时间域和频率域二阶同步压缩变换及其在储层识别中的应用
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摘要
从时间域推导出时间域二阶同步压缩短时傅里叶变换和时间域二阶同步压缩小波变换,从频率域推导出频率域二阶同步压缩短时傅里叶变换和频率域二阶同步压缩小波变换,通过公式推导结果可以得到二阶同步压缩变换的统一形式,这一规律可以推广到其他二阶同步压缩线性时频变换中去。将二阶同步压缩小波变换应用到实际地震资料处理中。结果表明:该方法可以得到非常高的时频分辨率,能够有效识别储层及有利圈闭,所得结果与测井资料相吻合;相对于传统线性时频分析方法和一阶同步压缩变换方法,二阶同步压缩变换可以使能量更加聚焦到时频脊上,提高时频域分辨率。
In this paper, we derive the second-order synchrosqueezing short-time Fourier transform and the second-order synchrosqueezing wavelet transform in time domain and frequency domain respectively, and obtain a unified form of the second-order synchrosqueezing transform. This law can be extended to other second-order synchrosqueezing linear time-frequency transforms. The actual seismic data processed by the second-order synchrosqueezing wavelet transform show that the method has a very high time-frequency resolution and can effectively identify the reservoirs and favorable traps. The results obtained are consistent with the logging data.Compared with the traditional linear time-frequency methods and the first-order synchrosqueezing transforms, the second-order synchrosqueezing transform can focus the energy more on the time-frequency ridge to improve the resolution in the time-frequency domain.
In this paper, we derive the second-order synchrosqueezing short-time Fourier transform and the second-order synchrosqueezing wavelet transform in time domain and frequency domain respectively, and obtain a unified form of the second-order synchrosqueezing transform. This law can be extended to other second-order synchrosqueezing linear time-frequency transforms. The actual seismic data processed by the second-order synchrosqueezing wavelet transform show that the method has a very high time-frequency resolution and can effectively identify the reservoirs and favorable traps. The results obtained are consistent with the logging data.Compared with the traditional linear time-frequency methods and the first-order synchrosqueezing transforms, the second-order synchrosqueezing transform can focus the energy more on the time-frequency ridge to improve the resolution in the time-frequency domain.
引文
[1] 王夕宾,郝延征,姚军,等.东营凹陷沙一段薄层湖相碳酸盐岩成因研究[J].中国石油大学学报(自然科学版),2016,40(1):27-34.WANG Xibin,HAO Yanzheng,YAO Jun,et al.Genetic research of flaggy lacustrine carbonate in the first Member of Shahejie Formation,Dongying Depression[J].Journal of China University of Petroleum(Edition of Natural Science),2016,40 (1):27-34.
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[13] LIU W,CAO S,LIU Y,et al.Synchrosqueezing transform and its applications in seismic data analysis[J].Journal of Seismic Exploration,2016,25(3):27-44.
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[18] JIANG Q,SUTER B W.Instantaneous frequency estimation based on synchrosqueezing wavelet transform[J].Signal Processing,2017,138:167-181.
[19] ZHANG Y,LI Z,WANG J.Time-varying spectral modeling deconvolution based on synchrosqueezed wavelet transform to improve seismic data resolution[C/OL]//2017 SEG International Exposition and Annual Meeting.Society of Exploration Geophysicists,2017,September 24-27[2018-06-22].https://doi.org/10.1190/segam2017-17586876.1.
[20] ZHANG Y,LI Z,WANG J.Seismic data resolution improvement by compensating time-frequency spectrum of synchrosqueezing wavelet transform[C/OL]//International Geophysical Conference,Qingdao,China,2017,April 17-20[2018-06-22].https://doi.org/10.1190/IGC2017-119.
[21] OBERLIN T,MEIGNEN S,PERRIER V.Second-order synchrosqueezing transform or invertible reassignment?towards ideal time-frequency representations[J].IEEE Trans Signal Processing,2015,63(5):1335-1344.
[22] OBERLIN T,MEIGNEN S.The second-order wavelet synchrosqueezing transform:2017 IEEE International Conference on Acoustics,Speech and Signal Processing (ICASSP),New Orleans,March 5-9,2017[C].Piscataway,NJ:IEEE,2017.
[2] 张鹏飞,刘惠民,王永诗,等.济阳坳陷太古界潜山储集体发育模式[J].中国石油大学学报(自然科学版),2017,41(6):20-29.ZHANG Pengfei,LIU Huimin,WANG Yongshi,et al.Development model of Archaeozoic buried hill reservoir in Jiyang Depression[J].Journal of China University of Petroleum (Edition of Natural Science),2017,41(6):20-29.
