A = UDV T 2 3 f -x 2 U M N V N N D M N σ Neelamani 4 i A σ 1 σ 2... σ M Curvelet Jin A = r σ i u i v T i 3 i = u i v T i M N 8 A

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1 GLOBAL GEOLOGY Vol. 35 No. 2 Jun SVD SVD SVD SVD SVD SVD P A doi /j. issn Method on random noise separation from poststack seismic data based on SVD JIANG Yu-hang 1 LIU Cai 1 SONG Chao 1 GAO Yue 2 LU Qi 1 1. College of Geo-exploration Science and Technology Jilin University Changchun China 2. Key Laboratory of Groundwater Resources and Environment Ministry of Education Jilin University Changchun China Abstract The authors present a new method of random noise separation from poststack seismic data based on SVD. If the events of seismic profile are horizontal or closely horizontal this method can separate the random noise from the seismic data validly and greatly improve the resolution of the seismic profile. In order to demonstrate the validity and high efficiency of de-noising method based on SVD the authors set up model experiments firstly then add random noise into the synthetic seismic data and field data. The noisy synthetic seismic data and field data with SVD method and wavelet threshold de-noising method have been processed respectively. The results show that compared with wavelet threshold de-noising method SVD method can separate the random noise from the seismic data more validly and efficiently. Key words SVD method wavelet threshold de-noising method random noise noise separation liucai@ jlu. edu. cn

544 35 2 A = UDV T 2 3 f -x 2 U M N V N N D M N σ Neelamani 4 i A σ 1 σ 2.

2 A = UDV T 2 3 f -x 2 U M N V N N D M N σ Neelamani 4 i A σ 1 σ 2... σ M Curvelet Jin A = r σ i u i v T i 3 i = u i v T i M N 8 A i Singular Value Decomposition SVD 3 9 SVD 1 M N 2 M N 10 A = x i j i = 1 2 M j = 1 2 N 30% 1 1 x i j A i j M < N A Hz m Fig. 1 1 Synthetic record and record with random noise

第2 期姜宇航刘财等基于 SVD 的叠后地震资料随机噪声分离方法表1 Table 1 545 模型参数表 Parameters of model 深度 / m 速度 / km s 1 密度 / kg m 3 第1 层 250 3. 8 1. 682 9 第2 层 250 4. 2 1. 723 1 第3 层 250 4. 6 1.

773 9 对加噪后的合成记录进行 SVD 分解得到奇异值排列图 2 得到的奇异值前两个远远大于其他奇异值所以对合成记录进行重构时设置其他所有奇异值为零只取前两个奇异值得到重构 11 地震记录图 3a 用小波分层阈值法对加噪后的合成记录进行去噪处理首先对信号进行小波 12 分析自动生成小波去噪阈值

3 第2 期姜宇航刘财等基于 SVD 的叠后地震资料随机噪声分离方法表1 Table 模型参数表 Parameters of model 深度 / m 速度 / km s 1 密度 / kg m 3 第1 层第2 层第3 层第4 层对加噪后的合成记录进行 SVD 分解得到奇异值排列图 2 得到的奇异值前两个远远大于其他奇异值所以对合成记录进行重构时设置其他所有奇异值为零只取前两个奇异值得到重构 11 地震记录图 3a 用小波分层阈值法对加噪后的合成记录进行去噪处理首先对信号进行小波 12 分析自动生成小波去噪阈值选取方案图3 Fig. 3 Fig. 2 加噪后的合成记录 SVD 后的奇异值排列 Singular value rank of the synthetic record after SVD SVD 去噪后的合成记录和小波分层阈值去噪后的合成记录 De-noising synthetic records with SVD and with wavelet threshold de-noising method 图4 Fig. 4 选取图2 SVD 法与分层阈值法分离出的随机噪声 Separated random noise with SVD method and wavelet threshold de-noising method

546 35 4 4 2 0. 002 0 0. 004 6 0. 003 4 0. 002 2 3b 3 SVD Table 2 Calculation time of SVD method and wavelet threshold de-noising method method for synthetic record SVD 4 SVD 2 SVD SVD 0. 012 460 1.

4 b 3 SVD Table 2 Calculation time of SVD method and wavelet threshold de-noising method method for synthetic record SVD 4 SVD 2 SVD SVD /s 4a 4b 3 SVD 5a % SVD 5b 5 Fig. 5 Field data and data with random noise SVD 3 SVD 6 20 Table 3 Calculation time of SVD method and wavelet 7a threshold de-noising method for field data b SVD /s SVD SVD 3 8a SVD 8 8b

De-noising field data with SVD method and wavelet threshold de-noising method 图8 Fig.

5 第2 期姜宇航刘财等基于 SVD 的叠后地震资料随机噪声分离方法图6 Fig. 6 图7 Fig. 7 Singular value rank of synthetic record after SVD SVD 去噪后的实际资料和小波分层阈值去噪后的实际资料 De-noising field data with SVD method and wavelet threshold de-noising method 图8 Fig. 8 加噪后的实际资料 SVD 后的奇异值排列 SVD 法与分层阈值法分离出的随机噪声 Separated random noise with SVD method and wavelet threshold de-noising method 547

6 J J. SHEN Ye JIANG Li. Prediction of hydrocarbon enrichment area by seismic high-low frequency information LIU Yang WANG Dian LIU Cai et al. Weighted me- J. Global Geology dian filter based on local correlation and its application to 4 poststack random noise attenuation J. Chinese Journal 1 SVD of Geophysics J LONG Yun HAN Li-guo DENG Wu-bin et al. Adaptive weighted improved window median filtering J. Global Geology SVD J LI Hong-yu YANG Chang-bao WU Yan-gang et al. Application of wavelet transform for de-noising and poten- 1. Bandelet tial field separation in gravity and magnetic data processing J. Global Geology D LIU Yan-fang. Seismic random noise remove based on the 9. Bandelet Transform master s degree thesis D. Harbin Harbin Institute of Technology Wang X. On the max /median filter J. IEEE Transactions on Signal Processing f-x J KANG Ye YU Cheng-ye JIA Wo et al. A study on noise-suppression method in f-x domain J. Oil Geophysical Prospecting Neelamani R Baurnstein A Gillard D et al. Coherent and random noise attenuation using the curvelet transform J. The Leading Edge Jin L Chen X H. The combination of wavelet transform and nonlinear filtering for time-lapse seismic difference a- nalysis J. Expanded Abstracts of SEG 78th Annual Meeting D ZHAN Yi. Study on pre-stack seismic data de-noising method doctor s degree thesis D. Chengdu Chengdu University of Technology AVA SVD HTI J LIU Cai LIU Yu-wei FENG Xuan et al. Invert crack density of HTI media by using SVD based PP-wave AVA data from crossing seismic survey lines J. Journal of Jilin University Earth Science Edition Donoho D L. De-noising by soft-thresholding J. IEEE Transactions on Information Theory

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