海量重力梯度张量数据多、弱异常源有序分离理论及快速反演算法研究

The potential field with weak anomalies and multi-causative sources are difficult separated and extracted in large scale data with multiple abnormal sources superposition, which is an accepted difficult problem in gravity prospecting. An innovative mutinary inverison algorithm for multi-causative sources using derivatives of Sigmoid function with higher core resolution will be researched in Geoscience BC project based on systematic research on influence factors and influence laws of the piecewise function in the planting inversion and binary inversion. A novel depth-weighting matrix is proposed, which counteracts the natural decay of the sensitivity matrix. The depth resolution of mutinary inverison is evaluated by depth resolution plot. To reveal the mechanism of the influence of mutinary inverison on the characterization of weak anomalies and multi-causative sources under complex condition, a adaptive mutinary inversion method is presented. Considering that weak anomaly source is easily overlap by the relatively large adjacent source, a horizontal attenuation function is proposed to suppress mutual interference between the adjacent anomaly sources and to extract weak anomalies and multi-causative sources one-by-one. According to the 3D forward and inversion of massively data is a time-consuming problem with high demands on computational and physical memory usage, a new fast method was proposed for updating sensitivity matrix. Through the above-mentioned research, this study lays a theoretical basis of extraction of weak anomalies and multi-causative for large scale gravity gradient tensor data in gravity prospecting.

如何从多异常源叠加的海量数据中提取勘探目标异常/弱异常信号一直是重力勘探资料解释中的一个关键问题，以Geoscience BC项目为依托，通过系统研究分段函数在种植反演和二进制反演等的主要影响因素与影响规律，利用Sigmoid函数的导数能扩展核心分辨率的特性，建立能表征多个异常源多进制反演方法；提出一个与场源衰减性质无关的深度加权函数，借助DRP工具，评价多进制反演中的深度分辨率优劣，开展自适应多进制反演方法研究，揭示于复杂条件下影响多进制反演表征多、弱异常源的机制；考虑弱异常源易于被邻近的相对较大的异常源所湮没这一问题，提出一个水平衰减函数，就抑制相邻异常源相互干扰趋势，及提取多/弱异常源的次序等问题开展研究；就正、反演研究中计算耗时过长和核矩阵内存消耗过大等问题，开展核函数快速更新方法研究。通过本项研究，将为提取大尺度重力梯度张量数据中的多、弱异常信号奠定一定的理论基础。

针对如何从多异常源叠加的海量数据中提取勘探目标异常/弱异常信号一直是重力勘探资料解释中的关键问题，充分利用Geoscience BC项目的重力资料、地质资料及地球物理解释成果，于海量、复杂条件下，揭示深度分辨率影响因素、影响多进制反演表征多、弱异常源的机制，及多、弱异常源的优化过程/提取次序等。具体研究成果如下：.①提出虚拟线线观测和虚拟面面观测方案，避免依赖于位场的对称性，实现适用于水平观测面的的快速算法；在此基础上，进行使用泰勒级数展开，提出了适用于非水平观测面的的重力梯度张量快速正演算法。.②利用灵敏度矩阵衰减特性，给出了多种构建深度加权矩阵及其相应预条件矩阵构建方法，避免位场多分量数据联合反演中难于确定衰减系数的问题。.③通过引入sigmoid函数实现二进制反演，以避免阶梯函数的块效应，模型试算与实际盐丘重力梯度张量数据反演结果及分析表明其在加快模型收敛速度的同时能够较好的反映模型位置和轮廓。.④考虑单一阶梯函数难于表征多个异常源，为此基于阶梯函数推广至多进制函数，利用全变差正则化项和L1小波正则化项构建混合正则化反演方法，采用分裂Bregman迭代方法求解其相应的最优化问题，再次基础上实现了基于多进制阶梯函数的反演方法，实际数据反演结果表明，多进制反演能有效地保留水平分辨率和深度分辨率信息。.⑤在L1范数的基础上，用累加求和分析替换迭代求解，避免计算或存储反演核系数矩阵，以减少内存占用和加快反演迭代；针对种植反演易于导致相邻异常源相互侵入，引入一个基于位场水平衰减特性加权函数来限制种子的作用范围，减弱相邻异常源相互侵入的趋势。.⑥针对常规欧拉反褶积仅通过欧拉反褶积解的构造指数的“色谱”难于评价、分离异常，引入三维核密度估计对欧拉反褶积解集综合分析，从而实现了欧拉反褶积对相邻异常有效分离、快速定位。