差分法声波地震合成的方法技术问题差分格式选取和变密度项取舍
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摘要
本文对复杂介质声波地震合成中的一些技术问题进行了研究。其中包括:差分方法中的网格假象与差分格式的关系及差分格式选取问题;普通声波方程和变密度声波方程合成的反射记录的差异及变密度项取舍问题。本文对田字型九点差分格式、十字形九点差分格式和五点差分格式的网格假象进行理论分析和数值计算,结果说明:田字形九点差分可以有效地压制网格引发的各向异性现象,在一定情况下也可以压制网格假频,其应用效果与差分权重系数有着很大的关系;十字形九点差分可以有效地压制网格假频,通常情况下其效果优于田字形九点差分。通过对比标准声波方程和变密度声波方程合成的反射记录说明变密度方程的反射系数更接近理论值。
Some technical issues about sonic seismic synthetic method in the complex media were studied.These include: 1.The relationship between alias and difference scheme,and the selection of difference scheme;2.The difference of synthesized reflection records between general acoustic equation and variable density acoustic wave equation,and the selection or abandonment of variable density item.This paper compared the 5-point difference scheme with 9-point difference scheme of two-dimensional acoustic wave modeling in a complex medium.The results showed that: square 9-point difference scheme is much more effective in avoiding grid anisotropy,and more effective in avoiding grid dispersion in some situations.The calculation result of square 9-point difference scheme depends on the parameters of difference scheme;Crisscross 9-point difference scheme is much more effective in avoiding grid alias;Crisscross nine-point difference scheme is usually more effective than square nine-point difference scheme in avoiding of alias;By comparing the synthesized reflection records of general acoustic equation and variable density acoustic wave equation,it shows the reflection coefficient of variable density equation is closer to the theoretical value.
Some technical issues about sonic seismic synthetic method in the complex media were studied.These include: 1.The relationship between alias and difference scheme,and the selection of difference scheme;2.The difference of synthesized reflection records between general acoustic equation and variable density acoustic wave equation,and the selection or abandonment of variable density item.This paper compared the 5-point difference scheme with 9-point difference scheme of two-dimensional acoustic wave modeling in a complex medium.The results showed that: square 9-point difference scheme is much more effective in avoiding grid anisotropy,and more effective in avoiding grid dispersion in some situations.The calculation result of square 9-point difference scheme depends on the parameters of difference scheme;Crisscross 9-point difference scheme is much more effective in avoiding grid alias;Crisscross nine-point difference scheme is usually more effective than square nine-point difference scheme in avoiding of alias;By comparing the synthesized reflection records of general acoustic equation and variable density acoustic wave equation,it shows the reflection coefficient of variable density equation is closer to the theoretical value.
引文
[1]Ahmad Zakaria,John Penrose,Frank Thomas.TheTwo Di mensional Numerical Modeling Of AcousticWave Propagation in Shallow Water[C].AustralianAcoustical Society Conference,Joondalup,2000.
[2]Alford R M,Kelly K R,Boore D M.Accuracy of fi-nite-difference modeling of acoustic wave propaga-tion[J].Geophysics,1974.39(6):834~842.
[3]Bording R P,Lines L R.Seismic modeling and i ma-ging with the complete wave equation[C].SEGCourse Notes N8,1997.
[4]Cerjan C,Kosloff D,Kosloff R.A nonreflectingboundary condition for discrete acoustic and elasticwave equations[J].Geopgysics,1985,50(4):705~708.
[5]Cole J B.A nearly exact second-order finite-difference ti me-domain wave propagation algorithmon a coarse grid[J].Computers in Physics,1994(8):730~734.
[6]Kelly K R,Ward R W.Sven Treitel.Synthetic Seis-mograms:A finite-difference Approach[J].Geo-physics,1976,41(1):2~27.
[7]Reynold A C.Boundary conditions for the numericalsolution of wave propagation problems[J].Geophys-ics,1978,43(1):1099~1110.
[8]Williams R S,Rechtien Richard D.The one-di men-sional elastic wave equation:Afinite-difference for-mulation for ani mated computer applications to fullwaveform propagation[J].Computers&Geosci-ences,1996,22(3):253~266.
[9]吴春玲,张霖斌.二维变密度声波波动方程的衍射层析成像[J].CT理论与应用研究,1994,3(3):5~10.
[2]Alford R M,Kelly K R,Boore D M.Accuracy of fi-nite-difference modeling of acoustic wave propaga-tion[J].Geophysics,1974.39(6):834~842.
[3]Bording R P,Lines L R.Seismic modeling and i ma-ging with the complete wave equation[C].SEGCourse Notes N8,1997.
[4]Cerjan C,Kosloff D,Kosloff R.A nonreflectingboundary condition for discrete acoustic and elasticwave equations[J].Geopgysics,1985,50(4):705~708.
[5]Cole J B.A nearly exact second-order finite-difference ti me-domain wave propagation algorithmon a coarse grid[J].Computers in Physics,1994(8):730~734.
[6]Kelly K R,Ward R W.Sven Treitel.Synthetic Seis-mograms:A finite-difference Approach[J].Geo-physics,1976,41(1):2~27.
[7]Reynold A C.Boundary conditions for the numericalsolution of wave propagation problems[J].Geophys-ics,1978,43(1):1099~1110.
[8]Williams R S,Rechtien Richard D.The one-di men-sional elastic wave equation:Afinite-difference for-mulation for ani mated computer applications to fullwaveform propagation[J].Computers&Geosci-ences,1996,22(3):253~266.
[9]吴春玲,张霖斌.二维变密度声波波动方程的衍射层析成像[J].CT理论与应用研究,1994,3(3):5~10.
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