【摘要】 Curvelet变换具有局部性、多尺度性和多方向性,在处理非稳态地震信号中具有较大的优势,可以利用Curvelet变换的压缩特性重建缺失的地震数据。本文首先分析了基于稀疏变换的缺失地震数据插值的基本原理,在反问题正则化理论框架下,针对L2范数约束和L1范数约束条件,分析了两种约束的差异,着重阐述了基于Curvelet变换的L1范数约束的插值方法,其优点在于对非线性同相轴不需要分窗口处理,并将凸集投影算法(POCS)引入到Curvelet变换的插值方法中,通过采用按指数规律衰减的阈值参数加快了迭代收敛的速度。理论和实际算例验证了Curvelet变换插值方法的有效性。更多还原

【Abstract】 Curvelet transform is suitable for nonstationary seismic data processing because it is multi-scale,multidirectional,and strictly localized.The compression attribute of Curvelet transform can be used for reconstruction of missing seismic data.In the paper,we first analyze the principle of missing seismic data interpolation using sparse transform.Then we discuss the difference between the interpolation methods with-norm and-norm restrictions in the inversion framework.We expatiate in detail on the interpolation method with-norm restriction,which do not need sliding windows for processing nonstationary seismic events.We introduce the Projections Onto Convex Sets(POCS) algorithm into the interpolation using Curvelet transform.The threshold in POCS algorithm is chosen to be exponentially decreased,which is a fast convergence method in iterative inversion.Synthetic and real data examples show that the interpolation method using Curvelet transform can effectively rebuild missing seismic data.更多还原