| 多频可控源电磁法三维有理函数Krylov子空间模型降阶正演算法研究 |
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| 引用本文： | 周建美,刘文韬,刘航,李貅,戚志鹏.多频可控源电磁法三维有理函数Krylov子空间模型降阶正演算法研究[J].地球物理学报,2018,61(6):2525-2536. |
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| 作者姓名： | 周建美 刘文韬 刘航 李貅 戚志鹏 |
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| 作者单位： | 长安大学地质工程与测绘学院, 西安 710054 |
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| 基金项目： | 国家自然科学基金重点项目（51139004），国家自然科学基金项目（41704108），中国博士后基金项目（332100150023），中央高校基本科研业务费（300102268106）联合资助. |
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| 摘 要： | 本文采用有理函数Krylov子空间模型降阶算法实现了同时求解多频可控源电磁法三维正演响应的快速计算.首先采用基于Yee氏交错网格的拟态有限体积法实现控制方程的空间离散，将任意频率的电场响应表示为关于频率参数的传递函数.采用有理函数Krylov子空间算法求解该传递函数.针对构建m维有理函数Krylov子空间需要求解m次（几十到上百）关于有理函数极点和离散控制方程系数矩阵的线性方程组的问题，本文提出采用单个重复极点的有理函数Krylov子空间模型降阶算法，结合直接法求解器PARDISO，采用Gram-Schmidt方法，只需要1次系数矩阵分解和m次矩阵回代即可实现有理函数Krylov子空间的构建，极大地减少了计算量.针对最优化有理函数极点选取问题，本文根据传递函数的有理函数Krylov子空间投影算法的误差分析理论，引入关于单个重复极点的收敛率函数，通过求解有理函数的最大收敛率直接给出最优化的单个重复极点公式.最终实现了不同发射频率的可控源电磁法三维正演响应的快速计算.分别计算了典型层状模型多发射频率的CSAMT和海洋CSEM的正演响应，通过与解析解的对比验证了本文算法在多发射频率正演的计算精度和计算效率；并通过一个三维海洋CSEM勘探设计最优化发射频率和接收区域选取的例子进一步说明本文算法的优点.
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| 关 键 词： | 可控源电磁法 三维正演 多频 有理函数Krylov子空间 模型降阶 |
| 收稿时间： | 2017-05-16 |
Research on rational Krylov subspace model order reduction algorithm for three-dimensional multi-frequency CSEM modelling |
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| ZHOU JianMei,LIU WenTao,LIU Hang,LI Xiu,QI ZhiPeng.Research on rational Krylov subspace model order reduction algorithm for three-dimensional multi-frequency CSEM modelling[J].Chinese Journal of Geophysics,2018,61(6):2525-2536. |
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| Authors: | ZHOU JianMei LIU WenTao LIU Hang LI Xiu QI ZhiPeng |
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| Institution: | School of Geological Engineering and Geomatics, Chang'an University, Xi'an 710054, China |
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| Abstract: | In this paper, a 3D forward modeling of multi-frequency controlled-source electromagnetic (CSEM) response is proposed by using the rational Krylov subspace model order reduction algorithm. Firstly, the staggered grid is used to simulate the mimetic finite volume space discretization of the governing equations. Then we obtain a system for electric field alone. The explicit solution of this system is given in terms of the transfer function form of the frequency parameter. Rational Krylov subspace model order reduction algorithm is used to solve the transfer function. It uses the Gram-Schmidt orthogonalization algorithm to construct the orthonormal basis vectors. Through the analysis of main time-consuming part of the rational Krylov subspace algorithm, we choose to adopt a repeat pole. A simple and fast algorithm for selecting optimization repeat pole is given according to the error analysis theory of rational function approximation. Further the basis vectors and projection matrix of rational Krylov subspace is constructed by only a matrix decomposition with direct method solver PARDISO. Then 3D response of multi-frequency CSEM is obtained. Finally, the computational accuracy and computational efficiency of the proposed algorithm are verified by comparing the results of the forward modeling with CSAMT and marine CSEM layered model. Then we use the proposed algorithm to calculate a typical 3D marine CSEM model to obtain the optimal transmission frequency and receiving area. |
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| Keywords: | CSEM 3D forward Multi-frequency Rational Krylov subspace Model order reduction |
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