二维直流电阻率倾斜各向异性自适应有限元正演

摘要

提出了一种二维直流电阻率倾斜各向异性自适应有限元数值模拟算法,利用对偶加权后验误差估计因子指导网格自动细化过程,并在易于模拟起伏地形和倾斜界面等复杂构造的非结构三角网格上实现了这种算法.模拟了水平两层电阻率倾斜各向异性模型的直流视电阻率,并将其与解析解以及电阻率各向同性模型的直流视电阻率进行了比较,结果表明,除了电源点附近测点的有限元数值解误差较大外,其它测点处相对误差都在1％以内,且电阻率各向异性对视电阻率曲线的峰值和形态都有明显影响.二维电流密度矢量图能够很好地解释视电阻率曲线峰值和形态随电阻率各向异性倾角变化而变化的现象.%In this paper,we propose an adaptive finite element (FE) numerical simulation algorithm for direct current (DC) resistivity in two-dimensional tilted anisotropy structures.This algorithm uses a dual weighting posteriori error estimation factor to guide the mesh automatic refining process,and it is implemented on unstructured triangular elements that facilitate simulation of complex structures characterized by undulating topography and tilted interfaces.We simulated the DC apparent resistivity of a two-layer resistivity tilted anisotropy model and compared it with the analytic solution and the DC apparent resistivity of the resistivity isotropy model.The results showed that the relative error of the finite element numerical solution in most measuring points was within 1 ％,the relative error of the measuring points near the power points was large,and the resistivity anisotropy had a significant effect on the peak and shape of the apparent resistivi ty curves.The phenomenon of the peak and the shape of the resistivity curves varying with the change in resistivity anisotropy dip angles can be explained using a two-dimensional current density vector diagram.