非均匀地震数据重建方法及其应用

Reconstruction of uneven seismic data and its application

（1. 中国海洋大学地球科学院，山东青岛 266003；2.中国科学院地质与地球物理研究所，北京 100029）

（Marine Geology College; Ocean University of China; Qingdao 266003; China）

将不规则地震数据重建问题归结为信息重建的地球物理反演问题。最小二乘方法求解时，引入离散傅氏变换（DFT）加权范数规则化策略，采用预条件共轭梯度法（PCG）求解，保证解的稳定性和收敛速度。处理线性同相轴假频问题时，采用YuleWalker方程由带限信号的低频功率谱预测高频功率谱，达到去假频目的。针对炮集三维叠前深度偏移中数据均匀化且尽可能覆盖速度体范围的要求，应用非均匀地震数据重建方法实现不均匀三维炮集数据内插、外推，避免以往植入空道的简单化处理，有效地扩大了偏移孔径信息。实际三维地震资料试算结果表明，偏移效果得到改善。

A new Fourier transform method has been proposed, which could reconstruct both uneven and aliasing seismic data. We formulated the reconstruction of band limited data as an inverse problem. The problem was solved by pre-conditional conjugate gradient method, in which a DFT-weighted norm regularization term was introduced during minimization with least square principles. To cope with linear event aliasing, high frequency power spectrum was estimated from the low frequency power spectrum of the band limited data via Yule-Walker equation. The proposed method was used to interpolate and extrapolate shot gathers, which overcomes the drawback of simply embedding zero traces. Tests on real data showed the method improved 3D shot prestack depth migration because the aperture of migration is enlarged.