基于改进线性Radon变换的井孔地震上下行波场分离方法

反射波场分离是井孔地震资料处理中极其重要的一个环节，波场分离的质量直接影响成像结果的精度.不管是VSP还是井间地震资料，其反射波时距曲线都近似直线型，根据这一特征，本文提出一种改进的线性Radon变换方法来进行井孔资料的反射波上下行波场分离.该方法基于频率域线性Radon变换，通过引入一个新的变量λ来消除变换算子对频率的依赖性，避免了求取每一频率分量对应的不同变换算子，显著降低了计算成本;文中在求解该方法对应的最小二乘问题时，引入了发展较为成熟的高分辨率Radon变换技术来进一步提高波场分离的精度.采用本文方法进行井孔地震资料的上下行波场分离可以在保证分离精度的前提下有效地提高计算效率.根据上下行波在λ-f域内分布的特殊性，设计简单的滤波算子就可实现上下行波场的分离.最后通过合成数据试算以及实际资料处理（VSP数据和井间地震数据）验证了该方法的可行性和有效性.

Wavefield separation by a modified linear Radon transform in borehole seismic

In borehole seismic, wavefield separation is an important issue which has great influence on data imaging. For both VSP and cross-well seismic data, the reflection time-distance curves are approximately straight lines. According to this characteristic, a modified linear Radon transform is presented in this paper for upgoing and downgoing wavefield separation in borehole seismic. On the basis of the frequency-domain linear Radon transform, this method is implemented by introducing a new variable λ so as to make the transform operator independent of the frequency, which avoids the calculation of different transform operators for each frequency component, large computational cost is decreased. Besides, in order to further improve the accuracy of wavefield separation, we introduce the sophisticated high-resolution Radon transform to deal with the least squares problem corresponding to this method in this paper. With the application of this method, significant improvement in accuracy and computational efficiency can be obtained in upgoing and downgoing wavefield separation for borehole seismic data. What's more, according to the particularity of the distribution of upgoing and downgoing wavefield in λ-f domain, wavefield separation can be easily performed by simple filter operators. Examples from synthetic data and real borehole seismic data (both VSP data and cross-well seismic data) proved that this method is feasible and valid.