基于NAD算子的高精度低数值频散地震波模拟方法
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摘要
基于二维声波方程,使用四阶截断的泰勒展开式离散时间偏导数,利用八阶精度的近似解析离散算子离散空间高阶偏导数,发展了一种八阶ONAD方法.通过数值误差、计算效率和复杂介质波场模拟等考察研究,结果均显示该方法在压制数值频散、计算效率和波场模拟精度等方面明显优越于四阶LAX-Wendroff Corrected(LWC)方法和八阶LWC方法.因此,八阶ONAD方法是一种有望在地震波模拟得到应用的十分有效的数值模拟方法.
The eighth-order ONAD method is developed for solving the 2-D acoustic wave equation.The new method uses the fourth-order truncated Taylor expansion to discretize partial derivative of time,and employs the eighth-order nearly analytic discrete operator discretize high-order partial derivatives of space.Through studying the numerical error,computational efficiency and complex medium wave-field simulations,those results show that this method is obviously superior to the fourth-order LAX-Wendroff Corrected(LWC)method and the eighth-order LWC method in suppressing the numerical dispersion,computational efficiency and simulation precision of wave-fields.Therefore,the eighth-order ONAD method is a very effective method of numerical simulation and can be applied in the seismic wave simulation.
The eighth-order ONAD method is developed for solving the 2-D acoustic wave equation.The new method uses the fourth-order truncated Taylor expansion to discretize partial derivative of time,and employs the eighth-order nearly analytic discrete operator discretize high-order partial derivatives of space.Through studying the numerical error,computational efficiency and complex medium wave-field simulations,those results show that this method is obviously superior to the fourth-order LAX-Wendroff Corrected(LWC)method and the eighth-order LWC method in suppressing the numerical dispersion,computational efficiency and simulation precision of wave-fields.Therefore,the eighth-order ONAD method is a very effective method of numerical simulation and can be applied in the seismic wave simulation.
引文
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Dablain M A.1986.The application of high-order differencing to the scalar wave equation[J].Geophysics,51(1):54-66.
Dong L G,Ma Z T,Cao J Z,et al.2000.A staggered-grid highorder difference method of one-order elastic wave equation[J].Chinese J.Geophys.(in Chinese),43(3):411-419.
Fei T,Larner K.1995.Elimination of numerical dispersion in finitedifference modeling and migration by flux-corrected transport[J].Geophysics,60(6):1830-1842.
Huang B S.1992.A program for two-dimensional seismic wave propagation by the pseudospectrum method[J].Comput.Geosci.,18(2-3):289-307.
Kelly K R,Ward R W,Treitel S,et al.1976.Synthetic seismograms;a finite-difference approach[J].Geophysics,41(1):2-27.
Komatitsch D,Vilotte J P.1998.The spectral element method:an efficient tool to simulate the seismic response of 2Dand 3D geological structures[J].Bull.Seism.Soc.Am.,88(2):368-392.
Lu M,Yang D H.2005.A modified nearly analytic discrete method and wavefield simulations in transversely isotropic media[J].Sci.in China(Ser.D Earth Sci.),48(8):132l-1328.
Ma X,Yang D H,Zhang J H.2010.Symplectic partitioned RungeKutta method for solving the acoustic wave equation[J].Chinese J.Geophys.(in Chinese),53(8):1993-2003,doi:10.3969/j.issn.0001-5733.2010.08.026.
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Tong P,Yang D H,Hua B L,et al.2013.A high-order stereomodeling method for solving wave equations[J].Bulletin of the Seismological Society of America,103(2):811-833.
Virieux J.1984.SH-wave propagation in heterogeneous media:velocity-stress finite-difference method[J].Geophysics,49(11):1933-1957.
Virieux J.1986.P-SV wave propagation in heterogeneous media:velocity-stress finite-difference method[J].Geophysics,51(4):889-901.
