探地雷达的正演模拟及有限差分波动方程偏移处理

Forward simulation of ground penetrating radar and its finite difference method wave equation migration processing

利用麦克斯韦方程和有限差分法,推导出雷达波的二维有限差分正演方程组,并运用该正演方程对“V”字形地电模型和同一斜面上的5个圆的地电模型进行正演合成,得到其相应的正演合成剖面;把该正演合成的剖面与实际模型相比,得出正演合成图与实际模型的示意图在形状上有一定的差别,这是剖面中异常点处的绕射波所致;为了提高雷达资料的解释精度,对正演合成的雷达剖面进行后处理,运用雷达上行波反向外推有限差分偏移法,对2个正演合成的雷达剖面进行偏移处理,通过对比偏移处理前后的雷达正演剖面,采用有限差分偏移法能使雷达正演剖面中的反射波归位,绕射波收敛,从而大大提高了雷达正演剖面的分辨率,有利于探地雷达剖面的地质解释和验证偏移方法的有效性。

Using Maxwell＇s equations and the principles of finite difference （FD） method, a radar wave forward system of equations of two dimensional FD was deduced, and the forward system of equations was used to synthesize the ＂V＂ style geoelectricity model and five circle geoelectricity models of the same inclined plane, and then the two corresponding forward synthesis sections were obtained. Comparing synthetic sections to those actual models, it is known that the forward synthesis sections have some discrepancies on the shape sketch map of the models, because there exists diffracted wave caused by a little bit of anomaly point in sections. In order to enhance the accuracy of explanation of radar data, the post processing to radar sections by forward simulation synthesis was carried out. At last, radar upgoing wave reverse extrapolate FD migration method was used to process the radar section coming from the forward simulation synthesis. By comparing the radar forward simulate sections before and after the migration processing, it is shown that FD migration method can make the reflection wave return to original position, and make the diffraction wave converge. The resolution of radar forward simulate sections can be enhanced highly, and it can instruct the geology explanation of ground penetrating radar sections and confirm the validity of migration method better.