地震信号高分辨率谱分解方法及应用
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摘要
地下介质的复杂性造成地震波在地下的传播是非稳定的，谱分解作为一种能够同时在时频域刻画地震信号，研究地震信号瞬时频率特征的技术被广泛应用。随着油气勘探程度的日益增大，地震勘探的目标由构造油气藏转为岩性油气藏，埋藏深、储层薄、物性差、非均质强等特性使得地震勘探的难度越来越大。针对这种情况，常规的谱分解技术由于其时频分辨率较低，已经不能满足高分辨率地震数据处理、解释的需求。
本文在回顾常规谱分解方法的基础上，实现了两种高分辨率地震数据谱分解技术—基于能量谱重排的小波变换(Reassigned wavelet transform, RWT)和压缩小波变换(Synchrosqueezing wavelet transform, SWT)谱分解，这两种方法都是建立在小波变换的基础上，相对于传统的小波变换，其时频分辨率都得到了提高，把这两种方法引入地震数据处理和解释领域，取得了较好的效果。
第一种高分辨率谱分解方法是基于能量谱重排的小波变换，该方法主要是针对小波变换后的时频能量，对其按照重新计算的位置（其局部重心）进行重排，从而达到提高时频分辨率的目的。文章详细阐述了这种方法的实现过程，并通过合成算例证实其相对于传统小波变换具有较高的时频分辨能力。利用该方法对叠后地震数据进行分频解释，体现出该方法的优势。从能谱重排小波变换的数学公式推导可以看到，虽然这种方法通过对小波变换结果进行一定的后续处理提高了其时频分辨能力，但它在数学上是不可逆的，这也就意味着如果想从这种方法得到的时频分析结果重构地震信号在数学上是不可实现的，这使得基于能量谱重排的小波变换在地震数据高分辨率处理方面的应用受限。
第二种高分辨率谱分解方法是压缩小波变换方法，不同于能谱重排小波变换，该方法只沿频率方向对小波变换复数谱进行重排，在提高时频分辨率的同时保持了其数学上的可逆性，这就为其在地震数据处理和解释中的应用提供了广阔的天地。文章在详细阐述该方法原理的基础上，提出了基于该方法的地震随机噪声和面波压制技术，合成算例和实际数据证明了这种方法在地震去噪中的有效性。与此同时，考虑地震噪声的影响，基于地震数据结构的自相似性，提出了自适应非局部均值地震噪声压制方法，大大改善了地震数据去噪效果。
针对复杂地区，由于地震波的传播和地下介质的吸收作用，造成地震资料分辨率降低，不能满足地震地质解释的精度。本文提出的基于压缩小波变换的提高分辨率技术，可以对深浅层地震剖面能量进行补偿，拓宽了地震资料的有效频带范围，提高了地震资料的分辨率，同时不破坏地震剖面同相轴的能量相对关系，有利于后续地质解释与岩性反演等工作，采用这种方法对实际地震资料进行处理，验证了方法的有效性。
地震波在地下传播过程中，除了球面扩散、大地的滤波作用等造成地震波能量的衰减，当在含油气储层中传播时，也会造成地震波能量的强衰减和地震波频率成分的改变，而这种衰减现象往往伴随着地震波的频散，这一点已经被广大科研工作者证实。本文结合谱分解方法和AVO方程，提出一种新的频散属性，该属性与纵波速度频散属性一样可以在一定程度上刻画储层的含流体情况，可以作为一种储层烃类预测的手段。
The propagation of seismic waves beneath the surface is non-stable because thecomplexity of subsurface. Spectral decomposition, which can describe the frequencycharacteristics varying with time of seismic signal, is widely used in geophysics. Withthe increase of oil/gas exploration, the exploration targets are shifting into litologicreservoirs, making it more and more difficult because of the complexity of reservoirs.For this reason, conventional spectral decomposition technology is unable to meet theseismic data processing and interpretation needs, and the development of new spectralanalysis technique with high resolution is imminent.
We first review the previous research on spectral decomposition, and thenintroduce two new techniques for high resolution spectral decomposition of seismicdata, including reassigned wavelet transform (RWT) and synchrosqueezing wavelettransform (SWT), which both are improved versions of original wavelet transform,making it helpful to seismic data processing and interpretation.
One kind of the new seismic spectral decomposition methods is reassignedwavelet transform based on energy reassigment, which assigning its energy to a newposition (its local gravity center). The paper shows how the reassigned wavelettransform works and we compare its resolution with wavelet transform by syntheticdata. We conduct this method on post-stack seismic profile and reveal hydrocarbonreservoir using low-frequency abnormity. Although the readability of time-frequencydistribution can be improved after energy reassignment, it is not invertible and thereconstruction of signal is difficult, which make its application in high-resolutionseismic processing limited.
Another high-resolution spectral decomposition method is synchrosqueezingwavelet transform, which is different from the reassigned wavelet transform, focusingthe time-frequency representation by squeezing its value along the frequency axis andoffers an exact reconstruction formula for signals. So it can be widely used in seismicdata processing and interpretation. The theory of synchrosqueezing wavelet transformis stated in this paper, and then we proposed two new denoising algorithms based on SWT, synthetic and field examples show these methods work well. And so on,considering the impact of seismic noise, we also propose an adaptive nonlocal meansseismic denoising method, which is based on the self-similarity of seismic datastructure.
Since the absorption of underground layers and seismic wave attenuation, theresolution of seismic data can not meet the accuracy of geophysical and geologicalinterpretation. This paper proposed a seismic frequency width extension method basedon SWT without destorying the energy relationship between relative phase axis,making it conducive to subsequent geological interpretation and lithology inversionwork. Real seismic data show our method performs well.
In addition to spherical spreading, filtering effect of earth, etc. It is known whenseismic signal penetrates through hydrocarbon reservoirs, its amplitude will showstrong attenuation and its high frequency components will be attenuated more thanlow-frequency components. This phenomenon is often accompanied by seismic wavedispersion, which has been confirmed by the majority of scientists. Combiningspectral decomposition with avo theory, a new dispersion attribute is proposed in thispaper, which can describe the presence of fluid in reservoirs partly like P-wavevelocity dispersion property, and can be used as a method for hydrocarbon detection.
