快速拟线性近似方法及三维频谱激电反演研究

Fast quasi-linear approximation and the three-dimensional spectrum of induced polarization inversion study

Zhdanov提出的拟线性(QL)近似方法有效解决了积分方程计算速度慢、占用内存多的缺陷,但因为三维频谱激电(SIP)换源频繁,每次换源都需要重新计算剖分单元的并矢格林函数和一次场,所以用该方法模拟三维SIP的速度仍然缓慢.本文根据一次场及格林函数的空间对称性,提出了一种适用于多源电磁法的快速QL近似正演方法.在此基础上,实现了Cole-Cole参数范围约束的三维SIP共轭梯度反演方法.理论试算结果表明:快速QL近似方法适用于三维SIP正演模拟,计算速度较QL近似方法有了很大提高;Cole-Cole参数范围约束的三维SIP共轭梯度反演方法对零频电阻率、极化率等参数的反演效果良好,将异常区域剖分成2000块时迭代一次只需约0.2s的时间,占用内存大约为140 MB.

The quasi-linear（QL）approximation method proposed by Zhdanov effectively tackles the problem of slow speed as well as high memory usage of integral equation method.However,as the location of transmitters of spectrum induced polarization method（SIP）needs to be changed in different modeling computation,we need to recalculate the green′s function and primary field each time,so the speed of three-dimensional SIP modeling based on QL is still slow.In this paper,we proposed a fast QL approximation method,which is based on the spatial character of primary field and Green′s tensor.After that,the Cole-Cole model was introduced to our modeling computation algorithm and then we inversed three-dimensional SIP theoretical data with conjugate gradient method and parameter constraints.The results of model trial shows that：on one hand,the fast QL approximation method has higher speed than QL approximation method and is more appropriate for three-dimensional SIP modeling.On the other hand,the inversion method in this paper can obtain good inversion results for SIP parameters such as direct current resistivity,intrinsic chargeability and so on.Normally,the computing time of single inversion iteration is about 0.2seconds and it takes up about 140 MB memory when the inhomogeneity domain is divided into two thousand blocks in the computing example.