Abstract：The spectral ratio method is currently one of the most commonly used Q factor estimation me-thods. When seismic data contains noise interfe-rence,the spectral ratio method has poor stability and the estimation result depends on the selected frequency band. This is because equal weights are used in the Q factor estimation by the spectral ratio method when the least-squares method is employed to fit a straight line. As a result, the fitting results are greatly affected by the abnormal values in the low and high frequency regions. To improve the stability of the spectral ratio method and reduce its dependence on the selection of frequency bands, this paper proposes the weighted spectral ratio method for Q factor estimation. During least-squares fitting, a Gaussian function is introduced as a weighting factor to reduce the weighting coefficients of signals with low signal-to-noise ratios. The peak frequency and variance of the Gaussian function are the centroid frequency and variance of the source wavelet,respectively. The model test indicates that the weighted spectral ratio method is more stable than the conventional spectral ratio method,and its dependence on frequency band selection is reduced. The application of actual VSP data further proves that the weighted spectral ratio method can estimate the Q factor stably and effectively.
WANG Y H.Inverse Q-filter for seismic resolution enhancement[J]. Geophysics, 2006, 71(3):V51-V60.
[2]
WANG S D, CHEN X H.Absorption-compensation method by L1-norm regularization[J]. Geophysics, 2014, 79(3):V107-V114.
[3]
WANG S D, SONG H J, YANG D F.Seismic attenuation compensation by Bayesian inversion[J]. Journal of Applied Geophysics, 2014, 111:356-363.
[4]
陈汉明, 周辉, 田玉昆. 分数阶拉普拉斯算子黏滞声波方程的最小二乘逆时偏移[J]. 石油地球物理勘探, 2020, 55(3):616-626.CHEN Hanming, ZHOU Hui, TIAN Yukun. Least-squares reverse-time migration based on a fractional Laplacian viscoacoustic wave equation[J]. Oil Geophysical Prospecting, 2020, 55(3):616-626.
[5]
刘金涛, 王孝, 王小卫, 等. 全局约束反演多道吸收补偿方法[J]. 石油地球物理勘探, 2021, 56(2):273-282.LIU Jintao, WANG Xiao, WANG Xiaowei, et al. Multi-channel absorption compensation method based on global constrained inversion[J]. Oil Geophysical Prospecting, 2021, 56(2):273-282.
[6]
MITTET R, SOLLIE R, HOKSTAD K.Prestack depth migration with compensation for absorption and dispersion[J]. Geophysics, 1995, 60(5):1485-1494.
[7]
HICKS G J, PRATT R G.Reflection waveform inversion using local descent methods:Estimating attenuation and velocity over a gas-sand deposit[J]. Geophysics, 2001, 66(2):598-612.
[8]
WINKLER K W, NUR A.Seismic attenuation:effects of pore fluids and frictional sliding[J]. Geophysics, 1982, 47(1):1-15.
[9]
ENGELHARD L.Determination of seismic-wave attenuation by complex trace analysis[J]. Geophysical Journal International, 1996, 125(2):608-622.
[10]
刘洋, 李向阳, 杨东方. 基于线性分解的解析信号法估算品质因子Q[J]. 石油地球物理勘探, 2018, 53(4):784-790.LIU Yang, LI Xiangyang, YANG Dongfang.Quality factor Q estimation with complex trace analysis based on linear decomposition[J]. Oil Geophysical Prospecting, 2018, 53(4):784-790.
[11]
TONN R.The determination of the seismic quality factor Q from VSP data:a comparison of different computational methods[J]. Geophysical Prospecting, 1991, 39(1):1-27.
[12]
QUAN Y L, HARRIS J M.Seismic attenuation tomography using the frequency shift method[J]. Geophysics, 1997, 62(3):895-905.
[13]
杨登锋, 秦成岗, 汪瑞良, 等. 能量谱质心频移法Q值估计[J]. 石油地球物理勘探, 2016, 51(5):863-867.YANG Dengfeng, QIN Chenggang, WANG Ruiliang, et al. Q factor estimation based on the centroid frequency shift of energy spectrum[J]. Oil Geophysical Prospecting, 2016, 51(5):863-867.
