四面体网格剖分下速度与反射界面的同时反演
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摘要
针对含起伏地表、不规则反射界面及速度异常体的复杂模型的走时正、反演问题,本文采用四面体单元进行模型参数化,实现多震相地震射线的追踪计算,且推导了四面体单元下走时关于速度、走时关于反射点深度的偏导数计算公式;结合共轭梯度法求解带约束的阻尼最小二乘反演问题,实现了多震相走时联合及同时反演成像;通过在同时反演中对不同种类Jacobi偏导元素做归一化处理,有效解决了不规则界面存在散射而导致的散射点所在区域射线过密、速度和界面过度更新问题。数值模拟结果表明:采用四面体单元进行模型参数化,复杂模型正演计算结果具有较高精度;同时反演可准确刻画不规则反射界面和速度异常体。因此,本文提出的走时成像方法具有有效性和实用性。
To conduct forward modeling and simultaneous inversion for a complex geological model with an irregular topography,or irregular reflectors,or irregular velocity anomaly,we propose in this paper simultaneous inversion using multi-phase travel-times in 3-D tetrahedral cell model.First we realize a multi-phase arrival tracking with a multistage modified shortest-path method,develop calculation formula of partial derivative of reflection depth about travel-times under a tetrahedral cell model.Then we solve a constrained-damped leastsquares inversion with a conjugated gradient method to simultaneously invert the velocity model and reflector geometry with multi-phase arrival time information.Finally we normalize the different Jacobi elements in the simultaneous inversion to eliminate undulated reflector scattering,which causes overhigh ray density and over-updated velocity issues.Numerical simulation results show that with the tetrahedral cell model parameterization,it is possible to maintain a high computational accuracy for forward modeling in the complex velocity model,and capture the irregular velocity anomaly and reflector geometry in the simultaneous inversion.Therefore,the proposed simultaneous travel-time inversion has a wide application in real problems.
To conduct forward modeling and simultaneous inversion for a complex geological model with an irregular topography,or irregular reflectors,or irregular velocity anomaly,we propose in this paper simultaneous inversion using multi-phase travel-times in 3-D tetrahedral cell model.First we realize a multi-phase arrival tracking with a multistage modified shortest-path method,develop calculation formula of partial derivative of reflection depth about travel-times under a tetrahedral cell model.Then we solve a constrained-damped leastsquares inversion with a conjugated gradient method to simultaneously invert the velocity model and reflector geometry with multi-phase arrival time information.Finally we normalize the different Jacobi elements in the simultaneous inversion to eliminate undulated reflector scattering,which causes overhigh ray density and over-updated velocity issues.Numerical simulation results show that with the tetrahedral cell model parameterization,it is possible to maintain a high computational accuracy for forward modeling in the complex velocity model,and capture the irregular velocity anomaly and reflector geometry in the simultaneous inversion.Therefore,the proposed simultaneous travel-time inversion has a wide application in real problems.
引文
[1]Aki K,Lee W H K.Determination of three dimensional velocity anomalies under a seismic array using first P arrival times from local earthquakes.Journal Geophysics Research,1976,81(23):4381-4399.
[2]成谷,马在田,耿建华等.地震层析成像发展回顾.勘探地球物理进展,2002,25(3):6-12.Cheng Gu,Ma Zaitian,Geng Jianhua et al.A review on the growth of seismic tomography.Progress in Exploration Geophysics,2002,25(3):6-12.
[3]成谷,张宝金.三角网格参数化在反射地震走时层析成像中的应用.中山大学学报:自然科学版,2006,45(5):128-132.Cheng Gu,Zhang Baojin.Application of triangle cell parameterization in travel-time tomography of reflection seismic data.Acta Scientiarum Naturalium Universitatis Sunyatseni,2006,45(5):128-132.
[4]尧德中,阮颖铮,刘光远.六角形网格波动方程数值模拟的傅氏变换算法.计算物理,1994,11(1):102-106.Yao Dezhong,Ruan Yingzheng,Liu Guangyuan.Wave equation numerical modeling of hexagonal sample by Fourier method.Chinese Journal of Computational Physics,1994,11(1):102-106.
[5]褚春雷,王修田.非规则三角网格有限差分法地震正演模拟.中国海洋大学学报(自然科学版),2005,35(1):43-48.Chu Chunlei,Wang Xiutian.Seismic modeling with a finite-difference method on irregular triangular grids.Periodical of Ocean University of China,2005,35(1):43-48.
