基于TV井地2.5D直流电阻率正则化反演

2.5D inversion of borehole-surface DC resistivity based on the total variation function

针对目前地面直流电阻率法所面临的勘探深度有限的问题,开展了基于TV井地2.5D直流电阻率正则化反演研究。首先从井地直流电满足的边值问题出发,采用三角单元二次插值有限元法推导了2.5D井地电阻率正演公式。为了提高计算效率,对边界采用近似处理、以及利用图论理论的矩阵重排与填入元分析方法,实现了稀疏矩阵的直接解法,大大提高了计算效率。为了能够提高反演结果的稳定以及对异常边界分辨能力,采用L曲线法求取正则化因子、TV的稳定因子以及共轭梯度方法进行反演目标函数的求解,研究表明,反演结果高效、准确。最后对不同井地观测方式的反演结果进行对比分析,得出井地直流电阻率异常特征和分布规律。

The 2.5Dregularization inversion for borehole-to-ground DC resistivity has been implemented in this paper,which is based on total variations（TV）to facing the problem that the ground DC resistivity exploration depth was limited.To start from the well satisfied boundary value problem,using the triangular unit finite element quadratic interpolation derived to2.5Dforward modeling formulation.While the approximate boundary treatment,as well as the use of graph theory matrix rearrangement and fill element analysis method to achieve a direct solution of sparse matrices,greatly improving the computational efficiency.In order to improve the stability of the inversion results and the ability to distinguish the exception of boundaries,using L-curve to achieve regularization factor,stability factor of the TV and the conjugate gradient method for solving the objective function,which have shown that efficiency and accuracy.Finally,the inversion results in different borehole-toground observation way were on the basis of contrastive analysis to reach the anomaly characteristics and distribution rule of borehole-to-ground dc resistivity.