As a numerical method based on the Galerkin variation, the numerical manifold method (NMM) adopts a dual covering system, which is convenient for constructing high-order manifold elements and performing adaptive analysis. In this paper, the NMM is used to simulate the electromagnetic response based on the structure of the undulating terrain existing in actual geophysical exploration. The relevant system equations are derived, and a penalty function method is proposed for dealing with boundary conditions. The simulation results validate the effectiveness and accuracy of this method. Through the simulation of ground barriers and ridge models, the effect of undulating terrain on the apparent resistivity and phase is investigated, which is potentially useful for examining the complex geoelectric model characteristics as well as for terrain correction of the detection results.

作为基于Galerkin变量的数值方法，数值流形方法（NMM）采用双重覆盖系统，方便构造高阶流形元素和进行自适应分析。本文将NMM用于基于实际地球物理勘探中存在的起伏地形的结构来模拟电磁响应。推导了相关的系统方程，提出了一种处理边界条件的罚函数法。仿真结果验证了该方法的有效性和准确性。通过模拟地面障碍和山脊模型，研究了起伏地形对视电阻率和相位的影响，