本文在回顾常规谱分解方法的基础上，实现了两种高分辨率地震数据谱分解技术—基于能量谱重排的小波变换(Reassigned wavelet transform, RWT)和压缩小波变换(Synchrosqueezing wavelet transform, SWT)谱分解，这两种方法都是建立在小波变换的基础上，相对于传统的小波变换，其时频分辨率都得到了提高，把这两种方法引入地震数据处理和解释领域，取得了较好的效果。
第一种高分辨率谱分解方法是基于能量谱重排的小波变换，该方法主要是针对小波变换后的时频能量，对其按照重新计算的位置（其局部重心）进行重排，从而达到提高时频分辨率的目的。文章详细阐述了这种方法的实现过程，并通过合成算例证实其相对于传统小波变换具有较高的时频分辨能力。利用该方法对叠后地震数据进行分频解释，体现出该方法的优势。从能谱重排小波变换的数学公式推导可以看到，虽然这种方法通过对小波变换结果进行一定的后续处理提高了其时频分辨能力，但它在数学上是不可逆的，这也就意味着如果想从这种方法得到的时频分析结果重构地震信号在数学上是不可实现的，这使得基于能量谱重排的小波变换在地震数据高分辨率处理方面的应用受限。
第二种高分辨率谱分解方法是压缩小波变换方法，不同于能谱重排小波变换，该方法只沿频率方向对小波变换复数谱进行重排，在提高时频分辨率的同时保持了其数学上的可逆性，这就为其在地震数据处理和解释中的应用提供了广阔的天地。文章在详细阐述该方法原理的基础上，提出了基于该方法的地震随机噪声和面波压制技术，合成算例和实际数据证明了这种方法在地震去噪中的有效性。与此同时，考虑地震噪声的影响，基于地震数据结构的自相似性，提出了自适应非局部均值地震噪声压制方法，大大改善了地震数据去噪效果。
针对复杂地区，由于地震波的传播和地下介质的吸收作用，造成地震资料分辨率降低，不能满足地震地质解释的精度。本文提出的基于压缩小波变换的提高分辨率技术，可以对深浅层地震剖面能量进行补偿，拓宽了地震资料的有效频带范围，提高了地震资料的分辨率，同时不破坏地震剖面同相轴的能量相对关系，有利于后续地质解释与岩性反演等工作，采用这种方法对实际地震资料进行处理，验证了方法的有效性。
地震波在地下传播过程中，除了球面扩散、大地的滤波作用等造成地震波能量的衰减，当在含油气储层中传播时，也会造成地震波能量的强衰减和地震波频率成分的改变，而这种衰减现象往往伴随着地震波的频散，这一点已经被广大科研工作者证实。本文结合谱分解方法和AVO方程，提出一种新的频散属性，该属性与纵波速度频散属性一样可以在一定程度上刻画储层的含流体情况，可以作为一种储层烃类预测的手段。
The propagation of seismic waves beneath the surface is non-stable because thecomplexity of subsurface. Spectral decomposition, which can describe the frequencycharacteristics varying with time of seismic signal, is widely used in geophysics. Withthe increase of oil/gas exploration, the exploration targets are shifting into litologicreservoirs, making it more and more difficult because of the complexity of reservoirs.For this reason, conventional spectral decomposition technology is unable to meet theseismic data processing and interpretation needs, and the development of new spectralanalysis technique with high resolution is imminent.
We first review the previous research on spectral decomposition, and thenintroduce two new techniques for high resolution spectral decomposition of seismicdata, including reassigned wavelet transform (RWT) and synchrosqueezing wavelettransform (SWT), which both are improved versions of original wavelet transform,making it helpful to seismic data processing and interpretation.
One kind of the new seismic spectral decomposition methods is reassignedwavelet transform based on energy reassigment, which assigning its energy to a newposition (its local gravity center). The paper shows how the reassigned wavelettransform works and we compare its resolution with wavelet transform by syntheticdata. We conduct this method on post-stack seismic profile and reveal hydrocarbonreservoir using low-frequency abnormity. Although the readability of time-frequencydistribution can be improved after energy reassignment, it is not invertible and thereconstruction of signal is difficult, which make its application in high-resolutionseismic processing limited.
Another high-resolution spectral decomposition method is synchrosqueezingwavelet transform, which is different from the reassigned wavelet transform, focusingthe time-frequency representation by squeezing its value along the frequency axis andoffers an exact reconstruction formula for signals. So it can be widely used in seismicdata processing and interpretation. The theory of synchrosqueezing wavelet transformis stated in this paper, and then we proposed two new denoising algorithms based on SWT, synthetic and field examples show these methods work well. And so on,considering the impact of seismic noise, we also propose an adaptive nonlocal meansseismic denoising method, which is based on the self-similarity of seismic datastructure.
Since the absorption of underground layers and seismic wave attenuation, theresolution of seismic data can not meet the accuracy of geophysical and geologicalinterpretation. This paper proposed a seismic frequency width extension method basedon SWT without destorying the energy relationship between relative phase axis,making it conducive to subsequent geological interpretation and lithology inversionwork. Real seismic data show our method performs well.
In addition to spherical spreading, filtering effect of earth, etc. It is known whenseismic signal penetrates through hydrocarbon reservoirs, its amplitude will showstrong attenuation and its high frequency components will be attenuated more thanlow-frequency components. This phenomenon is often accompanied by seismic wavedispersion, which has been confirmed by the majority of scientists. Combiningspectral decomposition with avo theory, a new dispersion attribute is proposed in thispaper, which can describe the presence of fluid in reservoirs partly like P-wavevelocity dispersion property, and can be used as a method for hydrocarbon detection.
引文
[1] Potter R K, Kopp G A, Kopp H G. Visible speech[M]. New York: Dover Publications, Inc.,1947.
[2] Partyka G, Gridley J, Lopez J. Interpretational applications of spectral decomposition inreservoir characterization[J]. The leading Edge,1999,18(3):353-360.
[3] Morlet J, Arens G, Fourgeau E, et al. Wave propagation and sampling theory—Part I:Complex signal and scattering in multilayered media[J]. Geophysics,1982,47(2):203-221.
[4] Abry P, Goncalves P, Flandrin P. Wavelet-based spectral analysis of1/f processes[C]. IEEEInternational Conference.1993.
[5] Stockwell R G, Mansinha L, Lowe R P. Localization of the complex spectrum: the Stransform[J]. IEEE Transactions on Signal Processing,1996,44(4):998-1001.
[6] Ville J. Theorie et Applications de la Notion de Signal Analytique[J]. Cables et Transmission,1948,2.
[7] Mallat S. A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way[M].Academic Press,2008.
[8] Sattar F, Salomonsson G. The use of a filter bank and the Wigner-Ville distribution fortime-frequency representation[J]. IEEE Transactions on Signal Processing,1999,47(6):1776-1783.
[9] Li Y, Li J, Zheng X. Channel system characterization using Wigner-Ville distribution-basedspectral decomposition[C]. SEG Technical Program Expanded Abstracts,2010,29(1):1418-1422.
[10] Neto E P D, Custaud M A, Frutoso J, et al. Smoothed pseudo Wigner-Ville distribution as analternative to Fourier transform in rats[J]. Autonomic Neuroscience-Basic&Clinical,2001,87(2-3):258-267.
[11] Marllat S, Zhang Z. Matching pursuits with time-frequency dictionaries[J]. Ieee Transactionson Antennas and Propagation,1993,41(12):3397-3415.
[12] Wang Y H. Seismic time-frequency spectral decomposition by matching pursuit[J].Geophysics,2007,72(1): V13-V20.
[13] Wang Y H. Multichannel matching pursuit for seismic trace decomposition[J]. Geophysics,2010,75(4): V61-V66.
[14] Huang N E. computer implicated empirical mode decomposition method, apparatus, andarticale of manufacture[J]. U.S. Patent Pending,1996.
