横向各向同性介质优化差分系数法地震波场数值模拟
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摘要
在应用有限差分法地震波场数值模拟过程中,数值频散是关键问题之一。为压制地震波场模拟中的数值频散,针对1阶速度—应力方程的交错网格空间离散差分算子,本文分别引入强约束条件和弱约束条件,构造了不同的Lagrange函数;然后通过求取条件极值得到优化差分算子。将其应用于横向各向同性(VTI)介质波场数值模拟,结果表明采用优化空间差分算子能有效压制数值频散,并可提高差分近似导数的精度。
In applying finite difference seismic wave field numerical simulation, the numerical dispersion is one of key issues. In order to suppress numerical dispersion in seismic wave field simulation the difference operator was discreted in staggered grid space of one-order velocity-stress equation, in this paper strong constraint condition and weak constraint condition were introduced, different Lagrange functions were constructed respectively, then optimized difference operator was obtained through estimation of conditional extremum. The optimized difference operator was applied to wave field numerical simulation in vertical transverse isotropic medium, the results show that the application of optimized space difference factor could effectively suppress numerical dispersion, and raise the accuracy of difference approximate derivative.
In applying finite difference seismic wave field numerical simulation, the numerical dispersion is one of key issues. In order to suppress numerical dispersion in seismic wave field simulation the difference operator was discreted in staggered grid space of one-order velocity-stress equation, in this paper strong constraint condition and weak constraint condition were introduced, different Lagrange functions were constructed respectively, then optimized difference operator was obtained through estimation of conditional extremum. The optimized difference operator was applied to wave field numerical simulation in vertical transverse isotropic medium, the results show that the application of optimized space difference factor could effectively suppress numerical dispersion, and raise the accuracy of difference approximate derivative.
引文
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[5]Wang Yuan,Wu Rongsheng.An opti mal spatial fi-nite-difference operator which reduces truncation er-ror to a muni mum.Advances in At mospheric Sci-ences,2002,19(3):468~484
[6]吴国忱,梁锴.VTI介质频率—空间域准P波正演模拟.石油地球物理勘探,2005,40(5):535~545
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[9]Virieux J.SH-wave propagation in heterogeneous media:Velocity-stress finite difference method.Geo-physics,1984,49(11):1933~1941
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[13]Du Qizhen,Li Bin and Hou Bo.Numerical modeling of seismic wavefields in transversely isotropic media with a compact staggered-grid finite difference scheme.Applied Geophysics,2009,6(1):42~49
[14]周家纪,王铎.用最佳差分方法计算P-SV波.哈尔滨工业大学学报,1994,26(1):85~89
[15]董良国,马在田,曹景忠等.一阶弹性波方程交错网格高阶差分解法.地球物理学报,2000,43(3):411~419
[2]Alford R M,Keily K R and Bore D M.Accuracy offinite difference modeling of the acoustic wave equa-tion.Geophyiscs,1974,39(6):834~842
[3]Dablain M A.The application of high-order differen-cing to the scalar wave equation.Geophysics,1986,51(1):54~65
[4]董良国,李培明.地震波传播数值模拟中的频散问题.天然气工业,2004,24(6):53~56
[5]Wang Yuan,Wu Rongsheng.An opti mal spatial fi-nite-difference operator which reduces truncation er-ror to a muni mum.Advances in At mospheric Sci-ences,2002,19(3):468~484
[6]吴国忱,梁锴.VTI介质频率—空间域准P波正演模拟.石油地球物理勘探,2005,40(5):535~545
[7]Madariaga R.Dynamics of an expanding circular fault.Bulletin of the Seismological Society of A-merica,1976,66(3):639~666
[8]杜启振,李宾.组合吸收边界条件下横向各向同性介质地震波场模拟.石油地球物理勘探,2009,44(2):173~178
[9]Virieux J.SH-wave propagation in heterogeneous media:Velocity-stress finite difference method.Geo-physics,1984,49(11):1933~1941
[10]Virieux J.P-SV wave propagation in heterogeneous media:Velocity-stress finite difference method.Geo-physics,1986,51(4):889~893
[11]Crase E.High-order(space and ti me)finite-difference and modeling of elastic wave equation.SEG Technical ProgramExpanded Abstracts,1990,9:987~991
[12]杜启振,孔丽云,韩世春.裂缝诱导各向异性双孔隙介质波场传播特征.地球物理学报,2009,52(4):1049~1058
[13]Du Qizhen,Li Bin and Hou Bo.Numerical modeling of seismic wavefields in transversely isotropic media with a compact staggered-grid finite difference scheme.Applied Geophysics,2009,6(1):42~49
[14]周家纪,王铎.用最佳差分方法计算P-SV波.哈尔滨工业大学学报,1994,26(1):85~89
[15]董良国,马在田,曹景忠等.一阶弹性波方程交错网格高阶差分解法.地球物理学报,2000,43(3):411~419
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