波动方程的变步长有限差分数值模拟
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摘要
有限差分算法是常用的正演模拟方法之一,其包含的地震信息丰富,且实现简单。传统的有限差分方法通常都采用均匀网格步长,在对含低速/高速介质、薄层/厚层介质的模型进行波场模拟时往往缺乏稳定性。文章介绍了一种可以有效解决上述问题的变网格算法,对常规有限差分法与变网格差分算法在内存需求、计算速率等方面的差别进行了比较,对变网格差分算法中的边界条件、时间积分的快速展开算法作了阐述,进而总结了变网格算法的优点。
The finite difference is one of common forward modeling methods, which contains abundant seismic information, and is easy to be realized. Traditional finite difference use usually uniform grids, the methods is lack of flexibility in numerical simulation of low-speed/high-speed medium,thin layer/thick layer. In this presentation, an algorithm of varying mesh is recommended, which has solved the problem described above. The difference of storage requirement and computational effort between traditional finite difference and the algorithm of varying mesh is discussed. And the boundary condition, rapid expansion method ( REM ) for the time integration of the algorithm of varying mesh are introduced, the advantages of this algorithm are summarized.
The finite difference is one of common forward modeling methods, which contains abundant seismic information, and is easy to be realized. Traditional finite difference use usually uniform grids, the methods is lack of flexibility in numerical simulation of low-speed/high-speed medium,thin layer/thick layer. In this presentation, an algorithm of varying mesh is recommended, which has solved the problem described above. The difference of storage requirement and computational effort between traditional finite difference and the algorithm of varying mesh is discussed. And the boundary condition, rapid expansion method ( REM ) for the time integration of the algorithm of varying mesh are introduced, the advantages of this algorithm are summarized.
引文
[1]余德平,波场数值模拟技术.勘探地球物理进展,2004,27(1):16~21
[2]D.Kosloff and E.Baysal.Forward modeling by a Fourier method.Geophysics,1982,47(10):1402~1412
[3]M.A.Dablain.The application of high-order differencing to the scalar wave equation.Geophysics,1986,51(1):54~66
[4]Cord Jastram,Alfred Behle.Acoustic modeling on a grid of verti-cally varying spacing.Geophysical Prospecting,1992,40(2):157~169
[5]J.E.Vidale.Comment on‘A comparison of finite-difference and Fourier-method calculations of synthetic seismograms’by C.R.Daudt et al.Bulletin of the seismological society of America.1990,80:493~495
[6]Dan Kosloff,A.Q.Filho,E.Tessmer.Numerical solution of the acoustic and elastic wave equations by a new rapid expandion method.Geophysical Prospecting.1989,37(4):383~394
[7]孙成禹,张吉辉.完全纵波方程有限差分波场模拟.石油地球物理勘探,2005,40(30):289~294
[8]O.Holberg.Computational aspects of the choice of operator and sampling interval for numerical differentiation in large-scale sim-ulation of wave phenomena.Geophysical Prospecting1987,35(6):625~655
[9]B.Fornberg.Generation of finite difference formulas on arbitrarily spaced grids.Mathematics of Computation,1988,51:699~706
[2]D.Kosloff and E.Baysal.Forward modeling by a Fourier method.Geophysics,1982,47(10):1402~1412
[3]M.A.Dablain.The application of high-order differencing to the scalar wave equation.Geophysics,1986,51(1):54~66
[4]Cord Jastram,Alfred Behle.Acoustic modeling on a grid of verti-cally varying spacing.Geophysical Prospecting,1992,40(2):157~169
[5]J.E.Vidale.Comment on‘A comparison of finite-difference and Fourier-method calculations of synthetic seismograms’by C.R.Daudt et al.Bulletin of the seismological society of America.1990,80:493~495
[6]Dan Kosloff,A.Q.Filho,E.Tessmer.Numerical solution of the acoustic and elastic wave equations by a new rapid expandion method.Geophysical Prospecting.1989,37(4):383~394
[7]孙成禹,张吉辉.完全纵波方程有限差分波场模拟.石油地球物理勘探,2005,40(30):289~294
[8]O.Holberg.Computational aspects of the choice of operator and sampling interval for numerical differentiation in large-scale sim-ulation of wave phenomena.Geophysical Prospecting1987,35(6):625~655
[9]B.Fornberg.Generation of finite difference formulas on arbitrarily spaced grids.Mathematics of Computation,1988,51:699~706
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