三角网格剖分下速度与反射界面的同时反演
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摘要
为了解决复杂速度模型中的走时正、反演问题,例如:含不规则起伏地表、不规则地下波阻抗界面、以及不规则速度异常体的复杂地学模型,本文采用三角网格单元模型参数化下的分区多步改进型最短路径算法,实现了多震相地震射线的追踪计算,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同时反演成像的方法技术.当界面起伏较大时出现散射,从而造成散射点所在区域射线密度过密,导致该区域内速度和界面的过度更新.为了克服上述问题,我们在同时反演中引入了射线密度的概念,从而有效地解决了上述过度更新问题.数值模拟实验表明:采用三角网格单元进行模型参数化,可保证在复杂模型中的正演计算具有较高的计算精度;同时反演中可以准确地刻画不规则异常体和不规则反射界面.因此,本文提出的走时成像方法技术具有较广的实用价值.
To conduct forward and simultaneous inversion in a complex velocity model, including an irregular topography, or irregular reflector,or irregular velocity anomaly,we in this paper realize a multi-phase arrival tracking with a multistage modified shortest-path method under a triangular cell model,and combine an inversion algorithm,that is the constrained damped least squares problem solved by a conjugated gradient method,to simultaneously invert the velocity model and reflector geometry with multi-phase arrival time information. Meanwhile,we introduce a concept of an equal ray density to overcome the over-updated velocity region,where the ray density is high,due to the scatter phenomenon caused by undulated reflector. The numerical simulation results show that with the triangular 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 traveltime inversion has a wide application in the real problem.
To conduct forward and simultaneous inversion in a complex velocity model, including an irregular topography, or irregular reflector,or irregular velocity anomaly,we in this paper realize a multi-phase arrival tracking with a multistage modified shortest-path method under a triangular cell model,and combine an inversion algorithm,that is the constrained damped least squares problem solved by a conjugated gradient method,to simultaneously invert the velocity model and reflector geometry with multi-phase arrival time information. Meanwhile,we introduce a concept of an equal ray density to overcome the over-updated velocity region,where the ray density is high,due to the scatter phenomenon caused by undulated reflector. The numerical simulation results show that with the triangular 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 traveltime inversion has a wide application in the real problem.
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].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[J].Pure Appl.Geophys.,162(11):2029-2049.
Bai C Y,Greenhalgh S.2006.3D local earthquake hypocenter determination with an irregular shortest-path method[J].Bulletin of the Seismological Society of America,96(6):2257-2268.
Bai C Y,Li X L,Tang X P.2011.Seismic wavefront evolution of multiply reflected,transmitted,and converted phases in 2D/3Dtriangular cell model[J].Journal of Seismology,15(4):637-652.
Bishop T N,Bube K P,Cutler R T,et al.1985.Tomographic determination of velocity and depth in laterally varying media[J].Geophysics,50(6):903-923.
B9hm G,Galuppo P,Vesnaver A.2000.3D adaptive tomography using Delaunay triangles and Voronoi polygons[J].Geophysical Prospecting,48(4):723-744.
Cheng G,Ma Z T,Geng J H,et al.2002.A review on the growth of seismic tomography[J].Progress in Exploration Geophysics(in Chinese),25(3):6-12.
Cheng G,Zhang B J.2006.Application of triangle cell parameterization in travel-time tomography of reflection seismic data[J].Acta Scientiarum Naturalium Universitatis Sunyatseni(in Chinese),45(5):128-132.
Curtis A,Snieder R.1997.Reconditioning inverse problems using the genetic algorithm and revised parameterization[J].Geophysics,62(5):1524-1532.
Huang G J,Bai C Y.2010.Simultaneous inversion with multiple traveltimes within 2-D complex layered media[J].Chinese J.Geophys.(in Chinese),53(12):2972-2981,doi:10.3969/j.issn.0001-5733.2010.12.021.
Jiang J X,Liu S H,Yan H Y.2006.Algorithm designing and realizing of TIN in VB[J].Surveying and Mapping of Sichuan,29(2):64-67.