Wang L,Yang D H,Deng X Y.2009.A WNAD method for seismic stress-field modeling in heterogeneous media[J].Chinese J.Geophys.(in Chinese),52(6):1526-1535.
Yang D H.2002.Finite element method of the elastic wave equation and wave field simulation in two-phase anisotropic media[J].Chinese J.Geophys.(in Chinese),45(4):575-583.
Yang D H,Liu E,Zhang Z J,et al.2002.Finite-difference modelling in two-dimensional anisotropic media using a fluxcorrected transport technique[J].Geophys.J.Int.,148(2):320-328.
Yang D H,Lu M,W u R S,et al.2004.An optimal nearly analytic discrete method for 2Dacoustic and elastic wave equations[J].Bul1.Seism.Sac.Am.,94(5):1982-1992.
Yang D H,Peng J M,Lu M,et al.2006a.A nearly analytical discrete method for wave-field simulations in 2Dporous media[J].Commun.Cornput.Phys.,1(3):528-547.
Yang D H,Peng J M,Lu M,et al.2006b.Optimal nearly analytic discrete approximation to the scalar wave equation[J].Bul1.Seisrn.Soc.Am.,96(3):1114-1130.
Yang D H,Teng J W,Zhang Z J,et al.2003.A nearly analytic discrete method for acoustic and elastic wave equations in anisotropic media[J].Bull.Seism.Soc.Am.,93(2):882-890.
Zhang Z J,Wang G J,Harris J M.1999.Multi-component wavefield simulation in viscous extensively dilatancy anisotropic media[J].Phys.Earth Planet Inter.,114(1-2):25-38.
董良国,马在田,曹景忠,等.2000.一阶弹性波方程交错网格高阶差分解法[J].地球物理学报,43(3):411-419.
卢明,杨顶辉.2005.一种改进的近似解析离散化方法及其横向各向同性波场模拟[J].中国科学(D辑:地球科学),35(1):72-78.
马啸,杨顶辉,张锦华.2010.求解声波方程的辛可分Runge-Kutta方法[J].地球物理学报,53(8):1993-2003,doi:10.3969/j.issn.0001-5733.2010.08.026.
宋国杰,杨顶辉,陈亚丽,等.2010.基于WNAD方法的非一致网格算法及其弹性波场模拟[J].地球物理学报,53(8):1985-1992,doi:10.3969/j.issn.00015733.2010.08.025.
王磊,杨顶辉,邓小英.2009.非均匀介质中地震波应力场的WNAD方法及其数值模拟[J].地球物理学报,52(6):1526-1535.
杨顶辉.2002.双相各向异性介质中弹性波方程的有限元解法及波场模拟[J].地球物理学报,45(4):575-583.
pyChapman C H,Shearer P M.1989.Ray tracing in azimuthally anisotropic media-Ⅱ:quasi-shear wave coupling[J].Geophys.J.Int.,96(1):65-83.
Chen K H.1984.Propagating numerical model of elastic wave in anisotropic in homogeneous media-finite element method[C].Symposium of 54th SEG,54:631-632.
Dablain M A.1986.The application of high-order differencing to the scalar wave equation[J].Geophysics,51(1):54-66.
Dong L G,Ma Z T,Cao J Z,et al.2000.A staggered-grid highorder difference method of one-order elastic wave equation[J].Chinese J.Geophys.(in Chinese),43(3):411-419.
Fei T,Larner K.1995.Elimination of numerical dispersion in finitedifference modeling and migration by flux-corrected transport[J].Geophysics,60(6):1830-1842.
Huang B S.1992.A program for two-dimensional seismic wave propagation by the pseudospectrum method[J].Comput.Geosci.,18(2-3):289-307.
Kelly K R,Ward R W,Treitel S,et al.1976.Synthetic seismograms;a finite-difference approach[J].Geophysics,41(1):2-27.
Komatitsch D,Vilotte J P.1998.The spectral element method:an efficient tool to simulate the seismic response of 2Dand 3D geological structures[J].Bull.Seism.Soc.Am.,88(2):368-392.
