A regularization theory-based method for time-frequency analysis and its applications
ZHANG Jin-Qiang1,2,3()
1. Key Laboratory of Shale Oil and Gas Exploration & Production,Sinopec,Beijing 102206,China 2. Sinopec Petroleum Exploration and Production Research Institute,Beijing 102206,China 3. State Key Laboratory of Shale Oil and Gas Enrichment Mechanisms and Effective Development,Beijing 100026,China
Time-frequency analysis (TFA) has been widely used in seismic exploration,thus it is crucial to develop a TFA algorithm with high time-frequency resolution.Given the limitations of conventional TFA methods,this study proposed a TFA method based on the regularization theory.The proposed method considers the signal in a short-time window as a superposition of harmonics with different frequencies and takes the TFA problem as an inverse problem.From this perspective,the TFA problem is ill-posed and needs to be solved based on the regularization theory to get a significant time-frequency spectrum.The solution methods under the conditions of L1 and L2 norm constraints and the minimum support constraint are commonly used in the regularization theory.This study investigated these solution methods and unified them into the same solution framework.Numerical analysis shows that the TFA method under the condition of the minimum support constraint yielded high time-frequency resolution.This method was systematically applied to the actual data of a specific study area,producing a time-frequency data volume with high time-frequency resolution.Moreover,the planar reservoir distribution was clearly characterized using a single-frequency data volume,demonstrating the promising application prospect of the method.
张金强. 基于正则化理论的时频分析方法及应用[J]. 物探与化探, 2023, 47(4): 965-974.
ZHANG Jin-Qiang. A regularization theory-based method for time-frequency analysis and its applications. Geophysical and Geochemical Exploration, 2023, 47(4): 965-974.
Qu Z D, He R Z, Zhang X H, et al. The time frequency domain phase filter and its application in noise suppression of teleseismic receiver functions[J]. Chinese Journal of Geophysics, 2017, 60(4):1389-1397.
Cao J, Wang L F, Ge X S, et al. Application of frequency-shared trace integration technique to reservoir prediction in Su59 gas field[J]. Chinese Journal of Engineering Geophysics, 2020, 17(2):154-159.
Yue Y X, Cai J X, Li B, et al. Application research of synchrosqueezing wavelet transform in the reservoir prediction[J]. Progress in Geophysics, 2018, 33(6):2498-2506.
Yang Y D, Zeng Q C, Guo X L, et al. High-precision seismic prediction of shale gas sweet spots based on matching pursuit algorithm[J]. Science Technology and Engineering, 2017, 17(4):180-185.
Li C H, Zhang F C, Yin X Y. The influential factors and accuracy of three time-freqency analyses[J]. Journal of Oil and Gas Technology:J. JPI, 2010, 32(4):239-242.
[12]
Qian S, Chen D. Discrete Gabor transform[J]. IEEE Transactions on Signal Processing, 1993, 41(7):2429-2439.
doi: 10.1109/78.224251
[13]
Sinha S, Routh P, Anno P. Instantaneous spectral attributes using scales in continuous-wavelet transform[J]. Geophysics, 2009, 74(2):WA137-WA142.
doi: 10.1190/1.3054145
Li S Y, Xu T J. A new high-resolution time-freqency method based on Wigner-Ville distribution and Chrip-Z transform[J]. Oil Geophysical Prospecting, 2022, 57(1):168-175.
Zhang X Y, Peng Z M, Zhang P, et al. Spectral decomposition of seismic signals based on fractional Wigner-Ville distribution[J]. Oil Geophysical Prospecting, 2014, 49(5):839-845.
[16]
Han J, Van D B M. Empirical mode decomposetion for seismic time-freqency analysis[J]. Geophysics, 2013, 78(2):O9-O19.
doi: 10.1190/geo2012-0199.1
[17]
Wang Y H. Seismic time-frequency spectral decom-position by matching pursuit[J]. Geophysics, 2007, 72(1):V13-V20.
doi: 10.1190/1.2387109
[18]
Mallat S, Zhang Z. Matching pursuit with time-freqency dictionaries[J]. IEEE Transactions on Signal Processing, 1993, 41(2):3397-3415.
doi: 10.1109/78.258082
[19]
Puryear C I, Portniaguine O N, Cobos C M, et al. Constraint least-square spectral analysis:Application to seismic data[J]. Geophysics, 2012, 77(5):V143-V167.
doi: 10.1190/geo2011-0210.1
Tian L, Hu J. Sparse shot-time Fourier transform spectral decomposition method and its application[J]. Progress in Geophysics, 2021, 36(6):2581-2587.
[22]
Zhang R, John C. Seismic sparse-layer reflectivity inversion using basis pursuit decomposition[J]. Geophysics, 2011, 76(6):R147-R158.
doi: 10.1190/geo2011-0103.1
[23]
Portniaguine O, Zhdanov M S. Focusing geophysical inversion images[J]. Geophysics, 1999, 64(3):874-887.
doi: 10.1190/1.1444596
[24]
Portniaguine O, Zhdanov M S. 3D magnetic inversion with data compression and image focusing[J]. Geophysics, 2002, 67(5):1532-1541.
doi: 10.1190/1.1512749
[25]
Partyka G A, Gridley J A, Lopez J A. Interpretational aspects of spectral decomposition in reservoir characterization[J]. The Leading Edge, 1999, 18(2):353-360.
doi: 10.1190/1.1438295
