中文摘要：

为了更准确地认识探地雷达（GPR）波在频散介质中的传播规律，从Maxwell方程组出发，在频散介质相对介电常数与频率满足Debye关系的条件下，经傅里叶变换，导出时间域GPR波电场和磁场的波动方程。对GPR波的电场波动方程采用伽辽金有限元法，推导频散介质中探地雷达二维有限元方程，采用透射吸收边界有效减弱截断边界的超强反射波，使得截断边界处的反射波充分吸收。利用依上述方法原理编制的程序分别对均匀模型和两圆状模型进行正演计算，验证该算法的正确性和可行性。研究结果表明：均匀频散介质中GPR子波的衰减比在非频散介质中的衰减要快得多，且GPR子波的宽度随着接收器与发射源距离的增加而变大；频散介质中异常体的反射波宽度比非频散介质中的反射波宽度大。

英文摘要：

In order to more accurately understand the propagation law of GPR （ground penetrating radar） wave in dispersive medium, the Fourier transform was adopted under the condition that relative dielectric constant in dispersive medium and frequency satisfied the Debye condition, and the wave equation of electromagnetic field was obtained in time domain based on the Maxwell equations. The wave equation of GPR electric field was taken as an example, and the 2-D finite element equation of GPR in dispersive medium was gotten by means of Galerkin finite element method. By combining transmitting absorbing boundary, the strong reflected wave on truncation boundary was effectively weakened and the reflected wave on truncation boundary was absorbed adequately. On the basis of the theory mentioned above, the program of its feasibility and effectiveness was tested by homogeneous and two-rounded models. The results show that compared with the modeling results of non-dispersive medium, the GPR wave in dispersive medium attenuates faster than that in non-dispersive medium, and the width of GPR wave in dispersive medium gets larger with the increase of the distance.Width of the reflected wave with the abnormal body in dispersive medium is larger than that of the reflected wave in non-dispersive medium.