Lu M,Yang D H.2005.A modified nearly analytic discrete method and wavefield simulations in transversely isotropic media[J].Sci.in China(Ser.D Earth Sci.),48(8):132l-1328.
Ma X,Yang D H,Zhang J H.2010.Symplectic partitioned RungeKutta method for solving the acoustic wave equation[J].Chinese J.Geophys.(in Chinese),53(8):1993-2003,doi:10.3969/j.issn.0001-5733.2010.08.026.
Song G J,Yang D H,Chen Y L,et al.2010.Non-uniform grid algorithm based on the WNAD method and elastic wave-field simulations[J].Chinese J.Geophys.(in Chinese),53(8):1985-1992,doi:10.3969/j.issn.00015733.2010.08.025.
Tong P,Yang D H,Hua B L,et al.2013.A high-order stereomodeling method for solving wave equations[J].Bulletin of the Seismological Society of America,103(2):811-833.
Virieux J.1984.SH-wave propagation in heterogeneous media:velocity-stress finite-difference method[J].Geophysics,49(11):1933-1957.
Virieux J.1986.P-SV wave propagation in heterogeneous media:velocity-stress finite-difference method[J].Geophysics,51(4):889-901.
Wang L,Yang D H,Deng X Y.2009.A WNAD method for seismic stress-field modeling in heterogeneous media[J].Chinese J.Geophys.(in Chinese),52(6):1526-1535.
Yang D H.2002.Finite element method of the elastic wave equation and wave field simulation in two-phase anisotropic media[J].Chinese J.Geophys.(in Chinese),45(4):575-583.
Yang D H,Liu E,Zhang Z J,et al.2002.Finite-difference modelling in two-dimensional anisotropic media using a fluxcorrected transport technique[J].Geophys.J.Int.,148(2):320-328.
Yang D H,Lu M,W u R S,et al.2004.An optimal nearly analytic discrete method for 2Dacoustic and elastic wave equations[J].Bul1.Seism.Sac.Am.,94(5):1982-1992.
Yang D H,Peng J M,Lu M,et al.2006a.A nearly analytical discrete method for wave-field simulations in 2Dporous media[J].Commun.Cornput.Phys.,1(3):528-547.
Yang D H,Peng J M,Lu M,et al.2006b.Optimal nearly analytic discrete approximation to the scalar wave equation[J].Bul1.Seisrn.Soc.Am.,96(3):1114-1130.
Yang D H,Teng J W,Zhang Z J,et al.2003.A nearly analytic discrete method for acoustic and elastic wave equations in anisotropic media[J].Bull.Seism.Soc.Am.,93(2):882-890.
Zhang Z J,Wang G J,Harris J M.1999.Multi-component wavefield simulation in viscous extensively dilatancy anisotropic media[J].Phys.Earth Planet Inter.,114(1-2):25-38.
董良国,马在田,曹景忠,等.2000.一阶弹性波方程交错网格高阶差分解法[J].地球物理学报,43(3):411-419.
卢明,杨顶辉.2005.一种改进的近似解析离散化方法及其横向各向同性波场模拟[J].中国科学(D辑:地球科学),35(1):72-78.
马啸,杨顶辉,张锦华.2010.求解声波方程的辛可分Runge-Kutta方法[J].地球物理学报,53(8):1993-2003,doi:10.3969/j.issn.0001-5733.2010.08.026.
宋国杰,杨顶辉,陈亚丽,等.2010.基于WNAD方法的非一致网格算法及其弹性波场模拟[J].地球物理学报,53(8):1985-1992,doi:10.3969/j.issn.00015733.2010.08.025.
王磊,杨顶辉,邓小英.2009.非均匀介质中地震波应力场的WNAD方法及其数值模拟[J].地球物理学报,52(6):1526-1535.
杨顶辉.2002.双相各向异性介质中弹性波方程的有限元解法及波场模拟[J].地球物理学报,45(4):575-583.
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