[15] Huang N E, Shen Z, Long S R, et al. The empirical mode decomposition and the Hilbertspectrum for nonlinear and non-stationary time series analysis[J]. Proceedings of the RoyalSociety of London, Series A: Mathematical, Physical and Engineering Sciences,1998,454:903–995.
[16] Huang N E,Wu M L,Long S R, et al. A confidence limit for the empirical mode decomposition and hilbert spect ral analysis[J]. Proc R Soc London.2003,45(9):2317-2345.
[17] Song H B, Bai Y, Pinheiro L, et al. Analysis of ocean internal waves imaged by multichannelreflection seismics, using ensemble empirical mode decomposition[J]. Journal of Geophysicsand Engineering,2012,9(3):302-311.
[18] Bekara M, van der Baan M. Random and coherent noise attenuation by empirical modedecomposition[J]. Geophysics,2009,74(5): V89-V98.
[19]徐善辉.基于Hilbert-Huang变换的地震噪声衰减与薄层预测技术研究[D].吉林大学,2012.
[20] Battista B M, Knapp C, McGee T, et al. Application of the empirical mode decompositionand Hilbert-Huang transform to seismic reflection data[J]. Geophysics,2007,72(2):H29-H37.
[21] Wu Z, and Huang N E. Ensemble Empirical Mode Decomposition: a Noise-Assisted DataAnalysis Method[J]. Advances in Adaptive Data Analysis,2009,01:1-49.
[22] Torres M E, Colominas M A, Schlotthauer G, and Flandrin P. A complete ensemble empiricalmode decomposition with adaptive noise[J]. IEEE International Conference on Acoustics,2011:4144–4147.
[23] Han J, van der Baan M. Empirical mode decomposition for seismic time-frequencyanalysis[J]. Geophysics,2013,78(2): O9-O19.
[24] Donoho D L. Compressed sensing[J]. Ieee Transactions on Information Theory,2006,52(4):1289-1306.
[25] Baraniuk R G. Compressive sensing[J]. Ieee Signal Processing Magazine,2007,24(4):118-120+124.
[26] Portniaguine O, Castagna J. Inverse spectral decomposition[J]. SEG Technical ProgramExpanded Abstracts,2004,23(1):1786-1789.
[27] Bonar D C, Sacchi M D. Complex spectral decomposition via inversion strategies[C]. SEGTechnical Program Expanded Abstracts,2010,29(1):1408-1412.
[28] Han L, Han L G, Li Z. Inverse spectral decomposition with the SPGL1algorithm[J]. Journalof Geophysics and Engineering,2012,9(4):423-427.
[29] Beck A, Teboulle M. A Fast Iterative Shrinkage-Thresholding Algorithm for Linear InverseProblems[J]. SIAM Journal on Imaging Sciences,2009,2(1):183-202.
[30] Chen S S B, Donoho D L, Saunders M A. Atomic decomposition by basis pursuit[J]. SIAMJournal on Scientic Computing,1998,20:33-61.
[31] Van den Berg E. Friedlander M P. Probing the Pareto frontier for basis pursuit solutions[J].SIAM J. Sci. Comput.,2008,31(2):890-912.
[32] Kodera K, De Villedary C, Gendrin R. A new method for the numerical analysis ofnon-stationary signals[J]. Physics of the Earth and Planetary Interiors,1976,12(2-3):142-150.
[33] Flandrin P, Auger F, Chassande-Mottin E. Time-frequency reassignment: from principles toalgorithms[J]. Applications in Time-Frequency Signal Processing,2003:179-203.
[34] Auger F, Flandrin P. Improving the readability of time-frequency and time-scalerepresentations by the reassignment method[J]. Signal Processing, IEEE Transactions on,1995,43(5):1068-1089.
[35] Wu X Y, Liu T Y. Spectral decomposition of seismic data with reassigned smoothed pseudoWigner-Ville distribution[J]. Journal of Applied Geophysics,2009,68:386-393.
[36]周家雄,张国栋,尚帅.基于重排Gabor变换的高分辨率谱分解[J].世界地质,2013,32(1):153-157.
[37] Li Han, David Bonar and Mauricio D. Sacchi. Seismic denoising by time-frequencyreassignment[C]. CSEG Expanded Abstracts,2012.
[38] Canales L L. Random noise reduction[C].54th Annual International Meeting. SEG ExpandedAbstracts,1984.
[39] Galbraith M. Random noise attenuation by f-x prediction. A tutorial[C].61st AnnualInternational Meeting, SEG, ExpandedAbstracts,1991:1428-1431.
[40]国九英,周兴元,杨慧珠.三维f-x,y域随机噪音衰减[J].石油地球物理勘探,1995,30(2):207-215.
[41]国九英,周兴元.用f-x域预测技术消除随机噪音[J].石油地球物理勘探,1992,27(5):655-661.
[42]苏贵士,周兴元,李承楚.频率空间三维F-xyz域预测去噪技术[J].石油地球物理勘探,1998,33(1):95-103.
[43] Jones I F, Levy S. Signal-to-noise ratio enhancement in multi channel seismic data via theKarhunen-Loeve transform[J]. Geophysical Prospecting,1987,35(1):12-32.
[44]岳承祺，唐权钧。用K-L变换提高多道地震记录的信噪比[J].石油地球物理勘探,1988,23(5):560-568.
[45]杨文采.非线性K-L滤波及其在反射地震资料处理中的应用[J].石油物探,1996,35(2):17-26.
[46] Lu W K. Adaptive noise attenuation of seismic images based on singular valuedecomposition and texture direction detection[J]. Journal of Geophysics and Engineering,2006,3(1),28–34.
[47] Yu Z, McMechan G A, Ferguson J F, et al. Adaptive wavelet filtering of seismic data in thewavelet transform domain[J]. Journal of Seismic Exploration,2002,11(3):223-246.
[48] Yu Z, Ferguson J, Mcmechan G, and Anno P. Wavelet-Radon domain dealiasing andinterpolation of seismic data[J]. Geophysics,2007,72(2): V41-V49.
[49] Pazos A, Gonzalez M J, and Alguacil G. Non-linear filter, using the wavelet transform,applied to seismological records[J]. Journal of Seismology,2003,7(4):413-429.
[50] Wang D L, Tong Z F, Tang C, et al. An iterative curvelet thresholding algorithm for seismicrandom noise attenuation[J]. Applied Geophysics,2010,7(4):315-324.
[51] Zhang Z Y, Zhang X D, Yu H Y, et al. Noise suppression based on a fast discrete curvelettransform[J]. Journal of Geophysics and Engineering,2010,7(1):105-112.
[52] Herrmann F J, Wang D L, Hennenfent G, et al. Curvelet-based seismic data processing: Amultiscale and nonlinear approach[J]. Geophysics,2008,73(1): A1-A5.
[53] Donno D, Chauris H, and Noble M. Curvelet-based multiple prediction[J]. Geophysics,2010,75(6): Wb255-Wb263.
[54] Yilmaz O Z. Seismic data analysis processing, inversion, and interpretation of seismicdata[M]. Society of Exploration Geophysicists,2001.
[55] Stewart R R, Schieck D G.3-D F-K filtering[J]. Journal of Seismic Exploration,1993,2:41-54.
