多重网格方法的大地电磁正演模拟与分析
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摘要
计算大型线性方程组是大地电磁正演问题的重要部分。求解线性方程组的一般迭代算法都可以有效光滑高频误差分量,但对低频误差分量的光滑效率比较差,严重制约了正演模拟的效率。为了有效提高二维大地电磁正演模拟的效率,本文从求解大型线性方程组入手,初步引入了多重网格方法。通过分析多重网格方法在一维问题上的应用,介绍了多重网格方法的基本原理,并证明了该方法可以高效地光滑高频误差分量和低频误差分量。
本文采用有限单元法进行二维正演模拟,求得每层网格上的刚度矩阵和方程右端项,并根据模拟特点设计了多重网格方法的循环策略。为了证明多重网格方法在大地电磁二维正演模拟中优越性,本文选用了三种高效的迭代方法,即广义最小残余法、QR分解的最小二乘法和双共轭梯度稳定法,通过比较这些算法在多重网格方法处理前后的计算结果,得到多重网格方法在大地电磁二维正演模拟中的特点。
首先对水平层状模型进行了模拟,定量分析了多重网格方法在计算精度上的优越性；其次分别对地下不均匀体模型和起伏地形模型进行了模拟,定性分析了多重网格方法在迭代次数、计算速度和精度上的优越性。
Solving large linear equations is an important part of the magnetotelluric forward modeling work. For general iterative algorithms, the high-frequency error components can be smoothed effectively, but the smooth efficiency of the low-frequency error components are relatively poor, so, this seriously hampered the effects of forward simulation. In order to improve the two-dimensional magnetotelluric forward modeling efficiency, the multi-grid methods has been introduced to the two-dimensional magnetotelluric forward modeling. By analyzing the application of multi-grid method in one-dimensional problem, the basic principles of multi-grid method has been introduced, and it is proved that this method can efficiently smooth both high-frequency error component and low frequency error component.
In this paper, the finite element method is used in the two-dimensional forward modeling. In meeting the simulation characteristics, the computing strategy of multi-grid method has been designed. Inorder to fully prove the superiority of multi-grid method, which is applied in the two-dimensional magnetotelluric forward modeling, three efficient iterative algorithms are selected to be compared with multi-grid method, they are the GMRES, the LSQR and the BICGSTAB.
First, the horizontal layered model has been simulated, and the advantages of multi-grid method on calculation accuracy has been quantitative analyzed and proved; secondly, the model of underground heterogeneous has been simulated, and the advantages of multi-grid method on iteration times, calculate speed and accuracy have been analyzed and proved; finally, the model of rolling topography has been simulated, and proved that multi-grid method can effectively suppress the impact of topography.
本文采用有限单元法进行二维正演模拟,求得每层网格上的刚度矩阵和方程右端项,并根据模拟特点设计了多重网格方法的循环策略。为了证明多重网格方法在大地电磁二维正演模拟中优越性,本文选用了三种高效的迭代方法,即广义最小残余法、QR分解的最小二乘法和双共轭梯度稳定法,通过比较这些算法在多重网格方法处理前后的计算结果,得到多重网格方法在大地电磁二维正演模拟中的特点。
首先对水平层状模型进行了模拟,定量分析了多重网格方法在计算精度上的优越性；其次分别对地下不均匀体模型和起伏地形模型进行了模拟,定性分析了多重网格方法在迭代次数、计算速度和精度上的优越性。
Solving large linear equations is an important part of the magnetotelluric forward modeling work. For general iterative algorithms, the high-frequency error components can be smoothed effectively, but the smooth efficiency of the low-frequency error components are relatively poor, so, this seriously hampered the effects of forward simulation. In order to improve the two-dimensional magnetotelluric forward modeling efficiency, the multi-grid methods has been introduced to the two-dimensional magnetotelluric forward modeling. By analyzing the application of multi-grid method in one-dimensional problem, the basic principles of multi-grid method has been introduced, and it is proved that this method can efficiently smooth both high-frequency error component and low frequency error component.
In this paper, the finite element method is used in the two-dimensional forward modeling. In meeting the simulation characteristics, the computing strategy of multi-grid method has been designed. Inorder to fully prove the superiority of multi-grid method, which is applied in the two-dimensional magnetotelluric forward modeling, three efficient iterative algorithms are selected to be compared with multi-grid method, they are the GMRES, the LSQR and the BICGSTAB.
First, the horizontal layered model has been simulated, and the advantages of multi-grid method on calculation accuracy has been quantitative analyzed and proved; secondly, the model of underground heterogeneous has been simulated, and the advantages of multi-grid method on iteration times, calculate speed and accuracy have been analyzed and proved; finally, the model of rolling topography has been simulated, and proved that multi-grid method can effectively suppress the impact of topography.
引文
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