基于L-BFGS算法和同时激发震源的频率多尺度全波形反演
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摘要
全波形反演可以利用叠前地震波场的运动学和动力学信息重建地下速度结构,具有揭示复杂地质背景下构造与岩性细节信息的潜力。然而,庞大的计算量和存储空间需求,限制了全波形反演的发展。在频率多尺度全波形反演中将L-BFGS数值优化算法与同时激发震源技术相结合的方法来改善这一现状。首先,对Marmousi模型进行了速度反演:在计算过程中明显发现对计算机内存的占用减少,最终反演结果与实际Marmousi模型的拟合误差为0.095 9,较小;采用10个频带单炮震源正演384炮所需时间约为32 640s,而采用同时激发震源(384炮)正演一次所需时间仅约为700s。然后,基于高速楔形体模型进行了抗噪能力研究:原始含噪地震记录信噪比为11.147 3dB;对反演得到的速度模型进行正演,其地震记录信噪比为22.251 8dB。最后,基于逆冲断层模型进行了反演速度扰动能力研究,反演得到的最终模型很清晰,与具有速度扰动特性的实际模型非常接近,拟合误差仅为0.036 0。数值模拟试验结果表明:此方法反演精度高,内存开销较小,能够显著提高计算效率,并且具有良好的抗噪能力,能够反演出具有速度扰动特性的介质。
Full waveform inversion(FWI) can reconstruct underground velocity while utilizing the kinematic and dynamic information of pre-stack seismic data,which could reveal detail information of the structure and lithology under complex geological background.However,huge calculating amount and storage space requirements confine the development of full waveform inversion.A combined method of L-BFGS algorithm and simultaneous sources technology is applied to ameliorate this problem during frequency multi-scale full waveform inversion.First we carry out velocity inversion based on the Marmousi model.It can be obviously found that the memory spending has been improved considerably in the process of calculation,and the fitting error between the final inversion result and true Marmousi model is as small as 0.095 9.Meanwhile,single shot forward modeling 384 times takes about 32 640 seconds when using 10 frequency bands,while simultaneous sources which contain 384 shots forward modeling one time needs only about 700 seconds.Then we conduct research on the anti-noise ability based on the high-speed wedge model.The signal to noise ratio of original seismic data is 11.147 3 dB,while the signal to noise ratio of the seismic data obtained from forward modeling based on inversion velocity model is 22.251 8 dB.Finally we conduct research on inversing the medium with velocity perturbation based on the thrust fault model.The final inversion model is very clear and very satisfied with the real model with velocity perturbation characteristics,and the fitting error between them is only 0.036 0.Numerical simulation experiment result indicates that the inversion precision of this method is higher enough,and the memory spending is less,which could significantly increase calculation efficiency.What is more,this method has good anti-noise ability,and could inverse the medium with velocity perturbation characteristics.
Full waveform inversion(FWI) can reconstruct underground velocity while utilizing the kinematic and dynamic information of pre-stack seismic data,which could reveal detail information of the structure and lithology under complex geological background.However,huge calculating amount and storage space requirements confine the development of full waveform inversion.A combined method of L-BFGS algorithm and simultaneous sources technology is applied to ameliorate this problem during frequency multi-scale full waveform inversion.First we carry out velocity inversion based on the Marmousi model.It can be obviously found that the memory spending has been improved considerably in the process of calculation,and the fitting error between the final inversion result and true Marmousi model is as small as 0.095 9.Meanwhile,single shot forward modeling 384 times takes about 32 640 seconds when using 10 frequency bands,while simultaneous sources which contain 384 shots forward modeling one time needs only about 700 seconds.Then we conduct research on the anti-noise ability based on the high-speed wedge model.The signal to noise ratio of original seismic data is 11.147 3 dB,while the signal to noise ratio of the seismic data obtained from forward modeling based on inversion velocity model is 22.251 8 dB.Finally we conduct research on inversing the medium with velocity perturbation based on the thrust fault model.The final inversion model is very clear and very satisfied with the real model with velocity perturbation characteristics,and the fitting error between them is only 0.036 0.Numerical simulation experiment result indicates that the inversion precision of this method is higher enough,and the memory spending is less,which could significantly increase calculation efficiency.What is more,this method has good anti-noise ability,and could inverse the medium with velocity perturbation characteristics.
引文
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[14]Berkhout A J.Changing the Mindset in Seismic DataAcquisition[J].The Leading Edge,2008,27(7):924-938.
[15]Neelamani R,Krohn C E,Krebs J R,et al.EfficientSeismic Forward Modeling Using Simultaneous Ran-dom Sources and Sparsity[J].Geophysics,2010,75(6):WB15-WB27.
