基于LSQR算法的二维声波方程频率域正演模拟与数值实现
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摘要
频率域正演是频率域全波形反演的基础,高效准确地完成频率域正演计算是目前该领域的一个热门问题。这里利用优化17点差分格式和PML完全匹配层构建波场,并使用LSQR算法求解波场,通过在简单层状模型和Overthrust模型上计算验证可知,LSQR算法可大幅提高频率域正演的计算速度和模拟精度,从而为此方向的研究提供一个可行的技术手段。
The frequency domain forward is the basis of the freguency domain full-waveform inversion(FWI).How to efficiently and accurately complete the frequency domain computation is a hot issue in this field at present. In this paper, we use the optimized 17 point difference scheme and PML to construct wave field, and the use of the LSQR algorithm for solving the wave field. Through simple layered model and the Overthrust model calculation show that LSQR algorithm can greatly improve the calculation speed and accuracy of frequency domain modeling. Therefore, a feasible technical means is provided for the study of this direction.
The frequency domain forward is the basis of the freguency domain full-waveform inversion(FWI).How to efficiently and accurately complete the frequency domain computation is a hot issue in this field at present. In this paper, we use the optimized 17 point difference scheme and PML to construct wave field, and the use of the LSQR algorithm for solving the wave field. Through simple layered model and the Overthrust model calculation show that LSQR algorithm can greatly improve the calculation speed and accuracy of frequency domain modeling. Therefore, a feasible technical means is provided for the study of this direction.
引文
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[4] STEKL I,Pratt K G. Frequency-domain finite accurate differences visco-elastic modeling by using rotated operators[J].Geophysics,1998,63(5):1779-1794.
[5] MIN J,SHIN C,KWON B,et al.Improved frequency-do-main elastic wave modeling using weighted-averaging difference operators[J].Geophysics,2000,65(3):884-895.
[6] HUSTEDT B,OPERT S,VIRIEUX J.Mixed-grid and staggered grid finite-difference methods for frequency-domain acoustic wave modeling[J].Geophysics,2004,157(3):1269-1296.
[7] 吴国忱,梁锴.VTI 介质频率-空间域准P波正演模拟[J].石油地球物理勘探,2005,40(5):535-545.WU G C,LIANG K.Quasi P-wave forward modeling in frequency-space domain in VTI media[J].Oil Geophysical Prospecting,2005,40(5):535-545.(In Chinese)
[8] 吴国忱,罗彩明,梁锴.TTI介质弹性波频率空间域有限差分数值模拟[J].吉林大学学报(地球科学版),2007,37(5):1023-1033.WU G C,LUO C M,LIANG K.Frequency-space domain finite difference numerical simulation of elastic wave in TTI media[J].Journal of Jilin University(Earth Science Edition),2007,37(5):1023-1033.(In Chinese)
[9] 任浩然,王华忠,龚婷.标量地震波频率-空间域有限差分法数值模拟[J].石油物探,2009,48(01):20-26.REN H R,WANG H Z,GONG T.Numerical simulation of scaslar seismic wave using frequency-space finite difference method[J].Geophysical Prospecting for Petroleum,2009,48(01):20-26.(In Chinese)
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[13] 刘伊克,常旭.地震层析成像反演中解的定量评价及其应用[J].地球物理学报,2000,43(2):251-256.LIU Y K,CHANG X.Quantitative assessment of inversion solution of seismic tomographys and its application[J].ChineseJ.Geophys,2000,43(2):251-256.(In Chinese)
[14] 杨文采.地球物理反演的理论与方法[M].北京:地质出版社,1997.YANG W C.Theory and methods in geophysical inversion[M].Beijing:Geological Publishing House,1997.(In Chinese)
[15] 刘劲松,刘福田,刘俊,等.地震层析成像LSQR算法的并行化[J].地球物理学报,2006,49(2):540-545.LIU J S,LIU F T,LIU J,et al.Parallel LSQR algorithms used in seismic tomography[J].Chinese Journal of Geophysics,2006,49(2):540-454.(In Chinese)
[16] 曹书红,陈景波.声波方程频率域高精度正演的 17 点格式及数值实现[J].地球物理学报,2012,55(10):3440-3449.CAO S H,CHEN J B.A 17-point scheme and its numerical implementation for high-accuracy modeling of frequency-domain acoustic equation[J].Chinese Journal of Geophysics,2012,55(10):3440-3449.(In Chinese)
[17] 董良国,李培明.地震波传播数值模拟中的频散问题[J].天然气工业,2004,24(6):53-56.DONG L G,LI P M.Dispersive problem in seismic wave propagation numerical modeling[J].Natural Gas Industry,2004,24(6):53-56.(In Chinese)
[18] 李国平,姚逢昌,石玉梅,等.有限差分法地震波数值模拟的几个关键问题[J] .地球物理学进展,2011,26(2):469-476.LI G P,YAO F C,SHI Y M,et al. Several key problems of numerical simulation of seismic waves by finite difference method[J]. Progress in Geophysics,2011,26(2):469-476.(In Chinese)
[19] 王守东.声波方程完全匹配层吸收边界[J].石油地球物理勘探,2003,38(1):31-34.WANG S D.Absorbing boundary condition for acoustic wave equation by perfectly matched layer[J].Oil Geophysical Prospecting,2003,38(1):31-34.(In Chinese)
[20] 陈可洋.完全匹配层吸收边界条件研究[J].石油物探,2010,49(5):472-477.CHEN K Y.Study on the boundary condition of fully matched layer absorption[J].Geophysical Prospecting For Petroleum,2010,49(5):472-477.(In Chinese)
[21] 陈可洋.声波完全匹配层吸收边界条件的改进算法[J].石油物探,2009,48(1):76-79.CHEN K Y.An improved algorithm for absorbing boundary conditions at the fully matched layer of soundwaves[J].Geophysical Prospecting For Petroleum,2009,48(1):76-79.(In Chinese)
[22] 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):1227-1232.HAN L,HAN L G,LI X,et al.PML boundary conditions for second-order acoustic wave equations and variable grid parallel computation in frequency-domain modeling[J].Journal of Jilin University(Earth Science Edition),2011,41(4):1227-1232.(In Chinese)
[23] BERENGER J P.A perfectly matched 1ayer for the absorption of electromagnetic waves[J].Compote Phys,1994,114:185-200.
