基于盲源分析的重力梯度张量多异常源分离理论及算法研究

The potential field with weak anomalies and multi-causative is difficult separation and extraction in gravity prospecting,which is an accepted difficult problem.An innovative potential field separation theory and algorithm will be researched through blind analysis extraction with order and accuracy for weak anomalies and multi-causative based on the advantage of tensor gradient gravity such as high sensitivity, information rich and strong anti-interference ability,etc. Regarding difficult to estimation causative number in superimposed anomaly in gravity prospecting, a novel source indicator will be proposed using the optimal solution of tensor Euler deconvolution to avoid solving underdetermined blind source separation problem. A new discrimination techniques will be studied ,which provides better constrained solutions for ill-condition of Euler homogeneous equation based on multi-parameter regularization parameter.Multi-parameter regularization nonlinear blind source separation will be considered for suppress noise. The order of blind signal extraction will be established according to their probability calculated by Hypergeometric probability density estimation or kernel density estimation of optimal solution of tensor Euler deconvolution to using blind source separation extract the causative signal one-by-one. Through the above-mentioned research, the new potential field separation method will be proposed based on nonlinear underdetermined blind source separation with specify extraction order and signals number technology, which can provide the technology of distinguish and extraction of weak gravity in spuerimposed anomaly, and fine marked in three-dimensional space,etc. This project has important scientific significance and application value in data processing and inversion of full tensor gradient gravity .

重力勘探中经常遇到多个复杂目标体而导致异常场源难以分离这一公认难题，利用重力梯度张量灵敏度高、信息量丰富、抗干扰能力强的特征，开展基于盲分析的重力梯度张量的多、弱异常场源的有序、准确分离基础理论研究。针对多场源叠加异常中场源数目难于确定的问题，提出了利用张量欧拉反褶积优解作为源指示器，规避求解欠定盲源分离问题；针对欧拉齐次方程的病态特征，开展了基于单一/多正则化重力梯度张量的欧拉反褶积剔除谬解方法的研究；考虑噪声影响，研究非线性多正则化的盲源分离抗噪问题；提出了利用欧拉解集优解的超几何概率密度估计/核密度估计大小作为盲抽取次序，有序、逐一抽取多异常场源。通过本项目研究，有望提出一套可准确确定异常场源数目及盲抽取次序的超定盲源分离算法，实现重力勘探领域复杂构造条件下多、弱异常信息的识别、提取与三维精细标示等，这对于促进重力梯度张量数据处理和资料反演解释方面具有重要科学意义和应用价值。

重力勘探中经常遇到多个复杂目标体而导致异常场源难以分离这一公认难题，利用重力梯度张量灵敏度高、信息量丰富、抗干扰能力强的特征，开展基于盲分析的重力梯度张量的多、弱异常场源的有序、准确分离基础理论研究。.针对直立六面体难于拟合复杂地质构造，任意六面体空间关系不明确难于满足反演需求，提出了计算量小、适合复杂地质构造、且无数值奇点的任意四面体解析解，及自适应正演计算策略；针对点元法计算时间长、基于等效几何构架的重力异常响应的计算依赖于位场的对称性，且其计算加速性能与地球物理模型剖分数仅为线性关系等难于满足海量数据反演需求，提出了重力梯度张量快速正演算法；针对在地球物理中单一正则化方法都有一定的侧重性，在最小分裂Bregman迭代算法框架下，引入基于全变差正则化项和多尺度小波L1正则化项构建混合正则化反演，以避免在异常边界上出现过度正则化效应，从而有效地勾勒异常物性边界；提出了不依赖于场源衰减特性的深度加权矩阵和的预条件矩阵方法，从而加快反演实施；针对欧拉线性方程组的条件数过大，易于导致欧拉解集中良解占优率低的问题，采用奇异值分解总体最小二乘法，构造阈值函数对解集进行过滤，并开展自适应误差估计策略张量欧拉反褶积算法的研究；在非线性瞬态盲源问题框架下，采用基于概率密度函数估计的信号源盲分离算法，引入基于欧拉解的多维核密度估计，实现了重力/重力梯度张量数据的盲源分离，采用模糊聚类对混叠源数进行估计，采用Huber范数对聚类中心水平位置快速估计，利用水平衰减函数避免异常源相互干扰，从而实现多个异常源的并行盲抽取。.本项目提出一套可准确确定异常场源数目及盲抽取次序的盲源分离算法，实现重力勘探领域复杂构造条件下多、弱异常信息的识别、提取与三维精细标示，促进重力梯度张量数据处理和资料反演解释方面研究。