Coal Geology & Exploration


With the development of high precision seismic exploration technology, the use of high fidelity methods to improve the SNR of seismic data becomes the key to denoising. Curvelet threshold method can effectively suppress random noise, but at the same time the method is easy to produce pseudo Gibbs shock phenomenon, resulting in local distortion of the signal, thus affecting the processing effect. To solve this problem, a method of seismic signal denoising based on compressing sensing(CS) is presented in this paper. The method uses the difference between sparse representation of random noise and effective signal in curvelet sparse domain to suppress the separation of random noise. Seismic data are transformed into curvelet domain; Curvelet coefficients are reset by using the compression perception theory and the total variation regularization algorithm; Reconstructed seismic data after curvelet inversion are used to suppress noise. The theoretical model and practical data show that the proposed method can avoid the signal distortion caused by the pseudo-Gibbs phenomenon and further improve the signal-to-noise ratio of the data.


random noise, curvelet transform, compressing sensing, total variation regularization




[1] LU Wenkai. Adaptive noise attenuation of seismic images based on singular value decomposition and texture direction detection[J]. Journal of Geophysics and Engineering,2006,3(1):28-34.

[2] 沈鸿雁,李庆春. 频域奇异值分解(SVD)地震波场去噪[J]. 石油地球物理勘探,2010,45(2):185-189. SHEN Hongyan,LI Qingchun. SVD(singular value decomposition) seismic wave field noise elimination in frequency domain[J]. Oil Geophysical Prospecting,2010,45(2):185-189.

[3] 蔡加铭,周兴元,吴律. f-x域算子外推去噪技术研究[J]. 石油地球物理勘探,1999,34(3):325-331. CAI Jiaming,ZHOU Xingyuan,WU Lyu. A technique for noise elimination using operator extrapolation f-x domain[J]. Oil Geophysical Prospecting,1999,34(3):325-331.

[4] 熊定钰,钱忠平,赵波,等. 用优频算子外推改善f-x域滤波性能[J]. 石油地球物理勘探,2011,46(2):211-216. XIONG Dingyu,QIAN Zhongping,ZHAO Bo,et al. Pre-dominant frequency band operator extrapolation to improve noise attenuation in f-x domain[J]. Oil Geophysical Prospecting,2011,46(2):211-216.

[5] 俞寿朋,蔡希玲,苏永昌. 用地震信号多项式拟合提高叠加剖面信噪比[J]. 石油地球物理勘探,1988,23(2):131-139. YU Shoupeng,CAI Xiling,SU Yongchang. Improvement of signal-to-noise ratio of stack section using polynomial fitting of seismic signals[J]. Oil Geophysical Prospecting,1988,23(2):131-139.

[6] 钟伟,杨宝俊,张智. 多项式拟合技术在强噪声地震资料中的应用研究[J]. 地球物理学进展,2006,21(1):184-189. ZHONG Wei,YANG Baojun,ZHAGH Zhi. Research on application of polynomial fitting technique in highly noisy seismic data[J]. Progress in Geophysics,2006,21(1):184-189.

[7] 王书明,王家映. 高阶统计量在大地电磁测深数据处理中的应用研究[J]. 地球物理学报,2004,47(5):929-935. WANG Shuming,WANG Jiaying. Application of higher-order statistics in magnetotelluric data processings[J]. Chinese Journal of Geophysics,2004,47(5):929-935.

[8] HERRMANN F J,WANG Deli,HENNENFENT G,et al. Curvelet-based seismic data processing:A multiscale and nonlinear approach[J]. Geophysics,2008,73(1):1-5.

[9] 张恒磊,张云翠,宋双,等. 基于Curvelet域的叠前地震资料去噪方法[J]. 石油地球物理勘探,2008,43(5):508-513. ZHANG Henglei,ZHANG Yuncui,SONG Shuang,et al. Curvelet domain-based prestack seismic data denoise method[J]. Oil Geophysical Prospecting,2008,43(5):508-513.

[10] 张恒磊,刘天佑,张云翠. 基于高阶相关的Curvelet域和空间域的倾角扫描噪声压制方法[J]. 石油地球物理勘探,2010,45(2):208-214. ZHANG Henglei,LIU Tianyou,ZHANG Yuncui. High order correlation based dip angle scanning noise elimination method in curvelet domain and space domain[J]. Oil Geophysical Prospecting,2010,45(2):208-214.

[11] BOASHASH B,MESBAH M. Signal enhancement by time-frequency peak filtering[J]. IEEE Transactions on Signal Processing,2004,52(4):929-937.