[56] Chapman C H. Generalized Radon transforms and slant stacks[J]. Geophys. J. Roy. Astr. Soc.,1981,54(2):481-518.
[57] Stoffa P L, Bubl P, diebold J B and Wenzel F. Diret mapping of seismic data to the domain ofintercept time and ray parameter plane-wave decomposition[J]. Geophysics,1981,46(2):255-267.
[58] Trad D, Sacchi M D, and Ulrych T J. A hybrid linear-hyperbolic radon transform[J]. Journalof Seismic Exploration,2001,9(4):303-318.
[59] Wang J F, Ng M, and Perz M. Seismic data interpolation by greedy local Radon transform[J].Geophysics,2010,75(6): Wb225-Wb234.
[60] Shankar U, Singh S S, and Sain K. Signal enhancement and multiple suppression usingRadon transform: an application to marine multichannel seismic data[J]. Marine GeophysicalResearches,2009,30(2):85-93.
[61] Xiong D, Zhao W, and Zhang J F. Hybrid-domain high-resolution parabolic Radon transformand its application to demultiple[J]. Chinese Journal of Geophysics-Chinese Edition,2009,52(4):1068-1077.
[62] Michell A R, Kelamis P G. Efficient tau-p hyperbolic velocity filtering[J]. Geophysics,1990,55(5):619-625.
[63] Elboth T, Presterud I V, and Hermansen D. Time-frequency seismic data de-noising[J].Geophysical Prospecting,2010,58(3):441-453.
[64] Parolai S. Denoising of Seismograms Using the S Transform[J]. Bulletin of the SeismologicalSociety of America,2009,99(1):226-234.
[65] Wang Y H. Seismic time-frequency spectral decomposition by matching pursuit[J].Geophysics,2007,72(1): V13-V20.
[66] Kulesh M, Diallo M S, Holschneider M, et al. Polarization analysis in the wavelet domainbased on the adaptive covariance method[J]. Geophysical Journal International,2007,170(2):667-678.
[67] Yu Z and Garossino P G A. High-energy noise attenuation of seismic data in thewavelet-transform domain[J]. Integrated Computer-Aided Engineering,2005,12(1):57-67.
[68] Pinnegar C R and Eaton D W. Application of the S transform to prestack noise attenuationfiltering[J]. Journal of Geophysical Research-Solid Earth,2003,108(B9):562-569.
[69] Galiana M, Herranz J R, Giner J, et al. De-noising of short-period seismograms by waveletpacket transform[J]. Bulletin of the Seismological Society of America,2003,93(6):2554-2562.
[70] Corso G, Kuhn P S, Lucena L S, et al. Seismic ground roll time-frequency filtering using thegaussian wavelet transform[J]. Physica a-Statistical Mechanics and Its Applications,2003,318(3-4):551-561.
[71]黄绪德.反褶积与地震道反演[M].北京:石油工业出版社.1992.
[72]李庆忠.走向精确勘探的道路[M].北京:石油工业出版社.1994.
[73] Futerman W I. Dispersive body waves[J]. Journal of Geophysical Research,1962,67(13):5279-5291.
[74] Tonn R. The determination of the seismic quality factor Q from Vsp data: a comparison ofdifferent computational methods[J]. Geophysical Prospecting,1991,39(1):1-27.
[75] Zhang C, Ulrych T J. Estimation of quality factors from CMP records[J]. Geophysics,2002,67(5):1542-1547.
[76] Liu Y, Wei X C. Interval Q Inversion From CMP Gathers: part I-absorption equation[C]. SEGAnnual Meeting.2005.
[77] Liu Y, Wei X C. Interval Q Inversion From CMP Gathers: Part II-Absorption Equation[C].SEG Annual Meeting.2005.
[78] Hale D. Q-adaptive deconvolution[R]. Stanford Exploration Rroject Report,1982,30:133-158.
[79] Bickel S, Natarajan R. Plane-wave Q deconvolution[J]. Geophysics,1985,50(9):1426-1439.
[80] Wang Y. A stable and efficient approach of inverse Q filtering[J]. Geophysics,2002,67(2):657-663.
[81] Wang Y. Inverse Q-filter for seismic resolution enhancement[J]. Geophysics,2006,71(3):V51-V60.
[82]李鲲鹏,张学工,李衍达.基于小波包分解的地层吸收补偿[J].地球物理学报,2000,43(4):542~549
[83]刘喜武,年静波,刘洪.基于广义S变换的吸收衰减补偿方法[J].石油物探,2006,45(1):9~14.
[84] Tian Jianhua, Song Wei, Yang Feizhou. Enhancing the resolution of seismic data based on thegeneralized S-transform[J]. Pet. Sci.,2009,6:153~157.
[85]汪小将,陈宝书,曹思远. HHT振幅频率恢复处理技术研究与应用[J].中国海上油气,2009,21(1):19-22.
[86] Chopra S, Castagna J P, Portniaguine O. Seismic resolution and thin-bed reflectivityinversion[C]. CSEG Expanded Abstracts,2006.
[87] Puryear C, Castagna J P. Layer-thickness determination and stratigraphic interpretation usingspectral inversion: Theory and application[J]. Geophysics,2008,73(2):37-48.
[88] Chopra S, Castagna J P, Xu Y. Thin-bed reflectivity inversion and some application[J]. FirstBreak,2009,27(5):17-24.
[89] Zoeppritz K. On the reflection and penetration of seismic waves through unstable layers[J].Erdbebenwellen VIIIB, Goettinger Nachr.,1919,1:66-84.
[90] Koefoed O. On the effect of poisson's ratios of rock strata on the reflection coefficients ofplane waves[J]. Geophysical Prospecting,1955,3(4):381-387.
[91] Bortfeld R. Approximations to the Reflection and Transmission Coefficients of PlaneLongitudinal and Transverse Waves[J]. Geophysical Prospecting,1961,9(4):485-502.
[92] Ostrander W J. Plane-wave reflection coefficients for gas sands at nonnormal angles ofincidence[J]. Geophysics,1984,49(10):1637-1648.
[93] Shuey R T. A simplification of the Zoeppritz equations[J]. Geophysics,1985,50(4):609-614.
[94] Smith G, Gidlow P. Weighted stacking for rock property estimation and detection of gas[J].Geophysical Prospecting,1987,35(9):993-1014.
[95] Hilterman F. Is AVO the seismic signature of lithology? A case history of Ship Shoal-SouthAddition[J]. The Leading Edge,1990,9(6):15-22.
[96]郑晓东. Zoeppritz方程的近似及其应用[J].石油地球物理勘探,1991,26(2):126-144.
[97] Mallick S. A simple approximation to the P-wave reflection coefficient and its implication inthe inversion of amplitude variation with offset data[J]. Geophysics,1993,58(4):544-552.
[98] Chapman M, Zatsepin S V, Crampin S. Derivation of a microstructural poroelastic model[J].Geophysical Journal International,2002,151(2):427-451.
[99] Chapman M. Frequency-dependent anisotropy due to meso-scale fractures in the presence ofequant porosity[J]. Geophysical Prospecting,2003,51(1):369-379.
