Prestack seismic inversion with reweighted L1-norm sparse constraints
ZHAO Yun1,2, WEN Xiaotao1,2, YIN Chuan3, HAN Wenming3, LI Chenlong1,2
1. State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Chengdu University of Technology, Chengdu, Sichuan 610059, China; 2. College of Geophysics, Chengdu University of Technology, Chengdu, Sichuan 610059, China; 3. CNOOC International Energy Services (Beijing) Co., Ltd., Beijing 100010, China
Abstract：Low sparsity pseudo-layers and low resolution of traditional sparse-constrained inversion lead to difficulty in thin-layer identification.To this end，we propose a prestack seismic inversion method based on reweighted L1-norm sparse constraints，namely to combine the reflection coefficients of the formation with the elements of the reweighted matrix，and the reflection coefficients are further reweighted to optimize and construct the inversion objective function.In addition，the alternating direction method of multipliers （ADMM） is used to transform the nonlinear inversion objective function containing multiple parameters into multiple easily solvable single-parameter linear subproblems，and iterative shrinkage thresholding algorithm （ISTA） is introduced to solve the mixed norm optimal solution of the subproblems.Unlike the traditional L1-norm sparse constraints，which only consider the position information of the reflection boundary，the reweighted L1-norm exploits the amplitude information of the reflection boundary，which can more fully utilize the sparsity of the L1-norm to obtain more accurate formation velocity boundary and density boundary through the prestack seismic inversion and weaken the velocity pseudo-layer phenomenon existing in the traditional L1-norm inversion results.The model test and the application of the measured data in the field data demonstrate that the profile boundaries of P- and S-wave velocities and density obtained by the proposed method are more accurate，with higher resolution，better identification ability for thin layers，and the pseudo-layer phenomenon is greatly reduced.It can provide a more accurate data basis for the subsequent prediction of other geophysical parameters.
印海燕.AVO叠前反演方法研究[D].山东青岛: 中国石油大学(华东),2008.YIN Haiyan.The Study on Methods of AVO Prestack Inversion[D].China University of Petroleum(East China),Qingdao,Shandong,2008.
WANG L,ZHOU H,WANG Y,et al.Three-parameter prestack seismic inversion based on L1-2 minimization[J].Geophysics,2019,84(5): R753-R766.
[4]
WANG D,GAO J,SUN F,et al.An improved TV-type variational regularization method for seismic impedance inversion[J].IEEE Geoscience and Remote Sensing Letters,2022,19: 7505205.
[5]
ZHANG Y,WU W,ZHANG M,et al.Multitrace impedance inversion based on structure-oriented regularization[J].IEEE Geoscience and Remote Sensing Letters,2022,19: 7503805.
[6]
蔺营.基于混合先验信息的随机反演方法研究[D].山东青岛: 中国石油大学(华东),2020.LIN Ying.Study of Stochastic Inversion Method Based on Mixed Prior Information[D].China University of Petroleum(East China),Qingdao,Shandong,2020.
[7]
BERKHOUT A J.Least-squares inverse filtering and wavelet deconvolution[J].Geophysics,1977,42(7):1369-1383.
TAYLOR H L,BANKS S C,MCCOY J F.Deconvolution with the L1 norm[J].Geophysics,1979,44(1): 39-52.
[10]
THEUNE U.JENSAS I Ø,EIDSVIK J.Analysis of prior models for a blocky inversion of seismic AVA data[J].Geophysics,2010,75(3): C25-C35.
[11]
KONG D,PENG Z,FAN H,et al.Seismic random noise attenuation using directional total variation in the shearlet domain[J].Journal of Seismic Exploration,2016,25(4): 321-338.
[12]
ZHANG F,DAI R,LIU H.Seismic inversion based on L1-norm misfit function and total variation regularization[J].Journal of Applied Geophysics,2014,109: 111-118.
[13]
GUITTON A.Blocky regularization schemes for full-waveform inversion[J].Geophysical Prospecting,2012,60(5): 870-884.
[14]
李昕洁,王维红,郭雪豹,等.全波形反演正则化方法对比[J].石油地球物理勘探,2022,57(1): 129-139.LI Xinjie,WANG Weihong,GUO Xuebao,et al.Comparison of regularization methods for full-waveform inversion[J].Oil Geophysical Prospecting,2022,57(1): 129-139.
