NAN FangZhou,
XU Ya,
LIU Wei et al
.2018.Denoising methods of OBS data based on sparse representation.Chinese Journal Of Geophysics,61(4): 1519-1528,doi: 10.6038/cjg2018L0130
Denoising methods of OBS data based on sparse representation
NAN FangZhou1,2,3, XU Ya1,2, LIU Wei1,2,3, LIU LiHua1,2, HAO TianYao1,2,3, YOU QingYu1,2,3
1. Institute of Geology and Geophysics, Chinese Academy of Sciences, Key Laboratory of Petroleum Resource Research, CAS, Beijing 100029, China; 2. Institutions of Earth Science, Chinese Academy of Sciences, Beijing 100029, China; 3. University of Chinese Academy of Sciences, Beijing 100049, China
Abstract:Noise suppression is the basis for OBS data interpretation and subsequent inversion. Combining Curvelet transform and compression sensing, we propose a noise suppression method for OBS data using sparse representation. Comparing to the wavelet method, the Curvelet transform has advantage in identifying linear anomalies on a parabolic scale, which permits to reconstruct OBS data in a sparse representation domain. The sparse data is enhanced and reconstructed by the means of compression sensing, followed by transforming the coefficient to get iterative filtered by the cooling threshold of L1, then an optimal coefficient is resolved. Our study shows iterative filtering in the Curvelet domain with a cooling threshold can be utilized in noise suppression of OBS data. Comparison of wavelet and Curvelet transforms shows that the Curvelet method has a better S/N ratio in the circumstance of the same amount iterations of noise suppression. We use this new method to enhance the OBS data signal acquired from the Bohai Bay experiment and show clearer identification of the seismic phases and better S/N ratios, which facilitates picking up seismic phases from data and subsequent inversion of velocity models.
Bai L S, Liu Y K, Lu H Y, et al. 2014. Curvelet-domain joint iterative seismic data reconstruction based on compressed sensing. Chinese Journal of Geophysics (in Chinese), 57(9):2937-2945, doi:10.6038/cjg20140919. Candès E J, Donoho D L. 2000. Curvelets:A surprisingly effective nonadaptive representation for objects with edges. Palo Alto:Stanford University California Department of Statistics. Candès E J, Donoho D L. 2004. New tight frames of Curvelets and optimal representations of objects with piecewise C2 singularities. Communications on Pure and Applied Mathematics, 57(2):219-266. Candès E, Demanet L, Donoho D, et al. 2006a. Fast discrete Curvelet transforms. Multiscale Modeling & Simulation, 5(3):861-899. Candès E J, Romberg J, Tao T. 2006b. Robust uncertainty principles:Exact signal reconstruction from highly incomplete frequency information. IEEE Transactions on Information Theory, 52(2):489-509. Chen S S, Donoho D L, Saunders M A. 2001. Atomic decomposition by basis pursuit. Siam Review, 43(1):129-159. Daubechies I. 1992. Ten Lectures on Wavelets. Philadelphia:Society for Industrial and Applied Mathematics. Daubechies I, Defrise M, De Mol C. 2004. An iterative thresholding algorithm for linear inverse problems with a sparsity constraint. Communications on Pure and Applied Mathematics, 57(11):1413-1457. Donoho D L. 2006. Compressed sensing. IEEE Transactions on Information Theory, 52(4):1289-1306. Donoho D L, Tsaig Y, Drori I, et al. 2012. Sparse solution of underdetermined systems of linear equations by stagewise orthogonal matching pursuit. IEEE Transactions on Information Theory, 58(2):1094-1121. Gabor D. 1946. Theory of communication. Part 1:The analysis of information. Journal of the Institution of Electrical Engineers-Part Ⅲ:Radio and Communication Engineering, 93(26):429-441. Hao T Y, You Q Y. 2011. Progress of homemade OBS and its application on ocean bottom structure survey. Chinese Journal of Geophysics (in Chinese), 54(12):3352-3361, doi:10.3969/j.issn.0001-5733.2011.12.033. Herrmann F J, Verschuur E. 2004. Curvelet-domain multiple elimination with sparseness constraints.