地震波数值模拟中差分近似的各向异性分析
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摘要
有限差分算法存在固有的数值频散问题,在正演过程中会严重干扰有效波场,降低地震波场的分辨率。针对此,从最简单的平面波数值理论分析出发,推导了任意高阶有限差分近似条件下相对相速度和相对群速度的计算公式,给出了求解最佳Courant数的计算方法,分析了差分近似造成的各向异性效应。理论分析和数值实例研究表明,正演数值模拟的精度与最小波长节点数、Courant数、有限差分近似阶数这3个因素密切相关,通过合理调节这3个量可以提高有效波场区域的数值模拟精度,拓宽正演波场的频带宽度,提高数值模拟的计算效率。
The finite difference algorithm has its inherent numerical dispersion problem,which seriously disturb the effective wavefield during forward simulation and therefore decrease the resolution of seismic wavefield.In order to solve the problem,starting from the analysis of the simplest plane wave numerical theory,we derived the formula of relative phase velocity and group velocity under the condition of arbitrary high-order finite-difference approximation, and gave the computational method for acquiring the optimum Courant number,and then analyzed the anisotropic effects due to finite difference approximation.The theory analysis and numerical examples show that the precision of seismic wave forward numerical modeling has close relationship with the least wavelength nodes, the Courant number and the finite-difference approximating order. Rationally adjusting the three factors can improve the numerical modeling precision in the effective wavefield region,extend the frequency bandwidth of the forward modeling wavefield and improve the computational efficiency of the numerical simulation.
The finite difference algorithm has its inherent numerical dispersion problem,which seriously disturb the effective wavefield during forward simulation and therefore decrease the resolution of seismic wavefield.In order to solve the problem,starting from the analysis of the simplest plane wave numerical theory,we derived the formula of relative phase velocity and group velocity under the condition of arbitrary high-order finite-difference approximation, and gave the computational method for acquiring the optimum Courant number,and then analyzed the anisotropic effects due to finite difference approximation.The theory analysis and numerical examples show that the precision of seismic wave forward numerical modeling has close relationship with the least wavelength nodes, the Courant number and the finite-difference approximating order. Rationally adjusting the three factors can improve the numerical modeling precision in the effective wavefield region,extend the frequency bandwidth of the forward modeling wavefield and improve the computational efficiency of the numerical simulation.
引文
[1]江凡,杨锴,程玖兵.复杂地表有限差分波动方程向上基准面校正[J].石油物探,2006,45(1):15-20
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[13]Fei T,Larner K.Elimination of numerical dispersion in finite-difference modeling and migration by fluxcorrected transport[J].Geophysics,1995,60(6): 1830-1842
[14]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[J].地球物理学报,2000,43(3): 411-419
[15]裴正林,牟永光.地震波传播的数值模拟[J].地球物理学进展,2004,19(4):933-941
[16]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
[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
[18]吴国忱,王华忠.波场模拟中的数值频散分析与校正策略[J].地球物理学进展,2005,20(1):58-65
[19]宁刚,熊章强,陈持.波动方程有限差分正演模拟误差来源分析[J].物探与化探,2008,32(2):203-206
[2]陈可洋,杨微,吴清岭,等.几种地震波叠后深度偏移方法的比较[J].勘探地球物理进展,2009,32(4): 257-260
[3]Carcione J M,Herman G C,Kroode A P E.Seismic modeling[J].Geophysics,2002,67(4):1304-1325
[4]Levander A R.Four-order finite-difference P-SV seismograms[J].Geophysics,1988,53(11 ): 1425-1436
[5]李信富,李小凡,张美根.地震波数值模拟方法研究综述[J].防灾减灾工程学报,2007,27(2):241-248
[6]Abdolrahim J.有限差分法合成记录地震图中的网格频散[J].地震学报,1994,16(3):310-318
[7]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
[8]陈可洋,杨微.优化的三维地震波旁轴近似吸收边界条件[J].勘探地球物理进展,2009,32(3):179-181, 206
[9]陈可洋,刘洪林,杨微,等.随机介质模型的改进方法及应用[J].大庆石油地质与开发,2008,27(5):124- 126,131
[10]Alford R M,Kelly K R,Boore D M.Accuracy of finite -difference modeling of the acoustic wave equation [J].Geophysics,1974,39(6):834-842
[11]Marfurt K J.Accuracy of finite difference and finite element modeling of the scalar and elastic equations [J].Geophysics,1984,49(5):533-549
[12]Dablain M A.The application of high-differencing to the scalar wave equation[J].Geophysics,1986,51 (1):54-66
[13]Fei T,Larner K.Elimination of numerical dispersion in finite-difference modeling and migration by fluxcorrected transport[J].Geophysics,1995,60(6): 1830-1842
[14]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[J].地球物理学报,2000,43(3): 411-419
[15]裴正林,牟永光.地震波传播的数值模拟[J].地球物理学进展,2004,19(4):933-941
[16]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
[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
[18]吴国忱,王华忠.波场模拟中的数值频散分析与校正策略[J].地球物理学进展,2005,20(1):58-65
[19]宁刚,熊章强,陈持.波动方程有限差分正演模拟误差来源分析[J].物探与化探,2008,32(2):203-206
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