[15]
张雨强,文晓涛,吴昊,等.基于Lp拟范数稀疏约束和交替方向乘子算法的波阻抗反演[J].石油物探,2022,61(5): 856-864.ZHANG Yuqiang,WEN Xiaotao,WU Hao,et al.Seismic acoustic impedance inversion using Lp quasi-norm sparse constraint and alternating direction multiplier algorithm[J].Geophysical Prospecting for Petroleum,2022,61(5): 856-864.
[16]
SUN J,LI Y.Adaptive Lp inversion for simultaneous recovery of both blocky and smooth features in a geophysical model[J].Geophysical Journal International,2014,197(2): 882-899.
[17]
PÉREZ D O,VELIS D R,SACCHI M D.Three-term inversion of prestack seismic data using a weighted l2,1 mixed norm[J].Geophysical Prospec-ting,2017,65(6): 1477-1495.
[18]
王治强,曹思远,陈红灵,等.基于TV约束和Toeplitz矩阵分解的波阻抗反演[J].石油地球物理勘探,2017,52(6): 1193-1199,1245.WANG Zhiqiang,CAO Siyuan,CHEN Hongling,et al.Wave impedance inversion based on TV regularization and Toeplitz-sparse matrix factorization[J].Oil Geophysical Prospecting,2017,52(6): 1193-1199,1245.
[19]
LI S,PENG Z M,WU H.Prestack Multi-Gather simultaneous inversion of elastic parameters using multiple regularization constraints[J].Journal of Earth Science,2018,29(6): 1359-1371.
[20]
HUANG G,CHEN X,LUO C,et al.Pre‐stack seismic inversion based on L1-2-norm regularized logarithmic absolute misfit function[J].Geophysical Prospec-ting,2020,68(8): 2419-2443.
[21]
WANG G,CHEN S.Pre-Stack seismic inversion with L1-2-Norm regularization via a proximal DC algorithm and adaptive strategy[J].Surveys in Geophysics,2022,43(6): 1817-1843.
[22]
耿伟恒,陈小宏,李景叶,等.基于 L1-2 正则化的地震波阻抗“块”反演[J].石油地球物理勘探,2022,57(6):1409-1417.GENG Weiheng,CHEN Xiaohong,LI Jingye,et al.Seismic“blocky”acoustic impedance inversion based on L1-2 regularization[J].Oil Geophysical Prospecting,2022,57(6): 1409-1417.
[23]
BOYD S,PARIKH N,CHU E,et al.Distributed optimization and statistical learning via the alternating direction method of multipliers[J].Foundations and Trends in Machine Learning,2011,3(1): 1-122.
[24]
GHADIMI E,TEIXEIRA A,SHAMES I,et al.Optimal parameter selection for the alternating direction method of multipliers (ADMM):quadratic problems[J].IEEE Tran- sactions on Automatic Control,2015,60(3): 644-658.
[25]
唐超,文晓涛,王文化.基于最小范数优化交错网格有限差分系数的波动方程数值模拟[J].石油地球物理勘探,2021,56(5): 1039-1047.TANG Chao,WEN Xiaotao,WANG Wenhua.Numerical simulation of wave equations based on minimum-norm optimization of staggered-grid finite-difference coefficients[J].Oil Geophysical Prospecting,2021,56(5): 1039-1047.
[26]
AKI K,RICHARDS P G.Quantitative Seismology:Theory and Methods[M].W.H.Freeman & Co.,San Franciso,1980.
[27]
CANDÈS E J,WAKIN M B,BOYD S P.Enhancing sparsity by reweighted ℓ1 minimization[J].Journal of Fourier Analysis and Applications,2008,14(5): 877-905.
[28]
吴昊.基于压缩感知的地震波成像及反演方法研究[D].四川成都: 电子科技大学,2020.WU Hao.Research on Seismic Imaging and Inversion Based on Compression Sensing[D].University of Electronic Science and Technology of China,Chengdu,Sichuan,2020.
[29]
HANSEN P C.Analysis of discrete ill-posed problems by means of the L-curve[J].SIAM Review,1992,34(4): 561-580.
[30]
RANATUNGA T,TONG S T Y,YANG Y J.An approach to measure parameter sensitivity in watershed hydrological modelling[J].Hydrological Sciences Journal,2017,62(1): 76-92.
