LIU Baotong1, LIU Qiyuan2, HUANG Yijian3, KANG Xuefu1, LIU Donglin1, JIANG Yingshuang1
1. School of Electronic Information and Electrical Engineering, Tianshui Normal University, Tianshui, Gansu 741001, China; 2. School of Mathematics, Sichuan University, Chengdu, Sichuan 610064, China; 3. State Key Laboratory of Continental Dynamics, Department of Geology, Northwest University, Xi'an, Shaanxi 710069, China
Abstract：The three-parameter W transform （TPWT） is an effective tool for analyzing non-stationary signals, and it has been successfully used in oil and gas reservoir identification. However, the reversibility of TPWT has not been discussed in detail in previous studies. Therefore, this paper first reviewed the basic principles of TPWT and theoretically analyzed the reversibility of TPWT. Both the theoretical analysis and numerical calculation results show that：①TPWT not only solves the problems of low time resolution at lowfrequencies and shift of the distribution centroid of the time-frequency spectral energy toward higher frequencies in S transform （ST） but also overcomes the amplitude splitting phenomenon of the time-frequency spectrum at the dominant frequency in W transform （WT）, which can characterize hydrocarbon reservoirs more accurately and is more beneficial for seismic interpretation.②In theory, TPWT is not strictly reversible but an approximately reversible transform tool, which is different from Fourier transform （FT） and ST.③The numerical calculation results of a synthetic seismogram and a real seismogram show that compared with original seismic data, the relative errors of seismic data reconstructed by inverse TPWT are 11.47%~21.35%, or in other words, the theoretical irreversibility leads to significant reconstruction errors, seriously affecting the application range of TPWT. TPWT is not applicable in fields that require data reconstruction such as denoising and high-resolution processing.
LIU B,LIU Q,KANG X.Application of improved time-frequency representation to local noise removal[J].Journal of Petroleum Exploration and Production Technology,2021, 11(5):2091-2096.
[2]
GUO Longyu,LIU Cai,LIU Yang.Filtering methods attenuate seismic data noise[J].Progress in Geophy-sics,2018,33(5):1890-1896.国胧予,刘财,刘洋.滤波类方法衰减地震数据噪声[J].地球物理学进展,2018,33(5):1890-1896.
[3]
LI R, ZHU X, ZHOU Y, et al.Generalized W transform and its application in gas-bearing reservoir characterization[J]. IEEE Geoscience and Remote Sensing Letters,2022,DOI:10.1109/LGRS.2021.3108836.
[4]
CHEN H,PENG L,CHEN X,et al.A three-para-meter W transform and its application to gas reservoir identification[J]. Geophysics,2022,87(5):V521-V532.
[5]
LI Siyuan,XU Tianji.A new high-resolution time-frequency analysis method based on Wigner-Ville distribution and Chirp-Z transform[J].Oil Geophysical Prospecting,2022,57(1):168-175, 211.李思源,徐天吉.基于Wigner-Ville分布与Chrip-Z变换的高分辨时频分析方法[J].石油地球物理勘探,2022,57(1):168-175, 211.
[6]
HAO Yaju,ZHANG Hua,ZHANG Sheng,et al.High-resolution self-adaptive Gabor time-frequency analysis method based on group-sparse regularized inversion[J].Oil Geophysical Prospecting,2023,58(2):412-421.郝亚炬,张华,张生,等.应用组稀疏正则化反演的高分辨率自适应Gabor时频分析方法[J].石油地球物理勘探, 2023, 58(2):412-421.
[7]
LU Wenkai,ZHANG Xuegong,LI Yanda,et al.Fitting a zero-offset seismic trace in time-frequency domain[J].Oil Geophysical Prospecting,2001,36(1):56-59,71.陆文凯,张学工,李衍达,等.时频域零炮检距地震道拟合[J].石油地球物理勘探,2001,36(1):56-59, 71.
[8]
GAO Jianhu,YONG Xueshan,LIU Hong.Study of reservoir prediction technology in frequency donain[J].Natural Gas Geoscience,2007,18(6):808-812.高建虎,雍学善,刘洪.频率域储层预测技术研究[J].天然气地球科学,2007,18(6):808-812.
[9]
DAUBECHIES I.Ten Lectures on Wavelets[M]. Society for Industrial and Applied Mathematics,PA,United States,1992.
STOCKWELL R G,MANSINHA L,LOWE R P. Localization of the complex spectrum:the S transform[J].IEEE Transactions on Signal Processing,1996,44(4):998-1001.
[12]
MCFADDEN P D,COOK J G,FORSTER L M. Decomposition of gear vibration signals by the generalized S transform[J].Mechanical Systems and Signal Processing,1999, 13(5):691-707.
[13]
PINNEGAR C R,EATON D W.Application of the S transform to prestack noise attenuation filtering[J].Journal of Geophysical Research,2003,108(B9):ESE9.1-ESE9.10.
[14]
PINNEGAR C R, MANSINHA L.The S-transform with windows of arbitrary and varying shape[J].Geophysics,2003, 68(1):381-385.
[15]
LI D,CASTAGNA J, GOLOSHUBIN G. Investigation of generalized S-transform analysis windows for time-frequency analysis of seismic reflection data[J].Geophysics, 2016,81(3):V235-V247.
[16]
EBROM D.The low-frequency gas shadow on seismic sections[J].The Leading Edge,2004,23(8):772-772.
[17]
Ten KROODE F,BERGLER S,CORSTEN C,et al. Broadband seismic data-The importance of low frequencies[J].Geophysics,2013,78(2):WA3-WA14.
[18]
LIU Lanfeng,LIU Quanxin,YONG Xueshan,et al. Hydrocarbon detection using instantaneous energy spectrum of low frequency based on general S transform[J].Natural Gas Geoscience,2005,16(2):238-241.刘兰锋,刘全新,雍学善,等.基于广义S变换的低频瞬时能量谱油气检测技术[J].天然气地球科学,2005,16(2):238-241.
[19]
LIU Junjie,CHEN Xuehua,WU Haojie,et al.Sparse generalized S-transform and its application to detection of low-frequency seismic anomalies in reservoirs[J].Oil Geophysical Prospecting,2023,58(3):690-699.刘俊杰,陈学华,吴昊杰,等.稀疏广义S变换及其在储层地震低频异常检测中的应用[J].石油地球物理勘探,2023, 58(3):690-699.
WANG Y.The W transform[J].Geophysics,2021,86(1):V31-V39.
[22]
LIU B T.Numerical S transform:Error analysis and application[C].Proceedings of 2015 International Conference on Computer Science and Environmental Engineering,2015,1336-1342.
[23]
SIMON C,VENTOSA S,SCHIMMEL M,et al.The S-transform and its inverses:side effects of discretizing and filtering[J].IEEE Transactions on Signal Processing,2007, 55(10):4928-4937.
[24]
CHEN Lin,SONG Haibin.The estimation of instantaneous frequency of seismic signal[J].Chinese Journal of Geophysics, 2009,52(1):206-214.陈林,宋海斌.地震信号瞬时频率的估算[J].地球物理学报,2009,52(1):206-214.
[25]
ZHANG Meng,WANG Huazhong,SUI Zhiqiang,et al. Seismic instantaneous frequency extraction based on empirical mode decomposition and wavelet transform[J].Oil Geophysical Prospecting,2016,51(3):565-571.张猛,王华忠,隋志强,等.基于经验模态分解和小波变换的地震瞬时频率提取方法及应用[J].石油地球物理勘探, 2016,51(3):565-571.
