分区多步最短路径极值法多值多次反射波追踪
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摘要
基于网格单元扩展的射线追踪算法,如:较为流行的有限差分解程函方程法和最短路径法均是建立在费马(最小走时)原理基础上的射线追踪算法,只能进行单值(最小走时)的多次反射波的追踪.然而当介质速度反差较大或存在复杂反射界面(如:常见的向斜、背斜、透镜体、塌陷构造等)时,将出现波前的自相缠绕(即蝴蝶结现象),相应的地震射线则为多值射线.为了模拟计算这种多值多次反射波,本文提出了一种多值地震射线追踪算法,即分区多步最短路径极值算法,可进行含复杂反射界面速度模型中的多值多次反射波射线的追踪计算.其基本原理是:将炮点和和检波器均设为震源,分别进行下行波射线追踪至离散反射界面,求出各个反射点走时和路径,进而将反射点处的走时加起来,形成叠加‘走时'曲线(三维时为曲面),再对该曲线(或曲面)求极值点,极值点所对应的反射点即为该炮一检对的反射点位置,最后将炮—反射点—检波器的走时及相应路径连接,从而实现了多值多次反射波的追踪计算.该方法原理简单,计算精度高,计算速度快,适应复杂介质的能力强.通过误差分析并与快速行进法之间的对比分析,认为分区多步最短路径极值法是一种行之有效的多值多次反射波的计算方法.
The grid-based raytracing algorithms,such as the finite-difference eikonal equation solver and the shortestpath method,are all based on the Fermat(minimum travel time) principle,which is able to track the first reflected arrivals only.In heterogeneous media involving a relatively larger velocity contrast or complex reflected interface.The seismic wavefronts are self-intersected,as a result,the rays are multi-paths.In order to simulate such multivalued and multiple reflected arrivals,we put forward an algorithm to trace the multivalued and multiple reflected arrivals.it referred as the extreme value algorithm based on the multistage modified shortest-path method,which is capable of tracking the multivalued and multiple reflected arrivals in velocity model included complex reflected interfaces.The principles of the extreme value are that;we firstly conduct down-wind raytracing from both sources and receivers to the sampled reflected interfaces and record the traveltimes and raypaths at each sampled reflected point,and sum up traveltime value at each reflected point,and form a stacked' traveltime-distance' curve(or surface for 3D case); secondly we solve extremum values for this stacked'traveltime-distance'curve(or surface),in which the location of the extreme points are the reflected points;finally we link the raypaths and add traveltimes from the source to the reflected point,and then to the receiver.Thus the multivalued and multiple reflected arrivals are successfully traced. This algorithm has a simple principle,high accuracy,fast CPU time and easy adaptation for complex media. Compared with the fast marching method and error analysis,it is evident that the extreme value of the multistage shortest-path method is a feasible and efficient algorithm for tracking the multivalued and multiple reflected arrivals.
The grid-based raytracing algorithms,such as the finite-difference eikonal equation solver and the shortestpath method,are all based on the Fermat(minimum travel time) principle,which is able to track the first reflected arrivals only.In heterogeneous media involving a relatively larger velocity contrast or complex reflected interface.The seismic wavefronts are self-intersected,as a result,the rays are multi-paths.In order to simulate such multivalued and multiple reflected arrivals,we put forward an algorithm to trace the multivalued and multiple reflected arrivals.it referred as the extreme value algorithm based on the multistage modified shortest-path method,which is capable of tracking the multivalued and multiple reflected arrivals in velocity model included complex reflected interfaces.The principles of the extreme value are that;we firstly conduct down-wind raytracing from both sources and receivers to the sampled reflected interfaces and record the traveltimes and raypaths at each sampled reflected point,and sum up traveltime value at each reflected point,and form a stacked' traveltime-distance' curve(or surface for 3D case); secondly we solve extremum values for this stacked'traveltime-distance'curve(or surface),in which the location of the extreme points are the reflected points;finally we link the raypaths and add traveltimes from the source to the reflected point,and then to the receiver.Thus the multivalued and multiple reflected arrivals are successfully traced. This algorithm has a simple principle,high accuracy,fast CPU time and easy adaptation for complex media. Compared with the fast marching method and error analysis,it is evident that the extreme value of the multistage shortest-path method is a feasible and efficient algorithm for tracking the multivalued and multiple reflected arrivals.