[24] 陈可洋.标量声波波动方程高阶交错网格有限差分法[J].中国海上油气,2009,21(4):232-236.CHEN K Y.High-order staggered-grid finite difference scheme for scalar acoustic wave equation[J].China Offshore Oil And Gas,2009,21(4):232-236.(In Chinese)
[25] 裴正林.三维各向同性介质弹性波方程交错网格高阶有限差分法模拟[J] .石油物探,2005,44(4):308-315.PEI Z L.Simulation of three dimensional isotropic medium elastic wave equation with staggered grid high order finite difference method[J].Geophysical ProspectingFor Petroleum,2005,44(4):308-315.(In Chinese)
[26] 裴正林,牟永光.地震波传播数值模拟[J].地球物理学进展,2004,19(4):933-941.PEI Z L,MOU Y G.Numerical simulation of seismic wave propagation[J].Progress in Geophysics,2004,19(4):933-941.(In Chinese)
[27] 殷文.基于频率域高阶有限差分法的正演模拟及并行算法[J].吉林大学学报(地球科学版),2008,38(1):144-151.YING W,Forward modeling and parallel algorithm based on high-order finite-difference method in frequency domain[J].Journal of Jilin University(Earth Science Edition),2008,38(1):144-151.(In Chinese)
[2] SHIN C S.Nonlinear Elastic wave Inversion by Blocky Parameterization[D].Tulsa:University of Tulsa,1988.
[3] JO C,SHIN C,SUH J.An optimal 9-point finite-difference frequency space 2-D scalar wave extrapolator [J].Geophysics,1996,61(2):529-537.
[4] STEKL I,Pratt K G. Frequency-domain finite accurate differences visco-elastic modeling by using rotated operators[J].Geophysics,1998,63(5):1779-1794.
[5] MIN J,SHIN C,KWON B,et al.Improved frequency-do-main elastic wave modeling using weighted-averaging difference operators[J].Geophysics,2000,65(3):884-895.
[6] HUSTEDT B,OPERT S,VIRIEUX J.Mixed-grid and staggered grid finite-difference methods for frequency-domain acoustic wave modeling[J].Geophysics,2004,157(3):1269-1296.
[7] 吴国忱,梁锴.VTI 介质频率-空间域准P波正演模拟[J].石油地球物理勘探,2005,40(5):535-545.WU G C,LIANG K.Quasi P-wave forward modeling in frequency-space domain in VTI media[J].Oil Geophysical Prospecting,2005,40(5):535-545.(In Chinese)
[8] 吴国忱,罗彩明,梁锴.TTI介质弹性波频率空间域有限差分数值模拟[J].吉林大学学报(地球科学版),2007,37(5):1023-1033.WU G C,LUO C M,LIANG K.Frequency-space domain finite difference numerical simulation of elastic wave in TTI media[J].Journal of Jilin University(Earth Science Edition),2007,37(5):1023-1033.(In Chinese)
[9] 任浩然,王华忠,龚婷.标量地震波频率-空间域有限差分法数值模拟[J].石油物探,2009,48(01):20-26.REN H R,WANG H Z,GONG T.Numerical simulation of scaslar seismic wave using frequency-space finite difference method[J].Geophysical Prospecting for Petroleum,2009,48(01):20-26.(In Chinese)
[10] PAIGE C C,SAUNDERS M A.LSQR:an algorithm for sparse liner equation and sparse least squares[J].ACM Transactins on Mathematical Software,1982,8(1):43-71.
