不依赖子波的弹性波混合域全波形反演
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摘要
震源子波的准确性直接影响全波形反演的建模效果,获取准确的实际子波十分困难。本文基于去子波影响的褶积法,提出弹性波混合域不依赖子波的全波形反演策略。基于二阶弹性波应力—位移方程的混合域反演理论,把观测地震记录与模拟记录的特征道、模拟记录与观测记录的特征道在频率域做乘积运算,构造了不依赖子波的弹性波混合域全波形反演目标函数,推导了反传震源的理论公式。最后,对Overthrust模型进行试算,得到了较好的反演结果,验证了该方法的可行性。
The accuracy of seismic wavelet can directly affect the modeling effect of full waveform inversion.In practice,it is very difficult to get the exact wavelet.In view of this problem,we develop a strategy of elastic wave full waveform inversion in hybrid domain based on the convolution for wavelet-influence removal.Based on the second-order elastic wave stress-displacement equation,we carry out a theoretical calculation of full waveform inversion.The objective function of the full waveform inversion of the elastic wave in hybrid domain is obtained by the multiplication of seismic records with characteristic traces of simulated records and the multiplication of simulated records with characteristic traces of seismic records.The theoretical formula of the reverse source is derived.Finally,numerical calculations on the Overthrust model obtain good inversion results,which verify the feasibility of the proposed approach in hybrid domain.
The accuracy of seismic wavelet can directly affect the modeling effect of full waveform inversion.In practice,it is very difficult to get the exact wavelet.In view of this problem,we develop a strategy of elastic wave full waveform inversion in hybrid domain based on the convolution for wavelet-influence removal.Based on the second-order elastic wave stress-displacement equation,we carry out a theoretical calculation of full waveform inversion.The objective function of the full waveform inversion of the elastic wave in hybrid domain is obtained by the multiplication of seismic records with characteristic traces of simulated records and the multiplication of simulated records with characteristic traces of seismic records.The theoretical formula of the reverse source is derived.Finally,numerical calculations on the Overthrust model obtain good inversion results,which verify the feasibility of the proposed approach in hybrid domain.
引文
[1] 杨勤勇,胡光辉,王立歆.全波形反演研究现状及发展趋势[J].石油物探,2014,53(1):77-83.YANG Qinyong,HU Guanghui,WANG Lixin.Research status and development trend of full waveform inversion[J].Geophysical Prospecting for Petroleum,2014,53(1):77-83.
[2] 苗永康.基于L-BFGS算法的时间域全波形反演[J].石油地球物理勘探,2015,50(3):469-474.MIAO Yongkang.Full waveform inversion in time domain based on limited-memory BFGS algorithm[J].Oil Geophysical Prospecting,2015,50(3):469-474.
[3] 史才旺,何兵寿.基于主成分分析和梯度重构的全波形反演[J].石油地球物理勘探,2018,53(1):95-104.SHI Caiwang,HE Bingshou.Full waveform inversion based on principal component analysis and gradient reconstruction[J].Oil Geophysical Prospecting,2018,53(1):95-104.
[4] 李海山,杨午阳,雍学善.三维一阶速度—应力声波方程全波形反演[J].石油地球物理勘探,2018,53(4):730-736.LI Haishan,YANG Wuyang,YONG Xueshan.Three-dimensional full waveform inversion based on the first-order velocity-stress acoustic wave equation[J].Oil Geophysical Prospecting,2018,53(4):730-736.
[5] Tarantola A.Inversion of seismic reflection data in the acoustic approximation[J].Geophysics,1984,49(8):1259-1266.
[6] Tarantola A.Inverse Problem Theory and Methods for Model Parameter Estimation[M].Society for Industrial & Applied Mathematics,Philadelphia Pa,2005,12:342.
[7] Tarantola A.A strategy for nonlinear elastic inversion of seismic reflection data[J].Geophysics,1986,5(5):1893-1903.
[8] 梁展源,吴国忱,王玉梅.基于波动方程重建震源子波的三维全波形反演[J].石油地球物理勘探,2017,52(6):1200-1207.LIANG Zhanyuan,WU Guochen,WANG Yumei.A 3D full waveform inversion method based on reconstructed source wavelet with wave equation[J].Oil Geophysical Prospecting,2017,52(6):1200-1207.
[9] Bunks C,Saleck F,Zaleski S,et al.Multiscale seismic waveform inversion[J].Geophysics,1995,60(5):1457-1473.
[10] Pica A J,Diet P,Tarantola A.Nonlinear inversion of seismic reflection data in laterally invariant medium[J].Geophysics,1990,55(1):284-292.
[11] Pratt R G.Seismic waveform inversion in the frequency domain,Part 1:Theory and verification in a physical scale model[J].Geophysics,1999,64(3):888-901.
[12] Pratt R G.Inverse theory applied to multi-source cross-hole tomography,part 2:Elastic wave-equation method[J].Geophysical Prospecting,1990,38(3):311-329.