引文
[1]Vinje V,Iversen E,Gjφystdal H.Traveltime and amplitude estimation using wavefront construction[J].Geophysics,1993,58:1157- 1166.
[2]Vinje V,Iversen E,Astebφl K,Gjφystdal H.Estimation of multivalued arrivals in 3D models using wavefront construction []].Geophysical Prospecting,1996,44:819-842.
[3]Vinje V,Astebol K,Iversen E.Gjoystdal H.3-D ray modelling by wavefront construction in open models[J].Geophysical Prospecting,1999,64:1912-1919.
[4]Symes W W,Qian J.A slowness matching eulerian method for multivalued solutions of eikonal equaions[J].SIAM J Sci Comput,2003,19:501-526.
[5]Sethian J A.Level set methods and fast marching methods [D].Cambridge University Press,Cambridge,1999.
[6]Rawlinson N,Sambridge M,Hauser J.Multipathing,reciprocal traveltime fields and raylets[J].Geophys J Int,2010,181:1077 -1092.
[7]Benamou J D.Direct computation of mullivaiued phase space solutions for Hamilton-Jacobi equations[J].Comm Pure Appl Math,1999,52:1443-1475.
[8]Hauser J,Sambridge M,Rawlinson N.Multiarrival wavefront tracking and its applications[J].Geochem.Geophys.Geosyst., 2008,9,Q11001,doi:10.1029/2008GC002069.
[9]Bai C Y,Tang X P,Zhao R,2009.2-D/3-D multiply transmitted, converted and reflected arrivals in complex layered media with the modified shortest path method[J].Geophys J Int,2009, 179:201-214.
[10]Bai C Y,Huang G J and Zhao R.2D/3D irregular shortest-path raytracing for multiple arrivals and its applications[J]. Geophys J Int,2010,revision submitted.
[11]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 3D layered media with the shortest path mcthod[J].Chinese J.Geophys, 2009,52(5):1130-1138.
[12]唐小平,白超英.最短路径算法下二维层状介质中多次波追踪[J].地球物理学进展,2009,24(6):2087-2096. Tang X P,Bai C Y.Multiple raytracing in 2D layered media with the shortest path method[J].Progress in geophys(in Chinese),2009,24(6):2087-2096.
[13]Hole J A and Zelt B C.3-D finite-difference reflection travel times[J].Geophys J Int,1995,121:427-434.
[14]Riahi M A,Juhlin C.3-D interpretation of reflected arrival times by finite-difference techniques[J].Geophysics,1994, 59:844-849.
[15]Podvin P,Lecomte I.Finite difference computation of travcltimes in very contrasted velocity models:A massively parallel approach and its associated tools.Geophys J Inter,1991,105: 271-284.
[16]赵爱华,丁志峰.宽角反射地震波走时模拟的双重网格法[J].地球物理学报,2005,48(5):1141-1147. Zhao A H,Ding Z F.A double-grid algorithm for calculating traveltimes of wide-angular reflection wave[J].Chinese J. Geophys(in Chinese),2005,48(5):1141—1147.
[17]赵爱华,张中杰.三维复杂介质中转换波走时快速计算[J].地球物理学报,2004,47(4):702-707. Zhao A H,Zhang Z J.Fast calculation of converted wave traveltime in 3D complex media[J].Chinese J.Geophys(in Chinese),2004,47(4).702—707.
[18]王童奎,张美根,李小凡,等.PS转换波界面二次源法射线追踪[J].地球物理学进展,2007,22(1):165-170. Wang T K,Zhang M G,Li X F,et al.Interface point as secondary sources method ray tracing PS converted waves[J]. Progress in geophys(in Chinese),2007,22(1),165-170.
[19]Rawlinson N,Sambridge M.Multiple reflection and transmission phases in complex layered media using a multistage fast marching method[J].Geophysics,2004,69:1338-1350.
[20]De Kool M,Rawlinson N,Sambridge M.A practical gridbased method for tracking multiple refraction and reflection phases in three-dimensional heterogeneous media[J]. Geophys J Int,2006,167:253-270.
