Comparison of linear and nonlinear time-frequency analysis on seismic signals
Huang Yucheng1, Zheng Xiaodong1, Luan Yi2, Yang Tingqiang1
1. Research Institute of Petroleum Exploration & Development, PetroChina, Beijing 100083, China; 2. Faculty of Science, The Chinese University of Hong Kong, Hong Kong 999077, China
Abstract:In this paper,we discuss the resolution,computational efficiency,and robustness of currently used seismic time-frequency analysis methods based on synthetic signals and real seismic data.In synthetic signal analysis,the time-frequency energy concentration of linear methods are generally weak,yet they are preferred in the low signal-to-noise (SNR) situation for their high computational efficiency,among which the continuous wavelet transform (CWT) is considerably robust; nonlinear methods are unstable with noisy data except for smoothed pseudo Wigner-Ville distribution (SPWVD) and general linear Chirplet transform (GLCT).However,nonlinear methods may reach much higher time-frequency resolution with high SNR.Thin-beds and the distribution of geologic features could be clearly identified using these methods.In real seismic data analysis,compared with linear methods like short time Fourier transform and CWT,reservoir reflection interfaces and sedimentary facies belts are better delineated on common frequency sections and time slices obtained by robust nonlinear methods like SPWVD and GLCT.
Morlet G,Fourgeau E,Giard D.Wave propagation and sampling theory,part I:complex signal and scattering inmultilayered media.Geophysics,1982,47(2):203-221.
[2]
Okaya D A,Karageorgi E,McEvilly T V et al.Removing vibrator-induced correlation artifacts by filtering in frequency-uncorrelated time space.Geophysics,1992,57(7):916-926.
[3]
Chakraborty A,Okaya D.Frequency-time decomposition of seismic data using wavelet-based methods.Geophysics,1995,60(6):1906-1916.
[4]
Grubb H J,Walden A T.Characterizing seismic time series using the discrete wavelet transform.Geophysical Prospecting,1997,45(2):183-205.
[5]
李宏兵,赵文智,曹宏等.小波尺度域含气储层地震波衰减特征.地球物理学报,2004,47(5):892-898.Li Hongbing,Zhao Wenzhi,Cao Hong et al.Characteristics of seismic attenuation of gas reservoirs in wavelet domain.Chinese Journal of Geophysics,2004,47(5):892-898.
[6]
Partyka G,Gridley J,Lopez J.Interpretational applications of spectral decomposition in reservoir characterization.The Leading Edge,1999,18(3):353-360.
[7]
Castagna J P,Sun S,Robert W S.Instantaneous spectral analysis:Detection of low-frequency shadows associated with hydrocarbons.The Leading Edge,2003,22(2):120-127.
[8]
Liu J,Wu Y,Han D et al.Time-frequency decomposition based on Ricker wavelet.SEG Technical Program Expanded Abstracts,2004,23:1937-1940.
[9]
Liu J,Marfurt K.Matching pursuit decomposition using Morlet wavelets.SEG Technical Program Expanded Abstracts,2005,24:786-789.
[10]
Liu J,Marfurt K J.Instantaneous spectral attributes to detect channels.Geophysics,2007,72(2):P23-P31.
[11]
Wang Y.Seismic time-frequency spectral decomposi-tion by matching pursuit.Geophysics,2007,72(1):V13-V20.
[12]
Wang Y.Multichannel matching pursuit for seismic trace decomposition.Geophysics,2010,75(4):V61-V66.
[13]
Sinha S,Routh S P,Anno D P et al.Spectral decomposition of seismic data with continuous-wavelet transform.Geophysics,2005,70(6):P19-P25.
[14]
Pinnegar C R,Lalu M.The S-transform with windows of arbitrary and varying shape.Geophysics,2003,68(1):381-385.
[15]
高静怀,陈文超,李幼铭等.广义S变换与薄互层地震响应分析.地球物理学报,2003,46(4):526-532.Gao Jinghuai,Chen Wenchao,Li Youmin et al.Gene-ralized S transform and seismic response analysis of thin interbeds.Chinese Journal of Geophysics,2003,46(4):526-532.
[16]
陈学华,贺振华,黄德济.基于广义S变换的地震资料高效时频谱分解.石油地球物理勘探,2008,43(5):530-534.Chen Xuehua,He Zhenhua and Huang Deji.High-efficient time-frequency spectrum decomposition of seismic data based on generalized S transform.OGP,2008,43(5):530-534.
[17]
陈学华,贺振华,黄德济等.时频域油气储层低频阴影检测.地球物理学报,2009,52(1):215-221.Chen Xuehua,He Zhenhua,Huang Deji et al.Low frequency shadow detection of gas reservoirs in time-frequency domain.Chinese Journal of Geophysics,2009,52(1):215-221.
[18]
徐阳,罗明璋,王智等.广义S变换与二维离散小波变换联合压制面波.石油物探,2018,57(3):395-403.Xu Yang,Luo Mingzhang,Wang Zhi et al.Surface wave suppression using generalized S-transform and 2D discrete wavelet transform.GPP,2018,57(3):395-403.
