基于矢量有限元的大地电磁快速三维正演研究

Research on fast three-dimensional forward algorithm of magnetotelluric sounding based on vector finite element

本文采用直接求解器PARDISO且无需散度校正的正演方案,求解矢量有限元法对应的大型线性方程组,获得不同地形(水平和起伏)条件下地电模型的大地电磁响应,提高了大地电磁三维正演计算的速度。在中等规模计算条件下,通过本文的计算方法与带散度校正的迭代求解法对比,计算速度可提高十倍以上。

The finite element method has the characteristics of strong adaptability in simulating the electromagnetic response of rugged topography and complex geological bodies.In recent years,it has been widely used in the three-dimensional(3D)forward modeling of magnetotelluric(MT)sounding.However,the finite element method also has some shortcomings in terms of computational efficiency.The large amount of calculation and long running time of the method are the main factors that lead to the lag of the practical process of the 3D MT inversion technology based on the finite element method compared with the 3D MT inversion technology based on the finite difference method.In order to improve the 3D forward speed of MT,the authors adopt the forward modeling scheme which uses the direct solver PARDISO and does not need divergence correction to solve the large-scale linear equations corresponding to the vector finite element method,and obtain the MT response of the geoelectric model under such different terrain conditions as flat and rugged topography.Under the conditions of medium-scale calculation,through the comparison between the direct solution method without divergence correction and the iterative solution method with divergence correction,the authors have detected that the direct solution method without divergence correction has advantages in calculation accuracy and calculation time,especially in the calculation.In terms of time,the ratio of the calculation speed of the direct solution and the iterative solution is raised by more than ten times.