基于区域分解算法的大地电磁二维正演研究

发布时间：2018-06-24 05:36

本文选题：大地电磁 + 正演模拟　；参考：《东华理工大学》2017年硕士论文

【摘要】：随着勘探精细化和三维探测的发展,大规模和海量数据的电磁法三维正反演计算成为当前研究难点和热点问题之一。近年来,电磁法三维正反演在计算速度提升、算法优化和并行加速等方面取得重大进步;但受内存空间、计算效率以及正演精度等限制,仍难于在实际勘探中得到广泛应用。区域分解算法(DDM)将大规模问题转化成若干小问题进行独立求解,极大缩小计算规模并节省内存空间,已成为解决大规模复杂数值问题的有力手段。据此,本文以大地电磁(MT)二维正演为例,开展多种区域分解算法研究及对比分析,为大规模电磁法三维快速正反演研究提供参考和依据。本文首先简要介绍MT二维有限差分正演的基本理论,然后介绍区域分解算法的子域剖分方式及分解模式。在此基础上,提出四种不同区域分解算法(基于元素剖分的Schur补偿算法(E_Schur)、分级区域分解算法(HDD)、基于顶点剖分的Schur补偿算法(V_Schur)和Schwarz交替法(Schwarz))实现MT二维正演模拟。最后,利用典型地电模型试算验证算法的准确性和可行性,并对子域分解方法、子域剖分形状、子域剖分组合、子域数目以及子域重叠大小等对区域分解算法的计算效率和影响因素进行综合分析,综合评价各种不同区域分解算法的计算效率和所需内存空间大小。通过多个典型地电模型大地电磁二维正演模拟,及与传统全域正演算法相比表明,四种区域分解算法的CPU计算时间均随子域数目增多而增加,所需内存随子域数目增多而降低;其中E_Schur、HDD和V_Schur三种方法所需内存随子域数目增多先急剧下降,后呈缓慢上升,但总体仍比全域求解所需内存少。Schwarz交替法所需内存随子域数目增加而降低,重叠子域组合方式和重叠规模大小对计算效率有一定影响,需进行合理优化。四种区域分解算法中,HDD算法的计算效率相对较好,E_Schur补偿算法次之,Schwarz交替法最慢。综上所诉,区域分解算法能大大降低计算所需内存,求解大规模问题具有极大优势,为电磁法多维大规模问题的正反演计算提供了一种新的思路。
[Abstract]:With the development of fine exploration and 3D exploration, electromagnetic forward and inverse calculation of large-scale and massive data has become one of the most difficult and hot issues. In recent years, electromagnetic 3D forward and inverse modeling has made great progress in computing speed, algorithm optimization and parallel acceleration, but limited by memory space, computational efficiency and forward precision, it is still difficult to be widely used in practical exploration. Domain decomposition algorithm (DDM) has become a powerful method to solve large scale complex numerical problems by transforming large scale problems into some small problems and solving them independently, greatly reducing the computational scale and saving memory space. Therefore, taking magnetotelluric (MT) two-dimensional forward modeling as an example, this paper carries out the research and comparative analysis of various domain decomposition algorithms, which provides a reference and basis for the large-scale electromagnetic three-dimensional fast forward and inverse modeling research. In this paper, the basic theory of MT 2-D finite difference forward modeling is introduced briefly, then the subdomain subdivision and decomposition mode of domain decomposition algorithm are introduced. On the basis of this, four different domain decomposition algorithms (Esteon Schur), hierarchical domain decomposition (HDD), vertex subdivision Schur compensation (VSP Schur) and Schwarz alternating (Schwarz) are proposed to realize MT 2D forward modeling. Finally, the accuracy and feasibility of the algorithm are verified by the typical geoelectric model, and the subdomain decomposition method, subdomain partition shape, subdomain subdivision combination, The computational efficiency and influencing factors of domain decomposition algorithm are analyzed synthetically, such as the number of subdomains and the overlap size of subdomains, and the computational efficiency and the required memory space of different domain decomposition algorithms are evaluated synthetically. Compared with the traditional global forward algorithm, the CPU computing time of the four domain decomposition algorithms increases with the increase of the number of subfields, and the required memory decreases with the increase of the number of subdomains. Among them, the memory requirement of the three methods of "ESchurn HDD" and "VSch Schur" decreases sharply with the increase of the number of subfields, and then increases slowly, but in general, the memory required by the alternating method of ".Schwarz" is less than that of the whole domain, and decreases with the increase of the number of subfields. The combination of overlapping subdomains and the size of overlapped subdomains have a certain effect on the calculation efficiency, which need to be optimized reasonably. Among the four domain decomposition algorithms, HDD algorithm has better computational efficiency than the ESM Schur compensation algorithm, followed by Schwarz alternating algorithm. In summary, the domain decomposition algorithm can greatly reduce the memory required for computing, and has a great advantage in solving large-scale problems, which provides a new way for the forward inversion calculation of electromagnetic multi-dimensional large-scale problems.
【学位授予单位】：东华理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：P631.325

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