[19]
Li Y,Zheng X.Spectral decomposition using Wigner-Ville distribution with applications to carbonate reservoir characterization.The Leading Edge,2008,27(8):1050-1057.
[20]
Wu X,Liu T.Spectral decomposition of seismic data with reassigned smoothed pseudo Wigner-Ville distribution.Journal of Applied Geophysics,2009,68(3):386-393.
[21]
Han J,Mirko V D B.Empirical mode decomposition for seismic time-frequency analysis.Geophysics,2013,78(2):O9-O19.
[22]
曹思远,邴萍萍,路交通等.利用改进希尔伯特-黄变换进行地震资料时频分析.石油地球物理勘探,2013,48(2):246-254.Cao Siyuan,Bing Pingping,Lu Jiaotong et al.Seismic data time-frequency analysis by the improved Hilbert-Huang transform.OGP,2013,48(2):246-254.
[23]
薛雅娟,曹俊兴.聚合经验模态分解和小波变换相结合的地震信号衰减分析.石油地球物理勘探,2016,51(6):1148-1151.Xue Yajuan and Cao Junxing. Seismic attenuation ana-lysis using ensemble empirical mode decomposition and wavelet transform.OGP,2016,51(6):1148-1155.
[24]
刘晗,张建中,黄忠来.基于同步挤压S变换的地震信号时频分析.石油地球物理勘探,2017,52(4):689-695.Liu Han,Zhang Jianzhong and Huang Zhonglai.Time-frequency analysis of seismic data using synchro-squeezing S transform.OGP,2017,52(4):689-695.
[25]
Khonde K,Rastogi R.Recent developments in spec-tral decomposition of seismic data (techniques and applications):a review.Proceedings of the 10th Biennial International Conference & Exposition,2013.
[26]
Marfurt K J,Kirlin R L.Narrow-band spectral analysis and thin-bed tuning.Geophysics,2001,66(4):1274-1283.
[27]
Odebeatu E,Zhang J,Chapman M et al.Application of spectral decomposition to detection of dispersion anomalies associated with gas saturation.The Leading Edge,2006,25(2):206-210.
[28]
Oliveira S,Vilhena O,da Costa E.Time-frequency spectral signature of Pelotas Basin deep water gas hydrates system.Marine Geophysical Researches,2010,31(1):89-97.
[29]
Wang X,Chen T,Cui R et al.Spectral decomposition method for predicting magmatic intrusion into a coal bed.International Journal of Mining Science and Technology,2012,22(4):447-452.
[30]
Gabor D.Theory of communication,Part 1:The ana-lysis of information.Journal of the Institution of Electrical Engineers,Part Ⅲ:Radio and Communication Engineering,1946,93(26):429-441.
[31]
张贤达.现代信号处理.北京:清华大学出版社,2002.
[32]
Qian S.Introduction to Time-frequency and Wavelet Transforms.Prentice Hall,USA,2002.
[33]
Stockwell R G,Mansinha L,Lowe R P.Localization of the complex spectrum:the S transform.IEEE Transactions on Signal Processing,1996,44(4):998-1001.
[34]
Pinnegar C R,Mansinha L.Time-local spectral analysis for non-stationary time series:The S-transform for noisy signals.Fluctuation & Noise Letters,2003,3(3):L357-L364.
[35]
Pinnegar C R,Mansinha L.The bi-Gaussian S-trans-form.SIAM Journal on Scientific Computing,2003,24(5):1678-1692.
[36]
Pinnegar C R,Mansinha L.Time-local Fourier analysis with a scalable,phase-modulated analyzing function:the S-transform with a complex window.Signal Processing,2004,84(84):1167-1176.
[37]
李振春,刁瑞,韩文功等.线性时频分析方法综述.勘探地球物理进展,2010,33(4):239-246.Li Zhenchun,Diao Rui,Han Wengong et al. Review on linear time-frequency analysis methods.Progress in Exploration Geophysics,2010,33(4):239-246.
[38]
Wigner E.On the quantum correction for thermody-namic equilibrium.Physical Review,1932,40(5):749-759.
[39]
张贤达,保铮.非平稳信号处理与分析.北京:国防工业出版社,2001.
[40]
Zhong J,Huang Y.Time-frequency representation based on an adaptive short-time Fourier transform.IEEE Transactions on Signal Processing,2010,58(10):5118-5128.
[41]
Pei S C,Huang S G.STFT with adaptive window width based on the Chirp rate.IEEE Transactions on Signal Processing,2012,60(8):4065-4080.
[42]
Huang N E,Shen Z,Long S R et al.The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis.Proceedings of the Royal Society of London Series A:Mathematical,Physical and Engineering Sciences,1998,454(1971):903-995.
[43]
Wu Z,Huang N E.Ensemble empirical mode decomposition:A noise assisted data analysis method.Advances in Adaptive Data Analysis,2009,1(1):1-41.
[44]
Torres M E,Colominas M A,Schlotthauer G et al.A complete ensemble empirical mode decomposition with adaptive noise.Proceedings of the IEEE International Conference on Acoustics,Speech and Signal Processing,2011.
