【作者】 赵宁；

【导师】 王绪本；

【作者基本信息】 成都理工大学 ， 固体地球物理， 2014， 博士

【摘要】 随着人们日益增长的能源需求以及近些年技术的逐步成熟,在过去十年中,海洋可控源电磁方法(MCSEM)在油气勘探领域获得了广泛的关注。尽管海洋三维地震反射数据已经提供了高精度的地质构造信息,以及含油气构造的指示信息,但不同的岩石属性可能产生相同的AVO特征,因此,单靠地震方法不能有效提升储层钻探成功率。近年来,电磁勘探成果表明,当储层孔隙结构中含油气和水合物等成分时,相对于围岩展现出高电阻率异常,往往电阻率相差50倍以上。如此显著的电性差异,表明电磁勘探方法对储层很敏感,具有明显的应用潜力。但是,由于海洋电磁三维正反演问题难度大,也是制约方法有效性实施的瓶颈。本文通过三维MCSEM基于可扩展并行的自适应矢量有限元算法和基于库仑规范的耦合势有限体积算法,对目前海洋电磁中多场源发射计算量巨大、低感应数、MCSEM观测装置参数对异常响应影响和利用MCSEM进行储层监测等方面分别进行探讨。主要研究成果包括：(1)在可扩展并行的三维MCSEM矢量有限元算法中,为了消除源点处场值的奇异性问题,把电场分为一次场和二次场分别进行计算。一次场通过解析方法进行求解,二次场的二阶偏微分方程采用h型自适应策略的矢量有限元方法进行离散。h型自适应加密是一个计算数值解、估计残差型后验误差、加密/放粗调整网格以及重新计算的迭代过程,最终使得误差几乎在网格上平均分布,从而在节省计算资源的前提下,提高计算精度。(2)在进行并行计算时,为了保证负载平衡,采用开源的METIS区域分解软件包将全局计算区域分解为若干个子区域,每个子区域只与它相邻子区域存在耦合关系,从而保证各进程并行计算时进程问通信量最少。(3)三维电磁问题中系数矩阵的条件数通常很大,利用Krylov子空间法对方程进行求解过程中,想要构造一个高效的预条件使得方程快速收敛是很困难的。另外,海洋电磁通常采用多场源点观测,对于一个确定的模型和频率,离散得到的刚度矩阵就确定了,改变场源点只会改变方程的右端项,如果采用迭代解法进行求解,计算量随着右端项的增加而增加,这时就体现出直接解法的巨大优势。本文采用MUMPS中的并行多波前(Multifrontal)策略的直接解法进行计算。(4)在三维海洋电磁数值模拟中,实际采用的频率往往比较低,无论是三维有限元法或是有限体积法,最终都会导致数值算法离散形成的方程组为病态方程组,产生低感应数问题。为克服低频发射导致的低感应数问题,有效提高三维电磁数值计算效率。本文建立一种基于耦合势的三维有限体积算法,利用库仑规范条件将麦克斯韦方程变换为与其等价的矢势与标势相耦合的亥姆霍兹方程,将其在Yee氏交错网格上进行数值离散,可得到一个复系数稀疏线性方程组。为减少保存方程所需的内存空间,把方程存储为CSR(行压缩)格式。为提高Krylov子空间法的迭代速度,采用不完全LU分解预处理的对称拟最小残差法(SQMR)求解大型复系数方程。(5)本文利用基于耦合势的三维有限体积算法,通过改变MCSEM观测装置参数讨论相应的异常响应影响,并且研究了海洋电磁法对海底储层进行监测的可行性。上述研究成果表明,矢量有限单元法的优势在于能够精确描述复杂地质体、提高数值模拟精度。而从减少计算量、提高计算效率的角度来看,有限体积法比矢量有限元法更适合于简单地电模型。本文矢量有限元算法计算结果针对多源问题具有速度快和精度高的优点,耦合势有限体积算法解决了海洋电磁环境下低频发射所带来的低感应数(LIN)问题,大大加快了求解线性方程组的收敛速度,提高了计算精度。这两种算法的成功实现,为进一步开展观测系统设计和反演计算提供了良好的基础。更多还原

