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通过引入Cole-Cole模型,推导了2.5维复电阻率满足的边值问题.利用前期开发的地球物理正反演统一框架,从钢度矩阵的特点出发、结合基于符号分析的矩阵直接解法,设计实现了适合复电阻法的快速正演算法.该算法首先对边界进行了近似的处理,经处理的钢度矩阵只与供电频率及波数有关,而与供电点无关;其次设计了基于图论理论的矩阵重排与填入元分析算法,实现了改进的Cholesky算法(即LDLT算法);根据钢度矩阵特征及LDLT特点设计了高效的2.5D复电阻率计算流程,对于同一剖分结构只需进行一次符号分析,同频和波数的条件下所有供电点只需一次LDLT分解.利用快速算法,研究了Cole-Cole模型描述异常体的复电阻率振幅、相位、频散率值等参数的异常特征.
By introducing the Cole-Cole model, the boundary value problem of 2.5-D complex resistivity is deduced. Based on the unified framework of geophysical forward and backward developed in the past, based on the characteristics of the steel matrix and the matrix direct solution based on symbolic analysis, A fast forward algorithm is proposed, which is suitable for the complex resistance method. The algorithm first approximates the boundary. The processed steel degree matrix is only related to the supply frequency and wave number, but has nothing to do with the supply point. Secondly, Matrix rearrangement and fill in the meta-analysis algorithm to achieve an improved Cholesky algorithm (LDLT algorithm); according to the characteristics of the steel matrix and LDLT features efficient 2.5D complex resistivity calculation process is designed for the same split structure only After a symbolic analysis, the same frequency and wavenumber conditions, only one LDLT decomposition is required for all the power supply points.Using the fast algorithm, the anomalies of complex resistivity amplitude, phase, dispersion rate and other parameters of Cole-Cole model anomalies are studied feature.