基于COMSOL的起伏地形三维大地电磁数值模拟

3D Magnetotelluric Modeling With Undulating Terrain Based on COMSOL

COMSOL是一个多物理场仿真软件,笔者尝试将其应用于大地电磁法的数值模拟,研究起伏地形对大地电磁响应的影响及解决方案。本文由麦克斯韦方程组出发,施加第一类边界条件,将地形起伏数字化为参数化曲面,导入COMSOL进行计算。在对COMSOL的精度进行了验证的基础上,分析不同频点所需内存以及自由度,然后选择合适的频点进行研究。将三维起伏地形的模拟结果与无地形起伏时的结果进行对比,总结出山谷、山峰地形对三维大地电磁响应的影响,发现在XY模式下,地形对视电阻率的影响大于相位,在视电阻率等值线图中能够清晰地看出起伏地形的轮廓,而在YX模式下,地形对相位的影响大于对视电阻率的影响。最后,利用“比值法”进行地形校正,校正前由于起伏地形影响,在异常体附近会出现部分视电阻率数值跳跃现象,通过校正有效抑制了起伏地形对异常体附近视电阻率的影响,校正后的视电阻率曲线整体上移,并且异常体周围的视电阻率值也趋于背景场值,获得了较好的效果。

COMSOL is a multi-physical field simulation software.This work applied it to the numerical simulation of the magnetotelluric(MT)method to study the influence of undulating terrain on MT response and its solution.Based on Maxwell's equations,the first kind of boundary conditions are applied to the model and the topographic relief is digitized into a parameterized surface,which is imported into COMSOL for calculation.On the basis of verifying the accuracy of COMSOL,the required memory and degrees of freedom for different frequency points are analyzed,and then the appropriate frequency points are selected for research.We compare three-dimensional undulating terrain simulation results with that without terrain relief,and examine the influence of the valley and the mountain terrain on three-dimensional MT response.Research suggests that in the XY mode,the influence of terrain is greater than that of the phase of resistivity,and the apparent resistivity in the contour map can clearly show the outline of undulating terrain.Under the mode of YX,topography has more effect on phase than on apparent resistivity.Finally,the“ratio method”is used to make topographic correction to remove the jump of some apparent resistivity values near the abnormal body due to original terrain.Through such correction,the influence of undulating terrain on apparent resistivity near the abnormal body is effectively restrained.After the correction,the apparent resistivity curve is shifted overall upward,and the apparent resistivity values around the abnormal body tend to be the background field,meaning good results obtained.