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基于curvelet变换的缺失地震数据插值方法

Keywords: 地震数据,重建,curvelet变换,凸集投影,l2范数,l1范数

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Abstract:

?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。

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