分数阶拉普拉斯算子黏滞声波方程的最小二乘逆时偏移

doi:10.13810/j.cnki.issn.1000-7210.2020.03.017

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摘要衰减补偿型逆时偏移方法能沿波的传播路径对地震波所经历的振幅衰减和相位畸变进行补偿，可提高成像精度和分辨率，但该方法需模拟呈指数增长的地震波场，存在数值不稳定问题。为此，在最小二乘反演理论框架下，基于分数阶拉普拉斯算子黏滞声波方程，推导其对应的Born正演模拟算子和伴随方程，利用反演思路逐步补偿地震波的吸收衰减，解决了传统衰减补偿型逆时偏移方法的不稳定问题。该最小二乘逆时偏移方法采用新颖的常分数阶拉普拉斯算子黏滞声波方程描述地震波的衰减和频散，与实际广泛使用的常Q模型匹配精度高；在反演算法方面，使用限域拟牛顿（L-BFGS）方法计算反射率模型的更新量。Marmousi模型数据和实际数据的偏移算例证实，所提黏滞声波最小二乘逆时偏移方法能稳定地补偿介质的黏滞性，获得高分辨率的地下反射率模型。

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关键词 ：最小二乘逆时偏移, 分数阶拉普拉斯算子, 黏滞声波, 地震成像

Abstract：The attenuation-compensated reverse-time migration (Q-RTM) compensates for amplitude loss and phase distortion along the entire wave propagatiing path,so it can enhance seismic imaging accuracy and resolution.However,since Q-RTM requires to solve an amplitude-boosted wave equation to simulate exponentially increased amplitude,it is not stable.A novel least-squares Q-RTM (LSQRTM) is proposed to stably invert a subsurface reflectivity model.The LSQRTM is based on viscoacoustic Born forward modeling and its adjoint operator that are derived from a new fractional Laplacian viscoacoustic wave equation.The wavefield simulated by the fractional Laplacian viscoacoustic wave equation can well match realistic attenuation and dispersion predicted by a constant-Q model.The L-BFGS algorithm is used in least-squares inversion to calculate the descent direction to update the reflectivity model.Used for Marmousi model and real data,the LSQRTM can stably compensate for the viscosity of the medium and provide a reflectivity model with high resolution.

Key words： least-squares reverse-time migration fractional Laplacian viscoacoustic seismic imaging

收稿日期: 2019-08-22

PACS:

P631

基金资助:本项研究受国家重点研发计划项目“多信息相容约束高效全波形反演方法研究”（2018YFA0702502）、国家自然科学基金青年项目“基于高维最优传输距离目标函数的衰减介质全波形反演研究”（41804111）、国家自然科学基金重点项目“变分数阶拉普拉斯算子粘滞声波方程正演、逆时偏移和全波形反演研究”（41630314）和中国石油大学（北京）科研启动基金课题“全波形反演方法研究”（ZX20180021）等联合资助。

通讯作者: 周辉,北京市昌平区府学路18号中国石油大学(北京)地球物理学院,102249。Email:huizhou@cup.edu.cn E-mail: huizhou@cup.edu.cn

作者简介: 陈汉明,博士,1987年生;2010年本科毕业于长江大学勘查技术与工程专业,2013年获中国石油大学(北京)地球探测与信息技术专业硕士学位,2017年获该校地质资源与地质工程专业博士学位,并留校工作;现为中国石油大学(北京)地球物理学院讲师,SEG/EA-GE会员;主要从事复杂波动方程数值模拟、复杂介质波场传播、波动方程偏移成像和全波形反演等方面的研究;已在国内外SCI/EI期刊发表第一作者论文十余篇。

引用本文:

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. Oil Geophysical Prospecting, 2020, 55(3): 616-626.

