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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,仪仪提高一维(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.
Based on the grid precision, the way of forming the system equations, the boundary conditions and the preconditioned linear operators, the MT finite difference numerical solution is compared in this paper. For three homogeneous half-space A comparison of the one-dimensional MT response of the model shows that the reduction of the thickness of the first floor while maintaining the variation of the thickness between the layers within a reasonable range can improve the accuracy of both the home field and the auxiliary field simultaneously.With the normal center grid method (home field and auxiliary field are defined in the cell Top Center) When calculating two-dimensional (2-D) TM mode responses, a second-order difference equation should be constructed from the Maxwell first-order difference equation so that changes in model resistivities can be taken more fully into account. Shows that the accuracy of the instrument in improving the accuracy of one-dimensional (1D) boundary values is limited to improve the accuracy of 2-D MT finite difference numerical solution. The linear operator is very important to improve the efficiency of MT solution. A simple comparison further shows Appropriate preconditions coupled with good linear operators, such as the DILU-BICGSTAB method used to solve 2-D MT in the paper, not only accelerate convergence but also reduce the number of iterations.