球坐标系下多震相走时三参数同时反演成像
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摘要
球坐标系下多震相走时三参数(速度、震源位置和反射界面)同时反演需要解决两个关键问题:(1)球坐标系下3D速度模型中多次透射、反射(折射)及转换波精确、快速的射线追踪;(2)同时反演时三种不同参数间的强耦合问题.为此,我们将直角坐标系下分区多步不规则最短路径算法推广至球坐标系中,进行区域或者全球尺度的多震相射线追踪.然后将其与适合多参数同时反演的子空间算法相结合,形成一种球坐标系下联合多震相走时三参数同时反演的方法技术.与双参数(速度和反射界面或速度和震源位置)同时反演的数值模拟对比分析显示:三参数与双参数的同时反演结果大体接近,并且它们对到时数据中可容许的随机噪声不太敏感.结果说明本文中的同时反演成像为一种提高成像分辨率,同时反演速度、震源位置和反射界面的有效方法.
To guarantee computational precision and improve the resolution of seismic traveltime tomography at a regional or global scale,we conduct a 3D simultaneous inversion of three different parameters(velocity,hypocenter location and reflector geometry)in spherical coordinates with multi-phase travel times.For this task,there are two key issues:(1)It needs an efficient and accurate arrival tracking algorithm for multiply transmitted,reflected(or refracted)and converted waves in a 3D variable velocity model with embedded velocity discontinuities(or subsurface interfaces),and(2)A subdimensional inversion solver is required which can easily search for different types of model parameters to balance the tradeoff between the different types of model parameter updated in the simultaneous inversion process.For these purposes,we first extend a popular grid/cell-based wavefront expanding ray tracing algorithm(the multistage irregular shortest-path ray tracing method,shorted as ISPM),which previously worked only in Cartesian coordinates at a local scale,to spherical coordinatesappropriate to a regional or global scale.In 3Dspherical coordinates a trapezoidal prism cell is used to divide the spherical earth model,except for the global and other irregular subsurface interfaces,where a trapezoidal cone is used.And in one previous paper we have discussed the computational accuracy of the multistage ISPM algorithm against the analytic solution of AK135 Travel Time Table for 49 kinds of global phases and concluded that the computational accuracy can be tuned to within the 0.1sabsolute time error when it works in the spherical coordinates.We then incorporate the subspace method to formulate a simultaneous inversion algorithm,in which the multiple classes of arrivals(including direct and reflected arrivals from different velocity discontinuities)can be used to simultaneously update the velocity fields,hypocenter location and reflector geometries.In order to illustrate the performance of inversion for three model class parameters,we have selected a regional model at a scale of 20°×20°×700km.In the numerical experiment,different phases are used.For comparison,we design three different schemes.The first one is to simultaneously update both the velocity field and the source locations(referred as V + S inversion),the second is to simultaneously invert both the velocity field and the reflector positions(referred as V+R inversion),while the third scheme updates all three model parameter classes simultaneously(referred as V+R+S inversion).To account for picking uncertainty,random noise was added to the multiple sets of arrivals according to the expected picking errors.The inversion results show that the reconstructed velocity fields exhibit similar anomalous structures to the true field,but only partially being recovered.Interestingly,the recovered velocity fields are nearly the same regardless whether the two parameter class inversion or three parameter class inversion is attempted.The updated two subsurface interfaces are almost identical,no matter whether the V+R or the V+R+S simultaneous inversion algorithm is used.For the hypocenter location,the V+S inversion has a slightly better convergence to the real source locations than the V+R+S inversion,due to only two classes of the model parameters being updated in the simultaneous inversion process,but the difference is not so significant.The above results verify that the V+R+S simultaneous inversion scheme is feasible and applicable due to the almost equal capability with the constrained two model parameter class inversions(V+S or V+R).All three scheme algorithms are quite tolerant to modest errors in the travel time picks,which makes them robust enough for practical applications.The results show that the V+R+S simultaneous inversion method is an efficient and feasible scheme for updating the velocity field,reflector geometry and hypocenter location.
