大地电磁有限差分数值解对比

基于网格精度、形成系统方程的方式、边界条件以及预条件线性算子等，文中对大地电磁（MT）有限差分数值解作了对比.对不同网格剖分方式下的三个均匀半空间模型的一维MT响应对比显示，在降低首层厚度的同时保持层间厚度变化在合理范围可以同时提高主场和辅助场的精度.在利用正常中心网格法（主场和辅助场都定义在单元顶面的中心）计算二维（2-D）TM模式响应时，应该从Maxwell一次差分方程开始组建二次差分方程，这样可以更充分考虑模型电阻率的变化.在对边界值如何影响数值解的测试表明，仅仅提高一维（1-D）边界值的精度对提高2-D MT有限差分数值解的精度是有限的.线性算子对提高MT解的效率十分重要，简单的对比进一步表明合适的预条件再配合好的线性算子（如文中求解2-D MT时所采用的DILU-BICGSTAB方法）不仅可以加速收敛，而且可以降低迭代次数.

COMPARISON OF FINITE DIFFERENCE NUMERICAL SOLUTIONS IN MAGNETOTELLURIC MODELLING

Different algorithms of the finite difference forward modeling for magnetotelluric sounding (MT) are compared focused on the grid resolution, ways to form system matrix, boundary conditions and preconditioning linear solvers. The MT responses of three half space models with different grids indicate that the accuracy of both the primary fields and auxiliary fields increases when the thickness of the first row decreases and the difference between successive rows is in a reasonable range. In the 2-D TM mode of the normal-center method (where the primary and auxiliary fields are defined at the center of top cell surface), the second order of Maxwell's difference equation is constructed from the first order of Maxwell's equations in order to consider model's resistivity variance. We also make a test how the boundary values affect the numerical solutions, and find that it can not greatly enhance the accuracy of the 2-D MT finite difference numerical solution by increasing the accuracy of the 1-D boundary values only. The linear solvers are important for an efficient solution of MT problems. The simple comparison shows that a suitable preconditioner combined with a good linear solver (for instance, the DILU-BICGSTAB method used for the 2-D MT problem in the article) can not only improve convergence, but also reduce iterative numbers.