复杂地表条件下基于线性插值和窄带技术的地震波走时计算
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摘要
为了在复杂地表条件下实现地震波走时计算,提出了一种基于线性插值和窄带技术的走时计算新方法.其中,线性插值用于局部走时计算,窄带技术用于局部波前捕获和追踪.为了逼近起伏地表,采用三角网和矩形网相结合的方法对速度模型进行剖分.为了得到局部走时计算公式,利用费马(Fermat)原理和关于入射点位置的限定条件.有关编程实践和数值试验表明:新方法不仅可以有效、灵活地处理地表高程的剧烈变化,而且还具有很好的适应性和稳定性,得到的计算结果满足波前传播规律.
For realizing the seismic traveltime computation under complex topographical conditions, we present a new method based on linear interpolation and narrow band technique. Here, the linear interpolation technique is used for carrying out the local traveltime computation, and the narrow band technique is used for capturing and propagating the wavefront. For fitting the complex topography, we use a hybrid grid, consisting of a triangular grid and a rectangular one, for dividing the velocity model into grid. For obtaining a formula for the local traveltime computation, we invoke the Fermat principle and a condition for limiting the position of the incident point. Programming practice and numerical tests show that the new method not only can treat the strong topographical change with effectiveness and flexibility, but also have satisfactory stability and adaptability to the complex velocity model. The results given by the new method consist with the laws on wave propagation.
For realizing the seismic traveltime computation under complex topographical conditions, we present a new method based on linear interpolation and narrow band technique. Here, the linear interpolation technique is used for carrying out the local traveltime computation, and the narrow band technique is used for capturing and propagating the wavefront. For fitting the complex topography, we use a hybrid grid, consisting of a triangular grid and a rectangular one, for dividing the velocity model into grid. For obtaining a formula for the local traveltime computation, we invoke the Fermat principle and a condition for limiting the position of the incident point. Programming practice and numerical tests show that the new method not only can treat the strong topographical change with effectiveness and flexibility, but also have satisfactory stability and adaptability to the complex velocity model. The results given by the new method consist with the laws on wave propagation.
引文
[1] Hubral P,Krey Th. Interval velocities fromseismic reflection time measurements. Tulsa: SEG,1980
[2] 杨文采.地球物理反演的理论与方法.北京:地质出版社,1997 Yang W C. Theory and Methods of Geophysical Inversion (in Chinese). Beijing: Geological Publishing House, 1997
[3] 井西利,杨长春,王世清.一种改进的地震反射层析成像方法.地球物理学报,2007,50(6) :1831-1836 Jing X L,Yang C C, Wang S S.A improved seismic reflection tomographic method. Chinese J.Geophys. (in Chinese), 2007,50(6) :1831-1836
[4] 瞿辰,周蕙兰,赵大鹏.使用纵波和横波走时层析成像研究菲律宾海板块西边缘带和南海地区的深部结构.地球物理学报,2007,50(6) :1757-1768 Qu C, Zhou H L, Zhao D P. Deep structure beneath the west margin of Philippine Sea Plate and South China Sea from P and S wave travel time tomography. Chinese J. Geophys. (in Chinese), 2007,50(6) :1757-1768
[5] Sun J. True-amplitude weight functions in 3D limited-aperture migration revisited. Geophysics, 2004, 69(4) :1025-1036
[6] Sun J. Limited-aperture migration. Geophysics, 2000, 65 (3) :584-595
[7] Sun J.On the aperture effect in 3D Kirchhoff-type migration. Geophysical Prospecting , 1999 ,47(5) :1045-1076
