地层格架正则化约束下的二维立体层析反演
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摘要
通过把地层格架信息作用于立体层析Fréchet导数矩阵,使得更新后的速度模型呈现出符合地质规律的块状特征.地层格架信息基于立体层析反演中得到的反射点位置进行非规则B样条插值拟合得到,因此在反演中它将会随着反射点位置的更新自然得到更新.与前人提出的保边缘层析算法或多层立体层析算法相比,本文提出的地层格架正则化无需引入混合正则化项或定义某种复杂的混合速度格式,更为直接也更容易实现.理论和实际数据算例证实了该正则化技巧的稳健性和可靠性,能够得到与实际地质构造特征更为一致的地质一致性反演结果.
This paper presents a regularization technique by incorporating the blocky geological boundary information into the Fréchet derivatives matrix of the stereo-tomography inversion.Using this method,the updated velocity model can automatically exhibit a blocky feature.The geological boundary information is updated based on the updated reflector positions,which can be provided by conventional stereo-tomography itself.Compared with the conventional tomography with mixed norms or the multi-layer stereo-tomography,the presented regularization technique does not depend on a hybrid regularization terms or a hybrid velocity format.It is more straightforward and easier to implement.The synthetic data example and the field seismic data case demonstrate the robustness of this method and its inversion results are more consistent with real geological structure.
This paper presents a regularization technique by incorporating the blocky geological boundary information into the Fréchet derivatives matrix of the stereo-tomography inversion.Using this method,the updated velocity model can automatically exhibit a blocky feature.The geological boundary information is updated based on the updated reflector positions,which can be provided by conventional stereo-tomography itself.Compared with the conventional tomography with mixed norms or the multi-layer stereo-tomography,the presented regularization technique does not depend on a hybrid regularization terms or a hybrid velocity format.It is more straightforward and easier to implement.The synthetic data example and the field seismic data case demonstrate the robustness of this method and its inversion results are more consistent with real geological structure.
引文
Alerini M,LambaréG,Baina R,et al.2007.Two-dimensional PP/PS-stereotomography:P-and S-waves velocities estimation from OBC data.Geophysical Journal International,170(2):725-736.
Billette F,LambaréG.1998.Velocity macro-model estimation from seismic reflection data by stereotomography.Geophysical Journal International,135(2):671-690.
Billette F,Le Bégat S,Podvin P,et al.2003.Practical aspects and applications of 2Dstereotomography.Geophysics,68(3):1008-1021.
Clapp R G,Biondi B L,Claerbout J F.2004.Incorporating geologic information into reflection tomography.Geophysics,69(2):533-546.
Costa J C,da Silva F J C,Gomes E N S,et al.2008.Regularization in slope tomography.Geophysics,73(5):VE39-VE47.
Farra V,Madariaga R.1987.Seismic waveform modeling in heterogeneous media by ray perturbation theory.Journal of Geophysical Research,92(B3):2697-2712.
Farra V,Madariaga R.1988.Non-linear reflection tomography.Geophysical Journal International,95(1):135-147.
Harlan W S.1995.Regularization by model reparameterization.http:∥www.billharlan.com/pub/papers/regularization.pdf.
Kosloff D,Sherwood J,Koren Z,et al.1996.Velocity and interface depth determination by tomography of depth migrated gathers.Geophysics,61(5):1511-1523.
Lambaré G,Guillaume P,Zhang X,et al.2013.Multi-layer nonlinear slope tomography.∥75th EAGE Conference&Exhibition.EAGE.
Li Z W,Yang K,Ni Y,et al.2014.Migration velocity analysis with stereo-tomography.Geophysical Prospecting for Petroleum(in Chinese),53(4):444-452.
Ni Y,Yang K,Chen B S.2013.Stereo-tomography inversion method:theory and application testing.Geophysical Prospecting for Petroleum(in Chinese),52(2):121-130,111.
