基于形态分量分析的含噪地震数据重建方法

doi:10.6038/pg2018BB0478

地球物理学进展 ›› 2019, Vol. 34 ›› Issue (2): 573-580.doi: 10.6038/pg2018BB0478

• 应用地球物理学Ⅰ（油气及金属矿产地球物理勘探） • 上一篇下一篇

基于形态分量分析的含噪地震数据重建方法

江萍¹,张凯^2,^*(),张医奎²,田鑫²

^1. 中国石油大学(华东)理学院,山东青岛 266580
^2. 中国石油大学(华东)地球科学与技术学院,山东青岛 266580

收稿日期:2018-06-18 修回日期:2018-12-12 出版日期:2019-04-20 发布日期:2019-05-13
通讯作者: 张凯 E-mail:zhksam@163.com
作者简介:江萍,女,1982年生,博士,副教授,主要从事应用物理学研究.(E-mail:pjiang@upc.edu.cn)
基金资助:
国家油气重大专项(2017ZX05032-003-002);山东省自然基金项目(ZR2017MD014);山东省重点研发计划项目(2018GHY115016);中央高校基本科研业务费专项资金共同资助(17CX02052);中央高校基本科研业务费专项资金共同资助(19CX02056A)

Noisy seismic data reconstruction method based on morphological component analysis framework

JIANG Ping¹,ZHANG Kai^2,^*(),ZHANG Yi-kui²,TIAN Xin²

^1. School of Science, China University of Petroleum(East China), Shandong Qingdao 266580, China
^2. School of Geoscience, China University of Petroleum(East China), Shandong Qingdao 266580, China

Received:2018-06-18 Revised:2018-12-12 Online:2019-04-20 Published:2019-05-13
Contact: Kai ZHANG E-mail:zhksam@163.com

摘要/Abstract

摘要：

随着当今勘探难度的增加,地震数据处理的精度也逐步提升,因此,对数据的完整度也提出了更高的要求.本文基于形态分量分析,采用离散余弦变换(DCT)字典和Shearlet字典的组合形式用于地震数据恢复重建,相比于其他稀疏变换具有更高的稀疏性、更强的稀疏表示能力.在MCA框架下,首先通过对地震数据中的局部奇异分量与平滑状分量分别采用DCT字典和Shearlet字典进行稀疏表示;而后,在重建的算法中加入指数阈值模型和指数阈值函数的块坐标松弛(BCR)算法来得到各个分量;最后,将不同字典得到的结果合并得到最终重建结果.通过合成数据实验和实际数据实验均表明,该方法能够有效地重建缺失地震数据,并且重建精度高于Curvelet字典与DCT字典组合、单一Shearlet字典、Shearlet字典与Curvelet字典组合.同时,通过对含噪数据以及不同信噪比的数据处理结果均验证了该方法具有较强的适应性.

关键词: 形态分量分析, 离散余弦变换(DCT), Shearlet变换, 地震数据重建, 压缩感知

Abstract:

Today,With the increasing difficulty of exploration,the precision of seismic data processing is also gradually improved. Therefore, higher requirements are put forward for the integrity of data. In this paper, a combination of Discrete Cosine Transform(DCT) dictionary and Shearlet dictionary is used for seismic data restoration and reconstruction based on Morphological Component Analysis(MCA). In comparison with other sparse transformations, Shearlet dictionary has higher sparsity and stronger sparse representation capability. In the MCA framework, DCT dictionary and Shearlet dictionary are used to sparse representation of local singular and smooth components in seismic data. Then we reconstruct each component by Block Coordinate Relaxation(BCR)algorithm with exponential threshold model and exponential threshold function. Finally, the results of different dictionaries are combined to obtain the final reconstruction results. Both synthetic and practical data experiments show that this method can effectively reconstruct missing seismic data, and the reconstruction accuracy is higher than Curvelet dictionary combined with DCT dictionary, single Shearlet dictionary, Shearlet dictionary combined with Curvelet dictionary. At the same time, through the data processing results of noise-containing data and different SNR, it is proved that this method has strong adaptability.

Key words: Morphological Component Analysis(MCA), Discrete Cosine Transform(DCT), Shearlet transform, Seismic data reconstruction, Compressed sensing

中图分类号:

P631

江萍, 张凯, 张医奎, 田鑫. 2019. 基于形态分量分析的含噪地震数据重建方法. 地球物理学进展, 34(2): 573-580. doi: 10.6038/pg2018BB0478.

JIANG Ping, ZHANG Kai, ZHANG Yi-kui, TIAN Xin. 2019. Noisy seismic data reconstruction method based on morphological component analysis framework. Progress in Geophysics. 34(2): 573-580. doi: 10.6038/pg2018BB0478.

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参考文献 22

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字典组合	Curvelet+DCT	Shearlet	Shearlet+Curvelet	Shearlet+DCT
SNR(dB)	34.5381	40.2652	41.6596	42.6748
PSNR(dB)	25.2825	28.1460	28.8433	29.3508

字典组合	Curvelet+DCT	Shearlet	Shearlet+Curvelet	Shearlet+DCT
SNR(dB)	10.6858	11.7176	12.1543	12.3262
PSNR(dB)	16.2043	16.7202	16.9385	17.0250

缺失程度	10%	20%	30%	40%	50%	60%	70%	80%	90%
SNR(dB)	47.0	46.0	35.3	30.2	19.8	9.6	4.5	2.8	1.1
PSNR(dB)	63.0	62.1	51.3	46.2	35.8	25.6	20.6	18.8	17.1

基于形态分量分析的含噪地震数据重建方法

Noisy seismic data reconstruction method based on morphological component analysis framework

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