隧道全空间瞬变电磁三维反演数值实现

发布时间：2018-02-04 09:21

本文关键词： 全空间瞬变电磁法三维有限差分三维正演三维反演　出处：《西南交通大学》2014年硕士论文　论文类型：学位论文

【摘要】：近年来,随着国家对交通基础设施的大力投入,众多长大隧道相继修建。在这些长大隧道的修建过程中出现了许多隧道施工安全事故,在这些事故中很多是由于地下水造成的,传统的超前地质预报方法由于受到自身特点的限制,对水的探测效果不佳,因此迫切需要找到一种探水方法。经过工程实践证明,瞬变电磁法可以比较精准的探测出地下水。但是隧道全空间中应用瞬变电磁法时是一个全空间的问题,隧道全空间中瞬变电磁法还缺乏系统的研究,尤其是与工程关系紧密的三维正、反演问题,论文正是在这种背景下展开研究的。瞬变电磁三维正演、反演问题是时下研究的热点问题。隧道全空间中的三维正、反演问题研究还处于探索阶段。论文在研究半空间的基础上,结合隧道全空间的特点推导了三维时域下的迭代差分方程,从数值计稳定性方面考虑介绍了时域下的数值色散、数值稳定性问题,并且得到数值稳定条件。论文主要完成了以下几个方面的工作： 1.边界条件的处理时,综合考虑隧道全空间的特点,引入了CPML边界条件。该边界条件能够极好的模拟电磁问题中的边界问题,减小了折射反射。 2.在研究三维正演问题时,为了保证模型的合理性,研究了经开挖隧道长度取值问题；不同尺寸低阻体对电磁响应的影响；不同低阻体的电磁响应等。这些结论能够为建立一个合理的模型提供参考。 3.在研究隧道全空间反演问题时,针对三维反演计算量大、耗时长的特点,采用了改进的特征反演法,有效的减少了计算时间,提高了效率。 4.提出了比较可行的反演路径,使得反演在满足一些限制条件的情况下能够顺利进行,同时提出了反演时控制矩阵病态的相关办法。
[Abstract]:In recent years, with the national investment in transportation infrastructure, many long tunnels have been built. In the process of construction of these long tunnels, there are many tunnel construction safety accidents. Many of these accidents are caused by underground water, and the traditional advanced geological prediction methods are limited by their own characteristics, so the detection effect of water is not good. Therefore, it is urgent to find a water detection method. Through engineering practice, it is proved that transient electromagnetic method can accurately detect groundwater. However, the application of transient electromagnetic method in the whole tunnel space is a full space problem. The transient electromagnetic method in the whole tunnel space is still lack of systematic research, especially the three-dimensional forward inversion problem which is closely related to engineering. Transient electromagnetic three-dimensional forward modeling, inversion problem is a hot issue in the current research. The research of three-dimensional forward inversion in the whole tunnel space is still in the exploration stage. This paper is based on the research of half-space. The iterative difference equations in 3D time domain are derived according to the characteristics of the whole tunnel space. The numerical dispersion and numerical stability in time domain are introduced from the point of view of numerical stability. And the numerical stability conditions are obtained. The main work of this paper is as follows: 1. When the boundary condition is processed, the CPML boundary condition is introduced considering the characteristics of the whole tunnel space. The boundary condition can simulate the boundary problem in the electromagnetic problem perfectly and reduce the refraction reflection. 2. In order to ensure the rationality of the model, the value of the length of the excavated tunnel is studied in order to ensure the rationality of the model. The influence of different sizes of low resistive bodies on the electromagnetic response; These conclusions can provide a reference for the establishment of a reasonable model. 3. In the study of the whole space inversion of tunnel, the improved feature inversion method is adopted in order to reduce the computation time and improve the efficiency because of the large amount of computation and the long time of 3D inversion. 4. A feasible inversion path is proposed, which enables the inversion to proceed smoothly under some restricted conditions. At the same time, the related methods of controlling the ill-condition of the matrix are put forward.
【学位授予单位】：西南交通大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：P631.325;U452.11

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