[6]蔡志成,顾汉明,成景旺等.大规模变网格三维地震正演MPI并行策略与实现.石油地球物理勘探,2017,52(3):468-476.Cai Zhicheng,Gu Hanming,Cheng Jingwang et al.Parallel large-scale variable grid 3D seismic wave modeling.OGP,2017,52(3):468-476.
[7]张伟.含起伏地形的三维非均匀介质中地震波传播的有限差分算法及其在强地面震动模拟中的应用[学位论文].北京:北京大学,2006.Zhang Wei.Finite Difference Seismic Wave Modeling in 3DHeterogeneous Media with Surface Topography and Its Implementation in Strong Ground Motion Study[D].Peking University,Beijing,2006.
[8]李波涛,杨长春,陈雨红等.基于波前面三角形网剖分的波前重建法三维射线追踪.地球物理学进展,2009,24(2):507-512.Li Botao,Yang Changchun,Chen Yuhong et al.3Dwavefront construction method ray tracing based on triangular grids layout on wavefront.Progress in Geophysics,2009,24(2):507-512.
[9]Yu S J,Liu R Z,Cheng J L.A minimum traveltime ray tracing global algorithm on a triangular net for propagating plane waves.Applied Geophysics,2010,7(4):348-356.
[10]Lan H,Zhang Z.Topography-dependent eikonal equation and its solver for calculating first-arrival traveltimes with an irregular surface.Geophysical Journal International,2013,193(2):1010-1026.
[11]Vinje V,stebl K,Iversen E et al.3-D ray modeling by wavefront construction in open models.Geophysics,1999,64(6):1912-1919.
[12]赵瑞,白超英.复杂层状模型中多次波快速追踪---一种基于非规则网格的最短路径算法.地震学报,2010,32(4):433-444.Zhao Rui,Bai Chaoying.Fast multiple ray tracing within complex layered media:The shortest path method based on irregular grid cells.Acta Seismologica Sinica,2010,32(4):433-444.
[13]Bai Chaoying,Li Xiaoling,Tang Xiaoping.Seismic wavefront evolution of multiply reflected,transmitted,and converted phases in 2D/3Dtriangular cell model.Journal of Seismology,2011,15(4):637-652.
[14]李晓玲,白超英,胡光义.起伏层状TI介质中多次波射线追踪.石油地球物理勘探,2013,48(6):924-931.Li Xiaoling,Bai Chaoying,Hu Guangyi.Multiple ray tracing in an undulated layered TI media.OGP,2013,48(6):924-931.
[15]李兴旺,白超英,李晓玲.四面体单元剖分下三维各向异性TI介质中多次波射线追踪.石油地球物理勘探,2017,52(1):48-55.Li Xingwang,Bai Chaoying,Li Xiaoling.Multiples raytracing in 3Danisotropic TI media with a tetrahedron cell model.OGP,2017,52(1):48-55.
[16]Tarantola A,Nercessian A.Three-dimensional inversion without blocks.Geophysical Journal International,1984,76(2):299-306.
[17]Sambridge M,Braun J,McQueen H.Geophysical parametrization and interpolation of irregular data using natural neighbours.Geophysical Journal International,1995,122(3):837-857.
[18]Gudmundsson O',Sambridge M.A regionalized upper mantle(RUM)seismic model.Journal Geophysical Research:Solid Earth,1998,103(B4):7121-7136.
[19]Curtis A,Snieder R.Reconditioning inverse problems using the genetic algorithm and revised parameterization.Geophysics,1997,62(5):1524-1532.
[20]B9hm G,Galuppo P,Vesnaver A.3Dadaptive tomography using Delaunay triangles and Voronoi polygons.Geophysical Prospecting,2000,48(4):723-744.
[21]Sambridge M and Faletiˇc R.Adaptive whole Earth tomography.Geochemistry,Geophysics,Geosystems,2003,4(3):1022,doi:10.1029/2001GC000213.
[22]于师建,刘润泽.三角网最小走时射线追踪层析成像.CT理论与应用研究,2013,22(3):401-408.Yu Shijian,Liu Ruize.Tomography of a minimum travel time ray tracing on a triangular net.CT Theory and Applications,2013,22(3):401-408.
