基于矩形网格的有限差分走时计算方法
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摘要
对于大多数速度场 ,地震波沿射线传播的初至波走时 ,可以用有限差分外推的方法在二维或三维数值网格上计算出来 .在保证精度的条件下 ,为提高计算效率和适应性 ,本文推导了基于任意矩形网格和局部平面波前近似的有限差分初至波走时计算方法 .另外 ,该方法对首波和散射波做了合适的处理 ,而且不会碰到传统射线法存在的阴影区和焦散区等问题 .简单模型和复杂的Marmousi模型试算的结果表明 ,该方法精度较高并适用于强纵、横向变速的复杂介质 .基于该方法的Kirchhoff叠前深度偏移 ,在主要构造和目的层位置的成像效果上基本达到了波动方程法叠前深度偏移的位置成像效果 .由于未考虑续至波等有效能量 ,在成像的保幅性上不如波动方程法叠前深度偏移的效果 ,但其计算效率则明显高于全格林函数法和波动方程法 .
To the most of velocity fields, the traveltimes of the first break that seismic waves propagate along rays can be computed on a 2-D or 3-D numerical grid by finite-difference extrapolation. Under ensuring accuracy, to improve calculating efficiency and adaptability, the calculation method of first-arrival traveltime of finite-difference is derived based on any rectangular grid and a local plane wavefront approximation. In addition, head waves and scattering waves are properly treated and shadow and caustic zones cannot be encountered, which appear in traditional ray-tracing. The testes of two simple models and the complex Marmousi model show that the method has higher accuracy and adaptability to complex structure with strong vertical and lateral velocity variation, and Kirchhoff prestack depth migration based on this method can basically achieve the position imaging effects of wave equation prestack depth migration in major structures and targets. Because of not taking account of the later arrivals energy, the effect of its amplitude preservation is worse than that by wave equation method, but its computing efficiency is higher than that by total Green′s function method and wave equation method.
To the most of velocity fields, the traveltimes of the first break that seismic waves propagate along rays can be computed on a 2-D or 3-D numerical grid by finite-difference extrapolation. Under ensuring accuracy, to improve calculating efficiency and adaptability, the calculation method of first-arrival traveltime of finite-difference is derived based on any rectangular grid and a local plane wavefront approximation. In addition, head waves and scattering waves are properly treated and shadow and caustic zones cannot be encountered, which appear in traditional ray-tracing. The testes of two simple models and the complex Marmousi model show that the method has higher accuracy and adaptability to complex structure with strong vertical and lateral velocity variation, and Kirchhoff prestack depth migration based on this method can basically achieve the position imaging effects of wave equation prestack depth migration in major structures and targets. Because of not taking account of the later arrivals energy, the effect of its amplitude preservation is worse than that by wave equation method, but its computing efficiency is higher than that by total Green′s function method and wave equation method.
引文
李振春.2002.多道集偏移速度建模方法研究[D]:[学位论文].上海:同济大学海洋与地球科学学院,17～33
王华忠,谢海兵,马在田.1997.有限差分法地震波走时计算[J].同济大学学报,25(3):318～321
张霖斌,刘迎曦.赵振峰.1993.有限差分法射线追踪[J].石油地球物理勘探,28(6):673～684
周洪波,张关泉.1994.复杂构造区域的初至波走时计算[J].地球物理学报,37(4):515～519
HillNR .2001.ProstackGaussian beanmdepthmigration[J].Geophysics,64(4):1240～1250
LeidenfrostA ,EttrichN ,GajewskiD ,etal.1999.Comparisonofsixdifferentmethodsforcalculatingtraveltimes[J].GeophysProsp,47(2):269～297
VersteegR .1994.TheMarmousiexperience:Velocitymodeldeterminationonasyntheticcomplexdataset[J].TheLeadingEdge,13(6):927～936
VidaleJ.1988.Finite differencecalculationoftraveltimes[J].BullSeismSocAmer,78(6):2062～2076
VidaleJ.1990.Finite differencecalculationoftraveltimesinthreedimensions[J].Geophysics,55(5):521～526
王华忠,谢海兵,马在田.1997.有限差分法地震波走时计算[J].同济大学学报,25(3):318～321
张霖斌,刘迎曦.赵振峰.1993.有限差分法射线追踪[J].石油地球物理勘探,28(6):673～684
周洪波,张关泉.1994.复杂构造区域的初至波走时计算[J].地球物理学报,37(4):515～519
HillNR .2001.ProstackGaussian beanmdepthmigration[J].Geophysics,64(4):1240～1250
LeidenfrostA ,EttrichN ,GajewskiD ,etal.1999.Comparisonofsixdifferentmethodsforcalculatingtraveltimes[J].GeophysProsp,47(2):269～297
VersteegR .1994.TheMarmousiexperience:Velocitymodeldeterminationonasyntheticcomplexdataset[J].TheLeadingEdge,13(6):927～936
VidaleJ.1988.Finite differencecalculationoftraveltimes[J].BullSeismSocAmer,78(6):2062～2076
VidaleJ.1990.Finite differencecalculationoftraveltimesinthreedimensions[J].Geophysics,55(5):521～526
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