探地雷达GPR正演模拟的时域有限差分实现

近年来，随着数字处理技术和电子技术的飞速发展，探地雷达（GPR）的实际应用范围迅速扩大，现已覆盖考古、矿产资源勘探、水文地质调查、岩土勘查、无损检测、工程建筑物结构调查、军事等众多领域，解决了很多工程实际问题，成为浅层勘探的有力工具.而探地雷达的理论研究与实际的应用相比，具有明显的滞后性.但是解释人员要达到精确地对探地雷达实际资料的进行解析，必须事先了解地质体的雷达反射剖面的特征，所以作为反演与解释基础的复杂地电模型的探地雷达正演模拟技术，就成了探地雷达理论研究的主要内容之一.本文以麦克斯韦两个旋度方程为基本出发点，运用K.S.Yee的空间网格模型理论和时域有限差分法的基本原理，推导出二维空间的探地雷达正演方程组，并详细地分析了差分格式中半空间步长与半时间步长的实现方法，及其雷达波电场与磁场分量在计算机上相互关系的C程序实现.然后讨论了数值频散关系及其产生原因，通过同时考虑时域有限差分法及Yee氏网格的特点，推导出了符合探地雷达实际传播规律的理想频散关系，作者自制了探地雷达正演程序，并分别计算了Mur超吸收边界条件及无边界条件下的雷达地电模型，通过对比可知，超吸收边界条件可利用，大大地减少截断边界处的干扰波，达到用有限区域达到在无限空间传播的效果.最后作者利用自制程序，对“V”字形和同一斜面上的五个圆的两个典型的探地雷达地电模型进行了正演模拟，得到了正演剖面图，消除了边界反射后的雷达剖面能很好地指导工作人员对雷达实测剖面的地质解释，同时使正演研究更符合实际的地质情况.

Finite difference time domain method of GPR forward simulation

This article takes two Maxwell's vorticity equations as basic departure point.Makes use of the principles of K.S.Yee's space grid model theory and the basic principle finite difference time domain method,deduces a GPR forward system of equation of two dimensional spaces.This article also detailedly analyzes the realization method of the half space step and the half time step in difference format,and the correlation of electric field component and magnetic field component of radar wave C program realization on computer.Then author discuss the numerical frequency dispersion relation and the producing reason.At the same time,It is deduced the ideal frequency dispersion relationship match to GPR actual dissemination regulation by considering the finite difference time domain method and the characteristics of Yee's grid.The author makes the GPR forward program by himself,and computes an electricity of radar model under the super absorbed boundary condition and without any boundary condition respectively.By comparison,when doing the the GPR forward simulation calculation,the super absorb the boundary condition can resolve the problem that how to use the finite region to attain the infinite space spreading nicely.At last,the author utilizes self-made program to process forward simulation to two typical geoelectricity model,and it obtaines the satisfied result,which can guide the staff member processing geology explain betterly to the actually radar section.