多波多分量高斯束叠前深度偏移
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摘要
本文对基于弹性波动理论的多波多分量高斯束偏移进行了完整且详细的分析和公式推导,实现了3D空间多分量(矢量)波场的直接成像.由于当前多数基于弹性波动方程的偏移方法只是假设应力边界条件为自由地表边界条件,这种假设不符合垂直地震剖面(VSP)和海底电缆(OBC)等地震数据.为此本文详细分析了实际应用中常见的三种弹性各向同性介质模型的应力边界条件:自由空间、海底和自由地表模型.在上行传播假设情况下,获得了应力边界条件与位移边界条件的关系式.在此基础上,准确推导了3D多波多分量高斯束波场延拓和偏移成像公式,并在偏移过程中实现了完整的多波型自动分离.由于常规的互相关成像条件不适用于矢量波场成像,本文引用了散度/旋度互相关成像条件.通过约定PS转换波的正向旋转方向解决了3D空间PS成像极性翻转问题.利用2D和3D模型数据偏移成像验证了我们所提出的多波多分量高斯束偏移方法的可行性.
Conventional migration methods based on the elastic wave equation assume that the boundary is a free surface,where the normal and shear stresses are all zero.This assumption is not consistent with many kinds of seismic data,such as VSP(Vertical Seismic Profile)and OBC(Ocean Bottom Cable).In this paper,we analyze the stress boundary conditions for three kinds of models,including free-space,ocean-bottom and free-surface models.Under the assumption of up-going propagation,the relationships between the stress boundary condition and displacement boundary condition in the three models are established.Based on these relationships we derive the multimode and multicomponent Gaussian beam′s continuation and migration equations accurately.The complete decomposition of wave modes is implemented automatically during the migration.Since the conventional cross-correlation image condition is not suitable for vector wave field imaging,we use cross-correlation of divergence and curl of vector wave fields.By setting the positive rotation direction of PS converted waves we solve the polarity reversal problem in a 3Dspace.Synthetic data from 2Dand 3D models are used to validate the feasibility of the approach we propose.
Conventional migration methods based on the elastic wave equation assume that the boundary is a free surface,where the normal and shear stresses are all zero.This assumption is not consistent with many kinds of seismic data,such as VSP(Vertical Seismic Profile)and OBC(Ocean Bottom Cable).In this paper,we analyze the stress boundary conditions for three kinds of models,including free-space,ocean-bottom and free-surface models.Under the assumption of up-going propagation,the relationships between the stress boundary condition and displacement boundary condition in the three models are established.Based on these relationships we derive the multimode and multicomponent Gaussian beam′s continuation and migration equations accurately.The complete decomposition of wave modes is implemented automatically during the migration.Since the conventional cross-correlation image condition is not suitable for vector wave field imaging,we use cross-correlation of divergence and curl of vector wave fields.By setting the positive rotation direction of PS converted waves we solve the polarity reversal problem in a 3Dspace.Synthetic data from 2Dand 3D models are used to validate the feasibility of the approach we propose.
引文
Alkhalifah T.1995.Gaussian beam depth migration for anisotropic media.Geophysics,60(5):1474-1484.
Berkhout A J,Wapenaar C P A.1989.One-way versions of the Kirchhoff integral.Geophysics,54(4):460-467.
Bleistein N,Cohen J K,Stockwell J W.2004.Multidimensional Seismic Imaging,Migration,and Inversion(in Chinese).Beijing:Science Press.
CervenV,Popov M M,Pencík L.1982.Computation of wave fields in inhomogeneous media-Gaussian beam approach.Geophys.J.Int.,70(1):109-128.
CervenV,Pencík L.1983.Gaussian beams and paraxial ray approximation in three-dimensional elastic inhomogeneous media.J.Geophys.,53:1-15.
CervenV.2001.Seismic Ray Theory.Cambridge University Press.
Chang W F,McMechan G A.1987.Elastic reverse-time migration.Geophysics,52(10):1365-1375.
Chang W F,McMechan G A.1994.3-D elastic prestack reversetime depth migration.Geophysics,59(4):597-609.
Dai T F,Kuo J T.1986.Real data results of Kirchhoff elastic wave migration.Geophysics,51(4):1006-1011.
