西分布约束和快速近端目标函数优化的三维重力反演方法

优化算法的选取在很大程度上影响着三维重力反演的计算效率，从而制约着三维重力反演的实用性.在复杂地质构造背景下，不同岩性单元之间可能会发生物性突变，产生尖锐边界.为此，本文提出了一种新的基于柯西分布约束和快速近端目标函数（Fast Proximal Objective Function，FPOF）优化的三维重力反演方法.FPOF优化方法的一个突出特点是在每一步迭代过程中逐一计算剖分网格内的未知密度参数，因此，有较低的计算复杂度和较高的计算效率.此外，目标函数中柯西范数（Cauchy norm）的引入会对反演结果施加稀疏性，有助于产生块状效果.理论模型测试表明，本文方法不仅能产生更加聚焦的反演效果，而且反演所需的时间也比传统的共轭梯度优化方法少.最后将本文方法应用于我国西部某地区实际重力数据，反演结果与已知的地质信息有较好的一致性.

3D gravity inversion based on Cauchy distribution constraint and fast proximal objective function optimization

The choice of an optimization algorithm affects computational efficiency of 3D gravity data inversion to a great extent and thereby constrains its application in the industry. In the context of complex subsurface geological settings, sharp boundaries may exist between different rock units that have large physical property contrasts. To this end, we propose a novel 3D gravity inversion method based on Cauchy distribution constraint and fast proximal objective function (FPOF) optimization. A salient characteristic of FPOF optimization is to calculate the unknown density in each subdivided unit of the inversion domain one by one at each iteration, thus reducing computational complexity and improving computational efficiency. In addition, the inclusion of Cauchy norm into objective function imposes sparseness on model parameters to be inverted and consequently facilitates a blocky density distribution. The test of synthetic data demonstrates that the proposed inversion method not only recovers more focused anomalous density bodies but also costs less run time than conventional CG optimization method. At last, the application of the proposed inversion method to real gravity data in the Western China shows that the recovered 3D density model agrees well with the known geological knowledge.