[3] 李永强,侯加根,刘钰铭,等.基于岩溶模式的溶洞储集体三维地质建模[J].中国石油大学学报(自然科学版),2016,40(5):43-50.LI Yongqiang,HOU Jiagen,LIU Yuming,et al.3D modeling of cave reservoirs based on karst patterns[J].Journal of China University of Petroleum (Edition of Natural Science),2016,40(5):43-50.
[4] DAUBECHIES I.A nonlinear squeezing of the continuous wavelet transform based on auditory nerve models[J].Wavelets in Medicine and Biology,1996:527-546.
[5] DAUBECHIES I,LU J,WU H T.Synchrosqueezed wavelet transforms:an empirical mode decomposition-like tool[J].Applied and Computational Harmonic Analysis,2011,30(2):243-261.
[6] OBERLIN T,MEIGNEN S,PERRIER V.The Fourier-based synchrosqueezing transform:2014 IEEE International Conference on Acoustics,Speech and Signal Processing (ICASSP),Florence,May 4-9,2014[C].Piscataway,NJ:IEEE,2014.
[7] HUANG Z,ZHANG J,ZHAO T,et al.Synchrosqueezing S-transform and its application in seismic spectral decomposition[J].IEEE Transactions on Geoscience and Remote Sensing,2016,54(2):817-825.
[8] YANG H,YING L.Synchrosqueezed wave packet transform for 2D mode decomposition[J].SIAM Journal on Imaging Sciences,2013,6(4):1979-2009.
[9] YANG H,YING L.Synchrosqueezed curvelet transform for two-dimensional mode decomposition[J].SIAM Journal on Mathematical Analysis,2014,46(3):2052-2083.
[10] HERRERA R H,HAN J,MIRKO V D B.Applications of the synchrosqueezing transform in seismic time-frequency analysis[J].Geophysics,2014,79(3):V55-V64.
[11] CHEN Y,LIU T,CHEN X,et al.Time-frequency analysis of seismic data using synchrosqueezing wavelet transform[C/OL]//2014 SEG International Exposition and Annual Meeting.Society of Exploration Geophysicists,2014,October 26-31[2018-06-22].https://doi.org/10.1190/segam2014-0034.1.
[12] WANG P,GAO J,WANG Z.Time-frequency analysis of seismic data using synchrosqueezing transform[J].IEEE Geoscience & Remote Sensing Letters,2014,11(12):2042-2044.
[13] LIU W,CAO S,LIU Y,et al.Synchrosqueezing transform and its applications in seismic data analysis[J].Journal of Seismic Exploration,2016,25(3):27-44.
[14] LI C,LIANG M.A generalized synchrosqueezing transform for enhancing signal time-frequency representation[J].Signal Processing,2012,92(9):2264-2274.
[15] CHEN H,LU L,XU D,et al.The synchrosqueezing algorithm based on generalized S-transform for high-precision time-frequency analysis[J].Applied Sciences,2017,7(8):769.
[16] HERRERA R H,TARY J B,van DER BAAN M.Time-frequency representation of microseismic signals using the synchrosqueezing transform[C/OL]//GeoConvention,Alberta,Canada,May 6-10,2013 [2018-06-22].https://www.geoconvention.com/archives/2013/094_GC2013_Time-Frequency_Representation.pdf.
[17] GHOLTASHI S,NAZARI SIAHSAR M A,ROSHANDELKAHOO A,et al.Synchrosqueezing-based transform and its application in seismic data analysis[J].Iranian Journal of Oil & Gas Science and Technology,2015,4(4):1-14.
[18] JIANG Q,SUTER B W.Instantaneous frequency estimation based on synchrosqueezing wavelet transform[J].Signal Processing,2017,138:167-181.
[19] ZHANG Y,LI Z,WANG J.Time-varying spectral modeling deconvolution based on synchrosqueezed wavelet transform to improve seismic data resolution[C/OL]//2017 SEG International Exposition and Annual Meeting.Society of Exploration Geophysicists,2017,September 24-27[2018-06-22].https://doi.org/10.1190/segam2017-17586876.1.
[20] ZHANG Y,LI Z,WANG J.Seismic data resolution improvement by compensating time-frequency spectrum of synchrosqueezing wavelet transform[C/OL]//International Geophysical Conference,Qingdao,China,2017,April 17-20[2018-06-22].https://doi.org/10.1190/IGC2017-119.
[21] OBERLIN T,MEIGNEN S,PERRIER V.Second-order synchrosqueezing transform or invertible reassignment?towards ideal time-frequency representations[J].IEEE Trans Signal Processing,2015,63(5):1335-1344.
[22] OBERLIN T,MEIGNEN S.The second-order wavelet synchrosqueezing transform:2017 IEEE International Conference on Acoustics,Speech and Signal Processing (ICASSP),New Orleans,March 5-9,2017[C].Piscataway,NJ:IEEE,2017.