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[1]	Dai W,Wang X,Schuster G T. Least-squares migration of multisource data with a deblurring filter[J]. Geophysics,2011,76(5):R135-R146.
[2]	Yao G,Jakubowicz H. Least-squares reverse-time migration[C]. SEG Technical Program Expanded Abstracts,2012,31:1-5.
[3]	Yao G,Jakubowicz H.Non-linear least-squares reverse-time migration[C]. SEG Technical Program Expanded Abstracts,2012,31:1-5.
[4]	Dai W,Fowler P,Schuster G T. Multi-source plane-wave least-squares reverse-time migration[J]. Geophysical Prospecting,2012,60(4):681-695.
[5]	Yao G,Jakubowicz H. Least-squares reverse-time migration in a matrix-based formulation[J]. Geophysical Prospecting,2016,64(3):611-621.
[6]	Wu D, Yao G, Cao J, et al.Least-squares RTM with L1 norm regularization[J]. Journal of Geophysics and Engineering,2016,13(5):666-673.
[7]	方修政,钮凤林,吴迪. 基于逆散射成像条件的最小二乘逆时偏移[J]. 地球物理学报,2018,61(9):3770-3782.FANG Xiuzheng,NIU Fenglin,WU Di. Least-squares reverse-time migration enhanced with the inverse scattering imaging condition[J]. Chinese Journal of Geophysics,2018,61(9):3770-3782.
[8]	Feng Z,Schuster G T. Elastic least-squares reverse-time migration[J]. Geophysics,2017,82(2):S143-S157.
[9]	Duan Y,Guitton A,Sava P. Elastic least-squares reverse time migration[J]. Geophysics,2017,82(4):S315-S325.
[10]	Ren Z,Liu Y,Sen M K. Least-squares reverse-time migration in elastic media[J]. Geophysical Journal International,2017,208(2):1103-1125.
[11]	Fang J,Zhou H,Chen H,et al. Source-independent elastic least-squares reverse time migration[J]. Geophysics,2019,84(1):S1-S16.
[12]	李振春,黄金强,黄建平,等. 基于平面波加速的VTI介质最小二乘逆时偏移[J]. 地球物理学报,2017,60(1):240-257.LI Zhenchun,HUANG Jinqiang,HUANG Jianping,et al. Fast least-squares reverse time migration based on plane-wave encoding for VTI media[J]. Chinese Journal of Geophysics,2017,60(1):240-257.
[13]	郭旭,黄建平,李振春,等. 基于一阶速度-应力方程的VTI介质最小二乘逆时偏移[J]. 地球物理学报,2019,62(6):2188-2202.GUO Xu,HUANG Jianping,LI Zhenchun,et al. Least-squares reverse time migration based on first-order velocity-stress wave equation in VTI media[J]. Chinese Journal of Geophysics,2019,62(6):2188-2202.
[14]	陈生昌,周华敏. 地震数据的反射波动方程最小二乘偏移[J]. 地球物理学报,2018,61(4):1413-1420.CHEN Shengchang,ZHOU Huamin. Least squares migration of seismic data with reflection wave equation[J]. Chinese Journal of Geophysics,2018,61(4):1413-1420.
[15]	Dai W,Schuster G T.Plane-wave least-squares re-verse-time migration[J]. Geophysics,2013,78(4):S165-S177.
[16]	Xue Z,Chen Y,Fomel S,et al. Seismic imaging of incomplete data and simultaneous-source data using least-squares reverse time migration with shaping re-gularization[J]. Geophysics,2016,81(1):S11-S20.
[17]	Chen Y,Chen H,Xiang K,et al. Preserving the discontinuities in least-squares reverse time migration of simultaneous-source data[J].Geophysics,2017,82(3):S185-S196.
[18]	Zhang Q,Mao W,Chen Y.Attenuating crosstalk noise of simultaneous-source least-squares reverse time migration with GPU-based excitation amplitude imaging condition[J]. IEEE Transactions on Geoscience and Remote Sensing,2019,57(1):587-597.
[19]	Claerbout J F. Toward a unified theory of reflector mapping[J]. Geophysics,1971,36(3):467-481.
[20]	Zhu T,Harris J M. Modeling acoustic wave propagation in heterogeneous attenuating media using decoupled fractional Laplacians[J]. Geophysics,2014,79(3):T105-T116.
[21]	吴玉,符力耘,陈高祥.基于分数阶拉普拉斯算子解耦的黏声介质地震正演模拟与逆时偏移[J].地球物理学报,2017,60(4):1527-1537.WU Yu,FU Liyun,CHEN Gaoxiang. Forward mode-ling and reverse time migration of viscoacoustic media using decoupled fractional Laplacians[J]. Chinese Journal of Geophysics,2017,60(4):1527-1537.
[22]	罗文山,陈汉明,王成祥,等. 时间域黏滞波动方程及其数值模拟新方法[J]. 石油地球物理勘探,2016,51(4):707-713.LUO Wenshan,CHEN Hanming,WANG Cheng-xiang,et al. A novel time-domain viscoacoustic wave equation and its numerical simulation[J].Oil Geophysical Prospecting,2016,51(4):707-713.
