任意四边形剖分二维MT有限元正演模拟

Two-dimensional magnetotelluric forward modeling by arbitrary quadrilateral finite element method

为了模拟实际的起伏地形,在前人研究的基础上,单元网格设计为任意四边形网格,单元内的场值双线性变化,采用了高斯数值积分法计算单元系数矩阵,并给出二维大地电场的辅助场表达式。通过模型算例表明,模拟结果与解析解的均方误差在1%以内,地形模型与前人的模拟结果相吻合。分析对比了两个不同坡度模型对视电阻率和相位的影响。采用任意四边形网格剖分法,降低了编程难度,可以方便地适应野外地形的起伏变化。

In order to easily model topography in field work,on the basis of predecessors'achievements,the arbitrary quad-rilateral element grid was used in the finite element method (FEM),and the electromagnetic field of models were designed to bilinear variation within each quadrilateral element in our numeric modeling.We deduced the specific formula to calculate the u-nit coefficient matrix by Gaussian numerical integral and the expression of the auxiliary field when using arbitrary quadratic ele-ment.Model calculation shows that the mean square error between the simulation results with the analytical solution is less than 1 percent,and the results of terrain model is consistent with the one of other scholar's.Through modeling of two ramp terrain modes with different pitch,comparing and analyzing the effect of the apparent resistivity and the phase.Due to the use of arbitrary quadrilateral element grid,the difficulty of programing was reduced,forward modeling can be more easily adapt to the topography variation.