最优化广义离散Shannon奇异核褶积微分算子地震波场模拟
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摘要
本文运用广义离散Shannon奇异核褶积微分算子(GDSCD)计算波动方程的空间导数,推导了一阶和二阶GDSCD的具体形式,并提出了系数优化方法,即在频率域逼近平面波的真实导数,得到不同半径和采样下限的最优权系数。通过计算滤波响应分析算子精度,与多种数值方法进行了对比。模型试算结果表明,本文构造的最优化GDSCD方法模拟地震波具有高精度、高效率的特点。
In this paper,we present an optimal generalized Shannon singular kernel convolution differentiator for solving seismic wave equation.Using generalized Shannon singular kernel convolution differentiator(GDSCD),the first and second order convolution differentiators are derived.Then an efficient method is developed to optimize the coefficients of the convolution differentiator.Many groups of optimal coefficients are obtained for various operator length and sampling rate per shortest wavelength.Compared with various numerical methods,the operator accuracy is discussed through filter response.Our results from model tests show that this new method has high accuracy and efficiency in seismic modeling.
In this paper,we present an optimal generalized Shannon singular kernel convolution differentiator for solving seismic wave equation.Using generalized Shannon singular kernel convolution differentiator(GDSCD),the first and second order convolution differentiators are derived.Then an efficient method is developed to optimize the coefficients of the convolution differentiator.Many groups of optimal coefficients are obtained for various operator length and sampling rate per shortest wavelength.Compared with various numerical methods,the operator accuracy is discussed through filter response.Our results from model tests show that this new method has high accuracy and efficiency in seismic modeling.
引文
[1]陈景波,秦孟兆.辛几何算法在射线追踪中的应用.数值计算与计算机应用,2000,21(4):255～265Chen Jingbo,Qin Mengzhao.Ray tracing by sym-plectic alogorithm.Journal of Numerical Methodsand Computer Applications,2000,21(4):255～265
[2]Kim S,Kerner C.3-D traveltime computation usingsecond order ENO scheme.Geophysics,1999,64(6):1867～1897
[3]Pao Y H,Varatharajulu V.Huygen's principle,radi-ation conditions,and intergral formulas for the scat-tering of elastic wave.J Acous Soc Am,1976,59(6):1361～1371
[4]Ursin B.Review of elastic and electromagnetic wavepropagation in horizontally layered media.Geophy-sics,1983,44(8):1063～1081
[5]胡英,陈辉,苏云等.基于双向介质BISQ模型的地震波正演模拟.石油地球物理勘探,2012,47(6):901～907Hu Ying,Chen Hui,Su Yun et al.Seismic wavemodelling of two-phase media based on BISQ model.OGP,2012,47(6):901～907
[6]Gazdag J.Modeling of the acoustic wave equationwith transform methods.Geophysics,1985,46(5):854～859
[7]薛东川,王尚旭.波动方程有限元叠前逆时偏移.石油地球物理勘探,2008,43(1):17～21Xue Dongchuan,Wang Shangxu.Wave equation fi-nite element prestack reverse-time migration.OGP,2008,43(1):17～21
[8]Komatitsch D.Spectral and Spectral-element Meth-ods for the 2 D and3 D Elastodynamics Equations inHeterogeneous Media[D].Institute de Physique duGlobe,Paris,France,1997
[9]Dormy E,Tarantola A.Numerical simulation of elas-tic wave propagation using a finite volume method.Journal of Geophysical Research,1995,100(B2):2123～2133
[10]Bayliss A,Jordan K E,Lemesurier B J,Turkel E.Afourth-order accurate finite-difference scheme for thecomputation of elastic wave.Bul Seism Soc Am,1986,76(4):1115～132
