三维LTI射线追踪极小值方程的快速数值解法
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摘要
线性走时插值(LTI)算法应用于三维射线追踪时,其向前处理过程中的极小值方程是超越方程,无法求出解析解.虽然可以采用网格剖分方式近似求解,网格剖分精度越大,计算结果越精确,但随着剖分精度的提高,向前处理的计算量会以N3的阶次增加,从而导致计算效率的降低.本文将最速下降法引入到LTI射线追踪算法的向前处理,提出了一种求解三维LTI超越方程的快速数值解法,该方法也不是一种精确求解方法,而是沿着负梯度方向不断逼近真实解.计算结果表明,该算法在兼顾射线追踪精度的同时能有效提高计算效率,计算速度快了3倍以上.
When linear traveltime interpolation(LTI) method is used in the three-dimensional ray tracing,the minimum equation employed in forward processing is a transcendental equation,thus the analytic solution can not been given.Though the approximate solution can be obtained by using the grid division method,the more precision of the grid division,the more accurate calculations,the calculating works in forward processing will be increased by the orders of N3 together with the increasing partition accuracy of the grid interface,consequently reducing the calculation efficiency.In this paper,the steepest descent method is introduced in the forward processing of LTI ray tracing and a fast algorithms for solving the three-dimensional LTI transcendental equation is put forward,The method is not an exact solution,but along the negative gradient direction continuous approximation to the true solution.The results show that this algorithm improves the calculation efficiency taking into account the accuracy of ray tracing at the same time,computational speed is faster more than three times at least.
When linear traveltime interpolation(LTI) method is used in the three-dimensional ray tracing,the minimum equation employed in forward processing is a transcendental equation,thus the analytic solution can not been given.Though the approximate solution can be obtained by using the grid division method,the more precision of the grid division,the more accurate calculations,the calculating works in forward processing will be increased by the orders of N3 together with the increasing partition accuracy of the grid interface,consequently reducing the calculation efficiency.In this paper,the steepest descent method is introduced in the forward processing of LTI ray tracing and a fast algorithms for solving the three-dimensional LTI transcendental equation is put forward,The method is not an exact solution,but along the negative gradient direction continuous approximation to the true solution.The results show that this algorithm improves the calculation efficiency taking into account the accuracy of ray tracing at the same time,computational speed is faster more than three times at least.
引文
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[10]徐萃微,孙绳武.计算方法引论[M].北京:高等教育出版社,2002:242-245.Xu Cuiwei,Sun Shengwu.Introduction to the Calcula-tion Method[M].Beijing:Higher Education Press,2002:242-245(Ch).
[2]Moser T J.Shortestpath calculation of seismic rays[J].Geophysics,1991,56(1):59-67.
[3]Vidale J E.Finite-difference calculation of travel timesin three dimensions[J].Geophysics,1990,55(5):521-526.
[4]和锐,杨建思,张翼.地震层析成像方法综述[J].CT理论与应用研究,2007,1:35-48.He Rui,Yang Jiansi,Zhang Yi.A review on the tech-nology of seismit tomography[J].Compoterized Tomo-graphy Theory and Applications,2007,1:35-48(Ch).
[5]张钋,刘洪,李幼铭.射线追踪方法的发展现状[J].地球物理学进展,2000,15(1):36-45.Zhang Po,Liu Hong,Li Youning.The situation andprogress of ray tracying method research[J].Progressin Geophysics,2000,15(1):36-45(Ch).
[6]张东,谢宝莲,杨艳,等.一种改进的线性走时插值射线追踪算法[J].地球物理学报,2009,52(01):200-205.Zhang Dong,Xie Baolian,Yang Yan,et al.A ray trac-ying method based on improved linear traveltime inter-polation[J].Chinese Journal of Geophysics,2009,52(01):200-205(Ch).
[7]张东,童海杰,杨艳,等.基于波前扩展的线性走时插值射线追踪算法[J].武汉大学学报(理学版),2010,56(6):649-654.Zhang Dong,Tong Haijie,Yang Yan,et al.Linear trav-eltime interpolation algorithm based on expandingwavefronts[J].Wuhan Univ(Nat Sci Ed),2010,56(6):649-654(Ch).
[8]Zhang Jianzhong,Huang Yueqin,Song Linping,et al.Fast and accurate 3-D ray tracing using bilinear travel-time interpolation and the wave front group marching[J].Geophysical Journal International,2011,184(3):1327-1340.
[9]张东,傅相如,杨艳,等.基于LTI和网格界面剖分的三维地震射线追踪算法[J].地球物理学报,2009,52(9):2370-2376.Zhang Dong,Fu Xiangru,Yang Yan,et al.3-D seismicray tracing algorithm based on LTI and partition ofgrid interface[J].Chinese Journal of Geophysics,2009,52(9):2370-2376(Ch).
[10]徐萃微,孙绳武.计算方法引论[M].北京:高等教育出版社,2002:242-245.Xu Cuiwei,Sun Shengwu.Introduction to the Calcula-tion Method[M].Beijing:Higher Education Press,2002:242-245(Ch).
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