最小二乘约束下的频谱分析技术及其应用
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摘要
时频分析方法是地震数据处理和解释领域的一个重要工具.本文基于最小二乘原理和正则化方法,提出了约束最小二乘时频分析方法.该方法是在有限支撑、非正交基函数空间下,通过迭代整形正则化方法求取信号傅里叶系数的一种时频分析方法.该方法是短时傅里叶变换时频分析方法的延伸和发展,具有较高的时频分析精度,能较准确地识别信号的频谱特征.理论分析和实际资料应用表明,该方法能够较精确的刻画储层的位置和边界,能够进一步提高储层预测的精度.
Time-frequency analysis is an important technical tool in seismic data analysis area.In this paper,we proposed the least square constrained method(LSCM)based on the least square and shaping regularization principles.This new method intends for computing the Fourier coefficients of interest signal under finite supported and non-orthogonal base space according to the least square and regularization principles.This is an extension of the short time Fourier transform(STFT).Comparisons with STFT using synthetic signals and real seismic data validates that the proposed method has better timefrequency resolution,can better identify the reservoir's boundaries and locations,further improve the accuracy of reservoir prediction.
Time-frequency analysis is an important technical tool in seismic data analysis area.In this paper,we proposed the least square constrained method(LSCM)based on the least square and shaping regularization principles.This new method intends for computing the Fourier coefficients of interest signal under finite supported and non-orthogonal base space according to the least square and regularization principles.This is an extension of the short time Fourier transform(STFT).Comparisons with STFT using synthetic signals and real seismic data validates that the proposed method has better timefrequency resolution,can better identify the reservoir's boundaries and locations,further improve the accuracy of reservoir prediction.
引文
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Castagna J P,Sun S,Siegfried R W.2003.Instantaneous spectral analysis:Detection of low-frequency shadows associated with hydrocarbons[J].The leading edge,22(2):120-127.
Chakraborty A,OKaya D.1995.Frequency-time decomposition of seismic data using wavelet-based methods[J].Geophysics,60(6):1906-1916.
Chen X H,He Z H,Huang D J,et al.2009.Low frequency shadow detection of gas reservoirs in time-frequency domain[J].Chinese J.Geophys.(in Chinese),52(1):215-221.
Ebrom D.2004.The low-frequency gas shadow on seismic sections[J].The Leading Edge,23(8):772.
Fomel S.2007.Shaping regularization in geophysical estimation problems[J].Geophysics,72(2):R29-R36.
Gassmann F.1951.ber die Elastizitt porser Medien[J].Vierteljahrsschrift der Naturforschenden Gesellschaft in Zürich,96(3):1-23.
Liu G C,Fomel S,Chen X H.2011.Time-frequency analysis of seismic data using local attributes[J].Geophysics,76(6):P23-P34.
Liu G C,Chen X H,Song J W.2013.Estimation of primaries and multiples by sparse inversion for OBS data with integration of streamer data[J].Chinese J.Geophys.(in Chinese),56(12):4288-4296,doi:10.6038/cjg20131231.
Mavko G,Nur A.1979.Wave propagation in partially saturated rocks[J].Geophysics,44(3):161-178.
Partyka G,Gridley J,Lopez J.1999.Interpretational applications of spectral decomposition in reservoir characterization[J].The Leading Edge,18(3):353-360.
Puryear C I,Portniaguine O N,Cobos C M,et al.2012.Constrained least-squares spectral analysis:Application to seismic data[J].Geophysics,77(5):V143-V167.
Sinha S,Routh P S,Anno P D,et al.2005.Spectral decomposition of seismic data with continuous-wavelet transform[J].Geophysics,70(6):P19-P25.
Tikhonov A N,Arsenin V Y.1977.Solitions of Ill-Posed Problems[M].V.H.Winston and Sons.
Vanìcek P.1969.Approximate spectral analysis by least-squares fit[J].Astrophysics and Space Science,4(4):387-391.
Wang Y H.2007.Seismic time-frequency spectral decomposition by matching pursuit[J].Geophysics,72(1):V13-V20.
Wang Y H.2010.Multichannel matching pursuit for seismic trace decomposition[J].Geophysics,75(4):V61-V66.
Wu G N,Cao S Y,Liu J J.2012a.Reassigned time-frequency decomposition and its application of hydrocarbon exploration[J].Progress in Geophys.(in Chinese),27(2):0596-0602,doi:10.6038/j.issn.1004-2903.2012.02.023.
Wu G N,Cao S Y,Sun N.2012b.Matching pursuit method based on complex seismic traces and its application of hydrocarbon exploration[J].Chinese J.Geophys.(in Chinese),55(6):2027-2034,doi:10.6038/j.issn.0001-5733.2012.06.024.
Xu S,Zhang Y,Pham D,et al.2005.Anti-leakage Fourier transform for seismic data regularization[J].Geophysics,70(4):V87-V95.
Yuan Y H,Wang Y B,Li Y K,et al.2013.A non-dyadic curvelet transform based least-squares matching algorithm and its application[J].Chinese J.Geophys.(in Chinese),56(4):1340-1349,doi:10.6038/cjg20130428.
Zhang F C,Li C H.2012.Orthogonal time-frequency atom based fast matching pursuit for seismic signal[J].Chinese J.Geophys.(in Chinese),55(1):277-283,doi:10.6038/j.issn.0001-5733.2012.01.027.
陈学华,贺振华,黄德济,等.2009.时频域油气储层低频阴影检测[J].地球物理学报,52(1):215-221.
刘国昌,陈小宏,宋家文.2013.基于稀疏反演的OBS数据多次波压制方法[J].地球物理学报,56(12):4288-4296,doi:10.6038/cjg20131231.