Piegl L,Tiller W.1997.B-spline programming concepts.∥The NURBS Book.Berlin,Heidelberg:Springer,593-628.
Prieux V,LambaréG,Operto S,et al.2013.Building starting models for full waveform inversion from wide-aperture data by stereotomography.Geophysical Prospecting,61(S1):109-137.
Ren L J,Sun X D,Li Z C,2014.The stereo-tomography based on eigen-wave attributes.∥Proceedings of the CPS/SEG Beijing2014International Geophysical Conference(in Chinese).Beijing:CPS/SEG.
Shao W D,Yang K,Xing F Y,et al.2017.Stereo-tomography in squared-slowness triangulated model.Chinese Journal of Geophysics(in Chinese),60(9):3574-3586,doi:10.6038/cjg20170923.
Van Vliet L J,Verbeek P W.1995.Estimators for orientation and anisotropy in digitized images.∥ASCI Imaging Workshop.Venray,NL,442-450.
Wang Y X,Yang K,Yang X C,et al.2016.A high-density stereotomography method based on the gradient square structure tensors algorithm.Chinese Journal of Geophysics(in Chinese),59(1):263-276,doi:10.6038/cjg20160122.
Wu X M,Hale D.2015.Horizon volumes with interpreted constraints.Geophysics,80(2):IM21-IM33.
Yang K,Xing F Y,Li Z W,et al.2016.3Dstereo-tomography based on the non-reduced Hamiltonian.Chinese Journal of Geophysics(in Chinese),59(9):3366-3378,doi:10.6038/cjg20160920.
Zelt C A,Smith R B.1992.Seismic traveltime inversion for 2-Dcrustal velocity structure.Geophysical Journal International,108(1):16-34.
Zhang X,Zhang J.2012.Edge preserving regularization for seismic traveltime tomography.∥2012SEG Annual Meeting.Las Vegas,Nevada:SEG,2830-3834.
Zhou H W.2006.Multiscale deformable-layer tomography.Geophysics,71(3):R11-R19.
李振伟,杨锴,倪瑶等.2014.基于立体层析反演的偏移速度建模应用研究.石油物探,53(4):444-452.
倪瑶,杨锴,陈宝书.2013.立体层析反演方法理论分析与应用测试.石油物探,52(2):121-130.
任丽娟,孙小东,李振春.2014.基于特征波属性参数的立体层析速度反演方法研究.∥CPS/SEG北京2014国际地球物理会议摘要.北京.
邵炜栋,杨锴,邢逢源等.2017.慢度平方三角网格立体层析反演方法.地球物理学报,60(9):3574-3586,doi:10.6038/cjg20170923.
王宇翔,杨锴,杨小椿等.2016.基于梯度平方结构张量算法的高密度二维立体层析反演.地球物理学报,59(1):263-276,doi:10.6038/cjg20160122.
杨锴,邢逢源,李振伟等.2016.基于非降阶汉密尔顿算子的三维立体层析反演.地球物理学报,59(9):3366-3378,doi:10.6038/cjg20160920.
Billette F,LambaréG.1998.Velocity macro-model estimation from seismic reflection data by stereotomography.Geophysical Journal International,135(2):671-690.
Billette F,Le Bégat S,Podvin P,et al.2003.Practical aspects and applications of 2Dstereotomography.Geophysics,68(3):1008-1021.
Clapp R G,Biondi B L,Claerbout J F.2004.Incorporating geologic information into reflection tomography.Geophysics,69(2):533-546.
Costa J C,da Silva F J C,Gomes E N S,et al.2008.Regularization in slope tomography.Geophysics,73(5):VE39-VE47.
Farra V,Madariaga R.1987.Seismic waveform modeling in heterogeneous media by ray perturbation theory.Journal of Geophysical Research,92(B3):2697-2712.
Farra V,Madariaga R.1988.Non-linear reflection tomography.Geophysical Journal International,95(1):135-147.
