高阶交错网格有限差分法弹性波叠前逆时深度偏移
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摘要
为了更好地研究复杂构造和速度分布条件下地震资料的精确成像方法,采用高阶交错网格有限差分法推导了各向同性介质弹性波动方程逆时偏移方程,给出计算所需的稳定性条件、多分量叠前逆时成像原理、吸收边界条件等,提出采用内插旅行时作为多分量记录叠前逆时成像条件,并对倾斜界面模型进行逆时偏移成像试验。偏移结果表明,该方法能够有效地处理复杂条件下的各向同性介质联合弹性波偏移成像问题,使地表接收到的复杂多波多分量弹性波场实现准确归位,理论模型中的倾斜截面和水平界面特征成像均较清晰准确。因此,该方法可为多分量资料叠前成像问题提供参考。
In order to study the accurate imaging method of seismic data in conditions of complex structure and velocity distribution,the paper uses High-order staggered-grid finite difference algorithm to obtain the equations of isotropic medium elastic wave equation reverse-time depth migration,gave the method's stable condition,pre-stack reverse-time imaging theory,absorbing boundary condition and so on,and uses interpolation arrival time as multi-components records’ pre-stack reverse-time image condition,and does reverse time migration experiment on tilted theoretical model.The imaging results show that the method can effectively deal with the problems of isotropic medium united elastic wave migration under the complex conditions,can achieve correct image of the multi-wave multi-components elastic wave field received by surface geophones,the tilted and horizontal interfaces in theoretical model can be relatively and correctly imaged,thus,the method can be a method reference for pre-stack image of multi-components data.
In order to study the accurate imaging method of seismic data in conditions of complex structure and velocity distribution,the paper uses High-order staggered-grid finite difference algorithm to obtain the equations of isotropic medium elastic wave equation reverse-time depth migration,gave the method's stable condition,pre-stack reverse-time imaging theory,absorbing boundary condition and so on,and uses interpolation arrival time as multi-components records’ pre-stack reverse-time image condition,and does reverse time migration experiment on tilted theoretical model.The imaging results show that the method can effectively deal with the problems of isotropic medium united elastic wave migration under the complex conditions,can achieve correct image of the multi-wave multi-components elastic wave field received by surface geophones,the tilted and horizontal interfaces in theoretical model can be relatively and correctly imaged,thus,the method can be a method reference for pre-stack image of multi-components data.
引文
[1]Whitemore,N.D.,1982,Migration:Fundamental issues and fu-ture developments.52nd Ann Internet.Mtg[C].,Dallas:Soc Ex-plor Geophys Publ Co,1982
[2]Loewenthal D,Mulfti I.R.Reverse-time migration in spatial fre-quency domain.Geophysics,1983,46:627～635
[3]Chang W F,McMechan G A.Reverse-time migration of offset vertical seismic profiling data using the excitation-time imaging condition.Geophysics,1986,51(1):67～80
[4]Gazdag J.Migration of vertical seismic profiles(VSP)using the phase shift plus interpolation(PSP)wave field continuation algo-rithm.Ann Mtg,Europ Assn Expolr Geophys[C].Oslo:Society of Exploration geophysicists Publ Co,1984
[5]Teng Y C,Dai T F.Finite-element prestack reverse time migration for elastic waves.Geophysics,1989,54(9):1204～1208
[6]张秉铭,董敏煜,李承楚等.各向异性介质中弹性波多分量联合逆时深度偏移.长春科技大学学报,2000,30(1):68～75
[7]张美根,王妙月.各向异性弹性波有限元叠前逆时偏移.地球物理学报,2001,44(5):711～719
[8]张美根,王妙月.各向异性弹性波叠后逆时深度偏移.石油物探,2002,41(3):259～263
[9]底青云,王妙月.弹性波有限元逆时偏移技术研究.地球物理学报,1997,40(4):570～579
[10]张会星,宁书年.弹性波动方程叠前逆时偏移.中国矿业大学学报,2002,31(5):372～375
[11]陈可洋.基于高阶有限差分的波动方程叠前逆时偏移方法.石油物探,2009,48(5):475～478
[12]王永刚,邢文军,谢万学等.完全匹配层吸收边界条件的研究.中国石油大学学报(自然科学版),2007,31(1):20～23
[13]陈可洋.声波完全匹配层吸收边界条件的改进算法.石油物探,2009,48(1):76～79
[14]董良国,马在田,曹景忠.一阶弹性波方程交错网格高阶差分解法稳定性研究.地球物理学报,2000,43(6):856～864
[15]陈可洋.标量声波波动方程高阶交错网格有限差分法.中国海上油气,2009,21(4):232～236
[2]Loewenthal D,Mulfti I.R.Reverse-time migration in spatial fre-quency domain.Geophysics,1983,46:627～635
[3]Chang W F,McMechan G A.Reverse-time migration of offset vertical seismic profiling data using the excitation-time imaging condition.Geophysics,1986,51(1):67～80
[4]Gazdag J.Migration of vertical seismic profiles(VSP)using the phase shift plus interpolation(PSP)wave field continuation algo-rithm.Ann Mtg,Europ Assn Expolr Geophys[C].Oslo:Society of Exploration geophysicists Publ Co,1984
[5]Teng Y C,Dai T F.Finite-element prestack reverse time migration for elastic waves.Geophysics,1989,54(9):1204～1208
[6]张秉铭,董敏煜,李承楚等.各向异性介质中弹性波多分量联合逆时深度偏移.长春科技大学学报,2000,30(1):68～75
[7]张美根,王妙月.各向异性弹性波有限元叠前逆时偏移.地球物理学报,2001,44(5):711～719
[8]张美根,王妙月.各向异性弹性波叠后逆时深度偏移.石油物探,2002,41(3):259～263
[9]底青云,王妙月.弹性波有限元逆时偏移技术研究.地球物理学报,1997,40(4):570～579
[10]张会星,宁书年.弹性波动方程叠前逆时偏移.中国矿业大学学报,2002,31(5):372～375
[11]陈可洋.基于高阶有限差分的波动方程叠前逆时偏移方法.石油物探,2009,48(5):475～478
[12]王永刚,邢文军,谢万学等.完全匹配层吸收边界条件的研究.中国石油大学学报(自然科学版),2007,31(1):20～23
[13]陈可洋.声波完全匹配层吸收边界条件的改进算法.石油物探,2009,48(1):76～79
[14]董良国,马在田,曹景忠.一阶弹性波方程交错网格高阶差分解法稳定性研究.地球物理学报,2000,43(6):856～864
[15]陈可洋.标量声波波动方程高阶交错网格有限差分法.中国海上油气,2009,21(4):232～236
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