%0 Journal Article
%T 3D DC Resistivity Inversion with Topography Based on Regularized Conjugate Gradient Method
%A Jian-ke Qiang
%A Xue Han
%A Shi-kun Dai
%J International Journal of Geophysics
%D 2013
%I Hindawi Publishing Corporation
%R 10.1155/2013/931876
%X During the past decades, we observed a strong interest in 3D DC resistivity inversion and imaging with complex topography. In this paper, we implemented 3D DC resistivity inversion based on regularized conjugate gradient method with FEM. The Fr¨¦chet derivative is assembled with the electric potential in order to speed up the inversion process based on the reciprocity theorem. In this study, we also analyzed the sensitivity of the electric potential on the earth¡¯s surface to the conductivity in each cell underground and introduced an optimized weighting function to produce new sensitivity matrix. The synthetic model study shows that this optimized weighting function is helpful to improve the resolution of deep anomaly. By incorporating topography into inversion, the artificial anomaly which is actually caused by topography can be eliminated. As a result, this algorithm potentially can be applied to process the DC resistivity data collected in mountain area. Our synthetic model study also shows that the convergence and computation speed are very stable and fast. 1. Introduction In DC resistivity exploration method, complex topography can generate artificial anomalies which will cause difficulty for the data interpretation. Based on Qiang and Luo¡¯s work [1] on 3D DC finite element resistivity modeling with complex topography, we conducted 3D regularized inversion and imaging for this complex model. The efficiency for 3D inversion problem depends primarily on 3 factors: efficient inversion algorithm, method for computing sensitivity matrix and the solver for a large liner system. Tripp et al. [2] introduced a method for calculating the sensitivity matrix, based on the relationship between electric potential and model parameter. This developed method for computing sensitivity matrix was successfully applied to a 2D DC resistivity inversion problem. Park and Van [3] introduced 3D inversion based on finite difference method. Sasaki [4] also described similar 3D inversion algorithm but based on finite element method. These introduced 3D inversion methods work well to recover shallow resistivity anomalies but fail to produce high-resolution image for the deep anomalous bodies. The synthetic model studies show that the recovered resistivity imaging is quite different from the true model if the anomaly is located deep underground. Zhang et al. [5] conducted the research on 3D DC resistivity inversion using conjugate gradient method. Loke and Barker [6] introduced the E-SCAN (pole-pole array) 3D inversion technique where the Fr¨¦chet derivative matrix can be
%U http://www.hindawi.com/journals/ijge/2013/931876/