基于多重网格法的MT正演模型边界截取

摘要

为了验证基于多重网格法边界截取的效果,通过数值模拟,分别对大地电磁法问题的均匀半空间模型和三层模型进行基于多重网格法的边界截取研究和分析.采用加权平均法产生粗网格上系数矩阵,并与传统的方法对比.研究结果表明:粗网格加权平均法的渐进收敛性明显比Galerkin法(采用简单的插值矩阵)的好,但比粗网格近似的几何法的渐进收敛性略差；收敛性的广义Fourier谱分析在大地电磁法中对介质的非连续性不敏感,不能区分模型参数变化所引起的收敛性变化；随着边界截取的增加,满足特定收敛标准的数值解与理论解偏差增大；当截取到的深度约为趋附深度的2倍时,截取后的计算结果接近理论值,说明基于多重网格法的边界截取有效.%Boundary truncation was applied for homogeneous half-space model and three-layer model based on the multigrid method. Compared to traditional coarse grid approximations, an average weighted method was used to generate the coarse grid approximation and general Fourier analysis was carried out for convergence analysis. Utilizing cycles or component of multi-grid method, the modeling area was reduced to improve modeling efficiency. The numerical results for boundary truncation were compared with numerical results by direct solver. The results show that the weighted average method has a better convergence behavior than Galerkin method and slightly poorer convergence than geometric method. General Fourier analysis is not sensitive to conductivity discontinuities and can not demonstrate the convergence differences caused by the discontinuities. As the truncation increases, deviation from the theoretical results becomes more obvious. When the boundary is truncated to around twice the skin depth, and the results are well approximated with theoretical results. In the log space (or just log frequency), when the truncated boundary value cannot well represent the real value, the calculated absolute electrical field (or phase) tends to move up and down at the same level with respect to frequency.