二维电性各向异性极化体的频率域响应

Frequency responses of a two-dimensional anisotropic polarization body

地球介质的大地电磁响应是电磁感应和激电效应的综合反应,传统的大地电磁正反演理论是基于电性各向同性和无极化效应的假设,而地球内部介质的电性各向异性现象和激发极化(IP)效应普遍存在,因此有必要研究含IP效应的各向异性地层条件下电磁场的响应特征。从Maxwell方程出发,推导出了二维倾斜各向异性地层条件下大地电磁场的响应,得到了一组TE和TM解耦的偏微分方程,利用Galerkin加权余量法形成大型稀疏有限元方程,采用不完全LU分解预条件因子的稳定双共轭梯度法对有限元方程进行求解。通过与1D各向异性结果的对比,验证了本文算法的可靠性。对设计的含IP效应的二维各向异性地电模型的计算发现,无论是视电阻率还是相位曲线均对地电体的电性各向异性特征表现敏感;IP效应对大地电磁场同样存在着不可忽视的影响,因此在激发极化或者各向异性特征突出的地区,应该考虑使用含IP效应或各向异性的地电模型进行大地电磁资料的处理与解释。研究结果对于指导频率域电磁方法的野外勘探,提高大地电磁资料的解释水平与应用效果都具有重要意义。

The magnetotelluric response of an underground medium derives from its combined reaction to electromagnetic induction and induced polarization(IP).The traditional magnetotelluric forward and inversion theories are based on the assumption of electrical isotropy and neglect the effect of polarization effect.However,electrical anisotropy and IP are common in underground media.It is therefore necessary to investigate the electromagnetic response of electrically anisotropic material susceptible of IP.Based on the Maxwell equation,the response of a two-dimensional tilted anisotropic formation was derived,and a set of partial differential equations decoupled by TE and TM were obtained.A large and sparse finite element equation was built using Galerkin-weighted residuals;the stabilized biconjugate gradients method with incomplete LU factorization preconditioning was used to solve the finite element equation.The comparison with the results obtained with a one-dimensional anisotropic configuration demonstrated the reliability of the proposed algorithm.By evaluating the two-dimensional anisotropic geoelectric model accounting for IP,it was found that both the apparent resistivity and the phase curve were sensitive to the anisotropy of the geoelectric object;the IP effect also was shown to have a non-negligible influence on the electromagnetic field in the object.In areas where IP or anisotropy are prominent,it is necessary to use geoelectric models that account for these features when processing and interpreting magnetotelluric data.The results presented in this paper are of great significance for guiding the electromagnetic exploration in the frequency domain and improving the interpretation of magnetotelluric data.