[16]Liu D C,Nocedal J.On the Limited Memory BFGSMethod for Large Scale Optimization[J].Mathemati-cal Programming,1989,45(1):503-528.
[17]张亚红.Focal变换及其在地震数据去噪和插值中的应用研究[D].长春:吉林大学,2010.Zhang Yahong.Focal Transformation Research andApplication in Seismic Data Denoising and Interpola-tion[D].Changchun:Jilin University,2010.
[18]王恩利.基于各向异性的复合介质弹性波场模拟与特征分析[D].长春:吉林大学,2008.Wang Enli.The Forward Modeling and Character A-nalysis for Complex Media Based on AnisotropicMedia[D].Changchun:Jilin University,2008.
[2]Tarantola A.A Strategy for Nonlinear Elastic Inver-sion of Seismic Reflection Data[J].Geophysics,1986,51(10):1893-1903.
[3]Marfurt K J.Accuracy of Finite-Difference and Finite-Element Modeling of the Scalar and Elastic Wave E-quation[J].Geophysics,1984,49(5):533-549.
[4]Pratt R G.Frequency-Domain Elastic Wave Modelingby Finite Differences:A Tool for Crosshole SeismicImaging[J].Geophysics,1990,55(5):626-632.
[5]Pratt R G,Worthington M H.Inverse Theory Ap-plied to Multi-Source Cross-Hole Tomography:Part1:Acoustic Wave-Equation Method[J].GeophysicalProspecting,1990,38(3):287-310.
[6]Pratt R G.Inverse Theory Applied to Multi-SourceCross-Hole Tomography:Part 2:Elastic Wave-Equa-tion Method[J].Geophysical Prospecting,1990,38(3):311-329.
[7]Pratt R G,Shin C,Hicks G J.Gauss-Newton andFull Newton Methods in Frequency-Space SeismicWaveform Inversion[J].Geophysical Journal Interna-tional,1998,133(2):341-362.
[8]Song Z M,Williamson P R,Pratt R G.Frequency-Domain Acoustic-Wave Modeling and Inversion ofCrosshole Data:Part 2:Inversion Method,SyntheticExperiments and Real-Data Results[J].Geophysics,1995,60(3):796-809.
[9]Sourbier F,Operto S,Virieux J,et al.FWT2D:AMassively Parallel Program for Frequency-DomainFull-Waveform Tomography of Wide-Aperture SeismicData:Part 1:Algorithm[J].Computers and Geosci-ences,2009,35(3):487-495.
[10]Pratt R G.Seismic Waveform Inversion in the Fre-quency Domain:Part 1:Theory and Verification in aPhysical Scale Model[J].Geophysics,1999,64(3):888-901.
[11]Nocedal J.Updating Quasi-Newton Matrices withLimited Storage[J].Mathematics of Computation,1980,35:773-782.
[12]Qin Z W(Tony).The Relationships Between CG,BFGS,and Two Limited-Memory Algorithms[J].Electronic Journal of Undergraduate Mathematics,2007,12:5-20.
[13]韩利,韩立国,李翔,等.二阶声波方程频域PML边界条件及频域变网格步长并行计算[J].吉林大学学报:地球科学版,2011,41(4):1226-1232.Han Li,Han Liguo,Li Xiang,et al.PML BoundaryConditions for Second-Order Acoustic Wave Equa-tions and Variable Grid Parallel Computation in Fre-quency-Domain Modeling[J].Journal of Jilin Univer-sity:Earth Science Edition,2011,41(4):1226-1232.
[14]Berkhout A J.Changing the Mindset in Seismic DataAcquisition[J].The Leading Edge,2008,27(7):924-938.
[15]Neelamani R,Krohn C E,Krebs J R,et al.EfficientSeismic Forward Modeling Using Simultaneous Ran-dom Sources and Sparsity[J].Geophysics,2010,75(6):WB15-WB27.
[16]Liu D C,Nocedal J.On the Limited Memory BFGSMethod for Large Scale Optimization[J].Mathemati-cal Programming,1989,45(1):503-528.
[17]张亚红.Focal变换及其在地震数据去噪和插值中的应用研究[D].长春:吉林大学,2010.Zhang Yahong.Focal Transformation Research andApplication in Seismic Data Denoising and Interpola-tion[D].Changchun:Jilin University,2010.
[18]王恩利.基于各向异性的复合介质弹性波场模拟与特征分析[D].长春:吉林大学,2008.Wang Enli.The Forward Modeling and Character A-nalysis for Complex Media Based on AnisotropicMedia[D].Changchun:Jilin University,2008.
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