[100] Chapman M, Maultzsch S, Liu E, et al. The effect of fluid saturation in an anisotropicmulti-scale equant porosity model[J]. Journal of Applied Geophysics,2003,54(3-4):191–202.
[101] Chapman M, Liu E, Li X Y. The influence of fluid-sensitive dispersion and attenuation onAVO analysis[J]. Geophysical Journal International,2006,167(1):89-105.
[102] Muller T M, Gurevich B. One-dimensional random patchy saturation model for velocityand attenuation in porous rocks[J]. Geophysics,2004,69:1166–1172.
[103] Muller T M, Lambert G, Gurevich B. Dynamic permeability of porous rocks and its seismicsignatures[J]. Geophysics,2007,72(5): E149–E158.
[104] Carcione J M, Picotti S. P-wave seismic attenuation by slowwave diffusion: Effects ofinhomogeneous rock properties[J]. Geophysics,2006,71(3): O1–O8.
[105] Norris A N. Low-frequency dispersion and attenuation in partially saturated rocks[J].Journal of the Acoustical Society of America,1993,94:359–370.
[106] Wilson A. Theory and Methods of Frequency-Dependent AVO Inversion[D]. England:University of Edinburgh,2010.
[107]吴小羊.基于频谱分析技术的频散AVO反演研究[D].北京:中国地质大学,2011.
[108]宁媛丽.频散介质基于反演谱分解的AVO方法研究[D].长春:吉林大学,2012.
[109] Gill P R, Wang A, Molnar A. The In-Crowd Algorithm for Fast Basis Pursuit Denoising[J].Signal Processing, IEEE Transactions on,2011,59(10):4595-4605.
[110] Rioul O, Flandrin P. Time-scale energy distributions: a general class extending wavelettransforms[J]. IEEE transactions on signal processing,1992,40(7):1746-1757.
[111] Flandrin, P., F. Auger, and E. Chassande-Mottin, Time-frequency reassignment:Fromprinciples to algorithms, in A. Papandreou-Suppappola, ed., Applications intime-frequency signal processing: CRC Press,2003:179–203.
[112] Liu C C, Han M, Chen B S, Han L G, Shang S. Reassigned wavelet spectral decompositionand its application in hydrocarbon detection[C]. SEG Technical Program ExpandedAbstracts,2013.
[113] Daubechies I, Lu J, Wu H T, Synchrosqueezed wavelet transforms: An empirical modedecomposition-like tool: Applied and Computational Harmonic Analysis[J],2011,30:243–261.
[114] Shang S, Han L G, Hu W. Seismic data analysis using synchrosqueezing wavelettransform[C]. SEG Technical Program Expanded Abstracts,2013.
[115] Herrera R H, Han J J, van der Baan M. Application of the synchrosqueezing transform inseismic time-frequency analysis[J]. Geophysics,2014,79(3): V55-V64.
[116] Daubechies I, Maes S. A nonlinear squeezing of the continuous wavelet transform based onauditory nerve models[J]. in Wavelets in Medicine and Biology,1996:527-546.
[117] Buades A, Coll B, Morel J M. A non-local algorithm for image denoising[C]. IEEEComputer Society Conference on Computer Vision and Pattern Recognition,2005:60-65.
[118] Buades A, Coll B, Morel J M. A review of image denoising algorithms, with a new one[J].SIAM Journal on Multiscale Modeling and Simulation,2005,4(2):490-530.
[119] Mahmoudi M, Sapiro G. Fast image and video denoising via nonlocal means of similarneighborhoods[J]. IEEE Signal Processing Letters,2005,12(12):839-842.
[120] Buades A, Coll B, Morel J M. Image denoising methods. A new nonlocal principle[J].SIAM Review,2010,52(1):113–147.
[121] Wang J, Guo Y, Ying Y, et al. Fast non-local algorithm for image denoising[C]. IEEEInternational Conference on Image Processing,2006:1429-1432.
[122] Sheng B, Li P, Sun H. Image-Based Material Restyling with Fast Non-local MeansFiltering[J]. ICIG,2009:841-846.
[123] Coupé P, Yger P, Prima S, et al. An optimized blockwise nonlocal means denoising filter for3-D magnetic resonance images[J]. IEEE Transactions on Medical Imaging,2008,27(4):425-441.
[124] Deledalle C. A, Denis L, Tupin F. Nl-insar:Nonlocal interferogram estimation[J]. IEEETransactions on Geoscience and Remote Sensing,2011,49(4):1441–1452.
[125] Bonar D, Sacchi M. Denoising seismic data using the nonlocal means algorithm[J].Geophysics,2012,77(1): A5-A8.
[126] Efros A. A, Leung T. K. Texture synthesis by non-parametric sampling[J]. ICCV,1999:1033-1038.
[127] Buades A, Coll B, Morel J M. Image and movie denoising by nonlocal means[J]. IJCV,2008,76(2):123-139.
[128] Manjón J V, Coupé P, Bonmatí M L, et al. Adaptive non-local means denoising of MRimages with spatially varying noise levels[J]. Journal of Magnetic Resonance Imaging,2010,31(1):192-203.
[129] Rutherford S R, Williams R H. Amplitude-versus-offset variations in gas sands[J].Geophysics,1989,54:680-688.
[130] Batzle M, Hofmann R, Han D, Castagna J. Fluids and frequency dependent seismic velocityof rocks[J]. The Leading Edge,2001,20:168–171.
[131] Ren H T, Goloshubin G, Hilerman F J. Poroelastic analysis of amplitude-versus-frequencyvariations[J]. Geophysics,2009,74(6): N41-N48.
[132] Teng L, Yang X C, et al. The frequency-angle-depended reflection of P wave influid-saturated porous rock[C]. SEG Expanded Abstracts,2013.
[133] Zong Z Y, Yin X Y, Wu G C. AVO inversion and poroelasticity with P-and S-wavemoduli[J]. Geophysics,2012,77(6): N17-N24.
[2] Partyka G, Gridley J, Lopez J. Interpretational applications of spectral decomposition inreservoir characterization[J]. The leading Edge,1999,18(3):353-360.
[3] Morlet J, Arens G, Fourgeau E, et al. Wave propagation and sampling theory—Part I:Complex signal and scattering in multilayered media[J]. Geophysics,1982,47(2):203-221.
[4] Abry P, Goncalves P, Flandrin P. Wavelet-based spectral analysis of1/f processes[C]. IEEEInternational Conference.1993.
[5] Stockwell R G, Mansinha L, Lowe R P. Localization of the complex spectrum: the Stransform[J]. IEEE Transactions on Signal Processing,1996,44(4):998-1001.
[6] Ville J. Theorie et Applications de la Notion de Signal Analytique[J]. Cables et Transmission,1948,2.
[7] Mallat S. A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way[M].Academic Press,2008.
[8] Sattar F, Salomonsson G. The use of a filter bank and the Wigner-Ville distribution fortime-frequency representation[J]. IEEE Transactions on Signal Processing,1999,47(6):1776-1783.
