二维复杂层状介质中地震多波走时联合反演成像
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摘要
采用新近提出的多次波射线追踪正演算法,结合共轭梯度法求解带约束的阻尼最小二乘最优化反演问题,分析讨论了利用多震相走时资料进行联合反演成像的方法及技术.考虑到不同震相走时的拾取误差不同,反演算法中引入了不同震相种类数据的权系数;由于同时反演速度模型和反射界面起伏中不同模型参数变化对走时影响程度的不同,Jacobi偏导矩阵元素中引入了不同参数的归一化因子;另外,为了克服射线密度过大(或过小)区域速度模型的过度(或欠)更新问题,反演算法中引入了等权射线密度的概念.几种数值模拟实例表明(含噪声敏感性试验):多波走时的联合或同时反演成像技术是一种提高走时成像空间分辨率,进而降低重建模型失真度行之有效的方法.
The newly developed multiple (reflected, transmitted and converted) arrival tracking algorithm and the conjugated gradient method are used to solve the constrained, damped least squares problem. We discuss and analyze the simultaneous inversion algorithm with different travel time datasets. In the inversion process we introduce different weighting factors according to the different picking errors of different arrivals, and normalize different parameters in Jacobian matrix elements to balance the influence on travel time due to the different contributions of velocity variation and depth of reflector. In order to overcome the velocity overestimation (or underestimation) in some regions where the ray density is very high (or low), the concept of equal weighted ray density is introduced into inversion process. The numerical results (including the noise-sensitivity tests both in travel times and velocity model perturbation) show that it is a practical and efficient way to improve the spatial resolution and reduce the artifact in reconstructing velocity distribution and reflective interface.
The newly developed multiple (reflected, transmitted and converted) arrival tracking algorithm and the conjugated gradient method are used to solve the constrained, damped least squares problem. We discuss and analyze the simultaneous inversion algorithm with different travel time datasets. In the inversion process we introduce different weighting factors according to the different picking errors of different arrivals, and normalize different parameters in Jacobian matrix elements to balance the influence on travel time due to the different contributions of velocity variation and depth of reflector. In order to overcome the velocity overestimation (or underestimation) in some regions where the ray density is very high (or low), the concept of equal weighted ray density is introduced into inversion process. The numerical results (including the noise-sensitivity tests both in travel times and velocity model perturbation) show that it is a practical and efficient way to improve the spatial resolution and reduce the artifact in reconstructing velocity distribution and reflective interface.
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.J Geophys Res,1976,81:4381～4399
[2] Rawlinson N,Sambridge M.Seismic traveltime tomography of the crust and lithosphere.Adv in Geophys,2003,46:81～198
[3] Zhao D,Kayal J R.Impact of seismic tomography on Earth sciences.Current Science,2000,79:1208～1214
[4] Zelt C A,Smith R B.Seismic travehime inversion for 2-D crustal velocity structure.Geophys J Int,1992,105:16～34
[5] Zelt C A,White D J.Crustal structure and tectonics of the southeastern Canadian Cordillera.J Geophys Res,1995,100:24255～24273
[6] Zelt C A,Hojka A M,Flueh E R,et al.3D simultaneous seismic refraction and reflection tomography of wide-angle data from the central Chilean margin.Geophys Res Lett,1999,26:2577～2580
[7] Zelt C A,Sain K,Naumenko J V,et al.Assessment of crustal velocity models using seismic refraction and reflection tomography.Geophys J Int,2003,153:609～626
[8] Zelt C A,Ellis R M,Zelt B C.Three-dimensional structure across the Tintina strike-slip fault,northern Canadian Cordillera,from seismic refraction and reflection tomography.Geophys J Int,2006,167:1292～1308
[9] Zhao D,Todo S,Lei S.Local earthquake reflection tomography of the Landers aftershock area.Earth Planet Sci Lett,2005,235:623～631
[10] Rawlinson N,Sambridge M.Multiple reflection and transmission phases in complex layered media using a multistage fast marching method.Geophysics,2004,69:1338～1350
[11] De Kool M,Rawlinson N,Sambridge M.A practical gridbased method for tracking multiple refraction and reflection phases in three-dimensional heterogeneous media.Geophys J Int,2006,167:253～270
[12] Bai C Y,Tang X P,Zhao R.2D/3D multiply transmitted,converted and reflected arrivals in complex layered media with the modified shortest path method.Geophys J Int,2009,179:201～214
