Abstract: After simplifying the borehole-to-surface electrical problem as a model with a vertical line source, the authors achieved 3D resistivity forward modeling of a vertical line source of electrical current using finite element method (FEM). The authors also achieved 3D resistivity inversion on the basis of iterative nonlinear damped least square method. Some simplified models were adopted to test both the forward and the inversion algorithms. The authors used “synthetic data” obtained from the forward modeling to inverse the target resistivity in the model. The authors also investigated the possible effects of data surveying region and noises on the inversion quality of target resistivity. This study would provide some theoretical background for enhancing the quality of inversion problem of borehole-to-surface electrical method.

Key words: 3D forward and inversion, borehole-to-surface electric method, finite element method (FEM)

摘要： 通过简化井地电法模型为垂直有限长线电流源作用下的三维地下介质模型，利用三维有限元法实现了垂直有限长线电流源作用下的三维地下介质电场的正演计算。应用非线性阻尼最小二乘迭代算法实现了地表电位数据的地下目标层电阻率反演，通过简化模型对相应计算程序进行了检验，证实了程序的可靠性。用给定模型正演得到的地表“理论合成数据”来反演地下异常体，并对数据测量范围和干扰水平对反演的影响进行了讨论。该研究可为提高井地电法反演质量提供部分理论指导依据。

关键词: 三维正, 反演, 井地电法, 有限元法