[9] Li Y, Li J, Zheng X. Channel system characterization using Wigner-Ville distribution-basedspectral decomposition[C]. SEG Technical Program Expanded Abstracts,2010,29(1):1418-1422.
[10] Neto E P D, Custaud M A, Frutoso J, et al. Smoothed pseudo Wigner-Ville distribution as analternative to Fourier transform in rats[J]. Autonomic Neuroscience-Basic&Clinical,2001,87(2-3):258-267.
[11] Marllat S, Zhang Z. Matching pursuits with time-frequency dictionaries[J]. Ieee Transactionson Antennas and Propagation,1993,41(12):3397-3415.
[12] Wang Y H. Seismic time-frequency spectral decomposition by matching pursuit[J].Geophysics,2007,72(1): V13-V20.
[13] Wang Y H. Multichannel matching pursuit for seismic trace decomposition[J]. Geophysics,2010,75(4): V61-V66.
[14] Huang N E. computer implicated empirical mode decomposition method, apparatus, andarticale of manufacture[J]. U.S. Patent Pending,1996.
[15] Huang N E, Shen Z, Long S R, et al. The empirical mode decomposition and the Hilbertspectrum for nonlinear and non-stationary time series analysis[J]. Proceedings of the RoyalSociety of London, Series A: Mathematical, Physical and Engineering Sciences,1998,454:903–995.
[16] Huang N E,Wu M L,Long S R, et al. A confidence limit for the empirical mode decomposition and hilbert spect ral analysis[J]. Proc R Soc London.2003,45(9):2317-2345.
[17] Song H B, Bai Y, Pinheiro L, et al. Analysis of ocean internal waves imaged by multichannelreflection seismics, using ensemble empirical mode decomposition[J]. Journal of Geophysicsand Engineering,2012,9(3):302-311.
[18] Bekara M, van der Baan M. Random and coherent noise attenuation by empirical modedecomposition[J]. Geophysics,2009,74(5): V89-V98.
[19]徐善辉.基于Hilbert-Huang变换的地震噪声衰减与薄层预测技术研究[D].吉林大学,2012.
[20] Battista B M, Knapp C, McGee T, et al. Application of the empirical mode decompositionand Hilbert-Huang transform to seismic reflection data[J]. Geophysics,2007,72(2):H29-H37.
[21] Wu Z, and Huang N E. Ensemble Empirical Mode Decomposition: a Noise-Assisted DataAnalysis Method[J]. Advances in Adaptive Data Analysis,2009,01:1-49.
[22] Torres M E, Colominas M A, Schlotthauer G, and Flandrin P. A complete ensemble empiricalmode decomposition with adaptive noise[J]. IEEE International Conference on Acoustics,2011:4144–4147.
[23] Han J, van der Baan M. Empirical mode decomposition for seismic time-frequencyanalysis[J]. Geophysics,2013,78(2): O9-O19.
[24] Donoho D L. Compressed sensing[J]. Ieee Transactions on Information Theory,2006,52(4):1289-1306.
[25] Baraniuk R G. Compressive sensing[J]. Ieee Signal Processing Magazine,2007,24(4):118-120+124.
[26] Portniaguine O, Castagna J. Inverse spectral decomposition[J]. SEG Technical ProgramExpanded Abstracts,2004,23(1):1786-1789.
[27] Bonar D C, Sacchi M D. Complex spectral decomposition via inversion strategies[C]. SEGTechnical Program Expanded Abstracts,2010,29(1):1408-1412.
[28] Han L, Han L G, Li Z. Inverse spectral decomposition with the SPGL1algorithm[J]. Journalof Geophysics and Engineering,2012,9(4):423-427.
[29] Beck A, Teboulle M. A Fast Iterative Shrinkage-Thresholding Algorithm for Linear InverseProblems[J]. SIAM Journal on Imaging Sciences,2009,2(1):183-202.
[30] Chen S S B, Donoho D L, Saunders M A. Atomic decomposition by basis pursuit[J]. SIAMJournal on Scientic Computing,1998,20:33-61.
[31] Van den Berg E. Friedlander M P. Probing the Pareto frontier for basis pursuit solutions[J].SIAM J. Sci. Comput.,2008,31(2):890-912.
[32] Kodera K, De Villedary C, Gendrin R. A new method for the numerical analysis ofnon-stationary signals[J]. Physics of the Earth and Planetary Interiors,1976,12(2-3):142-150.
[33] Flandrin P, Auger F, Chassande-Mottin E. Time-frequency reassignment: from principles toalgorithms[J]. Applications in Time-Frequency Signal Processing,2003:179-203.
[34] Auger F, Flandrin P. Improving the readability of time-frequency and time-scalerepresentations by the reassignment method[J]. Signal Processing, IEEE Transactions on,1995,43(5):1068-1089.
[35] Wu X Y, Liu T Y. Spectral decomposition of seismic data with reassigned smoothed pseudoWigner-Ville distribution[J]. Journal of Applied Geophysics,2009,68:386-393.
[36]周家雄,张国栋,尚帅.基于重排Gabor变换的高分辨率谱分解[J].世界地质,2013,32(1):153-157.
[37] Li Han, David Bonar and Mauricio D. Sacchi. Seismic denoising by time-frequencyreassignment[C]. CSEG Expanded Abstracts,2012.
[38] Canales L L. Random noise reduction[C].54th Annual International Meeting. SEG ExpandedAbstracts,1984.
[39] Galbraith M. Random noise attenuation by f-x prediction. A tutorial[C].61st AnnualInternational Meeting, SEG, ExpandedAbstracts,1991:1428-1431.
[40]国九英,周兴元,杨慧珠.三维f-x,y域随机噪音衰减[J].石油地球物理勘探,1995,30(2):207-215.
[41]国九英,周兴元.用f-x域预测技术消除随机噪音[J].石油地球物理勘探,1992,27(5):655-661.
[42]苏贵士,周兴元,李承楚.频率空间三维F-xyz域预测去噪技术[J].石油地球物理勘探,1998,33(1):95-103.
[43] Jones I F, Levy S. Signal-to-noise ratio enhancement in multi channel seismic data via theKarhunen-Loeve transform[J]. Geophysical Prospecting,1987,35(1):12-32.
[44]岳承祺，唐权钧。用K-L变换提高多道地震记录的信噪比[J].石油地球物理勘探,1988,23(5):560-568.
[45]杨文采.非线性K-L滤波及其在反射地震资料处理中的应用[J].石油物探,1996,35(2):17-26.
[46] Lu W K. Adaptive noise attenuation of seismic images based on singular valuedecomposition and texture direction detection[J]. Journal of Geophysics and Engineering,2006,3(1),28–34.
[47] Yu Z, McMechan G A, Ferguson J F, et al. Adaptive wavelet filtering of seismic data in thewavelet transform domain[J]. Journal of Seismic Exploration,2002,11(3):223-246.
[48] Yu Z, Ferguson J, Mcmechan G, and Anno P. Wavelet-Radon domain dealiasing andinterpolation of seismic data[J]. Geophysics,2007,72(2): V41-V49.