[13] 唐小平,白超英.最短路径算法下三维层状介质中多次波追踪.地球物理学报,2009,52(10) :2635～2643 Tang X P,Bai C Y.Multiple ray tracing within 3-D layered media with the shorted path method.Chinese J Geophys(in Chinese),2009,52(10) :2635～2643
[14] 唐小平,白超英.利用改进后的最短路径法追踪二维复杂层状介质中的多次波.地球物理学进展,2009,24(6) :2087～2096 Tang X P,Bai C Y.Multiple ray tracing within 2D layered media with the shorted path method.Progress in Geophys(in Chinese),2009,24(6) :2087～2096
[15] 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 R,Bai C Y.Fast multiple ray tracing within complex layered media:the shortest path method based on irregular grid cells.Acta Seismologica Sinica(in Chinese),2010,32 (4) :433～444
[16] Bai C Y,Huang G J,Zhao R.2D/3D irregular shortest-path ray tracing for multiple arrivals and its applications.Geophys J Int,2010,183:1596～1612
[17] Bai C Y,Greenhalgh S A,Zhou B.3-D ray tracing by using a modified shortest-path method.Geophysics,2007,72:T27～T36
[18] 刘福田.震源位置和速度结构的联合反演(Ⅰ)--理论和方法.地球物理学报,1984,27(2) :167～175 Liu F T.Simultaneous inversion of earthquake hypocenters and velocity structure(Ⅰ)-Theory and method.Chinese J Geophys(in Chinese),1984,27(2) :167～175
[19] 华龙标,刘福田.界面和速度反射联合成像--理论与方法.地球物理学报,1995,38(6) :750～756 Hua L B,Liu F T.Joint reflection imaging of velocity and interface-theory and method.Chinese J Geophys(in Chinese),1995,35(6) :750～756
[20] 李松林,吴宁远,宋占隆等.速度分布和界面位置的联合反演.地震学报,1997,19(4) :383～392 Li S L,Wu N Y,Song Z L,et al.Simultaneous inversion of velocity distribution and interface positions.Acta Seismologica Sinica(in Chinese),1997,19(4) :383～392
[21] 周龙泉,刘福田,陈晓非.三维介质中速度结构和界面的联合成像.地球物理学报,2006,49(4) :1062～1067 Zhou L Q,Liu F T,Chen X F.Simultaneous tomography of 3-D velocity structure and interface.Chinese J Geophys(in Chinese),2006,49(4) :1062～1067
[22] Kennett B L N,Sambridge M S,Williamson P R.Subspace methods for large inverse problem with multiple parameter classes.Geophysical Journal,1988,94:237～247
[23] McCaughey M,Satish S C.Simultaneous velocity and interface tomography of normal-incidence and wide-aperture seismic traveltime data.Geophys J Int,1997,131:87～99
[24] Hobro J W D,Satish S C,Minshull T A.Three-dimensional tomographic inversion of combined reflection and refraction seismic traveltime data.Geophys J Int,2003,152:79～93
[25] Greenhalgh S A,Zhou B,Green A.Solutions,algorithms and inter-relations for local minimization search geophysical inversion.J Geophys Eng,2006,3:101～113
[26] Menke W.Geophysical Data Analysis:Discrete Inverse Theory.San Diego,California:Academic Press Inc.,1984
[27] Meyerholtz K A,Szpakowski S A.Convolutional quelling in seismic tomography.Geophysics,1989,54:570～580
[28] Shaw P R,Orcutt J A.Waveform inversion of seismic refraction data and applications to young Pacific crust.Geophys J R Astr Soc,1985,82:375～414
[29] Tarantola A,Valette B.Generalized non-linear inverse problems solved using the least squares criterion.Rev Geophys Space Phys,1982,20:219～232
[30] Zhou B,Sinadinovski C,Greenhalgh S A.Iterative algorithm for the damped minimum norm,least-squares and constrained problem in seismic tomography.Exploration Geophysics,1992,23:497～505
[31] Bai C Y,Greenhalgh S A.3-D non-linear travel time tomography:imaging high contrast velocity anomalies.Pure Appl Geophys,2005,162:2029～2049
[32] Bishop T N,Bube R T,Cutler R T,et al.Tomographic determination of velocity and depth in laterally varying media.Geophysics,1985,50:903～923
[33] Bai C Y,Greenhalgh S A.3-D local earthquake hypocenter determination with an 'irregular' shortest-path method.Bull Seism Soc Am,2006,96:2257～2268
[2] Rawlinson N,Sambridge M.Seismic traveltime tomography of the crust and lithosphere.Adv in Geophys,2003,46:81～198
[3] Zhao D,Kayal J R.Impact of seismic tomography on Earth sciences.Current Science,2000,79:1208～1214
[4] Zelt C A,Smith R B.Seismic travehime inversion for 2-D crustal velocity structure.Geophys J Int,1992,105:16～34
[5] Zelt C A,White D J.Crustal structure and tectonics of the southeastern Canadian Cordillera.J Geophys Res,1995,100:24255～24273
[6] Zelt C A,Hojka A M,Flueh E R,et al.3D simultaneous seismic refraction and reflection tomography of wide-angle data from the central Chilean margin.Geophys Res Lett,1999,26:2577～2580
[7] Zelt C A,Sain K,Naumenko J V,et al.Assessment of crustal velocity models using seismic refraction and reflection tomography.Geophys J Int,2003,153:609～626