To guarantee computational precision and improve the resolution of seismic traveltime tomography at a regional or global scale,we conduct a 3D simultaneous inversion of three different parameters(velocity,hypocenter location and reflector geometry)in spherical coordinates with multi-phase travel times.For this task,there are two key issues:(1)It needs an efficient and accurate arrival tracking algorithm for multiply transmitted,reflected(or refracted)and converted waves in a 3D variable velocity model with embedded velocity discontinuities(or subsurface interfaces),and(2)A subdimensional inversion solver is required which can easily search for different types of model parameters to balance the tradeoff between the different types of model parameter updated in the simultaneous inversion process.For these purposes,we first extend a popular grid/cell-based wavefront expanding ray tracing algorithm(the multistage irregular shortest-path ray tracing method,shorted as ISPM),which previously worked only in Cartesian coordinates at a local scale,to spherical coordinatesappropriate to a regional or global scale.In 3Dspherical coordinates a trapezoidal prism cell is used to divide the spherical earth model,except for the global and other irregular subsurface interfaces,where a trapezoidal cone is used.And in one previous paper we have discussed the computational accuracy of the multistage ISPM algorithm against the analytic solution of AK135 Travel Time Table for 49 kinds of global phases and concluded that the computational accuracy can be tuned to within the 0.1sabsolute time error when it works in the spherical coordinates.We then incorporate the subspace method to formulate a simultaneous inversion algorithm,in which the multiple classes of arrivals(including direct and reflected arrivals from different velocity discontinuities)can be used to simultaneously update the velocity fields,hypocenter location and reflector geometries.In order to illustrate the performance of inversion for three model class parameters,we have selected a regional model at a scale of 20°×20°×700km.In the numerical experiment,different phases are used.For comparison,we design three different schemes.The first one is to simultaneously update both the velocity field and the source locations(referred as V + S inversion),the second is to simultaneously invert both the velocity field and the reflector positions(referred as V+R inversion),while the third scheme updates all three model parameter classes simultaneously(referred as V+R+S inversion).To account for picking uncertainty,random noise was added to the multiple sets of arrivals according to the expected picking errors.The inversion results show that the reconstructed velocity fields exhibit similar anomalous structures to the true field,but only partially being recovered.Interestingly,the recovered velocity fields are nearly the same regardless whether the two parameter class inversion or three parameter class inversion is attempted.The updated two subsurface interfaces are almost identical,no matter whether the V+R or the V+R+S simultaneous inversion algorithm is used.For the hypocenter location,the V+S inversion has a slightly better convergence to the real source locations than the V+R+S inversion,due to only two classes of the model parameters being updated in the simultaneous inversion process,but the difference is not so significant.The above results verify that the V+R+S simultaneous inversion scheme is feasible and applicable due to the almost equal capability with the constrained two model parameter class inversions(V+S or V+R).All three scheme algorithms are quite tolerant to modest errors in the travel time picks,which makes them robust enough for practical applications.The results show that the V+R+S simultaneous inversion method is an efficient and feasible scheme for updating the velocity field,reflector geometry and hypocenter location.
引文
Aki K,Lee W H K.1976.Determination of three-dimensional velocity anomalies under a seismic array using first P arrival times from local earthquakes:1.A homogeneous initial model.J.Geophys.Res.,81(23):4381-4399.
Bai C-Y,Greenhalgh S.2005.3-D non-linear travel-time tomography:Imaging high contrast velocity anomalies.Pure Appl.Geophys.,162(1):2029-2049.
Bai C Y,Huang G J,Zhao R.2010.2-D/3-D irregular shortestpath ray tracing for multiple arrivals and its applications.Geophys.J.Int.,183(3):1596-1612.
Bai C Y,Huang G J,Li Z S.2011.Simultaneous inversion combining multiple-phase travel times within 3D complex layered media.Chinese J.Geophys.(in Chinese),54(1):182-192,doi:10.3969/j.issn.0001-5733.2011.01.019.
Bijwaard H,Spakman W.1999.Fast kinematic ray tracing of firstand later-arriving global seismic phase.Geophys.J.Int.,139(2):359-369.