[11]Fornberg B.The pseudospectral method:Comparisonwith finite differences for the elastic wave equation.Geophysics,1987,52(4):483～501
[12]Fei T,Larner K.Elimination of numerical dispersionin finite difference modeling and migration by flux-corrected transport.Geophysics,1995,60(6):1830～
[13]Li X F,Wang W S,Lu M W et al.Structure-preser-ving modeling of elastic wave:a symplectic discretesingular convolution differetiator method.Geophys JIn,2012,188(3):1382～1392
[14]Mora P.Elastic fininte difference with convolutionaloperatrors.Stanford Exploration Project Report,California,1986:277～290
[15]Holberg O.Computation aspects of the choice of op-erator and sampling interval for numerical differntia-tion in large-scale simulation of wave phenomena.Ge-ophysical Prospecting,1987,35(6):629～655
[16]Zhou B,Greenhalgh S.Seismic scalar wave equationmodeling by a convolutonal differentiator.Bull SeismSoc Am,1992,82(1):289～303
[17]戴志阳,孙建国,查显杰.地震波场模拟中的褶积微分算子法.吉林大学学报(地球科学版),2005,35(4):520～524Dai Zhiyang,Sun Jianguo,Zha Xianjie.Seismic wavefield modeling with convolutional differentiator algo-rithm.Journal of Jilin University(Earth Science E-dition),2005,35(4):520～524
[18]龙桂华,赵宇波,赵家福.地震波数值模拟中的最优Shannnon奇异核褶积微分算子.地震学报,2011,33(5):650～662Long Guihua,Zhao Yubo,Zhao Jiafu.Optimal Shan-non singular kernel convolutional differentiator inseismic wave modeling.Acta Seismologica Sinica,2011,33(5):650～662
[19]Wei G W.Quasi wavelets and quasi interpolatingwavelets.Chemical Physics Letters,1998,296(3-4):215～220
[20]Qian L W.On the regularized whittaker-kotel'nikovShannon shampling formula.American MathematicalSociety,2002,131(4):1169～1176
[21]Feng B F,Wei G W.A comparison of the spectraland the discrete singular convolution schemes for theKdV-type equations.Journal of Computation Ap-plied Mathematics,2002,145(1):138～188
[22]龙桂华,李小凡,张美根.基于Shannon奇异核理论的褶积微分算子在地震波模拟中的应用.地球物理学报,2009,52(4):1014～1024Long Guihua,Li Xiaofan,Zhang Meigen.The appli-cation of convolutional differentiator in seismic model-ing based on Shannon singular kernel theory.ChineseJ Geophys,2009,52(4):1014～1024
[23]Jo C H,Shin C,Suh J H.An optimal 9-point,finite-difference,frequency-space,2-D scalar wave extrapo-lator.Geophysics,1996,61(2):529～537
[24]熊章强,毛承英.声波数值模拟中改进的非分裂式PML边界条件.石油地球物理勘探,2011,46(1):35～39Xiong Zhangqiang,Mao Chengying.Improved un-split PML boundary conditions in acoustic wave nu-merical simulation.OGP,2011,46(1):35～39
[2]Kim S,Kerner C.3-D traveltime computation usingsecond order ENO scheme.Geophysics,1999,64(6):1867～1897
[3]Pao Y H,Varatharajulu V.Huygen's principle,radi-ation conditions,and intergral formulas for the scat-tering of elastic wave.J Acous Soc Am,1976,59(6):1361～1371
[4]Ursin B.Review of elastic and electromagnetic wavepropagation in horizontally layered media.Geophy-sics,1983,44(8):1063～1081
[5]胡英,陈辉,苏云等.基于双向介质BISQ模型的地震波正演模拟.石油地球物理勘探,2012,47(6):901～907Hu Ying,Chen Hui,Su Yun et al.Seismic wavemodelling of two-phase media based on BISQ model.OGP,2012,47(6):901～907
[6]Gazdag J.Modeling of the acoustic wave equationwith transform methods.Geophysics,1985,46(5):854～859