[13] Brossier R,Operto S,Virieux J.Seismic imaging of complex onshore structure by 2D elastic frequency-domain full waveform inversion[J].Geophysics,2009,74(6):WCC105-WCC118.
[14] Operto S,Virieux J,Amestoy P,et al.3D finite-diffe-rence frequency-domain modeling of visco-acoustic wave propagation using a massively parallel direct solver:a feasibility study[J].Geophysics,2007,72(5):SM195-SM211.
[15] Sirgue L,Etgen J T,Albertin U.3D frequency domain waveform inversion using time domain finite diffe-rence methods[C].Extended Abstracts of 70th EAGE Conference & Exhibition,2008,F022.
[16] Fu L Y.Joint inversions of seismic data for acoustic impedance[J].Geophysics,2004,69(6):994-1004.
[17] 杨培杰,印兴耀.地震子波提取方法综述[J].石油地球物理勘探,2008,43(1):123-128.YANG Peijie,YIN Xingyao.Summary of seismic wavelet pick-up[J].Oil Geophysical Prospecting,2008,43(1):123-128.
[18] 陈健,戴永寿,张亚南,等.基于高阶统计量的地震子波提取方法评价[J].石油地球物理勘探,2013,48(3):497-503.CHEN Jian,DAI Yongshou,ZHANG Yanan,et al.Evaluation approaches for wavelet pickup based on high-order statistics[J].Oil Geophysical Prospecting,2013,48(3):497-503.
[19] Song Z M,Williamson P R,Pratt R G.Frequency-domain acoustic-wave modeling and inversion of crosshole data,PartⅡ:Inversion method,synthetic experiments and real-data results[J].Geophysics,1995,60(3):796-809.
[20] 胡勇,韩立国,许卓,等.基于精确震源函数的解调包络多尺度全波形反演[J].地球物理学报,2017,60(3):1088-1105.HU Yong,HAN Liguo,XU Zhuo,et al.Demodulation envelope multi-scale full waveform inversion based on precise seismic source function[J].Chinese Journal of Geophysics,2017,60(3):1088-1105.
[21] Choi Y,Shin C,Min D J,et al.Efficient calculation of the steepest descent direction for source-independent seismic waveform inversion:An amplitude approach[J].Journal of Computational Physics,2005,208(2):455-468.
[22] Choi Y,Alkhalifah T.Source-independent time-domain waveform inversion using convolved wavefields:Application to the Encoded Multisource Waveform Inversion[J].Geophysics,2011,76(5):R125-R134.
[23] 敖瑞德,董良国,迟本鑫.不依赖子波、基于包络的FWI初始模型建立方法研究[J].地球物理学报,2015,58 (6):1998-2010.AO Ruide,DONG Liangguo,CHI Benxin.Source-independent envelope-based FWI to build an initial model[J].Chinese Journal of Geophysics,2015,58(6):1998-2010.
[24] 王毓玮,董良国,黄超,等.降低弹性波全波形反演强烈非线性的分步反演策略[J].石油地球物理勘探,2016,51(2):288-294.WANG Yuwei,DONG Liangguo,HUANG Chao,et al.A multi-step strategy for mitigating severe nonli-nearity in elastic full-waveform inversion[J].Oil Geophysical Prospecting,2016,51(2):288-294.
[25] Crase E C,Wideman M Noble,Tarantola A.Nonlinear elastic inversion of land seismic reflection data[J].Journal of Geophysical Research,1992,97(B4):4685-4705.
[26] K?hn D.Time domain 2D elastic full waveform tomography[D].Christian-Albrechts-Universit?t zu Kiel,2011.
[27] Mora P.Nonlinear two-dimensional elastic inversion of multioffset seismic data[J].Geophysical Journal International,1987,201(3):1324-1334.
[2] 苗永康.基于L-BFGS算法的时间域全波形反演[J].石油地球物理勘探,2015,50(3):469-474.MIAO Yongkang.Full waveform inversion in time domain based on limited-memory BFGS algorithm[J].Oil Geophysical Prospecting,2015,50(3):469-474.
[3] 史才旺,何兵寿.基于主成分分析和梯度重构的全波形反演[J].石油地球物理勘探,2018,53(1):95-104.SHI Caiwang,HE Bingshou.Full waveform inversion based on principal component analysis and gradient reconstruction[J].Oil Geophysical Prospecting,2018,53(1):95-104.
[4] 李海山,杨午阳,雍学善.三维一阶速度—应力声波方程全波形反演[J].石油地球物理勘探,2018,53(4):730-736.LI Haishan,YANG Wuyang,YONG Xueshan.Three-dimensional full waveform inversion based on the first-order velocity-stress acoustic wave equation[J].Oil Geophysical Prospecting,2018,53(4):730-736.
[5] Tarantola A.Inversion of seismic reflection data in the acoustic approximation[J].Geophysics,1984,49(8):1259-1266.
[6] Tarantola A.Inverse Problem Theory and Methods for Model Parameter Estimation[M].Society for Industrial & Applied Mathematics,Philadelphia Pa,2005,12:342.
