网格剖分及其精度和计算量分析
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摘要
网格剖分程度直接影响着地震波正演数值模拟的计算精度及其计算量。以均匀介质模型为例,分析不同网格大小对波场模拟精度和计算量的影响,得出精细化网格剖分是实现高精度地震波正演模拟的有效方法,然而其计算量较大。以均匀倾斜介质模型为例,探讨倾斜地层网格剖分问题,数值实例分析不同震源频率对不同网格剖分方案引起的波场传播精度的影响,同时给出网格剖分的合理选取准则,并建立差分阶数和调节因子的近似函数关系。结合理论分析和数值试算表明,网格步长越大,倾斜界面网格剖分引起的台阶效应越严重,在网格步长满足合理的频散关系(精度)情况下,选择合理的非均匀网格剖分策略可以减小计算量,尤其是可以压制由倾斜地层网格剖分造成的虚假波场,并保证计算波场具有较高的信噪比和可信度,同时指出在适当减小网格剖分步长和提高差分近似阶数可以在保证计算精度的前提下提高计算效率。
Mesh Generation level can directly affect the accuracy and memory of seismic wave numerical simulation.The paper takes isotropic medium model as example to analyze the effect of different grid sizes on wave field simulating precision and calculated amount,and concludes that the fine grid can achieve the purpose of high-precision,but with disadvantage of calculated amount,then takes isotropic tilted medium model as another example to discuss the mesh generation problems on the tilted formation,uses numerical examples to analyze the wave field propagating effect of the different source frequency caused by different mesh generation strategy,and at the same time puts forward the rational mesh generation,and builds the approximating relationship between difference order and adjusted factor.The theoretical analysis and numerical experiments shows that the larger the grid step,the greater step effect induced by mesh generation of the tilted formation,under the condition of the grid size satisfying the rational dispersion relationship,selecting rational heterogametic mesh generation strategy can reduce the calculated amount,especially suppresses the bogus wave field raised by the mesh generation on the tilted formation,which ensures the numerical wave field with high S/N and credibility,and at the same time,points out that properly reducing the grid step and improving the difference order can improve the computational effect under the condition of ensuring the computational precision.
Mesh Generation level can directly affect the accuracy and memory of seismic wave numerical simulation.The paper takes isotropic medium model as example to analyze the effect of different grid sizes on wave field simulating precision and calculated amount,and concludes that the fine grid can achieve the purpose of high-precision,but with disadvantage of calculated amount,then takes isotropic tilted medium model as another example to discuss the mesh generation problems on the tilted formation,uses numerical examples to analyze the wave field propagating effect of the different source frequency caused by different mesh generation strategy,and at the same time puts forward the rational mesh generation,and builds the approximating relationship between difference order and adjusted factor.The theoretical analysis and numerical experiments shows that the larger the grid step,the greater step effect induced by mesh generation of the tilted formation,under the condition of the grid size satisfying the rational dispersion relationship,selecting rational heterogametic mesh generation strategy can reduce the calculated amount,especially suppresses the bogus wave field raised by the mesh generation on the tilted formation,which ensures the numerical wave field with high S/N and credibility,and at the same time,points out that properly reducing the grid step and improving the difference order can improve the computational effect under the condition of ensuring the computational precision.
引文
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[15]陈可洋,杨微,刘洪林,等.二阶弹性波动方程高精度交错网格波场分离数值模拟[J].物探与化探,2009,33(6):700-704.
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[18]陈可洋.各向异性弹性波动方程多分量联合叠后逆时偏移[J].内陆地震,2009,23(4):455-460.
[19]陈可洋.基于高阶有限差分的波动方程叠前逆时偏移方法[J].石油物探,2009,48(5):475-478.
[20]陈可洋,吴清岭,杨微,等.基于散度和旋度的弹性波波场分离数值模拟方法[J].物探与化探,2010,34(1):103-107.
[21]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[J].科学通报,2007,52(12):1 387-1 395.
[22]万永革,沈正康,王敏,等.根据GPS和InSAR数据反演2001年昆仑山口西地震同震破裂分布[J].地球物理学报,2008,51(4):1 074-1 084.
[23]陈可洋.地震波旅行时计算方法及其模型试验分析[J].石油物探,2010,49(2):153-157.
[24]陈可洋.高精度数值模拟多分量数据的采集[J].油气地球物理,2010,8(2):44-47.
[2]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.
[3]陈可洋.高阶弹性波动方程正演模拟及其逆时偏移成像研究(硕士学位论文)[D].黑龙江:大庆石油学院,2009.
[4]MoczoP.FinitedifferencetechniqueforSHwavesin2-Dmediausingirregulargrid:Application totheseismicresponseproblem[J].Geophysical Journal International,1989,99:321-329.
[5]Magnier,Peter,moro.Finite differences on minimal grid[J].Geophysics,1994,59(9):1 435-1 443.
[6]周家纪,王铎.用最佳差分方法计算P-SV波[J].哈尔滨工业大学学报,1994,26(1):85-89.
[7]Liu Y,Mrinal S K.An implicit staggered-grid finite-difference method for seismic modeling[J].Geophysical Journal Internation-al,2009,179(1):459-474.
[8]TessmerE,KosloffD,BehleA.Elasticwavepropagation simulation in thepresencesurfacetopography[J].GeophysJInternat,1992,108:621-632.
[9]Jastram C,Tessmer E.Elastic modeling on a grid with vertically varying spacing[J].Geophysical Prasp,1994,42:357-370.
[10]Falk J,Tessmer E,Gajevski D.Tube wave modeling by the finite-differences method with varying grid spacing[J].Pageoph,1996,14:77-93.
[11]Oprsal I,Zahradnik J.Elastic finite-difference method for irregular grids[J].Geophysics,1999,64(1):240-250.
[12]褚春雷,王修田.非规则三角网格有限差分法地震正演模拟[J].中国海洋大学学报,2005,35(1):43-48.
[13]陈可洋.标量声波波动方程高阶交错网格有限差分法[J].中国海上油气,2009,21(4):232-236.
[14]陈可洋.地震波数值模拟中差分近似的各向异性分析[J].石油物探,2010,49(1):19-22.
[15]陈可洋,杨微,刘洪林,等.二阶弹性波动方程高精度交错网格波场分离数值模拟[J].物探与化探,2009,33(6):700-704.
[16]陈可洋.三维随机建模方法及其波场模拟分析[J].勘探地球物理进展,2009,32(5):315-320.
[17]陈可洋.边界吸收中镶边法的评价[J].中国科学院研究生院学报,2010,27(2):170-175.
[18]陈可洋.各向异性弹性波动方程多分量联合叠后逆时偏移[J].内陆地震,2009,23(4):455-460.
[19]陈可洋.基于高阶有限差分的波动方程叠前逆时偏移方法[J].石油物探,2009,48(5):475-478.
[20]陈可洋,吴清岭,杨微,等.基于散度和旋度的弹性波波场分离数值模拟方法[J].物探与化探,2010,34(1):103-107.
[21]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[J].科学通报,2007,52(12):1 387-1 395.
[22]万永革,沈正康,王敏,等.根据GPS和InSAR数据反演2001年昆仑山口西地震同震破裂分布[J].地球物理学报,2008,51(4):1 074-1 084.
[23]陈可洋.地震波旅行时计算方法及其模型试验分析[J].石油物探,2010,49(2):153-157.
[24]陈可洋.高精度数值模拟多分量数据的采集[J].油气地球物理,2010,8(2):44-47.
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