Huang Z,Zhang J,Zhao T et al.Synchrosqueezing S-transform and its application in seismic spectral decomposition.IEEE Transactions on Geoscience & Remote Sensing,2015,54(12):1-9.
[47]
Thakur G,Wu H T.Synchrosqueezing-based recovery of instantaneous frequency from nonuniform samples.SIAM Journal on Mathematical Analysis,2011,43(5):2078-2095.
[48]
Mallat S,Zhang Z.Matching pursuits with time-frequency dictionaries.IEEE Transactions on Signal Processing,1993,41(12):3397-3415.
[49]
Qian S,Chen D.Signal representation using adaptive normalized Gaussian functions.Signal Processing,1994,36(1):1-11.
[50]
Mann S,Haykin S.The Chirplet transform:Physical considerations.IEEE Transactions on Signal Processing,1995,43(11):2745-2761.
[51]
Baraniuk R G,Jones D L.Wigner-based formulation of the Chirplet transform.IEEE Transactions on Signal Processing,1996,44(12):3129-3135.
[52]
Cui J,Wang W.The adaptive chirplet transform and visual evoked potentials.IEEE Transactions on Bio-medical Engineering,2006,53(7):1378-1384.
[53]
邹红星,戴琼海,李衍达等.FMm let变换的子空间.中国科学:E辑,2001,31(5):463-469.Zou Hongxing,Dai Qionghai,Li Yanda et al.Subspaces of FMm let transform.Science in China (Series E),2001,31(5):463-469.
[54]
Peng Z K,Meng G,Chu F L et al.Polynomial Chirplet transform with application to instantaneous frequency estimation.IEEE Transactions on Instrumentation & Measurement,2011,60(9):3222-3229.
[55]
Yang Y,Zhang W,Peng Z et al.Multicomponent signal analysis based on polynomial Chirplet transform.IEEE Transactions on Industrial Electronics,2013,60(9):3948-3956.
[56]
Yu G,Zhou Y.General linear Chirplet transform.MechanicalSystems and Signal Processing,2016,(70-71):958-973.
[57]
Puryear C I C.Constrained Least Squares Spectral Analysis:Application to Seismic Data[D].University of Houston,2012.
[58]
Lu W,Li F.Seismic spectral decomposition using deconvolutive short-time Fourier transform spectrogram.Geophysics,2013,78(2):V43-V51.
[59]
Sattari H,Gholami A,Siahkoohi H R.Seismic data analysis by adaptive sparse time-frequency decomposition.Geophysics,2013,78(5):V207-V217.
[60]
Zoukaneri I,Porsani M J.A combined Wigner-Ville and maximum entropy method for high-resolution time-frequency analysis of seismic data.Geophysics,2015,80(6):O1-O11.
[61]
Castagna J P,Sun S.Comparison of spectral decomposition methods.First break,2006,24(3):75-79.
[62]
Cohen L.Time-frequencyAnalysis.Prentice Hall PTR, New Jersey,1995.
[63]
Mallat S.A Wavelet Tour of Signal Processing:the Sparse Way.Academic Press,USA,2008.
[64]
陈学华,贺振华,黄德济.广义S变换及其时频滤波.信号处理,2008,24(1):28-31.Chen Xuehua,He Zhenhua,Huang Deji.Genearlized S transform and its time-frequency filtering.Signal Processing,2008,24(1):28-31.
[65]
Oberlin T,Meignen S,Perrier V.The Fourier-based synchrosqueezing transform.Proceedings of the 2014 IEEE International Conference on Acoustics,Speech and Signal Processing (ICASSP),2014.
[66]
Iatsenko D,McClintock P V E,Stefanovska A.Linear and synchrosqueezed time-frequency representations revisited:Overview,standards of use,resolution,reconstruction,concentration,and algorithms.Digital Signal Processing,2015,42:1-26.
[67]
Gribonval R.Fast matching pursuit with a multiscale dictionary of Gaussian chirps.IEEE Transactions on Signal Processing,2001,49(5):994-1001.
[68]
O'Neill J C,Flandrin P,Karl W C.Sparse representations with Chirplets via maximum likelihood estimation.IEEE Transactions on Signal Processing,2000,10(4):1-11.
[69]
Baraniuk R G,Flandrin P,Janssen A J et al.Measuring time-frequency information content using the Rényi entropies.IEEE Transactions on Information Theory,2001,47(4):1391-1409.
[70]
Vishwanath M,Owens R M,Irwin M J.The computational complexity of time-frequency distributions.Proceedings of the IEEE 6th SP Workshop on Statistical Signal and Array Processing,1992.
[71]
Wang Y H,Yeh C H,Young H W V et al.On the computational complexity of the empirical mode decomposition algorithm.Physica A:Statistical Mechanics and its Applications,2014,400:159-167.
[72]
O'Neill J C,Flandrin P.Chirp hunting.Proceedings of the Time-Frequency and Time-Scale Analysis,IEEE-SP International Symposium,1998.