[14]
YANG D F, LIU J, LI J N, et al. Q-factor estimation using bisection algorithm with power spectrum[J]. Geophysics, 2020, 85(3):V233-V248.
[15]
ZHANG C J, ULRYCH T J.Estimation of quality factors from CMP records[J]. Geophysics, 2002, 67(5):1542-1547.
[16]
WANG Y H.Stable Q analysis on vertical seismic profiling data[J]. Geophysics, 2014, 79(4):D217-D225.
[17]
DASGUPTA R, CLARK R A.Estimation of Q from surface seismic reflection data[J]. Geophysics, 1998, 63(6):2120-2128.
[18]
REINE C, VAN DER BAAN M, CLARK R A.The robustness of seismic attenuation measurements using fixed and variable-window time-frequency transforms[J]. Geophysics, 2009, 74(2):WA123-WA135.
[19]
DE CASTRO NUNES B I, DE MEDEIROS W E, DO NASCIMENTO A F, et al.Estimating quality factor from surface seismic data:a comparison of current approaches[J]. Journal of Applied Geophysics, 2011, 75(2):161-170.
[20]
PICOTTI S, CARCIONE J.Estimating seismic atte-nuation (Q) in the presence of random noise[J]. Journal of Seismic Exploration, 2006, 15(1):165-181.
[21]
曹思远, 谭佳, 高明, 等. 对数谱根式法Q值反演[J]. 石油地球物理勘探, 2014, 49(1):161-166.CAO Siyuan, TAN Jia, GAO Ming, et al.Seismic Q estimation with logarithmic spectrum equation root[J]. Oil Geophysical Prospecting, 2014, 49(1):161-166.
[22]
WANG S D, YANG D F, LI J N, et al.Q factor estimation based on the method of logarithmic spectral area difference[J]. Geophysics, 2015, 80(6):V157-V171.
[23]
刘国昌, 陈小宏, 杜婧, 等. 基于整形正则化和S变换的Q值估计方法[J]. 石油地球物理勘探, 2011, 46(3):417-422.LIU Guochang, CHEN Xiaohong, DU Jing, et al.Seismic Q estimation using S-transform with regularized inversion[J]. Oil Geophysical Prospecting, 2011, 46(3):417-422.
[24]
LIU G C, CHEN X H, RAO Y.Seismic quality factor estimation using frequency-dependent linear fitting[J]. Journal of Applied Geophysics, 2018, 156:1-8.
[25]
冯玮, 胡天跃, 常丁月, 等. 基于时变子波的品质因子估计[J]. 石油地球物理勘探, 2018, 53(1):136-146.FENG Wei, HU Tianyue, CHANG Dingyue, et al.Quality factor Q estimation based on time-varying wavelet[J]. Oil Geophysical Prospecting, 2018, 53(1):136-146.
[26]
郭锐, 林鹤, 王前, 等. 改进的Capon2D Q值估计方法及其应用[J]. 石油地球物理勘探, 2018, 53(增刊2):182-188.GUO Rui, LIN He, WANG Qian, et al.Modified Capon2D Q value estimation method and its application[J]. Oil Geophysical Prospecting, 2018, 53(S2):182-188.
SANGWAN P, KUMAR D, CHAKRABORTY S, et al.Nonlinear approach to spectral ratio method for estimation of seismic quality factor from VSP data[J]. Journal of Applied Geophysics, 2019, 167:33-41.
[29]
LI J N, WANG S X, YANG D F.An improved Q estimation approach:the weighted centroid frequency shift method[J]. Journal of Geophysics and Engineering, 2016, 13(3):399-411.
[30]
FUTTERMAN W I.Dispersive body waves[J]. Journal of Geophysical Research, 1962, 67(13):5279- 5291.
[31]
张海燕, 李庆忠. 几种常用解析子波的特性分析[J]. 石油地球物理勘探, 2007, 42(6):651-657.ZHANG Haiyan, LI Qingzhong.Analysis on feature of common analytic wavelets[J]. Oil Geophysical Prospecting, 20107, 42(6):651-657.
