基于ADI-FDTD法的探地雷达正演数值模拟及验证

Numerical simulation and verification of GPR forward modeling based on ADI-FDTD method

探地雷达(GPR)是一种应用前景广泛、用于探测和定位地下物体的浅层地球物理方法。通过开展探地雷达正演模拟研究,可以获得复杂地下结构的探地雷达图像回波特征。时域有限差分(FDTD)法受到稳定性和收敛性条件的限制,导致效率和精度低。交替方向隐式-时域有限差分(ADI-FDTD)法克服FDTD法的稳定性限制,可以选择更大的时间步长来提高计算效率。从原理出发,对ADI-FDTD法进行公式推导,在基于ADI-FDTD法的基础上进行卷积完全匹配层(CPML)的结合。通过进行ADI-FDTD法的时间稳定性仿真和不同材质、不同填充介质的双管,沙槽正演模拟实验,结果表明,ADI-FDTD法可以保证时间无条件稳定性,相同情况下可采用更大的时间步长进行正演模拟,提高正演效率。对不同管线、不同材质情况下的正演剖面曲线特征进行解译分析,最后与沙槽实测进行对比,证明得到的探测解译结果与实际状况达到较好的吻合。

Ground penetrating radar(GPR)is a shallow geophysical method with wide application prospects for detecting and locating underground objects.Through the forward simulation of GPR,the echo characteristics of GPR images of complex underground structures can be obtained.The finite difference time domain(FDTD)method is limited by the stability and convergence conditions,resulting in low efficiency and accuracy.The alternating direction implicit finite difference time domain(ADI-FDTD)algorithm overcomes the stability limitation of the traditional FDTD method,and can choose a larger time step to improve the computational efficiency.Starting from the principle,the formula of ADI-FDTD algorithm is derived.Based on ADI-FDTD algorithm,the convolution perfect matching layer(CPML)is combined.Through the time stability simulation of ADI-FDTD algorithm and the forward simulation experiment of double pipes and sand grooves with different materials and different filling media,it is concluded that ADI-FDTD algorithm can ensure the unconditional stability of time,and in the same case,a larger time step can be used for forward simulation to improve the forward efficiency.The forward profile curve characteristics of different pipelines with different materials are interpreted and analyzed,and finally compared with the actual measurement of sand trough,which shows that the detection interpretation results are in good agreement with the actual situation.