[23]何雷宇,严星,白超英.三角网格剖分下速度与反射界面的同时反演.地球物理学进展,2017,32(3):1140-1148.He Leiyu,Yan Xing,Bai Chaoying.Simultaneous inversion for velocity and reflector geometry with multiphase traveltimes in 2Dtriangular cell model.Progress in Geophysics,32(3):1140-1148.
[24]Si H.TetGen,a Delaunay-based quality tetrahedral mesh generator.ACM Transactions on Mathematical Software(TOMS),2015,41(2):1-36.
[25]Menke W.The resolving power of cross-borehole tomography.Geophysical Research Letters,1984,11(2):105-108.
[26]Meyerholtz K A,Pavlis G L,Szpakowski S A.Convolutional quelling in seismic tomography.Geophysics,1989,54(5):570-580.
[27]Tarantola A,Valette B.Generalized nonlinear inverse problems solved using the least squares criterion.Reviews of Geophysics,1982,20(2):219-232.
[28]Bai Chaoying,Greenhalgh S.3-D non-linear travel time tomography:Imaging high contrast velocity anomalies.Pure Applied Geophysics,2005,162(11):2029-2049.
[29]Zhou B,Greenhalgh S A,Sinadinovski C.Iterative algorithm for the damped minimum norm,least-squares and constrained problem in seismic tomography.Exploration Geophysics,1992,23(3):497-505.
[30]Sambridge M S.Non-linear arrival time inversion:constraining velocity anomalies by seeking smooth models in 3-D.Geophysical Journal International,1990,102(3):653-677.
[2]成谷,马在田,耿建华等.地震层析成像发展回顾.勘探地球物理进展,2002,25(3):6-12.Cheng Gu,Ma Zaitian,Geng Jianhua et al.A review on the growth of seismic tomography.Progress in Exploration Geophysics,2002,25(3):6-12.
[3]成谷,张宝金.三角网格参数化在反射地震走时层析成像中的应用.中山大学学报:自然科学版,2006,45(5):128-132.Cheng Gu,Zhang Baojin.Application of triangle cell parameterization in travel-time tomography of reflection seismic data.Acta Scientiarum Naturalium Universitatis Sunyatseni,2006,45(5):128-132.
[4]尧德中,阮颖铮,刘光远.六角形网格波动方程数值模拟的傅氏变换算法.计算物理,1994,11(1):102-106.Yao Dezhong,Ruan Yingzheng,Liu Guangyuan.Wave equation numerical modeling of hexagonal sample by Fourier method.Chinese Journal of Computational Physics,1994,11(1):102-106.
[5]褚春雷,王修田.非规则三角网格有限差分法地震正演模拟.中国海洋大学学报(自然科学版),2005,35(1):43-48.Chu Chunlei,Wang Xiutian.Seismic modeling with a finite-difference method on irregular triangular grids.Periodical of Ocean University of China,2005,35(1):43-48.
[6]蔡志成,顾汉明,成景旺等.大规模变网格三维地震正演MPI并行策略与实现.石油地球物理勘探,2017,52(3):468-476.Cai Zhicheng,Gu Hanming,Cheng Jingwang et al.Parallel large-scale variable grid 3D seismic wave modeling.OGP,2017,52(3):468-476.
[7]张伟.含起伏地形的三维非均匀介质中地震波传播的有限差分算法及其在强地面震动模拟中的应用[学位论文].北京:北京大学,2006.Zhang Wei.Finite Difference Seismic Wave Modeling in 3DHeterogeneous Media with Surface Topography and Its Implementation in Strong Ground Motion Study[D].Peking University,Beijing,2006.
[8]李波涛,杨长春,陈雨红等.基于波前面三角形网剖分的波前重建法三维射线追踪.地球物理学进展,2009,24(2):507-512.Li Botao,Yang Changchun,Chen Yuhong et al.3Dwavefront construction method ray tracing based on triangular grids layout on wavefront.Progress in Geophysics,2009,24(2):507-512.
[9]Yu S J,Liu R Z,Cheng J L.A minimum traveltime ray tracing global algorithm on a triangular net for propagating plane waves.Applied Geophysics,2010,7(4):348-356.
[10]Lan H,Zhang Z.Topography-dependent eikonal equation and its solver for calculating first-arrival traveltimes with an irregular surface.Geophysical Journal International,2013,193(2):1010-1026.
