地面频率域电磁法三维有限体积正演与截断牛顿法反演

发布时间：2018-06-23 23:27

本文选题：频率域电磁法 + 三维正反演　；参考：《吉林大学》2017年博士论文

【摘要】：地面频率域电磁法方法种类繁多,在深部地球结构探测、地热勘探、矿产勘查、油气勘查及环境与工程勘探等各个领域起到关键作用。随着电磁勘探技术的逐步发展以及“精细化”和“透明化”地质勘探的需求,实施地面频率域电磁法三维勘探与解释逐步成为常态。因而,频率域电磁法三维正反演成为大规模电磁数据精细化和定量解释的关键,然而受到多场源、正演模拟速度和精度、三维反演的适用性以及计算效率等问题的困扰,仍难于在实际勘探中获得应用。为此,本论文采用有限体积法求解Lorenz规范条件下耦合势对称方程实现任意场源频率域电磁法三维正演,并引入聚集多重网格求解技术实现大规模问题的线性代数方程组高精度快速求解;同时,提出一种“全局”优化算法—截断牛顿法及多种经典反演方法实现了地面频率域电磁法三维反演,并以大地电磁为例探讨该三维反演方法的适用性及其影响因素,期望以此建立地面频率域电磁三维正反演平台,为提高地面电磁勘探的三维精细化解释提供技术支撑。为了克服空气层和地表耦合以及不同场源类型、不同观测数据的频率域电磁法三维正演,本文首先从Maxwell方程出发,推导基于Lorenz规范条件的磁矢势和标势耦合对称方程,并采用有限体积技术对方程进行离散,得到大型对称稀疏线性代数方程组;然后利用一系列短导线(电性)源组合模拟各种不同类型场源,并采用预处理拟最小残差法(QMR)以及PARDISO、MUMPS等求解库进行求解,成功实现不同场源类型的地面频率域电磁法三维正演模拟。通过层状介质模型不同场源类型的三维正演模拟,并与一维解析解对比验证本文算法的准确性和有效性;进而,对典型地电模型在不同场源激发下频率域电磁法响应特征进行对比分析。为了加快地面频率域电磁三维正演的求解速度,将一种新型的代数多重网格算法—聚集多重网格算法(AGMG)引入到三维正演模拟中。本文从AGMG算法的粗化策略和套迭代技术出发,将AGMG和传统Krylov子空间(GCR、FCG)迭代算法进行耦合,提出五种不同AGMG求解算法。以大地电磁法为例,通过对典型复杂地电模型进行正演模拟,并与已有的大地电磁三维正反演程序(Mod EM)结果进行对比,验证本文算法的准确性。另外,将不同剖分网格和不同极化方式的正演模拟结果与QMR迭代算法进行对比表明,K-AGMG-GCR算法不仅能够改善AGMG算法的稳定性,同时还具有收敛精度高、速度快、计算效率高等优点。相对于现有Mod EM程序,K-AGMG-GCR算法能够提高计算速度数十倍,因此特别适合大规模地面频率域电磁三维正演问题。针对地面频率域电磁三维反演,本文引入一种全局优化信赖域算法和牛顿法结合的截断牛顿法(TRN)。首先,从最优化和正则化反演理论出发,建立频率域电磁法三维反演的目标函数、模型协方差矩阵及数据协方差表达式;并详细推导了不同类型频率域电磁法梯度、Hessian矩阵和Jacobi矩阵统一表达式;进而详细阐述了截断牛顿法的基本原理及关键技术(比如步长全局搜索、自适应截断误差算法以及正则化因子冷却法等);同时介绍了经典最优化反演算法-最速下降法(STD)、非线性共轭梯度法(NLCG)、高斯牛顿-共轭梯度法(GNCG)和有限内存拟牛顿法(L-BFGS)。最后,采用模块化设计思想及利用消息传递接口(MPI)实现并行加速,实现了不同算法地面频率域电磁法三维反演。本文以大地电磁三维反演为例,首先通过对比两个理论模型(高低组合模型、“拱桥”低阻模型)不同反演算法的结果,表明本文实现的反演算法(TRN、STD、NLCG、L-BFGS和GNCG)均能取得良好效果,与国际著名的大地电磁开源程序Mod EM效果相当;而本文所提出的TRN算法是一种收敛速度快、迭代次数少的全局优化算法,其反演效果与GNCG算法相当,优于梯度类反演算法(STD、NLCG、L-BFGS),并且改善了GNCG计算效率及局部优化的缺点。然后,本文以低阻隐伏矿体模型为例,探讨TRN反演算法的反演参数(正则化因子,初始截断误差、初始模型和网格剖分)以及观测数据(噪声水平、数据集、频点数和测点数)对反演结果的影响,表明TRN算法对初始模型依赖较小,同时具有较强的抗干扰能力。最后,将该算法应用于内蒙某地区的大地电磁实测数据处理中。通过与二维反演及地震解释地质剖面对比发现,TRN三维反演结果能够准确反演基底起伏情况,同时能够有效解决二维反演受三维异常体引起的畸变,进一步验证了TRN算法的可靠性。
[Abstract]:There are many kinds of electromagnetic methods in the ground frequency domain. It plays a key role in various fields, such as deep earth structure exploration, geothermal exploration, mineral exploration, oil and gas exploration, environment and engineering exploration. With the gradual development of electromagnetic exploration technology and the demand of "fine" and "transparent" geological exploration, ground frequency domain electromagnetic method is implemented. Three dimensional exploration and interpretation have gradually become normal. Therefore, the three-dimensional positive and inverse performance of the frequency domain electromagnetic method has become the key to the refinement and quantitative interpretation of large-scale electromagnetic data. However, it is still difficult to be applied in practical exploration by many sources, the speed and precision of the forward modeling, the applicability of the three-dimensional inversion and the efficiency of calculation. In this paper, the finite volume method is used to solve the coupling potential symmetric equation under the Lorenz standard to realize the three-dimensional forward modeling of the electromagnetic method in the frequency domain of any field source, and a high precision and rapid solution for the linear algebraic equations of large-scale problems is realized by the aggregation multigrid solving technique. At the same time, a "global" optimization algorithm, truncated Newton method, is proposed. The three-dimensional inversion of ground frequency domain electromagnetic method is realized by a variety of classical inversion methods. The applicability and influence factors of the three dimensional inversion method are discussed with magnetotelluric as an example. It is expected to establish the ground frequency domain electromagnetic three-dimensional positive and inverse platform to provide technical support for improving the three-dimensional fine interpretation of ground electromagnetic exploration. In this paper, the magnetic vector potential and the coupled symmetric equation of the magnetic vector potential based on the Lorenz standard conditions are derived from the Maxwell equation, and the finite volume technique is used to discrete the equations, and the large symmetric sparse linear algebraic equations are obtained. Then a series of short wire (Electrical) sources are used to simulate various types of field sources, and the pre processed quasi minimum residual method (QMR) and PARDISO, MUMPS and other solutions are used to solve them. The three-dimensional forward simulation of the ground