Davis T L.2001.Multicomponent seismology-The next wave.Geophysics,66(1):49.
Druzhinin A.2003.Decoupled elastic prestack depth migration.J.Appl.Geophys.,54(3-4):369-389.
Duan P F,Cheng J B,Chen A P,et al.2013.Local angle-domain Gaussian beam prestack depth migration in a TI medium.Chinese J.Geophys.(in Chinese),56(12):4206-4214,doi:10.6038/cjg20131223.
Gray S H.2005.Gaussian beam migration of common-shot records.Geophysics,70(4):S71-S77.
Gray S H,Bleistein N.2009.True-amplitude Gaussian-beam migration.Geophysics,74(2):S11-S23.
Hill N R.1990.Gaussian beam migration.Geophysics,55(11):1416-1428.
Hill N R.2001.Prestack Gaussian-beam depth migration.Geophysics,66(4):1240-1250.
Hokstad K.2000.Multicomponent Kirchhoff migration.Geophysics,65(3):861-873.
Huang Z Y,Sun J K,Zhu S J,et al.2007.Multicomponent Seismic Technology(in Chinese).Beijing:Petroleum Industry Press.
Kuo J T,Dai T F.1984.Kirchhoff elastic wave migration for the case of noncoincident source and receiver.Geophysics,49(8):1223-1238.
Li X L,Mao W J.2015.Multicomponent Gaussian beam migration in elastic medium.∥77th EAGE Conference and Exhibition.EAGE.
Li X Y.1997.Fractured reservoir delineation using multicomponent seismic data.Geophys.Prospecting,45(1):39-64.
Li X Y,Yuan J,Ziokowski A,et al.1999.Estimating Vp/Vsratio from converted waves-A 4C case example.∥61st EAGEConference and Exhibition.EAGE.
Mittet R.1994.Implementation of the Kirchhoff integral for elastic waves in staggered-grid modelling schemes.Geophysics,59(12):1894-1901.
Nowack R L,Sen M K,Stoffa P L.2003.Gaussian beam migration for sparse common-shot and common-receiver data.∥73rd Annual International Meeting,SEG Expanded Abstracts.Dallas,Texas,1114-1117.
Pao Y H,Varatharajulu V.1976.Huygens′principle,radiation conditions,and integral formulas for the scattering of elastic wave.J.Acoust.Soc.Am.,59(6):1361-1371.
Qian Z P,Chapman M,Li X Y,et al.2007.Use of multicomponent seismic data for oil-water discrimination in fractured reservoirs.The Leading Edge,26(9):1176-1184.
Ravasi M,Curtis A.2013.Elastic imaging with exact wavefield extrapolation for application to ocean-bottom 4Cseismic data.Geophysics,78(6):S265-S284.
Rechtien R D.1985.On“Kirchhoff elastic wave migration for the case of noncoincident source and receiver,”by John R.Kuo and Ting-fan Dai(GEOPHYSICS,49,1223-1238,August,1984).Geophysics,50(5):872.
Schleicher J,Tygel M,Ursin B,et al.2001.The KirchhoffHelmholtz integral for anisotropic elastic media.Wave Motion,34(4):353-364.
Sena A G,Toksoz M N.1993.Kirchhoff migration and velocity analysis for converted and nonconverted waves in anisotropic media.Geophysics,58(2):265-276.
Sun R,McMechan G A.1986.Pre-stack reverse-time migration for elastic waves with application to synthetic offset vertical seismic profiles.Proceedings of the IEEE,74(3):457-465.
Sun R,McMechan G A.2001.Scalar reverse-time depth migration of prestack elastic seismic data.Geophysics,66(5):1519-1527.
Sun R,McMechan G A,Lee C S,et al.2006.Prestack scalar reverse-time depth migration of 3D elastic seismic data.Geophysics,71(5):S199-S207.
Wapenaar C P A,HaiméG C.1990.Elastic extrapolation of primary seismic P-and S-waves.Geophys.Prospecting,38(1):23-60.
Xie X B,Wu R S.2005.Multicomponent prestack depth migration using the elastic screen method.Geophysics,70(1):S30-S37.