[7]薛东川,王尚旭.波动方程有限元叠前逆时偏移.石油地球物理勘探,2008,43(1):17～21Xue Dongchuan,Wang Shangxu.Wave equation fi-nite element prestack reverse-time migration.OGP,2008,43(1):17～21
[8]Komatitsch D.Spectral and Spectral-element Meth-ods for the 2 D and3 D Elastodynamics Equations inHeterogeneous Media[D].Institute de Physique duGlobe,Paris,France,1997
[9]Dormy E,Tarantola A.Numerical simulation of elas-tic wave propagation using a finite volume method.Journal of Geophysical Research,1995,100(B2):2123～2133
[10]Bayliss A,Jordan K E,Lemesurier B J,Turkel E.Afourth-order accurate finite-difference scheme for thecomputation of elastic wave.Bul Seism Soc Am,1986,76(4):1115～132
[11]Fornberg B.The pseudospectral method:Comparisonwith finite differences for the elastic wave equation.Geophysics,1987,52(4):483～501
[12]Fei T,Larner K.Elimination of numerical dispersionin finite difference modeling and migration by flux-corrected transport.Geophysics,1995,60(6):1830～
[13]Li X F,Wang W S,Lu M W et al.Structure-preser-ving modeling of elastic wave:a symplectic discretesingular convolution differetiator method.Geophys JIn,2012,188(3):1382～1392
[14]Mora P.Elastic fininte difference with convolutionaloperatrors.Stanford Exploration Project Report,California,1986:277～290
[15]Holberg O.Computation aspects of the choice of op-erator and sampling interval for numerical differntia-tion in large-scale simulation of wave phenomena.Ge-ophysical Prospecting,1987,35(6):629～655
[16]Zhou B,Greenhalgh S.Seismic scalar wave equationmodeling by a convolutonal differentiator.Bull SeismSoc Am,1992,82(1):289～303
[17]戴志阳,孙建国,查显杰.地震波场模拟中的褶积微分算子法.吉林大学学报(地球科学版),2005,35(4):520～524Dai Zhiyang,Sun Jianguo,Zha Xianjie.Seismic wavefield modeling with convolutional differentiator algo-rithm.Journal of Jilin University(Earth Science E-dition),2005,35(4):520～524
[18]龙桂华,赵宇波,赵家福.地震波数值模拟中的最优Shannnon奇异核褶积微分算子.地震学报,2011,33(5):650～662Long Guihua,Zhao Yubo,Zhao Jiafu.Optimal Shan-non singular kernel convolutional differentiator inseismic wave modeling.Acta Seismologica Sinica,2011,33(5):650～662
[19]Wei G W.Quasi wavelets and quasi interpolatingwavelets.Chemical Physics Letters,1998,296(3-4):215～220
[20]Qian L W.On the regularized whittaker-kotel'nikovShannon shampling formula.American MathematicalSociety,2002,131(4):1169～1176
[21]Feng B F,Wei G W.A comparison of the spectraland the discrete singular convolution schemes for theKdV-type equations.Journal of Computation Ap-plied Mathematics,2002,145(1):138～188
[22]龙桂华,李小凡,张美根.基于Shannon奇异核理论的褶积微分算子在地震波模拟中的应用.地球物理学报,2009,52(4):1014～1024Long Guihua,Li Xiaofan,Zhang Meigen.The appli-cation of convolutional differentiator in seismic model-ing based on Shannon singular kernel theory.ChineseJ Geophys,2009,52(4):1014～1024
[23]Jo C H,Shin C,Suh J H.An optimal 9-point,finite-difference,frequency-space,2-D scalar wave extrapo-lator.Geophysics,1996,61(2):529～537
[24]熊章强,毛承英.声波数值模拟中改进的非分裂式PML边界条件.石油地球物理勘探,2011,46(1):35～39Xiong Zhangqiang,Mao Chengying.Improved un-split PML boundary conditions in acoustic wave nu-merical simulation.OGP,2011,46(1):35～39
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