[11] BJORCK,A. DUFF,I.S.A direct method for the solution of sparse linear least squares problems[J].Linear Algebra and its Applications,1980,34(1):43-67.
[12] 刘伊克.地震层析成像的方法及应用研究[D].北京:中国科学院地球物理研究所,1988.LIU Y K. Method and application of seismic tomography[D].Beijing:Institute of Geophysics,Chinese Academy of Sciences,1988.(In Chinese)
[13] 刘伊克,常旭.地震层析成像反演中解的定量评价及其应用[J].地球物理学报,2000,43(2):251-256.LIU Y K,CHANG X.Quantitative assessment of inversion solution of seismic tomographys and its application[J].ChineseJ.Geophys,2000,43(2):251-256.(In Chinese)
[14] 杨文采.地球物理反演的理论与方法[M].北京:地质出版社,1997.YANG W C.Theory and methods in geophysical inversion[M].Beijing:Geological Publishing House,1997.(In Chinese)
[15] 刘劲松,刘福田,刘俊,等.地震层析成像LSQR算法的并行化[J].地球物理学报,2006,49(2):540-545.LIU J S,LIU F T,LIU J,et al.Parallel LSQR algorithms used in seismic tomography[J].Chinese Journal of Geophysics,2006,49(2):540-454.(In Chinese)
[16] 曹书红,陈景波.声波方程频率域高精度正演的 17 点格式及数值实现[J].地球物理学报,2012,55(10):3440-3449.CAO S H,CHEN J B.A 17-point scheme and its numerical implementation for high-accuracy modeling of frequency-domain acoustic equation[J].Chinese Journal of Geophysics,2012,55(10):3440-3449.(In Chinese)
[17] 董良国,李培明.地震波传播数值模拟中的频散问题[J].天然气工业,2004,24(6):53-56.DONG L G,LI P M.Dispersive problem in seismic wave propagation numerical modeling[J].Natural Gas Industry,2004,24(6):53-56.(In Chinese)
[18] 李国平,姚逢昌,石玉梅,等.有限差分法地震波数值模拟的几个关键问题[J] .地球物理学进展,2011,26(2):469-476.LI G P,YAO F C,SHI Y M,et al. Several key problems of numerical simulation of seismic waves by finite difference method[J]. Progress in Geophysics,2011,26(2):469-476.(In Chinese)
[19] 王守东.声波方程完全匹配层吸收边界[J].石油地球物理勘探,2003,38(1):31-34.WANG S D.Absorbing boundary condition for acoustic wave equation by perfectly matched layer[J].Oil Geophysical Prospecting,2003,38(1):31-34.(In Chinese)
[20] 陈可洋.完全匹配层吸收边界条件研究[J].石油物探,2010,49(5):472-477.CHEN K Y.Study on the boundary condition of fully matched layer absorption[J].Geophysical Prospecting For Petroleum,2010,49(5):472-477.(In Chinese)
[21] 陈可洋.声波完全匹配层吸收边界条件的改进算法[J].石油物探,2009,48(1):76-79.CHEN K Y.An improved algorithm for absorbing boundary conditions at the fully matched layer of soundwaves[J].Geophysical Prospecting For Petroleum,2009,48(1):76-79.(In Chinese)
[22] 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):1227-1232.HAN L,HAN L G,LI X,et al.PML boundary conditions for second-order acoustic wave equations and variable grid parallel computation in frequency-domain modeling[J].Journal of Jilin University(Earth Science Edition),2011,41(4):1227-1232.(In Chinese)
[23] BERENGER J P.A perfectly matched 1ayer for the absorption of electromagnetic waves[J].Compote Phys,1994,114:185-200.
[24] 陈可洋.标量声波波动方程高阶交错网格有限差分法[J].中国海上油气,2009,21(4):232-236.CHEN K Y.High-order staggered-grid finite difference scheme for scalar acoustic wave equation[J].China Offshore Oil And Gas,2009,21(4):232-236.(In Chinese)
[25] 裴正林.三维各向同性介质弹性波方程交错网格高阶有限差分法模拟[J] .石油物探,2005,44(4):308-315.PEI Z L.Simulation of three dimensional isotropic medium elastic wave equation with staggered grid high order finite difference method[J].Geophysical ProspectingFor Petroleum,2005,44(4):308-315.(In Chinese)
[26] 裴正林,牟永光.地震波传播数值模拟[J].地球物理学进展,2004,19(4):933-941.PEI Z L,MOU Y G.Numerical simulation of seismic wave propagation[J].Progress in Geophysics,2004,19(4):933-941.(In Chinese)
[27] 殷文.基于频率域高阶有限差分法的正演模拟及并行算法[J].吉林大学学报(地球科学版),2008,38(1):144-151.YING W,Forward modeling and parallel algorithm based on high-order finite-difference method in frequency domain[J].Journal of Jilin University(Earth Science Edition),2008,38(1):144-151.(In Chinese)
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