基于Curvelet变换的稀疏反褶积

doi:10.7623/syxb201301012

石油学报 ›› 2013, Vol. 34 ›› Issue (1): 107-114.DOI: 10.7623/syxb201301012

基于Curvelet变换的稀疏反褶积

孟大江 1,2 　王德利 1　冯　飞 1　黄　飞 1 　朱　恒 1

1.吉林大学地球探测科学与技术学院吉林长春 130026; 2.中海石油（中国）有限公司深圳分公司研究院广东广州 510240

收稿日期:2012-06-13 修回日期:2012-09-14 出版日期:2013-01-25 发布日期:2013-04-09
通讯作者: 王德利，男，1973年1月生，1998年获吉林大学学士学位，2002年获吉林大学地球探测与信息技术工学博士学位，现为吉林大学教授、博士生导师，主要从事各向异性介质波场正、反演理论和高精度地震勘探研究。
作者简介:孟大江，男，1986年6月生，2012年获吉林大学地球探测与信息技术工学硕士学位，现在中海石油（中国）有限公司深圳分公司研究院，主要从事地震资料解释、处理等工作。
基金资助:
国家重大科技专项（2011ZX05023-005-008）资助。

Sparse deconvolution based on the Curvelet transform

MENG Dajiang 1,2 　WANG Deli 1 　FENG Fei 1 　HUANG Fei 1　 ZHU Heng 1

Received:2012-06-13 Revised:2012-09-14 Online:2013-01-25 Published:2013-04-09

摘要/Abstract

摘要：

常规反褶积方法通常需要假设地层反射系数是稀疏的，然后再利用L1范数反褶积求得稀疏的反射系数来提高分辨率，但常规反褶积方法在提高分辨率的同时降低了信噪比，并且反褶积后同相轴的连续性会变差。针对上述问题，提出了基于Curvelet变换的反褶积方法。Curvelet变换对多维信号具有最好的稀疏表示，能获得最优的非线性逼近，因而可利用Curvelet变换来表示地震反射信号，将其引入到L1范数反褶积后，可利用稀疏的Curvelet系数来描述反射系数，从而无需地层反射信号是稀疏的假设。根据有效信号和随机噪声在Curvelet域中的分布特点，可通过阈值法来压制噪声提高信噪比，并且利用Curvelet变换对地震信号进行多维表示，可实现多维反褶积保持同相轴的连续性。最后，给出了一种阈值循环迭代算法来计算L1范数反褶积问题。研究结果表明，基于Curvelet变换的稀疏反褶积方法在提高地震分辨率的同时能有效地压制随机噪声，并保持同相轴的连续性。

关键词: 反褶积, 分辨率, 连续性, Curvelet变换, L¹范数, 信噪比

Abstract:

Traditional deconvolution methods usually need to assume a sparse distribution for seismic reflectivity, and then apply the L 1 norm deconvolution to get sparse reflectivity so as to improve resolution, but this doesn’t conform to reality. In addition, when traditional methods improve the resolution, they reduce the signal to noise ratio at the same time, making the continuity of a seismic profile poor. In view of these problems, the sparse deconvolution based on the Curvelet transform was proposed in the present paper. The Curvelet transform is characterized by an optimum sparseness expression for multidimensional signals to have the best nonlinear approximation, thus it can be used to express seismic reflectivity. When the Curvelet transform was introduced to the L 1 norm deconvolution, a sparse Curvelet coefficient representing reflectivity could be obtained without assuming the sparseness of reflectivity. In addition, according to the distribution characteristics of effective signals and noise the signal to noise ratio could be improved by using a threshold method to suppress noise, and consequently the multidimensional seismic deconvolution was obtained to maintain the continuity of seismic profiles. Finally, a threshold iterative algorithm was proposed to solve the L 1 norm deconvolution problem. The results show that this proposed method can effectively improve resolution and continuity of seismic profiles while suppressing random noise.

Key words: deconvolution, resolution, continuity, Curvelet transform, L¹ norm, signal to noise ratio

孟大江　王德利　冯　飞　黄　飞　朱　恒 . 基于Curvelet变换的稀疏反褶积[J]. 石油学报, 2013, 34(1): 107-114.

MENG Dajiang　WANG Deli　FENG Fei　HUANG Fei　ZHU Heng . Sparse deconvolution based on the Curvelet transform[J]. Editorial office of ACTA PETROLEI SINICA, 2013, 34(1): 107-114.

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基于Curvelet变换的稀疏反褶积

Sparse deconvolution based on the Curvelet transform

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