基于速度估计的改进型线性变换有限差分偏移在探地雷达中的应用

摘要

为了解决传统线性变换有限差分偏移算法对变速介质的高敏感性问题,对加入了速度变量的标量波动方程进行线性变换,在横向非均匀介质条件下,详细推导了包含混合因子项的线性变换差分偏移方程,实现了横向非均匀介质中陡倾角反射界面的正确归位,同时改进型算法可以灵活地选择混合因子项,这样就增强了原算法对复杂地质问题的适应能力,在此基础上结合速度估计算法,减小多次尝试输入法所产生的误差,提出一种基于速度估计的改进型线性变换有限差分偏移算法,并用该算法对实测探地雷达剖面进行了偏移处理,通过对比偏移前后的雷达资料得知,当横向非均匀介质中同时存在多次反射质点和主体反射层时,改进的偏移算法能有效地提高雷达剖面的偏移精度.%For the purpose of solving the problem of high velocity sensitivity of the traditional linear transformation of the finite difference migration algorithm, the paper applied the linear transformation to the scalar wave equation, in which the speed parameter is added. Through a series of detailed and accurate derivation, a new inhomogeneous wave equation is derived, which contains a mixed factor item. With the improved migration algorithm, the steep-dip reflection migration is achieved in the laterally inhomogeneous circumstances. Simultaneously, for the merit of the flexibility to select the mixed factor item, the adaptability of the traditional algorithm is enhanced when dealing with more complex geological problems, which also reflects the importance of the mixed factor item in different geological problems. In order to reduce the input errors, the paper combines the velocity estimates, and put forward an improved linear transformation of finite difference migration algorithm based on the velocity estimation. The migration accuracy is enhanced effectively after applying the improved algorithm to the real GPR (Ground Penetrating Radar) data processing, in which the main reflector and multiple reflection particles both exist.