三角形非结构化有限元GPR正演模拟

发布时间：2018-02-24 19:13

本文关键词： 探地雷达有限单元法透射边界条件数值模拟非结构化网格　出处：《湖南科技大学》2017年硕士论文　论文类型：学位论文

【摘要】：对于实际的地球物理模型的数值模拟,网格的划分对于拟合地球物理模型具有十分重要的意义。它直接影响着有限元数值模拟的求解效率以及计算精度。一般情况下,网格生成技术可以分为结构化网格和非结构化网格两大类。结构化网格具有统一的结构特点,生成速度快,结构单一,但是不能够满足复杂的地球物理模型的数值模拟。目前,非结构化网格划分技术在探地雷达的有限元数值模拟中应用的较少,相关的研究文献也相对较少。因此,本文研究了三角形非结构化网格下的探地雷达有限元数值模拟,并且建立了多种地球物理模型,进行了二维GPR有限元数值模拟、分析,归纳总结了雷达波在不同地质地球物理模型中的传播规律,对实际资料的解释工作具有十分重要的意义。本文在前人研究的基础上,重新推导了基于三角形网格划分的探地雷达有限元波动方程,并详细的给出了波动方程的解法。在数值模拟计算中,对加载透射了边界条件和没有加载透射边界条件的均匀模型开展了数值模拟,分析了透射边界的处理效果;简要分析了雷达波在介质水和空气的传播规律,分析了其中的差异;建立了道路路基病害模型、隧道地质超前预报模型以及顶管脱空模型等数学物理模型,分析了雷达波在不同模型中的传播规律。通过数值模拟可以发现:透射边界条件能够很好的抑制模型边界处所产生的干扰波;可以通过雷达波在介质中传播的多次反射波特征来区别介质水和介质空气;通过隧道地质超前预报与实测数据相结合,对于更好的判断雷达波在此类模型中的传播特点提供依据;通过对顶管脱空模型的进行数值模拟,发现探地雷达对于水泥混凝土顶管脱空能够取得很好的探测效果,对于钢顶管的脱空效果并不明显,与实测效果相符合。通过减小钢顶管壁的厚度,能够对脱空情况进行探测,但是效果并不明显。研究表明:非结构化网格对于物性参数复杂的的地球物理模型具有很好的适应性;非结构化网格剖分的质量好,单元易于控制,能够很好的实现自适应有限元,提高数值模拟的精度。
[Abstract]:For the numerical simulation of the actual geophysical model, the mesh division is very important for fitting the geophysical model. It directly affects the efficiency and accuracy of the finite element numerical simulation. Grid generation technology can be divided into structured grid and unstructured grid. Structured grid has the characteristics of uniform structure, fast generation speed and single structure, but it can not satisfy the numerical simulation of complex geophysical model. The unstructured mesh generation technique is seldom used in the finite element simulation of ground penetrating radar, and the related literatures are relatively few. Therefore, the finite element simulation of ground penetrating radar under triangular unstructured mesh is studied in this paper. Several geophysical models are established, 2D GPR finite element numerical simulation is carried out, and the propagation law of radar waves in different geophysical models is summarized. The interpretation of practical data is of great significance. Based on the previous studies, the finite element wave equation of ground penetrating radar based on triangular mesh division is rederived in this paper. The solution of wave equation is given in detail. In the numerical simulation, numerical simulation is carried out for the uniform model with and without the loading transmission boundary condition, and the processing effect of the transmission boundary is analyzed. The laws of radar wave propagation in medium water and air are analyzed briefly, and the difference between them is analyzed, and mathematical and physical models such as road subgrade disease model, tunnel geological advance prediction model and pipe jacking void model are established. The propagation law of radar wave in different models is analyzed. The numerical simulation shows that the transmission boundary condition can suppress the interference wave generated at the boundary of the model very well. It is possible to distinguish medium water from medium air by the characteristics of multiple reflection waves of radar wave propagating in medium, and combine tunnel geological advance prediction with measured data. Through numerical simulation of pipe jacking model, it is found that ground penetrating radar can achieve good detection effect for cement concrete pipe jacking. The emptying effect of steel jacking pipe is not obvious, which is consistent with the measured results. By reducing the thickness of steel jacking pipe wall, the void situation can be detected. But the effect is not obvious. The results show that the unstructured meshes have good adaptability to geophysical models with complex physical parameters, and the unstructured meshes are of good quality and easy to control. It can realize adaptive finite element well and improve the accuracy of numerical simulation.
【学位授予单位】：湖南科技大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：P631

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