用边界单元法模拟二维地形对大地电磁场的影响

本文用边界单元法模拟二维地形对大地电磁场的影响.首先用格林公式将二维大地电磁的边值问题转变成积分方程,然后用边界单元法解积分方程,得到地形上的大地电磁场和它的法向导数,由此可计算电阻率.与有限单元法相比,本方法剖分后的地形与实际地形的拟合程度高,向计算机输入原始数据的工作简单,可以在微机上计算地形引起的视电阻率.本方法适合于在野外生产现场进行大地电磁法的地形改正.计算表明,地形对H_x型波的影响比对E_x型波严重得多;随着周期的增长,地形对H_x型波的影响变得稳定.

MODELING 2-D TERRAIN EFFECT ON MT BY THE BOUNDARY ELEMENT METHOD

The boundary element method is used to model 2-D terrain effect on magnetotelluric field in this paper. First, the boundary value problem of 2-D magnetotelluric field is transformed into integral equation problems by use of Green's theorem. Then, the boundary element method is used to solve the integral equation and to get the magnetotelluric field and its normal derivative on the terrain. From these values, we can calculate the apparent resistivity caused by the terrain.The results calculated by this method are compared with those calculated by finite element method and by analytic method. The agreement is satisfactory.Compared with the finite element method, the boundary element method is simpler in element division and initial data preparation and requires less memory space. The configuration of terrain divided by the boundary element method is more consistent with the practical terrain. The method proposed in this paper can be run on a microcomputer. Therefore, the 2-D terrain correction for MT can become an applicable technique for field practice.The calculation results show that: in the case of Hx-polarization, the terrain effect is much severer than that in Ex-polarization, and it becomes stable as the period increases.