【Abstract】 With gradually increasing energy demand and developed techniques,marine electromagnetic methods have gained extensive attention in the oil and gas exploration industry over the past decade. Although the data of3D seismic reflection can provide high precision of geological structure information and instructions of oil and gas construction,different characteristics of rock properties may produce the same characteristics of AVO.So,seismic can not effectively improve the success rate of reservoir drilling.By analyzing related data, when the pore structure contains higher oil gas and hydrate and shows a high different resistivity relative to the surrounding rock, the resistivity often has a difference of more than50times.By a significant difference in electrical, electromagnetic prospecting method is sensitive to the reaction of the reservoir. To solve problems of large amount of calculation and the multiple field source emission and low number of induction in MCSEM, this article has studied the3D MCSEM based on the adaptive edge finite element algorithm with a scalable parallel and the coulomb-gauged finite volume method(FVM) of coupled vector-scalar potential.We discussed the MCSEM observation device parameters effect on abnormal response and reservoir monitoring by means of MCSEM.1.On account of scalable parallel vector finite element algorithm of three-dimensional MCSEM,In order to eliminate the singularity problem in the source point field,we divide the electric field into the primary and the secondary field before calculation.The primary field is solved by analytical methods, the second order partial differential equations of the second field is discreted by the method of vector finite element.h-adaptive refine is a iterative process of numerical solution calculation, estimating residual posterior error,refining/coarsening mesh and recalculating, consequently making errors distribute on the almost mesh.Thus on the premise of saving computational resources, the calculation accuracy can be improved.2.We use METIS software package to decompose the mesh. The global mesh is divided into many local mesh,data between the local mesh is only associated with the units on the boundary of the adjacent local mesh in order to ensure the data communication is the least during the parallel computing between each process.3.In three dimensional EM problems, when the matrix is discreted by the Maxwell equation,the condition number is usually large.when using Krylov subspace methods solve the equation,it is difficult to make the equation converge fastly during constructing an efficient precondition.In addition, the marine electromagnetic method usually adopts the way of multi-source measuring.The stiffness matrix is determined by a certain frequency and a certain model,so changing the field source will only change the right hand items of equation.If iterative method is used to solve the problem, the amounts of calculation will increase with the increasing of the right hand items.The direct method has a great advantage over the iterative method. In this paper, the method of parallel Multifrontal based on MUMPS is adopted.4.In the three-dimensional marine electromagnetic numerical simulation,the frequenciy is often relatively low.No matter the three dimensional finite element method or finite volume method is adopted, it can eventually lead to be ill conditioned equation which is discreted by the numerical algorithm.To solve the low number of induction,this paper establishes a kind of three dimensional finite volume algorithm based on coupled scalar-vector potential.Maxwell’s equations can be converted to meet the coupling potential Helmholtz equation of coulomb gauge.Using Yee’s staggered grid form large sparse complex coefficient of linear equation.By making use of distribution characteristics obtained in the discretization process of non-zero elements in the large sparse matrix, the row format compression method (CSR)is adopted to compresse and store the discrete equation coefficient matrix in order to save the storage space of the computer.To effectively reduce the condition number of coefficient matrix and improve iteration speed of Krylov subspace, the minimum residual method of incomplete LU decomposition preprocessing (SQMR) is adopted to solve large complex coefficient equations.5.Based on the three dimensional finite volume algorithm of coupling potential,we discuss the corresponding abnormal response by changing the parameters of MCSEM observation,and study the feasibility of reservoir monitoring in the bottom of the sea.The results show that the advantages of edge finite element method are that it can accurately describe the complex geological body and improve simulation accuracy. Compared with vector finite element method,finite volume method is more suitable for simply electric model, because it can reduce the amount of calculation and improve the computational efficiency. In this paper, calculation results of the vector finite element algorithm for multiple source problem have the advantages of high speed and precision.The coupled potential finite volume method can still keep high convergence speed and satisfactory numerical results at a lower frequency.These two kinds of algorithms provide a good foundation for further observation system design and inverse calculation.更多还原