中文摘要：

为了更好地模拟探地雷达（GPR）波在地下真实介质中的传播特征，首先采用随机过程的谱分解理论和混合型自相关函数理论构造随机介质模型，然后详细介绍无单元法在GPR正演模拟中的应用。在此基础上，利用无单元法对2个典型的随机介质模型进行正演计算，分析随机介质模型中GPR波的传播特征，并与均匀介质模型进行对比。模拟结果表明：随机介质模型理论能灵活、有效地描述地下实际介质的分布，具有适应性强、使用方便、灵活的优点；与均匀介质中GPR波的传播相比，随机介质中GPR波的传播由于受到小尺度异常的影响散射现象非常强烈，波形发生扭曲；随机介质中异常体产生的反射波形非常粗糙，甚至发生同相轴不连续的现象，并且反射波能量较弱，随机介质模型模拟所得的正演剖面与实测剖面更相符，更有利于指导雷达剖面的数据解译。

英文摘要：

In order to better simulate the propagation characteristics of ground penetrating radar （GPR） waves in the real underground medium, the random media models were constructed according to the theory of spectral factorization in stochastic processes and mixed autocorrelation function. Application of element free method in GPR forward modeling was introduced in detail. On this basis, forward modeling was carried out on two typical random media models by the element free method and the propagation characteristics of GPR wave in random media models were analyzed, and compared with those in homogeneous media models. The modeling results show that the theory of model in random media can flexibly and effectively describe the actual underground medium, with the advantage of strong adaptability, easiness and flexibility. Compared with the GPR wave propagation in homogeneous medium, GPR wave propagation in random medium has strong scattering phenomenon and the waveform is distorted due to the impact of small-scale anomalies; the reflection waveform generated by anomaly in random medium is very rough and has phase axis discontinuous phenomenon and the wave energy is weak. Forward section of random medium models is more consistent with the measured profiles and is more conducive to the interpretation of the radar profile data.