Li B T,Yang C C,Chen Y H,et al.2009.3D wavefront construction method ray tracing based on triangular grids layout on wavefront[J].Progress in Geophys.(in Chinese),24(2):507-512,doi:10.3969/j.issn.1004-2903.2009.02.019.
McCullagh M J,Ross C G.1980.Delaunay triangulation of a random data set for isarithmic mapping[J].The Cartographic Journal,17(2):93-99.
Sambridge M,Braun J,Mc Queen H.1995.Geophysical parametrization and interpolation of irregular data using natural neighbours[J].Geophysical Journal International,122(3):837-857.
Sambridge M,FaletiR.2003.Adaptive whole Earth tomography[J].Geochemistry,Geophysics,Geosystems,4(3),doi:10.1029/2001GC000213.
Tarantola A,Nercessian A.1984.Three-dimensional inversion without blocks[J].Geophysical Journal International,76(2):299-306.
Vinje V,stebΦl K,Iversen E,et al.1999.3-D ray modeling by wavefront construction in open models[J].Geophysics,64(6):1912-1919.
Yu S J,Liu R Z,Cheng J L.2010.A minimum traveltime ray tracing global algorithm on a triangular net for propagating plane waves[J].Applied Geophysics,7(4):348-356.
Yu S J,Liu R Z.2013.Tomography of a minimum travel time ray tracing on a triangular net[J].CT Theory and Applications(in Chinese),22(3):401-408.
Zhou B,Greenhalgh S A,Sinadinovski C.1992.Iterative algorithm fo the damped minimum norm,least-squares and constrained problem in seismic tomography[J].Explor.Geophys,23(3):497-505.
Zhou L Q,Liu F T,Chen X F.2006.Simultaneous tomography of 3-Dvelocity structure and interface[J].Chinese J.Geophys.(in Chinese),49(4):1062-1067,doi:10.3321/j.issn:0001-5733.2006.04.018.
成谷,马在田,耿建华,等.2002.地震层析成像发展回顾[J].勘探地球物理进展,25(3):6-12.
成谷,张宝金.2006.三角网格参数化在反射地震走时层析成像中的应用[J].中山大学学报(自然科学版),45(5):128-132.
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[J].地球物理学报,53(12):2972-2981,doi:10.3969/j.issn.0001-5733.2010.12.021.
江剑霞,刘少华,严汉英.2006.VB环境下不规则三角网的算法设计与实现[J].四川测绘,29(2):64-67.
李波涛,杨长春,陈雨红,等.2009.基于波前面三角形网格剖分的波前重建法三维射线追踪[J].地球物理学进展,24(2):507-512,doi:10.3969/j.issn.1004-2903.2009.02.019.
于师建,刘润泽.2013.三角网最小走时射线追踪层析成像[J].CT理论与应用研究,22(3):401-408.
周龙泉,刘福田,陈晓非.2006.三维介质中速度结构和界面的联合成像[J].地球物理学报,49(4):1062-1067,doi:10.3321/j.issn:0001-5733.2006.04.018.
Bai C Y,Greenhalgh S.2005.3-D non-linear travel-time tomography:Imaging high contrast velocity anomalies[J].Pure Appl.Geophys.,162(11):2029-2049.
Bai C Y,Greenhalgh S.2006.3D local earthquake hypocenter determination with an irregular shortest-path method[J].Bulletin of the Seismological Society of America,96(6):2257-2268.
Bai C Y,Li X L,Tang X P.2011.Seismic wavefront evolution of multiply reflected,transmitted,and converted phases in 2D/3Dtriangular cell model[J].Journal of Seismology,15(4):637-652.
Bishop T N,Bube K P,Cutler R T,et al.1985.Tomographic determination of velocity and depth in laterally varying media[J].Geophysics,50(6):903-923.
B9hm G,Galuppo P,Vesnaver A.2000.3D adaptive tomography using Delaunay triangles and Voronoi polygons[J].Geophysical Prospecting,48(4):723-744.
