Prestack Inversion Method with ATpV Regularization Based on Reweighted L1

doi:10.11885/j.issn.1674-5086.2022.08.20.02

Abstract

Abstract: Seismic prestack inversion can accurately obtain various parameters of underground reservoir media, and is one of the important technologies in oil and gas exploration and development. Due to unknown natural fators, seismic inversion is a typical ill-conditioned problem, and a regularization constraint objective function is usually used to alleviate the ill-conditioned inversion problem. However, the regularization constraint ignores the amplitude information of the stratigraphic boundary, and the reweighting method can overcome this problem well and restore the sparsity better. A pre-stack three-parameter inversion method for ATpV regularization based on reweighted L1 (ATpV-L1 method) is proposed. The reweighted L1 method is combined with ATpV regularization for the first time and introduced into the pre-stack inversion. The Alternating direction multiplier algorithm (ADMM) is used to establish the inversion framework, and the objective function is optimized in blocks, which effectively improves the convergence speed. The manuscript first introduces the ATpV-L1 method, and establishes the pre-stack inversion objective function based on ATpV-L1. Then the theoretical model data is used to compare the inversion results of the new method and the ATpV regularization method, and the effect of this method is verified. Finally, the actual data is used for experimental analysis, which further verifies the inversion accuracy of the new method and verifies the feasibility of the method. The experimental results show that the proposed method can effectively recover the sparsity of the inversion results and improve the inversion accuracy.

Key words: reweighted L1 method, ATpV regularization, prestack inversion, sparse constraint, ADMM, error analysis

CLC Number:

TE19
P631

PAN Shulin, CHEN Yaojie, YIN Cheng, GOU Qiyong, ZHANG Dongjun. Prestack Inversion Method with ATpV Regularization Based on Reweighted L1[J]. Journal of Southwest Petroleum University(Science & Technology Edition), 2024, 46(3): 13-26.

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URL: http://journal15.magtechjournal.com/Jwk_xnzk/EN/10.11885/j.issn.1674-5086.2022.08.20.02