[8] Zelt C A,Ellis R M,Zelt B C.Three-dimensional structure across the Tintina strike-slip fault,northern Canadian Cordillera,from seismic refraction and reflection tomography.Geophys J Int,2006,167:1292～1308
[9] Zhao D,Todo S,Lei S.Local earthquake reflection tomography of the Landers aftershock area.Earth Planet Sci Lett,2005,235:623～631
[10] Rawlinson N,Sambridge M.Multiple reflection and transmission phases in complex layered media using a multistage fast marching method.Geophysics,2004,69:1338～1350
[11] De Kool M,Rawlinson N,Sambridge M.A practical gridbased method for tracking multiple refraction and reflection phases in three-dimensional heterogeneous media.Geophys J Int,2006,167:253～270
[12] Bai C Y,Tang X P,Zhao R.2D/3D multiply transmitted,converted and reflected arrivals in complex layered media with the modified shortest path method.Geophys J Int,2009,179:201～214
[13] 唐小平,白超英.最短路径算法下三维层状介质中多次波追踪.地球物理学报,2009,52(10) :2635～2643 Tang X P,Bai C Y.Multiple ray tracing within 3-D layered media with the shorted path method.Chinese J Geophys(in Chinese),2009,52(10) :2635～2643
[14] 唐小平,白超英.利用改进后的最短路径法追踪二维复杂层状介质中的多次波.地球物理学进展,2009,24(6) :2087～2096 Tang X P,Bai C Y.Multiple ray tracing within 2D layered media with the shorted path method.Progress in Geophys(in Chinese),2009,24(6) :2087～2096
[15] 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 R,Bai C Y.Fast multiple ray tracing within complex layered media:the shortest path method based on irregular grid cells.Acta Seismologica Sinica(in Chinese),2010,32 (4) :433～444
[16] Bai C Y,Huang G J,Zhao R.2D/3D irregular shortest-path ray tracing for multiple arrivals and its applications.Geophys J Int,2010,183:1596～1612
[17] Bai C Y,Greenhalgh S A,Zhou B.3-D ray tracing by using a modified shortest-path method.Geophysics,2007,72:T27～T36
[18] 刘福田.震源位置和速度结构的联合反演(Ⅰ)--理论和方法.地球物理学报,1984,27(2) :167～175 Liu F T.Simultaneous inversion of earthquake hypocenters and velocity structure(Ⅰ)-Theory and method.Chinese J Geophys(in Chinese),1984,27(2) :167～175
[19] 华龙标,刘福田.界面和速度反射联合成像--理论与方法.地球物理学报,1995,38(6) :750～756 Hua L B,Liu F T.Joint reflection imaging of velocity and interface-theory and method.Chinese J Geophys(in Chinese),1995,35(6) :750～756
[20] 李松林,吴宁远,宋占隆等.速度分布和界面位置的联合反演.地震学报,1997,19(4) :383～392 Li S L,Wu N Y,Song Z L,et al.Simultaneous inversion of velocity distribution and interface positions.Acta Seismologica Sinica(in Chinese),1997,19(4) :383～392
[21] 周龙泉,刘福田,陈晓非.三维介质中速度结构和界面的联合成像.地球物理学报,2006,49(4) :1062～1067 Zhou L Q,Liu F T,Chen X F.Simultaneous tomography of 3-D velocity structure and interface.Chinese J Geophys(in Chinese),2006,49(4) :1062～1067
[22] Kennett B L N,Sambridge M S,Williamson P R.Subspace methods for large inverse problem with multiple parameter classes.Geophysical Journal,1988,94:237～247
[23] McCaughey M,Satish S C.Simultaneous velocity and interface tomography of normal-incidence and wide-aperture seismic traveltime data.Geophys J Int,1997,131:87～99
[24] Hobro J W D,Satish S C,Minshull T A.Three-dimensional tomographic inversion of combined reflection and refraction seismic traveltime data.Geophys J Int,2003,152:79～93
[25] Greenhalgh S A,Zhou B,Green A.Solutions,algorithms and inter-relations for local minimization search geophysical inversion.J Geophys Eng,2006,3:101～113
[26] Menke W.Geophysical Data Analysis:Discrete Inverse Theory.San Diego,California:Academic Press Inc.,1984
[27] Meyerholtz K A,Szpakowski S A.Convolutional quelling in seismic tomography.Geophysics,1989,54:570～580
[28] Shaw P R,Orcutt J A.Waveform inversion of seismic refraction data and applications to young Pacific crust.Geophys J R Astr Soc,1985,82:375～414
[29] Tarantola A,Valette B.Generalized non-linear inverse problems solved using the least squares criterion.Rev Geophys Space Phys,1982,20:219～232
[30] Zhou B,Sinadinovski C,Greenhalgh S A.Iterative algorithm for the damped minimum norm,least-squares and constrained problem in seismic tomography.Exploration Geophysics,1992,23:497～505
[31] Bai C Y,Greenhalgh S A.3-D non-linear travel time tomography:imaging high contrast velocity anomalies.Pure Appl Geophys,2005,162:2029～2049
[32] Bishop T N,Bube R T,Cutler R T,et al.Tomographic determination of velocity and depth in laterally varying media.Geophysics,1985,50:903～923
[33] Bai C Y,Greenhalgh S A.3-D local earthquake hypocenter determination with an 'irregular' shortest-path method.Bull Seism Soc Am,2006,96:2257～2268
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