[7] Tarantola A.A strategy for nonlinear elastic inversion of seismic reflection data[J].Geophysics,1986,5(5):1893-1903.
[8] 梁展源,吴国忱,王玉梅.基于波动方程重建震源子波的三维全波形反演[J].石油地球物理勘探,2017,52(6):1200-1207.LIANG Zhanyuan,WU Guochen,WANG Yumei.A 3D full waveform inversion method based on reconstructed source wavelet with wave equation[J].Oil Geophysical Prospecting,2017,52(6):1200-1207.
[9] Bunks C,Saleck F,Zaleski S,et al.Multiscale seismic waveform inversion[J].Geophysics,1995,60(5):1457-1473.
[10] Pica A J,Diet P,Tarantola A.Nonlinear inversion of seismic reflection data in laterally invariant medium[J].Geophysics,1990,55(1):284-292.
[11] Pratt R G.Seismic waveform inversion in the frequency domain,Part 1:Theory and verification in a physical scale model[J].Geophysics,1999,64(3):888-901.
[12] Pratt R G.Inverse theory applied to multi-source cross-hole tomography,part 2:Elastic wave-equation method[J].Geophysical Prospecting,1990,38(3):311-329.
[13] Brossier R,Operto S,Virieux J.Seismic imaging of complex onshore structure by 2D elastic frequency-domain full waveform inversion[J].Geophysics,2009,74(6):WCC105-WCC118.
[14] Operto S,Virieux J,Amestoy P,et al.3D finite-diffe-rence frequency-domain modeling of visco-acoustic wave propagation using a massively parallel direct solver:a feasibility study[J].Geophysics,2007,72(5):SM195-SM211.
[15] Sirgue L,Etgen J T,Albertin U.3D frequency domain waveform inversion using time domain finite diffe-rence methods[C].Extended Abstracts of 70th EAGE Conference & Exhibition,2008,F022.
[16] Fu L Y.Joint inversions of seismic data for acoustic impedance[J].Geophysics,2004,69(6):994-1004.
[17] 杨培杰,印兴耀.地震子波提取方法综述[J].石油地球物理勘探,2008,43(1):123-128.YANG Peijie,YIN Xingyao.Summary of seismic wavelet pick-up[J].Oil Geophysical Prospecting,2008,43(1):123-128.
[18] 陈健,戴永寿,张亚南,等.基于高阶统计量的地震子波提取方法评价[J].石油地球物理勘探,2013,48(3):497-503.CHEN Jian,DAI Yongshou,ZHANG Yanan,et al.Evaluation approaches for wavelet pickup based on high-order statistics[J].Oil Geophysical Prospecting,2013,48(3):497-503.
[19] Song Z M,Williamson P R,Pratt R G.Frequency-domain acoustic-wave modeling and inversion of crosshole data,PartⅡ:Inversion method,synthetic experiments and real-data results[J].Geophysics,1995,60(3):796-809.
[20] 胡勇,韩立国,许卓,等.基于精确震源函数的解调包络多尺度全波形反演[J].地球物理学报,2017,60(3):1088-1105.HU Yong,HAN Liguo,XU Zhuo,et al.Demodulation envelope multi-scale full waveform inversion based on precise seismic source function[J].Chinese Journal of Geophysics,2017,60(3):1088-1105.
[21] Choi Y,Shin C,Min D J,et al.Efficient calculation of the steepest descent direction for source-independent seismic waveform inversion:An amplitude approach[J].Journal of Computational Physics,2005,208(2):455-468.
[22] Choi Y,Alkhalifah T.Source-independent time-domain waveform inversion using convolved wavefields:Application to the Encoded Multisource Waveform Inversion[J].Geophysics,2011,76(5):R125-R134.
[23] 敖瑞德,董良国,迟本鑫.不依赖子波、基于包络的FWI初始模型建立方法研究[J].地球物理学报,2015,58 (6):1998-2010.AO Ruide,DONG Liangguo,CHI Benxin.Source-independent envelope-based FWI to build an initial model[J].Chinese Journal of Geophysics,2015,58(6):1998-2010.
[24] 王毓玮,董良国,黄超,等.降低弹性波全波形反演强烈非线性的分步反演策略[J].石油地球物理勘探,2016,51(2):288-294.WANG Yuwei,DONG Liangguo,HUANG Chao,et al.A multi-step strategy for mitigating severe nonli-nearity in elastic full-waveform inversion[J].Oil Geophysical Prospecting,2016,51(2):288-294.
[25] Crase E C,Wideman M Noble,Tarantola A.Nonlinear elastic inversion of land seismic reflection data[J].Journal of Geophysical Research,1992,97(B4):4685-4705.
[26] K?hn D.Time domain 2D elastic full waveform tomography[D].Christian-Albrechts-Universit?t zu Kiel,2011.
[27] Mora P.Nonlinear two-dimensional elastic inversion of multioffset seismic data[J].Geophysical Journal International,1987,201(3):1324-1334.