基于小波多分辨探地雷达三维正演模拟及偏移处理

通过对Maxwell方程进行离散化,导出DB2-MRTD算法的探地雷达3D差分公式,并开发探地雷达MRTD法正演程序,利用该程序对三维雷达模型进行正演模拟,得到其相应的正演合成三维剖视图及切片图;通过对这些模拟结果进行分析,验证MRTD法在探地雷达三维正演中的有效性;利用爆炸反射原理和浮动坐标变换,推导出三维探地雷达波动方程差分格式,并把波场外推矩阵在小波域进行求解,进而得到探地雷达小波域三维偏移算法及偏移处理程序,把该程序应用于正演结果中。对比偏移处理前、后的雷达资料发现,该三维偏移算法能使3D正演剖面中的反射波归位、绕射波收敛,极大地提高了雷达剖面的分辨率。

GPR three dimension forward simulation and migration processing with multi-resolution of wavelets

The GPR three-dimension finite difference formula of DB2-MRTD algorithm was deduced through dispersing the Maxwell equations. Based on this, MRTD forward simulation program of GPR was developed. Making use of this program, forward simulation to the 3D radar model was made and its 3D fence diagram and slice map of forward simulation synthesize were obtained. By analyzing these analog results, the validity of MRTD 3D forward simulation method in GPR was illuminated. Making use of the bursting reflection theory and floating coordinate transform, the finite difference format of GPR three-dimension wave equation was deduced. After the extrapolate matrix of wave field in the wavelets domain was solved, the migration algorithm of GPR three-dimension wave equation in wavelets domain and migration processing program was gotten. Comparing the radar data before and after the migration processing, the results show that this three-dimension migration algorithm can make the reflection wave return to the original position, and make the diffraction wave converge in the three-dimension sections. The lateral resolution of radar sections can be highly enhanced.