Cheng G,Ma Z T,Geng J H,et al.2002.A review on the growth of seismic tomography[J].Progress in Exploration Geophysics(in Chinese),25(3):6-12.
Cheng G,Zhang B J.2006.Application of triangle cell parameterization in travel-time tomography of reflection seismic data[J].Acta Scientiarum Naturalium Universitatis Sunyatseni(in Chinese),45(5):128-132.
Curtis A,Snieder R.1997.Reconditioning inverse problems using the genetic algorithm and revised parameterization[J].Geophysics,62(5):1524-1532.
Huang G J,Bai C Y.2010.Simultaneous inversion with multiple traveltimes within 2-D complex layered media[J].Chinese J.Geophys.(in Chinese),53(12):2972-2981,doi:10.3969/j.issn.0001-5733.2010.12.021.
Jiang J X,Liu S H,Yan H Y.2006.Algorithm designing and realizing of TIN in VB[J].Surveying and Mapping of Sichuan,29(2):64-67.
Li B T,Yang C C,Chen Y H,et al.2009.3D wavefront construction method ray tracing based on triangular grids layout on wavefront[J].Progress in Geophys.(in Chinese),24(2):507-512,doi:10.3969/j.issn.1004-2903.2009.02.019.
McCullagh M J,Ross C G.1980.Delaunay triangulation of a random data set for isarithmic mapping[J].The Cartographic Journal,17(2):93-99.
Sambridge M,Braun J,Mc Queen H.1995.Geophysical parametrization and interpolation of irregular data using natural neighbours[J].Geophysical Journal International,122(3):837-857.
Sambridge M,FaletiR.2003.Adaptive whole Earth tomography[J].Geochemistry,Geophysics,Geosystems,4(3),doi:10.1029/2001GC000213.
Tarantola A,Nercessian A.1984.Three-dimensional inversion without blocks[J].Geophysical Journal International,76(2):299-306.
Vinje V,stebΦl K,Iversen E,et al.1999.3-D ray modeling by wavefront construction in open models[J].Geophysics,64(6):1912-1919.
Yu S J,Liu R Z,Cheng J L.2010.A minimum traveltime ray tracing global algorithm on a triangular net for propagating plane waves[J].Applied Geophysics,7(4):348-356.
Yu S J,Liu R Z.2013.Tomography of a minimum travel time ray tracing on a triangular net[J].CT Theory and Applications(in Chinese),22(3):401-408.
Zhou B,Greenhalgh S A,Sinadinovski C.1992.Iterative algorithm fo the damped minimum norm,least-squares and constrained problem in seismic tomography[J].Explor.Geophys,23(3):497-505.
Zhou L Q,Liu F T,Chen X F.2006.Simultaneous tomography of 3-Dvelocity structure and interface[J].Chinese J.Geophys.(in Chinese),49(4):1062-1067,doi:10.3321/j.issn:0001-5733.2006.04.018.
成谷,马在田,耿建华,等.2002.地震层析成像发展回顾[J].勘探地球物理进展,25(3):6-12.
成谷,张宝金.2006.三角网格参数化在反射地震走时层析成像中的应用[J].中山大学学报(自然科学版),45(5):128-132.
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[J].地球物理学报,53(12):2972-2981,doi:10.3969/j.issn.0001-5733.2010.12.021.
江剑霞,刘少华,严汉英.2006.VB环境下不规则三角网的算法设计与实现[J].四川测绘,29(2):64-67.
李波涛,杨长春,陈雨红,等.2009.基于波前面三角形网格剖分的波前重建法三维射线追踪[J].地球物理学进展,24(2):507-512,doi:10.3969/j.issn.1004-2903.2009.02.019.
于师建,刘润泽.2013.三角网最小走时射线追踪层析成像[J].CT理论与应用研究,22(3):401-408.
周龙泉,刘福田,陈晓非.2006.三维介质中速度结构和界面的联合成像[J].地球物理学报,49(4):1062-1067,doi:10.3321/j.issn:0001-5733.2006.04.018.