[23]	Zhu T,Harris J M,Biondi B. Q-compensated reverse time migration[J].Geophysics,2014,79(3):S77-S87.
[24]	Sun J,Zhu T,Fomel S. Viscoacoustic modeling and imaging using low-rank approximation[J]. Geophy-sics,2015,80(5):A103-A108.
[25]	Li Q,Zhou H,Zhang Q,et al. Efficient reverse time migration based on fractional Laplacian viscoacoustic wave equation[J]. Geophysical Journal International,2016,204(1):488-504.
[26]	Wang Y,Zhou H,Chen H,et al. Adaptive stabilization for Q-compensated reverse time migration[J]. Geophysics,2018,83(1):S15-S32.
[27]	Zhao X,Zhou H,Chen H,et al. A stable approach for Q-compensated viscoelastic reverse time migration using excitation amplitude imaging condition[J]. Geophysics,2018,83(5):S459-S476.
[28]	Dutta G,Schuster G T. Attenuation compensation for least-squares reverse time migration using the visco-acoustic-wave equation[J]. Geophysics,2014,79(6):S251-S262.
[29]	李振春,郭振波,田坤. 黏声介质最小平方逆时偏移[J]. 地球物理学报,2014,57(1):214-228.LI Zhenchun, GUO Zhenbo, TIAN Kun. Least-squares reverse time migration in visco-acoustic me-dium[J].Chinese Journal of Geophysics,2014,57(1):214-228.
[30]	Guo P,McMechan G A. Compensating Q effects in viscoelastic media by adjoint-based least-squares reverse time migration[J]. Geophysics,2018,83(2):S151-S172.
[31]	曲英铭,李金丽,王云超,等. 最小二乘逆时偏移中黏弹性和各向异性的校正:以渤海湾地区地震数据为例[J]. 地球物理学报,2019,62(6):2203-2216.QU Yingming,LI Jinli,WANG Yunchao,et al. Correction of viscoelasticity and anisotropy in least-squares reverse time migration:a Bohai Bay seismic case study[J]. Chinese Journal of Geophysics,2019,62(6):2203-2216.
[32]	姚振岸,孙成禹,喻志超,等. 融合点扩散函数的预条件黏声最小二乘逆时偏移[J]. 石油地球物理勘探,2019,54(1):73-83.YAO Zhen'an,SUN Chengyu,YU Zhichao,et al. Preconditioned visco-acoustic least-squares reverse time migration integrated with point spread function[J].Oil Geophysical Prospecting,2019,54(1):73-83.
[33]	吴吉忠,左虎. 叠前衰减补偿时间偏移及GPU实现[J]. 石油地球物理勘探,2019,54(1):84-92.WU Jizhong, ZUO Hu. Attenuation compensation in prestack time migration and its GPU implementation[J].Oil Geophysical Prospecting,2019,54(1):84-92.
[34]	Kjartansson E. Constant Q-wave propagation and attenuation[J]. Journal of Geophysical Research,1979,84(B9):4737-4748.
[35]	蔡瑞乾,孙成禹,伍敦仕,等. 黏声波动方程变机制数有限差分正演[J]. 石油地球物理勘探,2019,54(3):529-538.CAI Ruiqian,SUN Chengyu,WU Dunshi,et al. Finite-difference numerical modeling with variable mechanisms for viscoacoustic wave equation[J]. Oil Geophysical Prospecting,2019,54(3):529-538.
[36]	Chen H,Zhou H,Li Q,et al. Two efficient modeling schemes for fractional Laplacian viscoacoustic wave equation[J]. Geophysics,2016,81(5):T233-T249.
[37]	Carcione J M.A generalization of the Fourier pseudospectral method[J]. Geophysics,2010,75(6):A53-A56.
[38]	Chen H,Zhou H,Rao R,et al.A matrix-transform numerical solver for fractional Laplacians viscoacoustic wave equation[J]. Geophysics,2019,84(4):T283-T297.
[39]	Chen H,Zhou H,Rao R,et al. Fractional Laplacian viscoacoustic wave equation low-rank temporal extrapolation[J]. IEEE Access,2019,7(1):93187-93197.
[40]	Chen H,Zhou H,Lin H,et al. Application of perfectly matched layer for scalar arbitrarily wide-angle wave equations[J]. Geophysics,2013,78(1):T29-T39.
[41]	Plessix R E.A review of the adjoint-state method for computing the gradient of a functional with geophysical applications[J]. Geophysical Journal International,2006, 167(2):495-503.
[42]	Métivier L,Brossier R. The SEISCOPE optimization toolbox:a large-scale nonlinear optimization library based on reverse communication[J].Geophysics,2016,81(2):F1-F15.
[43]	Nocedal J.Updating quasi-Newton matrices with limited storage[J]. Mathematics of Computation,1980,35(151):773-773.