[49] Pazos A, Gonzalez M J, and Alguacil G. Non-linear filter, using the wavelet transform,applied to seismological records[J]. Journal of Seismology,2003,7(4):413-429.
[50] Wang D L, Tong Z F, Tang C, et al. An iterative curvelet thresholding algorithm for seismicrandom noise attenuation[J]. Applied Geophysics,2010,7(4):315-324.
[51] Zhang Z Y, Zhang X D, Yu H Y, et al. Noise suppression based on a fast discrete curvelettransform[J]. Journal of Geophysics and Engineering,2010,7(1):105-112.
[52] Herrmann F J, Wang D L, Hennenfent G, et al. Curvelet-based seismic data processing: Amultiscale and nonlinear approach[J]. Geophysics,2008,73(1): A1-A5.
[53] Donno D, Chauris H, and Noble M. Curvelet-based multiple prediction[J]. Geophysics,2010,75(6): Wb255-Wb263.
[54] Yilmaz O Z. Seismic data analysis processing, inversion, and interpretation of seismicdata[M]. Society of Exploration Geophysicists,2001.
[55] Stewart R R, Schieck D G.3-D F-K filtering[J]. Journal of Seismic Exploration,1993,2:41-54.
[56] Chapman C H. Generalized Radon transforms and slant stacks[J]. Geophys. J. Roy. Astr. Soc.,1981,54(2):481-518.
[57] Stoffa P L, Bubl P, diebold J B and Wenzel F. Diret mapping of seismic data to the domain ofintercept time and ray parameter plane-wave decomposition[J]. Geophysics,1981,46(2):255-267.
[58] Trad D, Sacchi M D, and Ulrych T J. A hybrid linear-hyperbolic radon transform[J]. Journalof Seismic Exploration,2001,9(4):303-318.
[59] Wang J F, Ng M, and Perz M. Seismic data interpolation by greedy local Radon transform[J].Geophysics,2010,75(6): Wb225-Wb234.
[60] Shankar U, Singh S S, and Sain K. Signal enhancement and multiple suppression usingRadon transform: an application to marine multichannel seismic data[J]. Marine GeophysicalResearches,2009,30(2):85-93.
[61] Xiong D, Zhao W, and Zhang J F. Hybrid-domain high-resolution parabolic Radon transformand its application to demultiple[J]. Chinese Journal of Geophysics-Chinese Edition,2009,52(4):1068-1077.
[62] Michell A R, Kelamis P G. Efficient tau-p hyperbolic velocity filtering[J]. Geophysics,1990,55(5):619-625.
[63] Elboth T, Presterud I V, and Hermansen D. Time-frequency seismic data de-noising[J].Geophysical Prospecting,2010,58(3):441-453.
[64] Parolai S. Denoising of Seismograms Using the S Transform[J]. Bulletin of the SeismologicalSociety of America,2009,99(1):226-234.
[65] Wang Y H. Seismic time-frequency spectral decomposition by matching pursuit[J].Geophysics,2007,72(1): V13-V20.
[66] Kulesh M, Diallo M S, Holschneider M, et al. Polarization analysis in the wavelet domainbased on the adaptive covariance method[J]. Geophysical Journal International,2007,170(2):667-678.
[67] Yu Z and Garossino P G A. High-energy noise attenuation of seismic data in thewavelet-transform domain[J]. Integrated Computer-Aided Engineering,2005,12(1):57-67.
[68] Pinnegar C R and Eaton D W. Application of the S transform to prestack noise attenuationfiltering[J]. Journal of Geophysical Research-Solid Earth,2003,108(B9):562-569.
[69] Galiana M, Herranz J R, Giner J, et al. De-noising of short-period seismograms by waveletpacket transform[J]. Bulletin of the Seismological Society of America,2003,93(6):2554-2562.
[70] Corso G, Kuhn P S, Lucena L S, et al. Seismic ground roll time-frequency filtering using thegaussian wavelet transform[J]. Physica a-Statistical Mechanics and Its Applications,2003,318(3-4):551-561.
[71]黄绪德.反褶积与地震道反演[M].北京:石油工业出版社.1992.
[72]李庆忠.走向精确勘探的道路[M].北京:石油工业出版社.1994.
[73] Futerman W I. Dispersive body waves[J]. Journal of Geophysical Research,1962,67(13):5279-5291.
[74] Tonn R. The determination of the seismic quality factor Q from Vsp data: a comparison ofdifferent computational methods[J]. Geophysical Prospecting,1991,39(1):1-27.
[75] Zhang C, Ulrych T J. Estimation of quality factors from CMP records[J]. Geophysics,2002,67(5):1542-1547.
[76] Liu Y, Wei X C. Interval Q Inversion From CMP Gathers: part I-absorption equation[C]. SEGAnnual Meeting.2005.
[77] Liu Y, Wei X C. Interval Q Inversion From CMP Gathers: Part II-Absorption Equation[C].SEG Annual Meeting.2005.
[78] Hale D. Q-adaptive deconvolution[R]. Stanford Exploration Rroject Report,1982,30:133-158.
[79] Bickel S, Natarajan R. Plane-wave Q deconvolution[J]. Geophysics,1985,50(9):1426-1439.
[80] Wang Y. A stable and efficient approach of inverse Q filtering[J]. Geophysics,2002,67(2):657-663.
[81] Wang Y. Inverse Q-filter for seismic resolution enhancement[J]. Geophysics,2006,71(3):V51-V60.
[82]李鲲鹏,张学工,李衍达.基于小波包分解的地层吸收补偿[J].地球物理学报,2000,43(4):542~549
[83]刘喜武,年静波,刘洪.基于广义S变换的吸收衰减补偿方法[J].石油物探,2006,45(1):9~14.
[84] Tian Jianhua, Song Wei, Yang Feizhou. Enhancing the resolution of seismic data based on thegeneralized S-transform[J]. Pet. Sci.,2009,6:153~157.
[85]汪小将,陈宝书,曹思远. HHT振幅频率恢复处理技术研究与应用[J].中国海上油气,2009,21(1):19-22.
[86] Chopra S, Castagna J P, Portniaguine O. Seismic resolution and thin-bed reflectivityinversion[C]. CSEG Expanded Abstracts,2006.
[87] Puryear C, Castagna J P. Layer-thickness determination and stratigraphic interpretation usingspectral inversion: Theory and application[J]. Geophysics,2008,73(2):37-48.
[88] Chopra S, Castagna J P, Xu Y. Thin-bed reflectivity inversion and some application[J]. FirstBreak,2009,27(5):17-24.
[89] Zoeppritz K. On the reflection and penetration of seismic waves through unstable layers[J].Erdbebenwellen VIIIB, Goettinger Nachr.,1919,1:66-84.
[90] Koefoed O. On the effect of poisson's ratios of rock strata on the reflection coefficients ofplane waves[J]. Geophysical Prospecting,1955,3(4):381-387.
[91] Bortfeld R. Approximations to the Reflection and Transmission Coefficients of PlaneLongitudinal and Transverse Waves[J]. Geophysical Prospecting,1961,9(4):485-502.
