Development of the software of three-dimensional interpretation for electromagnetic tomography

电磁层析成像三维判读软件的开发

• 批准号: 07555332
• 负责人: SASAKI Yutaka
• 金额: $ 1.98万
• 依托单位: KYUSHU UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 1995
• 资助国家: 日本
• 起止时间: 1995 至 1996
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-07555332/
• 关键词: electromagnetic tomography; electromagnetic prospecting; 3-D modeling; finite-element method; 電磁誘導法探査; トモグラフィ

During the investigation of the applicability of the finite-element method (FEM) to 3-D modeling of electromagnetic tomography, it is found that the accuracy can be degraded significantly when the conductivity contrast is very high, or when the frequency used is low. This is due to the fact that the assumption on the continuity of the electric field is violated in the conventional FEM.Thus, in order to improve accuracy we used the edge element FEM and the staggered-grid finite difference method, both of which can take into account the discontinuity of the electric field. The modeling results show that good accuracy can be obtained for 3-D models with high conductivity contrast if the frequency is above about 100 Hz, and that the system of equations is more ill-conditioned as the frequency is lower. It is also found that successive overrelaxation (SOR) method mainly used in this study is not an adequate solver for the system of equations at lower frequencies, and that the biconjugate gradient method with a preconditioning is promising. We are planning to incorporate the divergence condition into our formulation, which is expected to reduce the condition numbers of the system materix and make the iterative process of the solution more stable. After completing 3-D modeling programs which give desired accuracy regardless of the frequency used, we are going to work on the 3-D inversion.

在研究有限元法 (FEM) 对电磁层析成像 3D 建模的适用性时，发现当电导率对比度非常高或使用的频率较低时，精度会显着降低。这是因为传统的有限元法违反了电场连续性的假设。因此，为了提高精度，我们采用了边缘单元有限元法和交错网格有限差分法，这两种方法都可以考虑电场的不连续性。建模结果表明，如果频率高于约 100 Hz，则具有高电导率对比度的 3-D 模型可以获得良好的精度，并且随着频率较低，方程组的病态性更强。研究还发现，本研究中主要使用的逐次过松弛（SOR）方法对于较低频率的方程组来说并不是一个足够的求解器，而带有预处理的双共轭梯度法是有前途的。我们计划将发散条件纳入我们的公式中，这有望减少系统矩阵的条件数并使求解的迭代过程更加稳定。完成 3-D 建模程序后，无论使用的频率如何，都能提供所需的精度，我们将进行 3-D 反演。

项目成果

Yutaka Sasaki: "Accuracy of FEM 3-D modeling in the electromagnetic methods" Proceedings of the 95th SEGJ Conference. 265-269 (1996)

Yutaka Sasaki：“电磁方法中 FEM 3-D 建模的准确性”第 95 届 SEGJ 会议论文集。

佐々木 裕: "電磁法におけるFEM3次元モデリングの精度" 物理探査学会第95回学術講演会講演論文集. 265-269 (1996)

Yutaka Sasaki：“电磁法中 FEM 3D 建模的精度”物理探索学会第 95 届学术会议论文集 265-269 (1996)。