[8] Sun I.On the limited aperture migration in two dimensions. Geophysics, 1998, 63(5) :984-994
[9] 程玖兵,王华忠,马在田.双平方根方程三维叠前深度偏移.地球物理学报,2003,46(5) :676-683 Cheng J B, Wang H Z, Ma Z T. Double square root equation 3D prestack depth migration. Chinese J. Geophys. (in Chinese), 2003, 46(5) :676-683
[10] 樊卫花,杨长春,孙传文等.三维地震资料叠前时间偏移应用研究.地球物理学进展,2007,22(3) :836-842 Fan W H, Yang C C, Sun C W, et al. Application of prestack time migration for three dimensional seismic data. Progress in Geophysics (in Chinese), 2007, 22(3) : 836-842
[11] 徐涛,徐果明,高尔根等.三维复杂介质的块状建模和试射射线追踪.地球物理学报,2004,47(6) :1118-1126 Xu T, Xu G M, Gao E G, et al. Block modeling and shooting ray tracing in complex 3-D media. ChineseJ. Geophys. (in Chinese), 2004, 47(6) :1118-1126
[12] Julian B R, Gubbins D. Three-dimensional seismic ray tracing. J.Geophys, 1977, 43:95-113
[13] Vinje V E A.3-D ray modeling by wavefront construction in open models. Geophys Prospect,1993, 64:1912-1919
[14] 韩复兴,孙建国,杨昊.不同插值算法在波前构建射线追踪中的应用与对比.计算物理,2008,25(2) :197-202 Han F X, Sun J G, Yang H. Interpolation algorithms in wavefront construction. Chinese Journal of Computational Physics (in Chinese), 2008, 25(2) :197-202
[15] 韩复兴,孙建国,杨 昊.基于C_语言实现波前构建射线追踪.石油地球物理勘探,2007,42(4) :475-481 Han F X, Sun J G, Yang H. Ray tracing by implementing C++ language-based wavefront construction approach. Oil Geophysical Prospecting (in Chinese), 2007, 42(4) :475-481
[16] Vidale J E. Finite-difference calculations of traveltimes. Bull Seism Soc Am, 1988,78:2062-2076
[17] Asakawa E K T. Seismic ray tracing using linear traveltime interpolation.Geophysical Prospecting , 1993, 41 (1) :99-111
[18] Moser T J.Shortest path calculation of seismic rays. Geophysics ,1991,56:59-67
[19] 张美根,贾豫葛,王妙月等.界面二次源波前扩展法全局最小走时射线追踪技术.地球物理学报,2006,49(4) :1169-1175 Zhang M G, Jia Y G,Wang M Y, et al. A global minimum traveltime ray tracing algorithm of wavefront expanding with interface points as secondary sources. Chinese J. Geophys. (in Chinese), 2006, 49(4) :1169-1175
[20] 秦孟兆,陈景波.Maslov渐近理论与辛几何算法.地球物理学报,2000,43(4) :523-533 Qin M Z, Chen J B. Maslov asymptotic theory and symplectic algorithm. Chinese J. Geophys. (in Chinese) , 2000,43(4) : 523-533
[21] 高亮,李幼铭,陈旭荣等.地震射线辛几何算法初探.地球物理学报,2000,43(3) :402-409 Gao L, Li Y M, Chen X R,et al. An attempt to seismic ray tracing with symplectic algorithm. Chinese J. Geophys. (in Chinese), 2000,43(3) :402-469
[22] 孙建国.复杂地表条件下地球物理场数值模拟方法评述.世界地质,2007,26(3) :345-362 Sun J G. Methods for numerical modeling of geophysical fields under complex topographical conditions: a critical review. Global Geology, 2007, 26(3) :345-362
[23] Sethian J A, Popovici A M. 3-D traveltime computation using the fast marching method. Geophysics, 1999, 64:516-523
[24] Sethian J A. Evolution, implementation, and application of level set and fast marching methods for advancing fronts. J. Comp Phys, 2001,169:503-555
[2] 杨文采.地球物理反演的理论与方法.北京:地质出版社,1997 Yang W C. Theory and Methods of Geophysical Inversion (in Chinese). Beijing: Geological Publishing House, 1997
[3] 井西利,杨长春,王世清.一种改进的地震反射层析成像方法.地球物理学报,2007,50(6) :1831-1836 Jing X L,Yang C C, Wang S S.A improved seismic reflection tomographic method. Chinese J.Geophys. (in Chinese), 2007,50(6) :1831-1836
[4] 瞿辰,周蕙兰,赵大鹏.使用纵波和横波走时层析成像研究菲律宾海板块西边缘带和南海地区的深部结构.地球物理学报,2007,50(6) :1757-1768 Qu C, Zhou H L, Zhao D P. Deep structure beneath the west margin of Philippine Sea Plate and South China Sea from P and S wave travel time tomography. Chinese J. Geophys. (in Chinese), 2007,50(6) :1757-1768