[92] Ostrander W J. Plane-wave reflection coefficients for gas sands at nonnormal angles ofincidence[J]. Geophysics,1984,49(10):1637-1648.
[93] Shuey R T. A simplification of the Zoeppritz equations[J]. Geophysics,1985,50(4):609-614.
[94] Smith G, Gidlow P. Weighted stacking for rock property estimation and detection of gas[J].Geophysical Prospecting,1987,35(9):993-1014.
[95] Hilterman F. Is AVO the seismic signature of lithology? A case history of Ship Shoal-SouthAddition[J]. The Leading Edge,1990,9(6):15-22.
[96]郑晓东. Zoeppritz方程的近似及其应用[J].石油地球物理勘探,1991,26(2):126-144.
[97] Mallick S. A simple approximation to the P-wave reflection coefficient and its implication inthe inversion of amplitude variation with offset data[J]. Geophysics,1993,58(4):544-552.
[98] Chapman M, Zatsepin S V, Crampin S. Derivation of a microstructural poroelastic model[J].Geophysical Journal International,2002,151(2):427-451.
[99] Chapman M. Frequency-dependent anisotropy due to meso-scale fractures in the presence ofequant porosity[J]. Geophysical Prospecting,2003,51(1):369-379.
[100] Chapman M, Maultzsch S, Liu E, et al. The effect of fluid saturation in an anisotropicmulti-scale equant porosity model[J]. Journal of Applied Geophysics,2003,54(3-4):191–202.
[101] Chapman M, Liu E, Li X Y. The influence of fluid-sensitive dispersion and attenuation onAVO analysis[J]. Geophysical Journal International,2006,167(1):89-105.
[102] Muller T M, Gurevich B. One-dimensional random patchy saturation model for velocityand attenuation in porous rocks[J]. Geophysics,2004,69:1166–1172.
[103] Muller T M, Lambert G, Gurevich B. Dynamic permeability of porous rocks and its seismicsignatures[J]. Geophysics,2007,72(5): E149–E158.
[104] Carcione J M, Picotti S. P-wave seismic attenuation by slowwave diffusion: Effects ofinhomogeneous rock properties[J]. Geophysics,2006,71(3): O1–O8.
[105] Norris A N. Low-frequency dispersion and attenuation in partially saturated rocks[J].Journal of the Acoustical Society of America,1993,94:359–370.
[106] Wilson A. Theory and Methods of Frequency-Dependent AVO Inversion[D]. England:University of Edinburgh,2010.
[107]吴小羊.基于频谱分析技术的频散AVO反演研究[D].北京:中国地质大学,2011.
[108]宁媛丽.频散介质基于反演谱分解的AVO方法研究[D].长春:吉林大学,2012.
[109] Gill P R, Wang A, Molnar A. The In-Crowd Algorithm for Fast Basis Pursuit Denoising[J].Signal Processing, IEEE Transactions on,2011,59(10):4595-4605.
[110] Rioul O, Flandrin P. Time-scale energy distributions: a general class extending wavelettransforms[J]. IEEE transactions on signal processing,1992,40(7):1746-1757.
[111] Flandrin, P., F. Auger, and E. Chassande-Mottin, Time-frequency reassignment:Fromprinciples to algorithms, in A. Papandreou-Suppappola, ed., Applications intime-frequency signal processing: CRC Press,2003:179–203.
[112] Liu C C, Han M, Chen B S, Han L G, Shang S. Reassigned wavelet spectral decompositionand its application in hydrocarbon detection[C]. SEG Technical Program ExpandedAbstracts,2013.
[113] Daubechies I, Lu J, Wu H T, Synchrosqueezed wavelet transforms: An empirical modedecomposition-like tool: Applied and Computational Harmonic Analysis[J],2011,30:243–261.
[114] Shang S, Han L G, Hu W. Seismic data analysis using synchrosqueezing wavelettransform[C]. SEG Technical Program Expanded Abstracts,2013.
[115] Herrera R H, Han J J, van der Baan M. Application of the synchrosqueezing transform inseismic time-frequency analysis[J]. Geophysics,2014,79(3): V55-V64.
[116] Daubechies I, Maes S. A nonlinear squeezing of the continuous wavelet transform based onauditory nerve models[J]. in Wavelets in Medicine and Biology,1996:527-546.
[117] Buades A, Coll B, Morel J M. A non-local algorithm for image denoising[C]. IEEEComputer Society Conference on Computer Vision and Pattern Recognition,2005:60-65.
[118] Buades A, Coll B, Morel J M. A review of image denoising algorithms, with a new one[J].SIAM Journal on Multiscale Modeling and Simulation,2005,4(2):490-530.
[119] Mahmoudi M, Sapiro G. Fast image and video denoising via nonlocal means of similarneighborhoods[J]. IEEE Signal Processing Letters,2005,12(12):839-842.
[120] Buades A, Coll B, Morel J M. Image denoising methods. A new nonlocal principle[J].SIAM Review,2010,52(1):113–147.
[121] Wang J, Guo Y, Ying Y, et al. Fast non-local algorithm for image denoising[C]. IEEEInternational Conference on Image Processing,2006:1429-1432.
[122] Sheng B, Li P, Sun H. Image-Based Material Restyling with Fast Non-local MeansFiltering[J]. ICIG,2009:841-846.
[123] Coupé P, Yger P, Prima S, et al. An optimized blockwise nonlocal means denoising filter for3-D magnetic resonance images[J]. IEEE Transactions on Medical Imaging,2008,27(4):425-441.
[124] Deledalle C. A, Denis L, Tupin F. Nl-insar:Nonlocal interferogram estimation[J]. IEEETransactions on Geoscience and Remote Sensing,2011,49(4):1441–1452.
[125] Bonar D, Sacchi M. Denoising seismic data using the nonlocal means algorithm[J].Geophysics,2012,77(1): A5-A8.
[126] Efros A. A, Leung T. K. Texture synthesis by non-parametric sampling[J]. ICCV,1999:1033-1038.
[127] Buades A, Coll B, Morel J M. Image and movie denoising by nonlocal means[J]. IJCV,2008,76(2):123-139.
[128] Manjón J V, Coupé P, Bonmatí M L, et al. Adaptive non-local means denoising of MRimages with spatially varying noise levels[J]. Journal of Magnetic Resonance Imaging,2010,31(1):192-203.
[129] Rutherford S R, Williams R H. Amplitude-versus-offset variations in gas sands[J].Geophysics,1989,54:680-688.
[130] Batzle M, Hofmann R, Han D, Castagna J. Fluids and frequency dependent seismic velocityof rocks[J]. The Leading Edge,2001,20:168–171.
[131] Ren H T, Goloshubin G, Hilerman F J. Poroelastic analysis of amplitude-versus-frequencyvariations[J]. Geophysics,2009,74(6): N41-N48.
[132] Teng L, Yang X C, et al. The frequency-angle-depended reflection of P wave influid-saturated porous rock[C]. SEG Expanded Abstracts,2013.
[133] Zong Z Y, Yin X Y, Wu G C. AVO inversion and poroelasticity with P-and S-wavemoduli[J]. Geophysics,2012,77(6): N17-N24.
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