Xu S Y,Li Y P,Ma Z T.1999.Separation of P-and S-wave fields via theτ-q transform.China Offshore Oil and Gas(Geology)(in Chinese),13(5):334-337.
Yan J,Sava P.2008.Isotropic angle domain elastic reverse-time migration.Geophysics,73(6):S229-S239.
Yan J,Sava P.2009.Elastic wave-mode separation for VTI media.Geophysics,74(5):WB19-WB32.
Yue Y B.2011.Study on Gaussian beam migration methods in complex medium[Ph.D.thesis](in Chinese).Qingdao:China University of Petroleum(East China).
Zhe J P,Greenhalgh S A.1997.Prestack multicomponent migration.Geophysics,62(2):598-613.
Zhu T F,Gray S,Wang D L.2006.Prestack Gaussian-beam depth migration in anisotropic media.∥76th Annual International Meeting,SEG Expanded Abstracts.New Orleans,Louisiana,2362-2366.
布莱斯坦N,科恩J K,斯托克韦尔J W.2004.多维地震成像、偏移和反演中的数学.北京:科学出版社.
段鹏飞,程玖兵,陈爱萍等.2013.TI介质局部角度域高斯束叠前深度偏移成像.地球物理学报,56(12):4206-4214,doi:10.6038/cjg20131223.
黄中玉,孙建库,朱仕军等.2007.多分量地震技术.北京:石油工业出版社.
许世勇,李彦鹏,马在田.1999.τ-q变换法波场分离.中国海上油气(地质),13(5):334-337.
岳玉波.2011.复杂介质高斯束偏移成像方法研究[博士论文].青岛:中国石油大学(华东).
Berkhout A J,Wapenaar C P A.1989.One-way versions of the Kirchhoff integral.Geophysics,54(4):460-467.
Bleistein N,Cohen J K,Stockwell J W.2004.Multidimensional Seismic Imaging,Migration,and Inversion(in Chinese).Beijing:Science Press.
CervenV,Popov M M,Pencík L.1982.Computation of wave fields in inhomogeneous media-Gaussian beam approach.Geophys.J.Int.,70(1):109-128.
CervenV,Pencík L.1983.Gaussian beams and paraxial ray approximation in three-dimensional elastic inhomogeneous media.J.Geophys.,53:1-15.
CervenV.2001.Seismic Ray Theory.Cambridge University Press.
Chang W F,McMechan G A.1987.Elastic reverse-time migration.Geophysics,52(10):1365-1375.
Chang W F,McMechan G A.1994.3-D elastic prestack reversetime depth migration.Geophysics,59(4):597-609.
Dai T F,Kuo J T.1986.Real data results of Kirchhoff elastic wave migration.Geophysics,51(4):1006-1011.
Davis T L.2001.Multicomponent seismology-The next wave.Geophysics,66(1):49.
Druzhinin A.2003.Decoupled elastic prestack depth migration.J.Appl.Geophys.,54(3-4):369-389.
Duan P F,Cheng J B,Chen A P,et al.2013.Local angle-domain Gaussian beam prestack depth migration in a TI medium.Chinese J.Geophys.(in Chinese),56(12):4206-4214,doi:10.6038/cjg20131223.
Gray S H.2005.Gaussian beam migration of common-shot records.Geophysics,70(4):S71-S77.
Gray S H,Bleistein N.2009.True-amplitude Gaussian-beam migration.Geophysics,74(2):S11-S23.
Hill N R.1990.Gaussian beam migration.Geophysics,55(11):1416-1428.
Hill N R.2001.Prestack Gaussian-beam depth migration.Geophysics,66(4):1240-1250.
Hokstad K.2000.Multicomponent Kirchhoff migration.Geophysics,65(3):861-873.
Huang Z Y,Sun J K,Zhu S J,et al.2007.Multicomponent Seismic Technology(in Chinese).Beijing:Petroleum Industry Press.
Kuo J T,Dai T F.1984.Kirchhoff elastic wave migration for the case of noncoincident source and receiver.Geophysics,49(8):1223-1238.
Li X L,Mao W J.2015.Multicomponent Gaussian beam migration in elastic medium.∥77th EAGE Conference and Exhibition.EAGE.
Li X Y.1997.Fractured reservoir delineation using multicomponent seismic data.Geophys.Prospecting,45(1):39-64.