//2004 SEG Annual Meeting. Denver, Colorado:SEG, 1333-1336. Herrmann F J, Wang D L, Hennenfent G, et al. 2007. Curvelet-based seismic data processing:A multiscale and nonlinear approach. Geophysics, 73(1):A1-A5. Herrmann F J, Hennenfent G. 2008. Non-parametric seismic data recovery with Curvelet frames. Geophysical Journal International, 173(1):233-248. Liu L H, Lv C C, Hao T Y, et al. 2012. Data processing methods of OBS and its development tendency in detection of offshore oil and gas resources. Progress in Geophysics (in Chinese), 27(6):2673-2684, doi:10.6038/j.issn.1004-2903.2012.06.047. Lustig M, Donoho D L, Santos J M, et al. 2008. Compressed sensing MRI. IEEE Signal Processing Magazine, 25(2):72-82. Ma J W, Plonka G. 2010. The curvelet transform. IEEE Signal Processing Magazine, 27(2):118-133. Ma J W. 2011. Improved iterative Curvelet thresholding for compressed sensing and measurement. IEEE Transactions on Instrumentation and Measurement, 60(1):126-136. Mallat S G, Zhang Z F. 1993. Matching pursuits with time-frequency dictionaries. IEEE Transactions on Signal Processing, 41(12):3397-3415. Needell D, Vershynin R. 2009. Uniform uncertainty principle and signal recovery via regularized orthogonal matching pursuit. Foundations of Computational Mathematics, 9(3):317-334. Oka A, Lampe L. 2009. A compressed sensing receiver for UWB impulse radio in bursty applications like wireless sensor networks. Physical Communication, 2(4):248-264. Patel V M, Chellappa R. 2013. Sparse Representations and Compressive Sensing for Imaging and Vision. Heidelberg:Springer. Pati Y C, Rezaiifar R, Krishnaprasad P S. 1993. Orthogonal matching pursuit:Recursive function approximation with applications to wavelet decomposition.//Proceedings of the 1993 Conference Record of the Twenty-Seventh Asilomar Conference on Signals, Systems and Computers. Pacific Grove, CA, USA:IEEE, 40-44. Pope G. 2009. Compressive sensing:A summary of reconstruction algorithms. Zürich:ETH, Swiss Federal Institute of Technology Zurich, Department of Computer Science. Shahidi R, Tang G, Ma J W, et al. 2013. Application of randomized sampling schemes to Curvelet-based sparsity-promoting seismic data recovery. Geophysical Prospecting, 61(5):973-997. Shan H, Ma J W, Yang H Z. 2009. Comparisons of wavelets, contourlets and curvelets in seismic denoising. Journal of Applied Geophysics, 69(2):103-115. Sun B B, Ma J W, Chauris H, et al. 2009. Solving wave equations in the Curvelet domain:A multi-scale and multi-directional approach. Annals of Clinical Biochemistry, 14(4):235-239. Tang G, Ma J W. 2010a. Application of total-variation-based curvelet shrinkage for three-dimensional seismic data denoising. IEEE Geoscience and Remote Sensing Letters, 8(1):103-107. Tang G. 2010b. Seismic data reconstruction and denoising based on compressive sensing and sparse representation (in Chinese). Beijing:Tsinghua University. Wu Z C, Liu T Y. 2008. Wavelet transform methods in seismic data noise attenuation. Progress in Geophysics (in Chinese), 23(2):493-499. Xu Y, Hao T Y, Zhou L H, et al. 2006. Review of Wavelet transform in potential field. Progress in Geophysics (in Chinese), 21(4):1132-1138. Yao S L. 2007. Study on methods of noise removing by wavelet and their applications to seismic data processing (in Chinese). Changsha:Central South University. Yin W T. 2010. Analysis and generalizations of the linearized Bregman method. SIAM Journal on Imaging Sciences, 3(4):856-877. You Q Y, Liu F T, Ran C R, et al. 2003. High frequency micro-power ocean bottom seismograph. Progress in Geophysics (in Chinese), 18(1):173-176. Zhang H, Chen X H, Yang H Y. 2011. Optimistic wavelet basis selection in seismic signal noise elimination. Oil Geophysical Prospecting (in Chinese), 2011, 46(1):70-75+164+170-171. 白兰淑, 刘伊克, 卢回忆等. 2014. 基于压缩感知的Curvelet域联合迭代地震数据重建. 地球物理学报, 57(9):2937-2945, doi:10.6038/cjg20140919. 郝天珧, 游庆瑜. 2011. 国产海底地震仪研制现状及其在海底结构探测中的应用. 地球物理学报, 54(12):3352-3361, doi:10.3969/j.issn.0001-5733.2011.12.033. 刘丽华, 吕川川, 郝天珧等. 2012. 海底地震仪数据处理方法及其在海洋油气资源探测中的发展趋势. 地球物理学进展, 27(6):2673-2684, doi:10.6038/j.issn.1004-2903.2012.06.047. 唐刚. 2010b. 基于压缩感知和稀疏表示的地震数据重建与去噪. 北京:清华大学, 2010. 吴招才, 刘天佑. 2008. 地震数据去噪中的小波方法. 地球物理学进展, 23(2):493-499. 徐亚, 郝天珧, 周立宏等. 2006. 位场小波变换研究进展. 地球物理学进展, 21(4):1132-1138. 姚胜利. 2007. 地震信号的小波去噪方法研究. 长沙:中南大学. 游庆瑜, 刘福田, 冉崇荣等. 2003. 高频微功耗海底地震仪研制. 地球物理学进展, 18(1):173-176. 张华, 陈小宏, 杨海燕. 2011. 地震信号去噪的最优小波基选取方法. 石油地球物理勘探, 46(1):70-75+164+170-171.