A method for calculating the P-to-S-wave velocity ratio through direct inversion of prestack multi-component seismic data based on the L1-2 norm constraint
HAN Lei1(), LI Jing-Ye1, GENG Wei-Heng2, WANG Yong-Ping1, YANG Qi-Yu1, ZHANG Yu-Ning1
1. College of Geophysics,China University of Petroleum(Beijing),Beijing 102249,China 2. School of Information Science and Technology,Tsinghua University,Beijing 100084,China
The ratio of compressional to shear wave velocities(hereafter referred to as the P-to-S-wave velocity ratio) is an essential parameter for lithology discrimination,reservoir characterization,and gas reservoir identification.Direct inversion of PP-wave seismic data to derive the P- and S-wave velocities has been a well-established technique.However,calculating the P-to-S-wave velocity ratio using the P- and S-wave velocities obtained through individual inversion may lead to cumulative errors.In contrast,since PS-wave data inherently contain S-wave velocity information,the joint inversion of PS-wave data can significantly improve the accuracy of the P-to-S-wave velocity ratio.This study employed the L1-2 norm to enhance the resolution of inversion results.Compared to the L1 and L2 norms,the L1-2 norm yielded sparser solutions with higher resolution.First,this study derived and assessed the accuracy of linearized forward modeling approximate formulas for PP- and PS-waves.Second,based on Bayesian theory,this study incorporated the L1-2 norm to construct an objective function for the direct inversion of the P-to-S-wave velocity ratio.Third,the objective function was solved to obtain the inversion result for the P-to-S-wave velocity ratio.The quantitative comparison of the correlation coefficients demonstrates that the inversion results based on the L1-2 norm outperform those based on the L1 or L2 norm,direct inversion is superior to indirect inversion,and joint inversion provides better results than individual inversion.Finally, the effectiveness and feasibility of the proposed method in this study were validated through inversions of synthetic and field data.
韩磊, 李景叶, 耿伟恒, 王永平, 杨骐羽, 张宇宁. 基于L1-2范数约束的叠前多分量地震数据直接反演纵横波速度比方法[J]. 物探与化探, 2025, 49(3): 620-630.
HAN Lei, LI Jing-Ye, GENG Wei-Heng, WANG Yong-Ping, YANG Qi-Yu, ZHANG Yu-Ning. A method for calculating the P-to-S-wave velocity ratio through direct inversion of prestack multi-component seismic data based on the L1-2 norm constraint. Geophysical and Geochemical Exploration, 2025, 49(3): 620-630.
Granli J R, Arntsen B, Sollid A, et al. Imaging through gas-filled sediments using marine shear-wave data[J]. Geophysics, 1999, 64(3):668-677.
[2]
Tsvankin I, Gaiser J, Grechka V, et al. Seismic anisotropy in exploration and reservoir characterization:An overview[J]. Geophysics, 2010, 75(5):75A15-75A29.
[3]
Dave H. Dynamic warping of seismic images[J]. Geophysics, 2013, 78(2):S105-S115.
[4]
Geng W H, Chen X H, Li J Y, et al. Warped P-SV wavelet distortion correction using a time-frequency adaptive shaping filter[J]. Geophysics, 2023, 88(2):V101-V112.
Zhang T Y, Lin K, Wen X T, et al. Direct inversion of P-wave to S-wave velocity ratio by Lp quasi-norm sparse constraints[J]. Oil Geophysical Prospecting, 2024, 59(2):230-237.
Cheng B J, Xu T J, Liang Q, et al. Gas identification using multi-wave velocity ratio parameters[J]. Oil Geophysical Prospecting, 2014, 49(2):307-315,220-221.
[7]
Compton S, Hale D. Estimating VP/VS ratios using smooth dynamic image warping[J]. Geophysics, 2014, 79(6):V201-V215.
[8]
Zhi L X, Chen S Q, Song B S, et al. Nonlinear PP and PS joint inversion based on the exact zoeppritz equations:A two-stage procedure[J]. Journal of Geophysics and Engineering, 2018, 15(2):397-410.
[9]
Donoho D L. Compressed sensing[J]. IEEE Transactions on Information Theory, 2006, 52(4):1289-1306.
[10]
Zhang R, Castagna J. Seismic sparse-layer reflectivity inversion using basis pursuit decomposition[J]. Geophysics, 2011, 76(6):R147-R158.
[11]
Yin P H, Lou Y F, He Q, et al. Minimization of L1-2 for compressed sensing[J]. SIAM Journal on Scientific Computing, 2015, 37(1):A536-A563.
Geng W H, Chen X H, Li J Y, et al. Seismic“blocky” acoustic impedance inversion based on L1-2 regularization[J]. Oil Geophysical Prospecting, 2022, 57(6):1409-1417,1260-1261.
[13]
聂文亮. 非凸L1-2正则化地震反演方法研究[D]. 成都: 成都理工大学, 2021.
[13]
Nie W L. Research on nonconvex L1-2 regularization seismic inversion method[D]. Chengdu: Chengdu University of Technology, 2021.
[14]
Aki K, Richards P G. Quantitative seismology theory and methods[M]. San Francisco: W.H. Freeman,1980.
Liu Y T, Li Y, Liao Z Q, et al. Study and application of high-precision direct inversion method of P-to-S-wave velocity ratio based on elastic impedance[J]. Progress in Geophysics, 2024, 39(3):1152-1163.
[16]
Wang P, Hu T Y. AVO approximation for PS-wave and its application in PP/PS joint inversion[J]. Applied Geophysics, 2011, 8(3):189-196.
[17]
Ramos A C B, Castagna J P. Useful approximations for converted-wave AVO[J]. Geophysics, 2001, 66(6):1721-1734.
Zhang S X, Yin X Y, Zhang F C. Prestack three term inversion method based on Trivariate Cauchy distribution prior constraint[J]. Oil Geophysical Prospecting, 2011, 46(5):737-743,836,663.
Zhou L, Liao J P, Li J Y, et al. Prediction method of reservoir oil-gas potential based on exact Zoeppritz equations[J]. Chinese Journal of Geophysics, 2021, 64(10):3788-3806.
Zhou L, Liao J P, Yuan C, et al. Time-lapse seismic inversion for fluid dynamic monitoring based on the exact Zoeppritz equations[J]. Progress in Geophysics, 2022, 37(5):2118-2128.