De Kool M,Rawlinson N,Sambridge M.2006.A practical gridbased method for tracking multiple refraction and reflection phases in three-dimensional heterogeneous media.Geophys.J.Int.,167(1):253-270.
Grand S P,Van der Hilst R D,Widiyantoro S.1997.Global seismic tomography:A snapshot of convection in the Earth.GSAToday,7(4):1-7.
Huang G J,Bai C Y.2010.Simultaneous inversion with multiple traveltimes within 2-D complex layered media.Chinese J.Geophys.(in Chinese),53(12):2972-2981,doi:10.3969/j.issn.0001-5733.2010.12.021.
Huang G J,Bai C Y,Greenhalgh S.2013.Fast and accurate global multiphase arrival tracking:the irregular shortest-path method in a 3-D spherical earth model.Geophys.J.Int.,194(3):1878-1892.
Huang G J,Bai C Y.2013.Simultaneous inversion of three model parameters with multiple classes of arrival times.Chinese J.Geophys.(in Chinese),56(12):4215-4225,doi:10.6038/cjg20131224.
Kennett B L N,Sambridge M S,Williamson P R.1988.Subspace methods for large inverse problems with multiple parameter classes.Geophys.J.Int.,94(2):237-247.
Kennett B L N,Engdahl E R,Buland R.1995.Constraints on seismic velocities in the earth from traveltimes.Geophys.J.Int.,122(1):108-124.
KlimeL,Kvasnicka M.1994.3-D network ray tracing.Geophys.J.Int.,116(3):726-738.
Moser T J.1991.Shortest path calculation of seismic rays.Geophysics,56(1):59-67.
Preston L A.2003.Simultaneous inversion of 3D velocity structure,hypocenter locations,and reflector geometry in Cascadia[Ph.D.thesis].Washington:University of Washington.
Preston L A,Creager K C,Grosson R S,et al.2003.Intraslab earthquakes:Dehydration of the Cascadia slab.Science,302(5648):1197-1200.
Rawlinson N,Sambridge M.2004.Multiple reflection and transmission phases in complex layered media using a multistage fast marching method.Geophysics,69:1338-1350.
Rawlison N,Sambridge M S.2003.Seismic traveltime tomography of the crust and lithosphere.Advances in Geophysics,46:81-198.
Sambridge M S.1990.Non-linear arrival time inversion:Constraining velocity anomalies by seeking smooth models in 3-D.Geophys.J.Int.,102(3):653-677.
Sambridge M S,Kennett B L N.1990.Boundary value ray tracing in a heterogeneous medium:A simple and versatile algorithm.Geophys.J.Int.,101(1):157-168.
Snoke J A,Lahr J C.2001.Locating earthquakes:At what distance can the earth no longer be treated as flat?Seism.Res.Lett.,72(5):538-541.
Su W J,Woodward R L,Dziewonski A M.1994.Degree 12model of shear velocity heterogeneity in the mantle.J.Geophys.Res.,99(B4):6945-6980.
Tang X P,Bai C Y.2009a.Multiple ray tracing in 2Dlayered media with the shortest path method.Progress in Geophysics(in Chinese),24(6):2087-2096,doi:10.3969/j.issn.1004-2903.2009.06.022.
Tang X P,Bai C Y.2009b.Multiple ray tracing within 3-D layered media with the shortest path method.Chinese J.Geophys.(in Chinese),52(10):2635-2643,doi:10.3969/j.issn.0001-5733.2009.10.024.
Tian Y,Huang S H,Nolet G,et al.2007.Dynamic ray tracing and traveltime corrections for global seismic tomography.J.Comp.Phys.,226(1):672-687.
Van der Hilst R D,Widiyantoro S,Engdahl E R.1997.Evidence for deep mantle circulation from global tomography.Nature,386(6625):578-584.
Vidale J E.1998.Finite-difference calculation of travel times.Bull.Seism.Soc.Am.,78(6):2062-2076.
Vidale J E.1990.Finite-difference calculation of traveltimes in three dimensions.Geophysics,55(5):521-526.
