地质雷达二维时域有限差分正演

【作者】 冯德山；

【导师】 戴前伟； 胡祥昭；

【作者基本信息】 中南大学 ， 地球探测与信息技术， 2004， 硕士

【摘要】 地质雷达是在高频微电子技术以及计算技术迅速发展的20世纪后期，此项技术才获得根本性的进展。由于它是一种非破坏性的原位探测技术，抗电磁干扰能力强，故可在各种噪声环境下工作，环境干扰小。同时地质雷达还具有工程上较满意的探测深度和分辨率，现场能直接提供实时剖面记录，图像清晰、直观；再上使用便携式微机控制数据采集、存储和处理，工作效率高，重复性好。地质雷达具有如此多的优点，故应用十分广泛；但是目前地质雷达亦还有待改进之处，如雷达图像的识别主要还停留在人工的肉眼和手工的基础上；所以对常见探测对象的物理正演模拟，有助于我们了解电磁波的传播规律，挖掘雷达波中更多有用信息。 作者在本文中首先以麦克斯韦方程组为出发点，着重于对麦克斯韦的两个旋度方程的分析，运用K.S.YEE氏的空间网格模型，并利用中心差商代替微商，把空间连续变量离散化，把电场进行规约化，得出二维空间的时域有限差分方程，即我们所要推导的地质雷达正演模拟方程；为了保证算法的精确性，我们对二维空间的TM电磁波(雷达波)进行数值稳定性分析及数值频散问题的讨论，推导出了数值稳定性条件表达式和理想频散关系；同时为了防止雷达模拟模型截断边界引起波的超强反射，我们推导出了超吸收边界条件，并把该条件运用到自制的用C语言编写的程序中，取得到了良好的效果。 在本论文中我们还讨论了地质雷达的*.dzt文件格式，并着重分析了*.dzt的头文件格式，在清楚地了解*.dzt文件格式的基础上，我们把头文件和用上面自制的程序模拟得到的数据用C语言的库函数fwrite写入到*.dzt雷达格式文件中，再将*.dzt雷达格式文件导入到随机配套的雷达处理软件中，得到了常见的几种规则模型的波形图。模拟结果的波形与实际探测的波形非常吻合，证明了用时域有限差分法在地质雷达正演模拟方面具有良好效果，并且用时域有限差分法模拟地质雷达模型的正演模拟结果对工程实践亦具有重要的指导意义，再加之时域有限差分法计算程序的对电磁场的广泛通用性，对不同的问题或不同的计算对象只需修改有关的少部分便可运用，故我们编制的程序对电磁场的模拟工作者亦有一定的参考价值。更多还原

【Abstract】 In period late of 20 century, the technology of ground penetrating radar acquiring basically development, just after the high frequency microelectronics technique and calculation technique get quick development. Because it is a exploration technique of not breaking the original property, and its ability of anti-electromagnetism interference is strong, therefore it can be work well under the environment of the all kinds of noise interference, the environment interference is small, too. It possesses the satisfactory exploration depth and distinguish rate in engineering, can offering the real time section record in the locale directly. The diagram clears, intuitionist. The convenient schlepping microcomputer controls the data collected, storage and handle, and the work efficiency is high, repetition is good. Ground penetrating radar (GPR) have so many advantage, therefore applied very extensive. But now it still exist some proportion to waiting for improvement, for example, distinguishing the GPR diagram primarily stays in the foundation of the artificial naked eye distinguish and handcraft identify. Therefore it is beneficial to us to understand the electromagnetic wave spreading regulation, and scoop out much more useful information from the GPR wave inside, through forward simulate the familiar penetrating object in physical.At first, in this text author set out analysis from Maxwell equation group, and put great emphasis on the two vortices equation of Maxwell equation group. Application K.S.YEE ’s space grid model, and the utilize center difference coefficient substitute for the differential coefficient. We can disperse the spatial continuous variable, regularization the electric field, and obtain the two dimension spatial time-domain finite-difference equation, which is the GPR forward simulate equation we request deducing. For guaranteeing the arithmetic accurate, we analyze the numerical value’s stability and discussion question of numerical value frequency dispersion to the two-dimension TM electromagnetic wave (GPR wave), deduce out numerical value’s stability expression and ideal frequency dispersion relation. At the same time in order to prevent the radar simulation model wave at the truncated boundary strong reflection.We deduce out the super absorb boundary condition, and make use of the condition into the self-regulating program write by C language, and obtained the good effect.In this thesis we discuss GPR *.dzt file format, and put great emphasis point on analyze radar *.dzt head file format. On basic of clearly understand the *.dzt file format. The head file and the data obtain by running and simulating the self-regulating program are been written into the file of *.dzt radar format using the function-base fwrite in C language. Afterward we transmit the *.dzt file of radar format into the radar dispose software that the machine equip, and get the wave diagram from several familiar formula model. The waves of imitate result and the waves of practical penetrate fit well. It proved that the finite-difference time-domain (FDTD) method can reach good effect in GPR forward simulate, besides the result of using finite-difference time-domain (FDTD) method forward simulate the GPR model have important guidance meaning for the engineering practice. Additionally finite-difference time-domain (FDTD) method calculating program have the extensive currency character in electromagnetism field. The program can be exerted only needing modification a little of relevant parts aim at different problem or different calculation object. Therefore the program of us authorized have a few of reference value to the electromagnetism field simulate operator.更多还原