[11]Vinje V,stebl K,Iversen E et al.3-D ray modeling by wavefront construction in open models.Geophysics,1999,64(6):1912-1919.
[12]赵瑞,白超英.复杂层状模型中多次波快速追踪---一种基于非规则网格的最短路径算法.地震学报,2010,32(4):433-444.Zhao Rui,Bai Chaoying.Fast multiple ray tracing within complex layered media:The shortest path method based on irregular grid cells.Acta Seismologica Sinica,2010,32(4):433-444.
[13]Bai Chaoying,Li Xiaoling,Tang Xiaoping.Seismic wavefront evolution of multiply reflected,transmitted,and converted phases in 2D/3Dtriangular cell model.Journal of Seismology,2011,15(4):637-652.
[14]李晓玲,白超英,胡光义.起伏层状TI介质中多次波射线追踪.石油地球物理勘探,2013,48(6):924-931.Li Xiaoling,Bai Chaoying,Hu Guangyi.Multiple ray tracing in an undulated layered TI media.OGP,2013,48(6):924-931.
[15]李兴旺,白超英,李晓玲.四面体单元剖分下三维各向异性TI介质中多次波射线追踪.石油地球物理勘探,2017,52(1):48-55.Li Xingwang,Bai Chaoying,Li Xiaoling.Multiples raytracing in 3Danisotropic TI media with a tetrahedron cell model.OGP,2017,52(1):48-55.
[16]Tarantola A,Nercessian A.Three-dimensional inversion without blocks.Geophysical Journal International,1984,76(2):299-306.
[17]Sambridge M,Braun J,McQueen H.Geophysical parametrization and interpolation of irregular data using natural neighbours.Geophysical Journal International,1995,122(3):837-857.
[18]Gudmundsson O',Sambridge M.A regionalized upper mantle(RUM)seismic model.Journal Geophysical Research:Solid Earth,1998,103(B4):7121-7136.
[19]Curtis A,Snieder R.Reconditioning inverse problems using the genetic algorithm and revised parameterization.Geophysics,1997,62(5):1524-1532.
[20]B9hm G,Galuppo P,Vesnaver A.3Dadaptive tomography using Delaunay triangles and Voronoi polygons.Geophysical Prospecting,2000,48(4):723-744.
[21]Sambridge M and Faletiˇc R.Adaptive whole Earth tomography.Geochemistry,Geophysics,Geosystems,2003,4(3):1022,doi:10.1029/2001GC000213.
[22]于师建,刘润泽.三角网最小走时射线追踪层析成像.CT理论与应用研究,2013,22(3):401-408.Yu Shijian,Liu Ruize.Tomography of a minimum travel time ray tracing on a triangular net.CT Theory and Applications,2013,22(3):401-408.
[23]何雷宇,严星,白超英.三角网格剖分下速度与反射界面的同时反演.地球物理学进展,2017,32(3):1140-1148.He Leiyu,Yan Xing,Bai Chaoying.Simultaneous inversion for velocity and reflector geometry with multiphase traveltimes in 2Dtriangular cell model.Progress in Geophysics,32(3):1140-1148.
[24]Si H.TetGen,a Delaunay-based quality tetrahedral mesh generator.ACM Transactions on Mathematical Software(TOMS),2015,41(2):1-36.
[25]Menke W.The resolving power of cross-borehole tomography.Geophysical Research Letters,1984,11(2):105-108.
[26]Meyerholtz K A,Pavlis G L,Szpakowski S A.Convolutional quelling in seismic tomography.Geophysics,1989,54(5):570-580.
[27]Tarantola A,Valette B.Generalized nonlinear inverse problems solved using the least squares criterion.Reviews of Geophysics,1982,20(2):219-232.
[28]Bai Chaoying,Greenhalgh S.3-D non-linear travel time tomography:Imaging high contrast velocity anomalies.Pure Applied Geophysics,2005,162(11):2029-2049.
[29]Zhou B,Greenhalgh S A,Sinadinovski C.Iterative algorithm for the damped minimum norm,least-squares and constrained problem in seismic tomography.Exploration Geophysics,1992,23(3):497-505.
[30]Sambridge M S.Non-linear arrival time inversion:constraining velocity anomalies by seeking smooth models in 3-D.Geophysical Journal International,1990,102(3):653-677.