[5] Sun J. True-amplitude weight functions in 3D limited-aperture migration revisited. Geophysics, 2004, 69(4) :1025-1036
[6] Sun J. Limited-aperture migration. Geophysics, 2000, 65 (3) :584-595
[7] Sun J.On the aperture effect in 3D Kirchhoff-type migration. Geophysical Prospecting , 1999 ,47(5) :1045-1076
[8] Sun I.On the limited aperture migration in two dimensions. Geophysics, 1998, 63(5) :984-994
[9] 程玖兵,王华忠,马在田.双平方根方程三维叠前深度偏移.地球物理学报,2003,46(5) :676-683 Cheng J B, Wang H Z, Ma Z T. Double square root equation 3D prestack depth migration. Chinese J. Geophys. (in Chinese), 2003, 46(5) :676-683
[10] 樊卫花,杨长春,孙传文等.三维地震资料叠前时间偏移应用研究.地球物理学进展,2007,22(3) :836-842 Fan W H, Yang C C, Sun C W, et al. Application of prestack time migration for three dimensional seismic data. Progress in Geophysics (in Chinese), 2007, 22(3) : 836-842
[11] 徐涛,徐果明,高尔根等.三维复杂介质的块状建模和试射射线追踪.地球物理学报,2004,47(6) :1118-1126 Xu T, Xu G M, Gao E G, et al. Block modeling and shooting ray tracing in complex 3-D media. ChineseJ. Geophys. (in Chinese), 2004, 47(6) :1118-1126
[12] Julian B R, Gubbins D. Three-dimensional seismic ray tracing. J.Geophys, 1977, 43:95-113
[13] Vinje V E A.3-D ray modeling by wavefront construction in open models. Geophys Prospect,1993, 64:1912-1919
[14] 韩复兴,孙建国,杨昊.不同插值算法在波前构建射线追踪中的应用与对比.计算物理,2008,25(2) :197-202 Han F X, Sun J G, Yang H. Interpolation algorithms in wavefront construction. Chinese Journal of Computational Physics (in Chinese), 2008, 25(2) :197-202
[15] 韩复兴,孙建国,杨 昊.基于C_语言实现波前构建射线追踪.石油地球物理勘探,2007,42(4) :475-481 Han F X, Sun J G, Yang H. Ray tracing by implementing C++ language-based wavefront construction approach. Oil Geophysical Prospecting (in Chinese), 2007, 42(4) :475-481
[16] Vidale J E. Finite-difference calculations of traveltimes. Bull Seism Soc Am, 1988,78:2062-2076
[17] Asakawa E K T. Seismic ray tracing using linear traveltime interpolation.Geophysical Prospecting , 1993, 41 (1) :99-111
[18] Moser T J.Shortest path calculation of seismic rays. Geophysics ,1991,56:59-67
[19] 张美根,贾豫葛,王妙月等.界面二次源波前扩展法全局最小走时射线追踪技术.地球物理学报,2006,49(4) :1169-1175 Zhang M G, Jia Y G,Wang M Y, et al. A global minimum traveltime ray tracing algorithm of wavefront expanding with interface points as secondary sources. Chinese J. Geophys. (in Chinese), 2006, 49(4) :1169-1175
[20] 秦孟兆,陈景波.Maslov渐近理论与辛几何算法.地球物理学报,2000,43(4) :523-533 Qin M Z, Chen J B. Maslov asymptotic theory and symplectic algorithm. Chinese J. Geophys. (in Chinese) , 2000,43(4) : 523-533
[21] 高亮,李幼铭,陈旭荣等.地震射线辛几何算法初探.地球物理学报,2000,43(3) :402-409 Gao L, Li Y M, Chen X R,et al. An attempt to seismic ray tracing with symplectic algorithm. Chinese J. Geophys. (in Chinese), 2000,43(3) :402-469
[22] 孙建国.复杂地表条件下地球物理场数值模拟方法评述.世界地质,2007,26(3) :345-362 Sun J G. Methods for numerical modeling of geophysical fields under complex topographical conditions: a critical review. Global Geology, 2007, 26(3) :345-362
[23] Sethian J A, Popovici A M. 3-D traveltime computation using the fast marching method. Geophysics, 1999, 64:516-523
[24] Sethian J A. Evolution, implementation, and application of level set and fast marching methods for advancing fronts. J. Comp Phys, 2001,169:503-555
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