http://journal15.magtechjournal.com/Jwk_xnzk/EN/Y2024/V46/I3/13

References

[1] ZOEPPRITZ K, ERDBEBENWELLEN B. On the reflection and penetration of seismic waves through unstable layers[J]. Goettinger Nachr, 1919(1):66-84.
[2] SHUEY R T. Simplification of Zoeppritz equations[J]. Geophysics, 1985, 50(4):609-614. doi:10.1190/1.1441-936
[3] BULAND A, OMRE H N. Bayesian linearized AVO inversion[J]. Geophysics, 2003, 68(1):185-198. doi:10.1190/1.1543206
[4] 毛宁波,谢涛,杨凯,等. 裂缝储层地震方位AVO正演模拟研究及应用[J]. 石油天然气学报, 2008, 30(5):59-63. doi:10.3969/j.issn.1000-9752.2008.05.014 MAO Ningbo, XIE Tao, YANG Kai, et al. Azimuthal AVO forward model for fractured reservoirs and its application[J]. Journal of Oil and Gas Technology, 2008, 30(5):59-63. doi:10.3969/j.issn.1000-9752.2008.05.014
[5] 张广智,王丹阳,印兴耀. 利用MCMC方法估算地震参数[J]. 石油地球物理勘探, 2011, 46(4):605-609. ZHANG Guangzhi, WANG Danyang, YIN Xingyao. Seismic parameter estimation using Markov Chain Monte Carlo Method[J]. Oil Geophysical Prospecting, 2011, 46(4):605-609.
[6] 宗兆云,印兴耀,张峰,等. 杨氏模量和泊松比反射系数近似方程及叠前地震反演[J]. 地球物理学报, 2012, 55(11):3786-3794. doi:10.6038/j.issn.0001-5733.2012.11.025 ZONG Zhaoyun, YIN Xingyao, ZHANG Feng, et al. Reflection coefficient equation and pre-stack seismic inversion with Young's modulus and Poisson ratio[J]. Chinese Journal of Geophysics, 2012, 55(11):3786-3794. doi:10.6038/j.issn.0001-5733.2012.11.025
[7] 张广智,杜炳毅,李海山,等. 页岩气储层纵横波叠前联合反演方法[J]. 地球物理学报, 2014, 57(12):4141-4149. doi:10.6038/cjg20141225 ZHANG Guangzhi, DU Bingyi, LI Haishan, et al. The method of joint pre-stack inversion of PP and P-SV waves in shale gas reservoirs[J]. Chinese Journal of Geophysics, 2014, 57(12):4141-4149. doi:10.6038/cjg20141225
[8] 张瑞,文晓涛,杨吉鑫,等. 杨氏模量和泊松比反射系数近似方程及地震叠前反演[J]. 石油地球物理勘探, 2019, 54(1):145-153. doi:10.13810/j.cnki.issn.1000-7210.2019.01.017 ZHANG Rui, WEN Xiaotao, YANG Jixin, et al. Twoterm reflection coefficient equation with Young's modulus and Poisson ratio and its prestack seismic inversion[J]. Oil Geophysical Prospecting, 2019, 54(1):145-153. doi:10.13810/j.cnki.issn.1000-7210.2019.01.017
[9] GE Zijian, PAN Shulin, LI Jingye, et al. Seismic AVA inversion of elastic and attenuative parameters in viscoelastic media using the Zoeppritz equations[J]. Journal of Applied Geophysics, 2022, 201:104643. doi:10.1016/j.jappgeo.2022.104643
[10] TIKHONOV A N. Regularization of incorrectly posed problems[J]. Soviet Mathematics Doklady, 1963, 4(6):1624-1627.
[11] RUDIN L I, OSHER S, FATEMI E. Nonlinear total variation based noise removal algorithms[J]. Physica D:Nonlinear Phenomena, 1992, 60(1-4):259-268. doi:10.1016/0167-2789(92)90242-F
[12] WANG Yanfei. Seismic impedance inversion using L1 norm regularization and gradient descent methods[J]. Journal of Inverse and Ill-Posed Problems, 2010, 18(7):823-838. doi:10.1515/jiip.2011.005
[13] ZHANG Fanchang, DAI Ronghuo, LIU Hanging. Seismic inversion based on L1-norm misfit function and total variation regularization[J]. Journal of Applied Geophysics, 2014, 109:111-118. doi:10.1016/j.jappgeo.2014.07.024
[14] LIU Cai, SONG Chao, LU Qi, et al. Impedance inversion based on L1 norm regularization[J]. Journal of Applied Geophysics, 2015, 120:7-13. doi:10.1016/j.jappgeo.2015.06.002
[15] GHOLAMI A. Nonlinear multichannel impedance inversion by total-variation regularization[J]. Geophysics, 2015, 80(5):217-224. doi:10.1190/GEO2015-0004.1
[16] GHOLAMI A. A fast automatic multichannel blind seismic inversion for high-resolution impedance recovery[J]. Geophysics, 2016, 81(5):357-364. doi:10.1190/GEO-2015-0654.1
[17] WANG Dehua, GAO Jinghua, ZHOU Hongan. Datadriven multichannel seismic impedance inversion with anisotropic total variation regularization[J]. Journal of Inverse and Ill-Posed Problems, 2018, 26(2):229-241. doi:10.1515/jiip-2017-0024
[18] WOODWORTH J T, CHARTRAND R. Compressed sensing recovery via nonconvex shrinkage penalties[J]. Inverse Problems, 2016, 32(7):075004. doi:10.1088/02665611/32/7/075004
[19] CHARTRAND R, YIN Wotao. Iteratively reweighted algorithms for compressive sensing[C]. Las Vegas:2008 IEEE International Conference, 2008. doi:10.1109/ICASSP.2008.4518498
[20] LI Shu, HE Yanmin, CHEN Yingpin, et al. Fast multi-trace impedance inversion using anisotropic total p-variation regularization in the frequency domain[J]. Journal of Geophysics and Engineering, 2018, 15(5):2171-2182. doi:10.1088/1742-2140/aaca4a
[21] CHEN Yingpin, PENG Zhenming, GHOLAMI A, et al. Seismic signal sparse time-frequency representation by Lp-quasinorm constraint[J]. Digital Signal Processing, 2019, 87:43-59. doi:10.1016/j.dsp.2019.01.010
[22] WU Hao, HE Yanmin, CHEN Yingpin, et al. Seismic acoustic impedance inversion using mixed second-order fractional ATpV regularization[J]. IEEE Access, 2020, 8:3442-3452. doi:10.1109/ACCESS.2019.2962552
[23] LIU Yangting, LIU Chenguang, XIE Chengliang, et al. A hybrid regularization operator and its application in seismic inversion[J]. IEEE Access, 2021, 9:378-387. doi:10.1109/ACCESS.2021.3106912
[24] CANDES E J, WAKIN M B, BOYD S P. Enhancing sparsity by reweighted L1 minimization[J]. Journal of Fourier Analysis and Applications, 2008, 14:877-905. doi:10.1007/s00041-008-9045-x
[25] RUSU C, DUMITRESCU B. Iterative reweighted L1 design of sparse FIR filters[J]. Signal Processing, 2012, 92(4):905-911. doi:10.1016/j.sigpro.2011.09.031
[26] MA Peifeng, LIN Hui, LAN Hengxing, et al. On the performance of reweighted L1 minimization for tomographic SAR imaging[J]. IEEE Geoscience and Remote Sensing Letters, 2015, 12(4):895-899. doi:10.1109/LGRS.2014.2365613
[27] 宋昱,孙文赟. 基于重加权L1范数的边缘保持图像平滑算法[J]. 华南理工大学学报(自然科学版), 2021, 49(6):109-121. doi:10.12141/j.issn.1000-565X.200231 SONG Yu, SUN Wenyun. Edge-preserving image smoothing algorithm based on reweighted L1 norm[J]. Journal of South China University of Technology (Natural Science Edition), 2021, 49(6):109-121. doi:10.12141/j.issn.1000-565X.200231
[28] HE Liangsheng, WU Hao, WEN Xiaotao, et al. Seismic acoustic impedance inversion using reweighted L1-norm sparse constraint[J]. IEEE Geoscience and Remote Sensing Letters, 2022, 19:1-5.
[29] AKI K I, RICHARDS P G. Quantitative seismology:Theory and methods[J]. Earth-Science Reviews, 1981, 17(3):296-297. doi:10.1016/0012-8252(81)90044-1