Zhao D P,Hasegawa A,Horiuchi S.1992.Tomographic imaging of P and S wave velocity structure beneath northeastern Japan.J.Geophys.Res.,97(B13):19909-19928.
Zhao D P,Lei J S.2004.Seismic ray path variations in a 3Dglobal velocity model.Phys.Earth Planet.Inter.,141(3):153-166.
Zhao D P,Todo S,Lei J S.2005.Local earthquake reflection tomography of the Landers aftershock area.EarthPlanet.Sci.Lett.,235(3-4):623-631.
Zhao R,Bai C Y.2010.Fast multiple ray tracing within complex layered media:The shortest path method based on irregular grid cells.Acta Seismologica Sinica(in Chinese),42(4):433-444.
白超英,黄国娇,李忠生.2011.三维复杂层状介质中多震相走时联合反演成像.地球物理学报,54(1):182-192,doi:10.3969/j.issn.0001-5733.2011.01.019.
黄国娇,白超英.2010.二维复杂层状介质中地震多波走时联合反演成像.地球物理学报,53(12):2972-2981,doi:10.3969/j.issn.0001-5733.2010.12.021.
黄国娇,白超英.2013.多震相走时联合三参数同时反演成像.地球物理学报,56(12):4215-4225,doi:10.6038/cjg20131224.
唐小平,白超英.2009a.最短路径算法下二维层状介质中多次波追踪.地球物理学进展,24(6):2087-2096,doi:10.3969/j.issn.1004-2903.2009.06.022.
唐小平,白超英.2009b.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,52(10):2635-2643,doi:10.3969/j.issn.0001-5733.2009.10.024.
赵瑞,白超英.2010.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,42(4):433-444.
Bai C-Y,Greenhalgh S.2005.3-D non-linear travel-time tomography:Imaging high contrast velocity anomalies.Pure Appl.Geophys.,162(1):2029-2049.
Bai C Y,Huang G J,Zhao R.2010.2-D/3-D irregular shortestpath ray tracing for multiple arrivals and its applications.Geophys.J.Int.,183(3):1596-1612.
Bai C Y,Huang G J,Li Z S.2011.Simultaneous inversion combining multiple-phase travel times within 3D complex layered media.Chinese J.Geophys.(in Chinese),54(1):182-192,doi:10.3969/j.issn.0001-5733.2011.01.019.
Bijwaard H,Spakman W.1999.Fast kinematic ray tracing of firstand later-arriving global seismic phase.Geophys.J.Int.,139(2):359-369.
De Kool M,Rawlinson N,Sambridge M.2006.A practical gridbased method for tracking multiple refraction and reflection phases in three-dimensional heterogeneous media.Geophys.J.Int.,167(1):253-270.
Grand S P,Van der Hilst R D,Widiyantoro S.1997.Global seismic tomography:A snapshot of convection in the Earth.GSAToday,7(4):1-7.
Huang G J,Bai C Y.2010.Simultaneous inversion with multiple traveltimes within 2-D complex layered media.Chinese J.Geophys.(in Chinese),53(12):2972-2981,doi:10.3969/j.issn.0001-5733.2010.12.021.
Huang G J,Bai C Y,Greenhalgh S.2013.Fast and accurate global multiphase arrival tracking:the irregular shortest-path method in a 3-D spherical earth model.Geophys.J.Int.,194(3):1878-1892.
Huang G J,Bai C Y.2013.Simultaneous inversion of three model parameters with multiple classes of arrival times.Chinese J.Geophys.(in Chinese),56(12):4215-4225,doi:10.6038/cjg20131224.
Kennett B L N,Sambridge M S,Williamson P R.1988.Subspace methods for large inverse problems with multiple parameter classes.Geophys.J.Int.,94(2):237-247.
Kennett B L N,Engdahl E R,Buland R.1995.Constraints on seismic velocities in the earth from traveltimes.Geophys.J.Int.,122(1):108-124.
KlimeL,Kvasnicka M.1994.3-D network ray tracing.Geophys.J.Int.,116(3):726-738.
Moser T J.1991.Shortest path calculation of seismic rays.Geophysics,56(1):59-67.