Li X Y,Yuan J,Ziokowski A,et al.1999.Estimating Vp/Vsratio from converted waves-A 4C case example.∥61st EAGEConference and Exhibition.EAGE.
Mittet R.1994.Implementation of the Kirchhoff integral for elastic waves in staggered-grid modelling schemes.Geophysics,59(12):1894-1901.
Nowack R L,Sen M K,Stoffa P L.2003.Gaussian beam migration for sparse common-shot and common-receiver data.∥73rd Annual International Meeting,SEG Expanded Abstracts.Dallas,Texas,1114-1117.
Pao Y H,Varatharajulu V.1976.Huygens′principle,radiation conditions,and integral formulas for the scattering of elastic wave.J.Acoust.Soc.Am.,59(6):1361-1371.
Qian Z P,Chapman M,Li X Y,et al.2007.Use of multicomponent seismic data for oil-water discrimination in fractured reservoirs.The Leading Edge,26(9):1176-1184.
Ravasi M,Curtis A.2013.Elastic imaging with exact wavefield extrapolation for application to ocean-bottom 4Cseismic data.Geophysics,78(6):S265-S284.
Rechtien R D.1985.On“Kirchhoff elastic wave migration for the case of noncoincident source and receiver,”by John R.Kuo and Ting-fan Dai(GEOPHYSICS,49,1223-1238,August,1984).Geophysics,50(5):872.
Schleicher J,Tygel M,Ursin B,et al.2001.The KirchhoffHelmholtz integral for anisotropic elastic media.Wave Motion,34(4):353-364.
Sena A G,Toksoz M N.1993.Kirchhoff migration and velocity analysis for converted and nonconverted waves in anisotropic media.Geophysics,58(2):265-276.
Sun R,McMechan G A.1986.Pre-stack reverse-time migration for elastic waves with application to synthetic offset vertical seismic profiles.Proceedings of the IEEE,74(3):457-465.
Sun R,McMechan G A.2001.Scalar reverse-time depth migration of prestack elastic seismic data.Geophysics,66(5):1519-1527.
Sun R,McMechan G A,Lee C S,et al.2006.Prestack scalar reverse-time depth migration of 3D elastic seismic data.Geophysics,71(5):S199-S207.
Wapenaar C P A,HaiméG C.1990.Elastic extrapolation of primary seismic P-and S-waves.Geophys.Prospecting,38(1):23-60.
Xie X B,Wu R S.2005.Multicomponent prestack depth migration using the elastic screen method.Geophysics,70(1):S30-S37.
Xu S Y,Li Y P,Ma Z T.1999.Separation of P-and S-wave fields via theτ-q transform.China Offshore Oil and Gas(Geology)(in Chinese),13(5):334-337.
Yan J,Sava P.2008.Isotropic angle domain elastic reverse-time migration.Geophysics,73(6):S229-S239.
Yan J,Sava P.2009.Elastic wave-mode separation for VTI media.Geophysics,74(5):WB19-WB32.
Yue Y B.2011.Study on Gaussian beam migration methods in complex medium[Ph.D.thesis](in Chinese).Qingdao:China University of Petroleum(East China).
Zhe J P,Greenhalgh S A.1997.Prestack multicomponent migration.Geophysics,62(2):598-613.
Zhu T F,Gray S,Wang D L.2006.Prestack Gaussian-beam depth migration in anisotropic media.∥76th Annual International Meeting,SEG Expanded Abstracts.New Orleans,Louisiana,2362-2366.
布莱斯坦N,科恩J K,斯托克韦尔J W.2004.多维地震成像、偏移和反演中的数学.北京:科学出版社.
段鹏飞,程玖兵,陈爱萍等.2013.TI介质局部角度域高斯束叠前深度偏移成像.地球物理学报,56(12):4206-4214,doi:10.6038/cjg20131223.
黄中玉,孙建库,朱仕军等.2007.多分量地震技术.北京:石油工业出版社.
许世勇,李彦鹏,马在田.1999.τ-q变换法波场分离.中国海上油气(地质),13(5):334-337.
岳玉波.2011.复杂介质高斯束偏移成像方法研究[博士论文].青岛:中国石油大学(华东).