高陡起伏地形GPR偏移的波场延拓及精度分析

摘要

Considering that ground penetrating radar (GPR) is obviously influenced by the inclination angle of reflecting interface, in order to improve the imaging accuracy of steep-dip rough terrains in GPR migration, the single differential operator was replaced by a cross differential operator(CDO), and a reverse-time migration method based on CDO was proposed, which completely changed the direction of wave-field extrapolation, and the implementation of CDO FD migration method was eventually achieved with the precise difference equations and corresponding boundary conditions of up-going GPR wave. Then a laterally variable velocity reflection model with steep-dip rough terrains was presented, particular attention was paid to the precision of wave-field extrapolation in laterally variable velocity, and from wave-field extrapolation precision, fidelity weight of wave amplitude, ability of energy convergence in steep-dip case and migration imaging section to analyze the imaging precision obtained by CDO FD migration method, FD method, F−K method and Kirchhoff method. The results show that the diffraction and scattering can be mostly converged with COD FD migration method, which shows that the COD FD migration method can deal with steep-dip rough terrains of GPR data.%基于高陡起伏地形对探地雷达波场的成像精度产生影响，将传统的单微分算子改进为交叉微分算子(CDO)；基于交叉微分算子的差分逆时偏移改变传统差分偏移算法的波场延拓方向，给出无近似的波场延拓差分公式、上行波边界条件和实现过程，得到能适应于高陡起伏地形的探地雷达偏移算法，然后以横向速度差异较大的高陡起伏反射模型为例，从波场延拓精度与解析结果、振幅保真加权值、高陡界面能量归位能力、成像剖面4方面分析交叉微分算子偏移法与传统方法的成像精度。研究结果表明：基于交叉微分算子的探地雷达偏移算法能够实现高陡界面的正确归位。