Preston L A.2003.Simultaneous inversion of 3D velocity structure,hypocenter locations,and reflector geometry in Cascadia[Ph.D.thesis].Washington:University of Washington.
Preston L A,Creager K C,Grosson R S,et al.2003.Intraslab earthquakes:Dehydration of the Cascadia slab.Science,302(5648):1197-1200.
Rawlinson N,Sambridge M.2004.Multiple reflection and transmission phases in complex layered media using a multistage fast marching method.Geophysics,69:1338-1350.
Rawlison N,Sambridge M S.2003.Seismic traveltime tomography of the crust and lithosphere.Advances in Geophysics,46:81-198.
Sambridge M S.1990.Non-linear arrival time inversion:Constraining velocity anomalies by seeking smooth models in 3-D.Geophys.J.Int.,102(3):653-677.
Sambridge M S,Kennett B L N.1990.Boundary value ray tracing in a heterogeneous medium:A simple and versatile algorithm.Geophys.J.Int.,101(1):157-168.
Snoke J A,Lahr J C.2001.Locating earthquakes:At what distance can the earth no longer be treated as flat?Seism.Res.Lett.,72(5):538-541.
Su W J,Woodward R L,Dziewonski A M.1994.Degree 12model of shear velocity heterogeneity in the mantle.J.Geophys.Res.,99(B4):6945-6980.
Tang X P,Bai C Y.2009a.Multiple ray tracing in 2Dlayered media with the shortest path method.Progress in Geophysics(in Chinese),24(6):2087-2096,doi:10.3969/j.issn.1004-2903.2009.06.022.
Tang X P,Bai C Y.2009b.Multiple ray tracing within 3-D layered media with the shortest path method.Chinese J.Geophys.(in Chinese),52(10):2635-2643,doi:10.3969/j.issn.0001-5733.2009.10.024.
Tian Y,Huang S H,Nolet G,et al.2007.Dynamic ray tracing and traveltime corrections for global seismic tomography.J.Comp.Phys.,226(1):672-687.
Van der Hilst R D,Widiyantoro S,Engdahl E R.1997.Evidence for deep mantle circulation from global tomography.Nature,386(6625):578-584.
Vidale J E.1998.Finite-difference calculation of travel times.Bull.Seism.Soc.Am.,78(6):2062-2076.
Vidale J E.1990.Finite-difference calculation of traveltimes in three dimensions.Geophysics,55(5):521-526.
Zhao D P,Hasegawa A,Horiuchi S.1992.Tomographic imaging of P and S wave velocity structure beneath northeastern Japan.J.Geophys.Res.,97(B13):19909-19928.
Zhao D P,Lei J S.2004.Seismic ray path variations in a 3Dglobal velocity model.Phys.Earth Planet.Inter.,141(3):153-166.
Zhao D P,Todo S,Lei J S.2005.Local earthquake reflection tomography of the Landers aftershock area.EarthPlanet.Sci.Lett.,235(3-4):623-631.
Zhao R,Bai C Y.2010.Fast multiple ray tracing within complex layered media:The shortest path method based on irregular grid cells.Acta Seismologica Sinica(in Chinese),42(4):433-444.
白超英,黄国娇,李忠生.2011.三维复杂层状介质中多震相走时联合反演成像.地球物理学报,54(1):182-192,doi:10.3969/j.issn.0001-5733.2011.01.019.
黄国娇,白超英.2010.二维复杂层状介质中地震多波走时联合反演成像.地球物理学报,53(12):2972-2981,doi:10.3969/j.issn.0001-5733.2010.12.021.
黄国娇,白超英.2013.多震相走时联合三参数同时反演成像.地球物理学报,56(12):4215-4225,doi:10.6038/cjg20131224.
唐小平,白超英.2009a.最短路径算法下二维层状介质中多次波追踪.地球物理学进展,24(6):2087-2096,doi:10.3969/j.issn.1004-2903.2009.06.022.
唐小平,白超英.2009b.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,52(10):2635-2643,doi:10.3969/j.issn.0001-5733.2009.10.024.
赵瑞,白超英.2010.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,42(4):433-444.