[21]Hauser J,Sambridge M,Rawlinson N.Phase space methods for multi-arrival wavefronts[J].Exploration Geophysics, 2006,37:331-339.
[2]Vinje V,Iversen E,Astebφl K,Gjφystdal H.Estimation of multivalued arrivals in 3D models using wavefront construction []].Geophysical Prospecting,1996,44:819-842.
[3]Vinje V,Astebol K,Iversen E.Gjoystdal H.3-D ray modelling by wavefront construction in open models[J].Geophysical Prospecting,1999,64:1912-1919.
[4]Symes W W,Qian J.A slowness matching eulerian method for multivalued solutions of eikonal equaions[J].SIAM J Sci Comput,2003,19:501-526.
[5]Sethian J A.Level set methods and fast marching methods [D].Cambridge University Press,Cambridge,1999.
[6]Rawlinson N,Sambridge M,Hauser J.Multipathing,reciprocal traveltime fields and raylets[J].Geophys J Int,2010,181:1077 -1092.
[7]Benamou J D.Direct computation of mullivaiued phase space solutions for Hamilton-Jacobi equations[J].Comm Pure Appl Math,1999,52:1443-1475.
[8]Hauser J,Sambridge M,Rawlinson N.Multiarrival wavefront tracking and its applications[J].Geochem.Geophys.Geosyst., 2008,9,Q11001,doi:10.1029/2008GC002069.
[9]Bai C Y,Tang X P,Zhao R,2009.2-D/3-D multiply transmitted, converted and reflected arrivals in complex layered media with the modified shortest path method[J].Geophys J Int,2009, 179:201-214.
[10]Bai C Y,Huang G J and Zhao R.2D/3D irregular shortest-path raytracing for multiple arrivals and its applications[J]. Geophys J Int,2010,revision submitted.
[11]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 3D layered media with the shortest path mcthod[J].Chinese J.Geophys, 2009,52(5):1130-1138.
[12]唐小平,白超英.最短路径算法下二维层状介质中多次波追踪[J].地球物理学进展,2009,24(6):2087-2096. Tang X P,Bai C Y.Multiple raytracing in 2D layered media with the shortest path method[J].Progress in geophys(in Chinese),2009,24(6):2087-2096.
[13]Hole J A and Zelt B C.3-D finite-difference reflection travel times[J].Geophys J Int,1995,121:427-434.
[14]Riahi M A,Juhlin C.3-D interpretation of reflected arrival times by finite-difference techniques[J].Geophysics,1994, 59:844-849.
[15]Podvin P,Lecomte I.Finite difference computation of travcltimes in very contrasted velocity models:A massively parallel approach and its associated tools.Geophys J Inter,1991,105: 271-284.
[16]赵爱华,丁志峰.宽角反射地震波走时模拟的双重网格法[J].地球物理学报,2005,48(5):1141-1147. Zhao A H,Ding Z F.A double-grid algorithm for calculating traveltimes of wide-angular reflection wave[J].Chinese J. Geophys(in Chinese),2005,48(5):1141—1147.
[17]赵爱华,张中杰.三维复杂介质中转换波走时快速计算[J].地球物理学报,2004,47(4):702-707. Zhao A H,Zhang Z J.Fast calculation of converted wave traveltime in 3D complex media[J].Chinese J.Geophys(in Chinese),2004,47(4).702—707.
[18]王童奎,张美根,李小凡,等.PS转换波界面二次源法射线追踪[J].地球物理学进展,2007,22(1):165-170. Wang T K,Zhang M G,Li X F,et al.Interface point as secondary sources method ray tracing PS converted waves[J]. Progress in geophys(in Chinese),2007,22(1),165-170.
[19]Rawlinson N,Sambridge M.Multiple reflection and transmission phases in complex layered media using a multistage fast marching method[J].Geophysics,2004,69:1338-1350.
[20]De Kool M,Rawlinson N,Sambridge M.A practical gridbased method for tracking multiple refraction and reflection phases in three-dimensional heterogeneous media[J]. Geophys J Int,2006,167:253-270.
[21]Hauser J,Sambridge M,Rawlinson N.Phase space methods for multi-arrival wavefronts[J].Exploration Geophysics, 2006,37:331-339.
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