[12] 林红波,李月,徐学纯. 压制地震勘探随机噪声的分段时频峰值滤波方法[J]. 地球物理学报,2011,54(5):1358-1366. LIN Hongbo,LI Yue,XU Xuechun. Segmenting time-frequency peak filtering method to attenuation of seismic random noise[J]. Chinese Journal of Geophysics,2011,54(5):1358-1366.

[13] 董恩清,刘贵忠,张宗平. 基于离散Gabor变换迭代时变滤波实现地震信号去噪[J]. 煤田地质与勘探,2000,28(6):48-51. DONG Enqing,LIU Guizhong,ZHANG Zongping. A denosing method of seismic data based on iterative time-variant filter of discrete gabor transform[J]. Coal Geology & Exploration,2000,28(6):48-51.

[14] 李貅,宋建平,马宇,等. 基于小波分析的TEM信号提取[J]. 煤田地质与勘探,2005,32(2):72-75. LI Xiu,SONG Jianping,MA Yu,et al. The abstract of TEM signal based on the wavelet analysis[J]. Coal Geology & Exploration,2005,32(2):72-75.

[15] 刘洋,FOMEL Sergey,刘财,等. 高阶seislet变换及其在随机噪声消除中的应用[J]. 地球物理学报,2009,52(8):2142-2151. LIU Yang,FOMEL S,LIU Cai,et al. High-order seislet transform and its application of random noise attenuation[J]. Chinese Journal of Geophysics,2009,52(8):2142-2151.

[16] 刘伟,曹思远,崔震. 基于压缩感知和TV准则约束的地震资料去噪[J]. 石油物探,2015,54(2):180-187. LIU Wei,CAO Siyuan,CUI Zhen. Random noise attenuation based on compressive sensing and TV rule[J]. Geophysical Prospecting for Petroleum,2015,54(2):180-187.

[17] CANDÈS E J,ROMBERG J,TAO T. Robust uncertainty principles:Exact signal reconstruction from highly incomplete frequency information[J]. IEEE Transactions on Information Theory,2004,52(2):489-509.

[18] CANDES E J,TAO T. Near-optimal signal recovery from random projections:Universal encoding strategies?[J]. IEEE Transactions on Information Theory,2006,52(12):5406-5425.

[19] MOHAMMAD R. Compressed sensing[M]. Heidelberg:Springer International Publishing,2013:9-22.

[20] TSAIG Y,DONOHO D L. Extensions of compressed sensing[J]. Signal Processing,2006,86(3):549-571.

[21] 王汉闯,陶春辉,陈生昌,等. 基于稀疏约束的地震数据高效采集方法理论研究[J]. 地球物理学报,2016,59(11):4246-4265. WANG Hanchuang,TAO Chunhui,CHEN Shengchang,et al. Study on highly efficient seismic data acquisition method and theory based on sparsity constraint[J]. Chinese Journal of Geophysics,2016,59(11):4246-4265.

[22] HENNENFENT G,HERRMANN F J. Simply denoise:Wavefield reconstruction via jittered undersampling[J]. Geophysics,2008,73(3):19-28.

[23] 白兰淑,刘伊克,卢回忆,等. 基于压缩感知的Curvelet域联合迭代地震数据重建[J]. 地球物理学报,2014,57(9):2937-2945. BAI Lanshu,LIU Yike,LU Huiyi,et al. Curvelet-domain joint iterative seismic data reconstruction based on compressed sensing[J]. Chinese Journal of Geophysics,2014,57(9):2937-2945.

[24] 韩立国,张莹,韩利,等. 基于压缩感知和稀疏反演的地震数据低频补偿[J]. 吉林大学学报(地球科学版),2012,42(增刊3):259-264. HAN Liguo,ZHANG Ying,HAN Li,et al. Compressed sensing and sparse inversion based low-frequency information compensation of seismic data[J]. Journal of Jilin University(Earth Science Edition),2012,42(S3):259-264.

[25] CANDES E,DEMANET L,DONOHD D,et al. Fast discrete curvelet transforms[J]. Multiscale Modeling & Simulation,2006,5(3):861-899.

[26] LI Chengbo. An efficient algorithm for total variation regularization with applications to the single pixel camera and compressive sensing[D]. Texas:Rice University,2010.

[27] 牛聪,詹毅,李辉峰. 对比地震记录信噪比的几种估算方法[J]. 物探化探计算技术,2006,28(1):5-9. NIU Cong,ZHAN Yi,LI Huifeng. Several estimation methods for comparison of signal to noise ratio of seismic records[J]. Computing Techniques for Geophysical and Geochemical Exploration,2006,28(1):5-9.

[28] DONOHO D L. De-noising by soft-thresholding[J]. IEEE Transactions on Information Theory,1995,41(3):613-627.



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