波动方程有限差分双变网格算法的精度分析
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摘要
应用双变网格(空间及时间)方法可对复杂储层地震波场进行精细模拟,且具有较高的计算效率,但空间变网格方法的缺点是在两种网格的边界处会引起数值噪声。为了更准确地对局部复杂构造进行数值模拟,本文从理论分析和数值模拟结果两方面对空间变网格的插值算法和变系数算法及变时间步长方法进行了定量研究和对比分析。通过对以上方法的定量误差分析,进而确定这些算法的适用范围。在数值模拟时通过选择合适的方法和参数,可以保证对微弱波场异常的模拟精度。
Dual-variable grid algorithm can be applied on fine simulation of wave fields of complex reservoirs with high calculation efficiency.However,with the variable space grid and variable time step,numerical noises would be generated at the interface of different grids and steps.In order to obtain more accurate numerical modeling results on locally complex structures,quantitative studies and comparisons on varying-space grids with interpolation method and variable coefficient method are implemented by theoretical analysis and numerical stimulation experiments.An error analysis of locally variable time step method is also conducted in this paper.Errors generated by each of the three methods mentioned above are then quantitatively studied to determine the application scope of each corresponding method.And thus the simulation accuracy can be guaranteed in case of weak anomaly of wave field by choosing appropriate method and parameters.
Dual-variable grid algorithm can be applied on fine simulation of wave fields of complex reservoirs with high calculation efficiency.However,with the variable space grid and variable time step,numerical noises would be generated at the interface of different grids and steps.In order to obtain more accurate numerical modeling results on locally complex structures,quantitative studies and comparisons on varying-space grids with interpolation method and variable coefficient method are implemented by theoretical analysis and numerical stimulation experiments.An error analysis of locally variable time step method is also conducted in this paper.Errors generated by each of the three methods mentioned above are then quantitatively studied to determine the application scope of each corresponding method.And thus the simulation accuracy can be guaranteed in case of weak anomaly of wave field by choosing appropriate method and parameters.
引文
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[9]李振春,张慧,张华.一阶弹性波方程的变网格高阶有限差分数值模拟.石油地球物理勘探,2008,43(6):711～716Li Zhenchun,Zhang Hui,Zhang Hua.Variable-grid high-order finite-difference numeric simulation of first-order e-lastic wave equation.OGP,2008,43(6):711～716
[10]黄超,董良国.可变网格与局部时间步长的高阶差分地震波数值模拟.地球物理学报,2009,52(1):176～186Huang Chao,Dong Liangguo.Variable space gridand local time step of the higher order differentialseismic wave numerical simulation.Chinese Journalof Geophysics,2009,52(1):176～186
[11]张慧,李振春.基于双变网格算法的地震波正演模拟.地球物理学报,2011,54(1):77～86Zhang Hui,Li Zhenchun.Seismic wave simulationmethod based on dual-variable grid.Chinese Journalof Geophysics,2011,54(1):77～86
[12]Tessmer E.Seismic finite-difference modeling withspatially varying time steps.Geophysics,2000,65(4):1290～1293
[13]Sergio Adriano and Moura Oliveira.A fourth-orderfinite-difference method for the acoustic wave equa-tion on irregular grids.Geophysics,2003,68(4):972～976
[2]Jastram C,Behle A.Acoustic modeling on a grid ofvertically varying spacing.Geophysical Prospecting,1992,40(1):157～169
[3]Jastram C,Tessemer E.Elastic modeling on a gridwith vertically varying spacing.Geophysical Pros-pecting,1994,42(2):357～370
[4]Wang Y,Schuster G T.Finite-difference variable gridscheme for acoustic and elastic wave equation model-ing.SEG Technical Program Expanded Abstracts,1996,15:674～677
[5]李胜军,孙成禹,倪长宽.声波方程有限差分数值模拟的变网格步长算法.工程地球物理学报,2007,4(3):207～212Li Shengjun,Sun Chengyu,Ni Changkuan.Acousticequation numerical modeling on a grid of varyingspacing.Chinese Journal of Engineering Geophy-sics,2007,4(3):207～212
[6]朱生旺,曲寿利,魏修成等.变网格有限差分弹性波动方程数值模拟方法.石油地球物理勘探,2007,42(6):634～639Zhu Shengwang,Qu Shouli,Wei Xiucheng et al.Numeric simulation by grid-various finite-differenceelastic wave equation.OGP,2007,42(6):634～639
[7]赵海波,王秀明.一种优化的交错变网格有限差分法及其在井间声波中的应用.科学通报,2007,52(12):1387～1395Zhao Haibo,Wang Xiuming.An optimized staggeredvariable grid finite difference method and its applica-tion to the crosswell acoustic modeling.Science Bul-letin,2007,52(12):1387～1395
[8]孙成禹,李胜军,倪长宽等.波动方程变网格步长有限差分数值模拟.石油物探,2008,47(2):123～128Sun Chengyu,Li Shengjun,Ni Changkuan et al.Wave equation numerical modeling by finite differencemethod with varying grid spacing.GPP,2008,47(2):123～128
[9]李振春,张慧,张华.一阶弹性波方程的变网格高阶有限差分数值模拟.石油地球物理勘探,2008,43(6):711～716Li Zhenchun,Zhang Hui,Zhang Hua.Variable-grid high-order finite-difference numeric simulation of first-order e-lastic wave equation.OGP,2008,43(6):711～716
[10]黄超,董良国.可变网格与局部时间步长的高阶差分地震波数值模拟.地球物理学报,2009,52(1):176～186Huang Chao,Dong Liangguo.Variable space gridand local time step of the higher order differentialseismic wave numerical simulation.Chinese Journalof Geophysics,2009,52(1):176～186
[11]张慧,李振春.基于双变网格算法的地震波正演模拟.地球物理学报,2011,54(1):77～86Zhang Hui,Li Zhenchun.Seismic wave simulationmethod based on dual-variable grid.Chinese Journalof Geophysics,2011,54(1):77～86
[12]Tessmer E.Seismic finite-difference modeling withspatially varying time steps.Geophysics,2000,65(4):1290～1293
[13]Sergio Adriano and Moura Oliveira.A fourth-orderfinite-difference method for the acoustic wave equa-tion on irregular grids.Geophysics,2003,68(4):972～976
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