武国宁,曹思远,刘建军.2012a.谱图重排的谱分解理论及其在储层探测中的应用[J].地球物理学进展,27(2):596-602,doi:10 .6038/j.issn.1004-2903.2012.02.023.
武国宁,曹思远,孙娜.2012b.基于复数地震记录的匹配追踪算法及其在储层预测中的应用[J].地球物理学报,55(6):2027-2034,doi:10.6038/j.issn.0001-5733.2012.06.024.
袁艳华,王一博,刘伊克,等.2013.基于非二次幂Curvelet变换的最小二乘匹配算法及其应用[J].地球物理学报,56(4):1340-1349,doi:10.6038/cjg20130428.
张繁昌,李传辉.2012.基于正交时频原子的地震信号快速匹配追踪[J].地球物理学报,55(1):277-283,doi:10.6038/j.issn.0001-5733.2012.01.027.
Castagna J P,Sun S,Siegfried R W.2003.Instantaneous spectral analysis:Detection of low-frequency shadows associated with hydrocarbons[J].The leading edge,22(2):120-127.
Chakraborty A,OKaya D.1995.Frequency-time decomposition of seismic data using wavelet-based methods[J].Geophysics,60(6):1906-1916.
Chen X H,He Z H,Huang D J,et al.2009.Low frequency shadow detection of gas reservoirs in time-frequency domain[J].Chinese J.Geophys.(in Chinese),52(1):215-221.
Ebrom D.2004.The low-frequency gas shadow on seismic sections[J].The Leading Edge,23(8):772.
Fomel S.2007.Shaping regularization in geophysical estimation problems[J].Geophysics,72(2):R29-R36.
Gassmann F.1951.ber die Elastizitt porser Medien[J].Vierteljahrsschrift der Naturforschenden Gesellschaft in Zürich,96(3):1-23.
Liu G C,Fomel S,Chen X H.2011.Time-frequency analysis of seismic data using local attributes[J].Geophysics,76(6):P23-P34.
Liu G C,Chen X H,Song J W.2013.Estimation of primaries and multiples by sparse inversion for OBS data with integration of streamer data[J].Chinese J.Geophys.(in Chinese),56(12):4288-4296,doi:10.6038/cjg20131231.
Mavko G,Nur A.1979.Wave propagation in partially saturated rocks[J].Geophysics,44(3):161-178.
Partyka G,Gridley J,Lopez J.1999.Interpretational applications of spectral decomposition in reservoir characterization[J].The Leading Edge,18(3):353-360.
Puryear C I,Portniaguine O N,Cobos C M,et al.2012.Constrained least-squares spectral analysis:Application to seismic data[J].Geophysics,77(5):V143-V167.
Sinha S,Routh P S,Anno P D,et al.2005.Spectral decomposition of seismic data with continuous-wavelet transform[J].Geophysics,70(6):P19-P25.
Tikhonov A N,Arsenin V Y.1977.Solitions of Ill-Posed Problems[M].V.H.Winston and Sons.
Vanìcek P.1969.Approximate spectral analysis by least-squares fit[J].Astrophysics and Space Science,4(4):387-391.
Wang Y H.2007.Seismic time-frequency spectral decomposition by matching pursuit[J].Geophysics,72(1):V13-V20.
Wang Y H.2010.Multichannel matching pursuit for seismic trace decomposition[J].Geophysics,75(4):V61-V66.
Wu G N,Cao S Y,Liu J J.2012a.Reassigned time-frequency decomposition and its application of hydrocarbon exploration[J].Progress in Geophys.(in Chinese),27(2):0596-0602,doi:10.6038/j.issn.1004-2903.2012.02.023.
Wu G N,Cao S Y,Sun N.2012b.Matching pursuit method based on complex seismic traces and its application of hydrocarbon exploration[J].Chinese J.Geophys.(in Chinese),55(6):2027-2034,doi:10.6038/j.issn.0001-5733.2012.06.024.
Xu S,Zhang Y,Pham D,et al.2005.Anti-leakage Fourier transform for seismic data regularization[J].Geophysics,70(4):V87-V95.
Yuan Y H,Wang Y B,Li Y K,et al.2013.A non-dyadic curvelet transform based least-squares matching algorithm and its application[J].Chinese J.Geophys.(in Chinese),56(4):1340-1349,doi:10.6038/cjg20130428.
Zhang F C,Li C H.2012.Orthogonal time-frequency atom based fast matching pursuit for seismic signal[J].Chinese J.Geophys.(in Chinese),55(1):277-283,doi:10.6038/j.issn.0001-5733.2012.01.027.
陈学华,贺振华,黄德济,等.2009.时频域油气储层低频阴影检测[J].地球物理学报,52(1):215-221.
刘国昌,陈小宏,宋家文.2013.基于稀疏反演的OBS数据多次波压制方法[J].地球物理学报,56(12):4288-4296,doi:10.6038/cjg20131231.
武国宁,曹思远,刘建军.2012a.谱图重排的谱分解理论及其在储层探测中的应用[J].地球物理学进展,27(2):596-602,doi:10 .6038/j.issn.1004-2903.2012.02.023.
武国宁,曹思远,孙娜.2012b.基于复数地震记录的匹配追踪算法及其在储层预测中的应用[J].地球物理学报,55(6):2027-2034,doi:10.6038/j.issn.0001-5733.2012.06.024.
袁艳华,王一博,刘伊克,等.2013.基于非二次幂Curvelet变换的最小二乘匹配算法及其应用[J].地球物理学报,56(4):1340-1349,doi:10.6038/cjg20130428.
张繁昌,李传辉.2012.基于正交时频原子的地震信号快速匹配追踪[J].地球物理学报,55(1):277-283,doi:10.6038/j.issn.0001-5733.2012.01.027.
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