frequency domain of different source types is successfully realized. The accuracy and effectiveness of the proposed algorithm are compared with one dimensional analytical solution. Then, the characteristics of the electromagnetic response of the typical geoelectric model in the frequency domain under different source excitation are compared and analyzed. In order to speed up the solving speed of the three dimensional forward electromagnetic field in the ground frequency domain, a new algebraic multigrid algorithm - aggregated multigrid is put forward. The algorithm (AGMG) is introduced into the 3D forward modeling. This paper, starting from the roughing strategy of AGMG algorithm and the set of iterative techniques, combines AGMG and the traditional Krylov subspace (GCR, FCG) iterative algorithm to propose five different AGMG algorithms. The results of Mod EM are compared to verify the accuracy of the proposed algorithm. In addition, the comparison between the forward modeling results of different mesh and different polarization modes and the QMR iterative algorithm shows that the K-AGMG-GCR algorithm can not only improve the stability of the AGMG algorithm, but also have high convergence precision, fast speed, and calculation. Compared with the existing Mod EM program, the K-AGMG-GCR algorithm can improve the computing speed dozens of times, so it is especially suitable for the large-scale ground frequency domain electromagnetic three dimensional forward problem. In view of the ground frequency domain electromagnetic 3D inversion, this paper introduces a global optimization trust region algorithm and Newton method combined truncated Newton method (TRN). First, Starting from the optimization and regularization inversion theory, the objective function, the model covariance matrix and the data covariance expression of the three dimensional inversion of the frequency domain electromagnetic method are established, and the unified expressions of the electromagnetic gradient, Hessian matrix and Jacobi matrix in different frequency domains are derived in detail, and then the basic principle of the truncated Newton method is described in detail and the basic principles of the truncated Newton method are elaborated. Key technologies (such as global search for step size, adaptive truncation error algorithm and regularization factor cooling method), and the classical optimal inversion algorithms - STD, nonlinear conjugate gradient (NLCG), Gauss Newton conjugate gradient (GNCG) and finite memory quasi Newton (L-BFGS). Finally, the modular design idea is adopted. And using the message transfer interface (MPI) to achieve parallel acceleration, the three dimensional inversion of electromagnetic method in the ground frequency domain of different algorithms is realized. This paper, taking the three dimensional magnetotelluric inversion as an example, first compares the results of two theoretical models (high and low combination model, arch bridge "low resistance model), and shows the inverse algorithm (TRN, STD) realized in this paper. NLCG, L-BFGS and GNCG can achieve good results, which are equivalent to the famous international magnetotelluric open source program Mod EM, and the TRN algorithm proposed in this paper is a global optimization algorithm with fast convergence speed and less iterative times. The inversion effect is equivalent to the GNCG algorithm, which is superior to the gradient inversion algorithm (STD, NLCG, L-BFGS), and improves GNCG. In this paper, the effect of the inversion parameters (regularization factor, initial truncation error, initial model and grid subdivision) and the effect of observation data (noise level, data set, frequency number and number of points) on the inversion results of the TRN inversion algorithm are discussed in this paper. The results show that the TRN algorithm is insidious to the initial results. The model is less dependent and has strong anti-interference ability. Finally, the algorithm is applied to the magnetotelluric data processing in a certain area of Inner Mongolia. By comparing with two-dimensional inversion and seismic interpretation, it is found that the TRN three-dimensional inversion results can accurately inverse the condition of the base undulation, and can effectively solve the two-dimensional inversion by three. The distortion caused by the dimension abnormal body further verifies the reliability of the TRN algorithm.
【学位授予单位】：吉林大学
【学位级别】：博士
【学位授予年份】：2017
【分类号】：P631.325

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