摘要
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.
In this paper,2.5 dimensional complex resistivity satisfy boundary value problem is given. We design and implementation of complex resistivity method for fast forward algorithm that based on development of geophysical forward and inversion unified framework, starting from the characteristics of steel Matrix and combing with the Matrix direct method which based on symbolic analysis.At the first,the algorithm approximates treatment on the boundary.And the treated steel matrix depends only on the power supply frequency and wave number,and have nothing to do with power＇s point;Secondly,we design a matrix rearrangement and fill element analysis method based on graph theory,and the Cholesky algorithm（LDLT algorithm）modified is achieved According to the 2.5D features of stiffness matrix and characteristics of LDLT,we designed the efficient complex resistivity calculation process,For the same mesh structure with just one symbolic analysis,with the same frequency and wave number, all power points only need one LDLT factorization.Based on Cole-Cole model, we studied the complex resistivity characters of anomalous body from the parameters analysis of amplitude,phase,dispersion rate value by this rapid algorithm.
出处
《地球物理学进展》
CSCD
北大核心
2014年第5期2326-2331,共6页
Progress in Geophysics
基金
国家自然科学基金(41304055,41304056)资助
