基于聚集代数多重网格法的CSAMT三维数值模拟研究

发布时间：2018-04-26 06:07

本文选题：可控源音频大地电磁法 + 交错网格有限差分法　；参考：《东华理工大学》2015年硕士论文

【摘要】：可控源音频大地电磁法(CSAMT)是地球物理勘探的重要手段之一,在矿产资源勘查和地质调查等多个领域得到了广泛的应用。由于传统的CSAMT一维和二维反演方法难以真实地反映复杂变化的介质结构,CSAMT三维反演技术的实用化问题迫在眉睫,而寻求一种高效、稳定的正演计算方法是推进CSAMT三维反演实用化进程的关键因素之一。因此本文开展基于聚集代数多重网格法的CSAMT三维数值模拟研究。本文从CSAMT满足的麦克斯韦方程出发,将总场分解为一次场和二次场,利用电磁场边界条件和傅里叶变换推导有限长电偶源激发的电磁场公式,并通过快速汉克尔变换实现快速计算。然后利用三维交错采样有限差分法推导出二次场中电、磁场分量满足的关系式,并通过变换消去磁场分量,将CSAMT三维数值模拟的二次场计算问题转换成仅关于电场分量的大型线性方程组的求解问题。为提高CSAMT数值模拟中迭代求解的速度,引入具有高速收敛性的聚集代数多重网格法(AGMG),重点研究AGMG的聚集粗化策略及求解过程的算法实现。针对CSAMT三维有限差分模拟中线性方程组的大型稀疏特性,采用AGMG法作为广义最小残差法(GCR)预处理算子实现线性方程组求解,开发了CSAMT三维正演软件。论文通过二维LAPLACE方程求解比较了算法的优越性,表明聚集代数多重网格-广义最小残差法(AGMG-GCR)相比传统的Krylov子空间迭代法(BCGSTAB,CG,BCG,GCR,DQGMRES,ILU-GCR)既有GCR算法的强稳定性,也有线性快速衰减和随网格剖分数增加迭代次数基本保存不变的特征。通过水平层状模型三维正演验证算法的正确性和稳定性,并对典型地电模型(低阻模型、高阻模型和组合模型)进行数值模拟,分析和总结其CSAMT三维响应特征,为野外数据采集和资料解释提供参考。
[Abstract]:Controlled source audio magnetotelluric (CSAMT) is one of the important means of geophysical exploration. It has been widely used in many fields, such as mineral resources exploration and geological investigation. Because the traditional CSAMT one and two dimensional inversion method is difficult to reflect the complex medium structure, the practical problem of CSAMT 3D inversion is forced to An efficient, stable forward calculation method is one of the key factors to promote the practical process of CSAMT 3D inversion. Therefore, this paper develops a three-dimensional numerical simulation of CSAMT based on the multigrid method of aggregation algebra. This paper, based on the Maxwell equation satisfied by CSAMT, decomposes the total field into one field and two fields. The electromagnetic field boundary condition and the Fu Liye transform are used to derive the electromagnetic field formula excited by a finite long couple source, and the Fast Hankel transform is used to calculate the electromagnetic field. Then the three dimensional staggered sampling finite difference method is used to deduce the relationship between the two fields and the magnetic field components, and the three-dimensional numerical simulation of CSAMT is simulated by changing the magnetic field components. The two field computation problem is converted to the solution of a large linear equation group with only an electric field component. In order to improve the speed of iterative solution in the CSAMT numerical simulation, a high speed convergent aggregation algebraic multigrid method (AGMG) is introduced, focusing on the aggregation and coarsening strategy of AGMG and the algorithm implementation of the solution process. The large sparse characteristic of the linear equation group in the finite difference simulation, the AGMG method is used as the generalized minimum residual method (GCR) to solve the linear equations, and the CSAMT 3D forward software is developed. The superiority of the algorithm is compared with the two-dimensional LAPLACE equation, and the multigrid generalized minimum residual method (AGMG-) of the aggregation algebra is shown. (AGMG- GCR) compared with the traditional Krylov subspace iterative method (BCGSTAB, CG, BCG, GCR, DQGMRES, ILU-GCR), it has both the strong stability of the GCR algorithm, the linear fast attenuation and the constant preservation of the number of iterations with the grid fraction. The low resistance model, the high resistance model and the combined model are used to carry out numerical simulation, analyze and summarize the three dimensional response characteristics of CSAMT, and provide reference for field data collection and data interpretation.

【学位授予单位】：东华理工大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：P631.325

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