Harlan W S.1995.Regularization by model reparameterization.http:∥www.billharlan.com/pub/papers/regularization.pdf.
Kosloff D,Sherwood J,Koren Z,et al.1996.Velocity and interface depth determination by tomography of depth migrated gathers.Geophysics,61(5):1511-1523.
Lambaré G,Guillaume P,Zhang X,et al.2013.Multi-layer nonlinear slope tomography.∥75th EAGE Conference&Exhibition.EAGE.
Li Z W,Yang K,Ni Y,et al.2014.Migration velocity analysis with stereo-tomography.Geophysical Prospecting for Petroleum(in Chinese),53(4):444-452.
Ni Y,Yang K,Chen B S.2013.Stereo-tomography inversion method:theory and application testing.Geophysical Prospecting for Petroleum(in Chinese),52(2):121-130,111.
Piegl L,Tiller W.1997.B-spline programming concepts.∥The NURBS Book.Berlin,Heidelberg:Springer,593-628.
Prieux V,LambaréG,Operto S,et al.2013.Building starting models for full waveform inversion from wide-aperture data by stereotomography.Geophysical Prospecting,61(S1):109-137.
Ren L J,Sun X D,Li Z C,2014.The stereo-tomography based on eigen-wave attributes.∥Proceedings of the CPS/SEG Beijing2014International Geophysical Conference(in Chinese).Beijing:CPS/SEG.
Shao W D,Yang K,Xing F Y,et al.2017.Stereo-tomography in squared-slowness triangulated model.Chinese Journal of Geophysics(in Chinese),60(9):3574-3586,doi:10.6038/cjg20170923.
Van Vliet L J,Verbeek P W.1995.Estimators for orientation and anisotropy in digitized images.∥ASCI Imaging Workshop.Venray,NL,442-450.
Wang Y X,Yang K,Yang X C,et al.2016.A high-density stereotomography method based on the gradient square structure tensors algorithm.Chinese Journal of Geophysics(in Chinese),59(1):263-276,doi:10.6038/cjg20160122.
Wu X M,Hale D.2015.Horizon volumes with interpreted constraints.Geophysics,80(2):IM21-IM33.
Yang K,Xing F Y,Li Z W,et al.2016.3Dstereo-tomography based on the non-reduced Hamiltonian.Chinese Journal of Geophysics(in Chinese),59(9):3366-3378,doi:10.6038/cjg20160920.
Zelt C A,Smith R B.1992.Seismic traveltime inversion for 2-Dcrustal velocity structure.Geophysical Journal International,108(1):16-34.
Zhang X,Zhang J.2012.Edge preserving regularization for seismic traveltime tomography.∥2012SEG Annual Meeting.Las Vegas,Nevada:SEG,2830-3834.
Zhou H W.2006.Multiscale deformable-layer tomography.Geophysics,71(3):R11-R19.
李振伟,杨锴,倪瑶等.2014.基于立体层析反演的偏移速度建模应用研究.石油物探,53(4):444-452.
倪瑶,杨锴,陈宝书.2013.立体层析反演方法理论分析与应用测试.石油物探,52(2):121-130.
任丽娟,孙小东,李振春.2014.基于特征波属性参数的立体层析速度反演方法研究.∥CPS/SEG北京2014国际地球物理会议摘要.北京.
邵炜栋,杨锴,邢逢源等.2017.慢度平方三角网格立体层析反演方法.地球物理学报,60(9):3574-3586,doi:10.6038/cjg20170923.
王宇翔,杨锴,杨小椿等.2016.基于梯度平方结构张量算法的高密度二维立体层析反演.地球物理学报,59(1):263-276,doi:10.6038/cjg20160122.
杨锴,邢逢源,李振伟等.2016.基于非降阶汉密尔顿算子的三维立体层析反演.地球物理学报,59(9):3366-3378,doi:10.6038/cjg20160920.