【摘要】 正反演技术是获取全面地下介质信息的关键，研究者们一直致力于发展稳定、高效、高精度的地球物理正演技术。直流电阻率法中间梯度装置的主要观测区域的初始电场可视为水平均匀电场，本文为实现对直流电阻率法的中间梯度装置的电位分布及视电阻率曲线响应正演模拟，采用有限差分方法对二维地电模型的均匀电场进行正演。在前人基础上，采用非均匀网格剖分电流主要影响范围，以减少网格数量，提高计算效率。本文首先从均匀电场满足的拉普拉斯方程边值问题出发，详细地分析了非均匀网格剖分、微分方程的差分离散、线性方程组的求解等各个步骤。其次，对均匀半空间模型试算并与模型解析解对比，结果表明，地表视电阻率响应的有限差分数值解与解析解吻合，验证了有限差分算法的正确性和稳定性。最后，对单个异常体的二维地电模型和多个异常体模型的电场进行正演计算，总结了异常体及其电场分布规律。本文形成的有限差分算法，对于均匀半空间验算的正演模拟中，计算时间为2.432 26 s,相对误差不超过1.5×10^-12%。在本文中的算例中，各个模型的视电阻率曲线图及电位等值线图都能较好地反应异常体的分布情况，说明本文的有限差分算法能对均匀外电场进行有效模拟，为实际测量数据的定性解释提供思路。更多还原

【Abstract】 Forward and inverse modeling techniques are key to obtaining comprehensive information about subsurface media. Researchers are dedicated to developing stable, efficient and high-precision geophysical forward modeling techniques. The initial electric field in the main observation area of the intermediate gradient device in the direct current resistivity method can be classied as a horizontal uniform electric field. In order to realize the forward simulation of the uniform electric field for a two-dimensional geo-electric model, this paper uses finite difference method to numerically simulate the potential distribution and apparent resistivity curve response of the intermediate gradient device in direct current resistivity method. Firstly, starting from the boundary value problem of Laplace’s equation satisfied by uniform electric field, we analyze each step of non-uniform grid division, difference discretization of differential equations and solution of linear equations in detail. Secondly, we calculate a homogeneous half-space model and compare it with analytical solutions. The results show that finite difference numerical solution is consistent with analytical solution for surface apparent resistivity response, which verifies correctness and stability of finite difference algorithm. Finally, we perform forward calculation on electric fields for two-dimensional geo-electric models with single anomaly body and multiple anomaly bodies respectively and summarize distribution rules of anomaly bodies and their electric fields. In examples presented in this paper, apparent resistivity curve graphs and potential contour maps for each model can reflect distribution situation of anomaly bodies well, indicating that finite difference algorithm presented in this paper can effectively simulate uniform external electric field, and provide ideas for qualitative interpretation of actual measurement data.更多还原