扩展矩形盒波前法与扩展波前法在初至波计算中的对比研究
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摘要
基于Vidale "扩展矩形盒波前法"的思想,通过有限差分求解程函方程,利用MATLAB编程计算了二维速度模型的初至时间。理论研究和模拟结果表明:扩展矩形盒波前法计算初至时间不会像射线追踪法一样出现盲区,具有较高的计算精度,可大大降低计算量;但在处理复杂结构模型和强速度界面时会出现不稳定现象,导致所计算的走时并非真正的初至时间。为了进一步提高计算精度、算法的稳定性和解决地震波传播的因果性问题,给出了结合局部算法的扩展波前法结果。由于扩展波前法结合局部算法遵循了因果性,适应复杂结构模型和强速度界面,但计算的大量时间要用于寻找波前上的最小初至时间,效率较低。
Traveltime calculation plays an important role in many areas of seismology,such as pre-stack migration,traveltime inversion,earthquake location and seismic tomography.In this paper,the author gets traveltime by solving eikonal equation with finite difference method.Based on Vidale expanding square wavefront idea,the traveltimes of first arriving seismic waves are computed through the forward modeling by programming with MATLAB software in two dimensions.Modeling computation shows that the "expanding square"method overcomes many problems of the ray tracing calculation,like shadow zones,with higher accuracy and improves computing efficiency.But this method isn't applicable to media with strong velocity contrast and complex velocity structure.Sometimes the computational traveltimes of the first arriving seismic waves with this method isn't real first arriving time,for it violates the causal laws.To improve the computational accuracy,the algorithm stability and to solve the causality of the propagating path of seismic waves,the paper presented a finite-difference scheme in which the solution region progresses outward from an "expanding wavefront"rather than an "expanding square"in combination with local algorithm.However,the expanding wavefront method is applicable to media with strong velocity contrast and complex velocity structure,which made the algorithm more robust and accuracy.But penalty results to a large increase in computational cost and programming effort.A lot of computing time wastes in finding the minimum travetimes of the first arriving seismic waves.
Traveltime calculation plays an important role in many areas of seismology,such as pre-stack migration,traveltime inversion,earthquake location and seismic tomography.In this paper,the author gets traveltime by solving eikonal equation with finite difference method.Based on Vidale expanding square wavefront idea,the traveltimes of first arriving seismic waves are computed through the forward modeling by programming with MATLAB software in two dimensions.Modeling computation shows that the "expanding square"method overcomes many problems of the ray tracing calculation,like shadow zones,with higher accuracy and improves computing efficiency.But this method isn't applicable to media with strong velocity contrast and complex velocity structure.Sometimes the computational traveltimes of the first arriving seismic waves with this method isn't real first arriving time,for it violates the causal laws.To improve the computational accuracy,the algorithm stability and to solve the causality of the propagating path of seismic waves,the paper presented a finite-difference scheme in which the solution region progresses outward from an "expanding wavefront"rather than an "expanding square"in combination with local algorithm.However,the expanding wavefront method is applicable to media with strong velocity contrast and complex velocity structure,which made the algorithm more robust and accuracy.But penalty results to a large increase in computational cost and programming effort.A lot of computing time wastes in finding the minimum travetimes of the first arriving seismic waves.
引文
[1]万永革.地震学导论[M].北京:科学出版社,2016.
[2]Vidale J.Finite-difference calculation of travel times[J].Bulletin of the Seismological Society of America,1988,78(6):2062-2076.
[3]熊彬,阮百尧.MATLAB在有限差分法中的应用[J].桂林工学院学报,2001,21(2):104-109.
[4]赵烽帆,马婷,徐涛.地震波初至走时的计算方法综述[J].地球物理学进展,2014,29(3):1102-1113.
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[6]Qin F H,Luo Y,Olsen K B,et al.Finite-difference solution of the eikonal equation along expanding wavefronts[J].Geophysics,1992,57(3):478-487.
[7]李文杰,魏修成,宁俊瑞,等.一种改进的利用程函方程计算旅行时的方法[J].石油地球物理勘探,2008,43(5):589-594.
[8]Van Avendonk H J A,Harding A J,Orcutt J A,et al.Hybird shortest path and ray bending method for traveltime and raypath calculations[J].Geophysics,2001,66(2):648-653.
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[10]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[J].地球物理学报,2009,52(10):2635-2643.
[11]韩果花,李川,黄明曦,等.二维复杂速度结构中的射线追踪[J].桂林理工大学学报,2013,33(3):425-429.
[12]Qian J L,Zhang Y T,Zhao H K.Fast sweeping methods for Eikonal equations on triangular meshes[J].SIAM Journal on Numerical Analysis,2007,45(1):83-107.
[13]兰海强,张智,徐涛,等.地震波走时场模拟的快速推进法和快速扫描法比较研究[J].地球物理学进展,2012,27(5):1863-1870.
[14]杨昊,孙建国,韩复兴,等.基于完全三叉树堆排序的波前扩展有限差分地震波走时快速算法[J].吉林大学学报(地球科学版),2010,40(1):188-194.
[15]张智,刘有山,徐涛,等.弹性波逆时偏移中的稳定激发振幅成像条件[J].地球物理学报,2013,56(10):3523-3533.
[2]Vidale J.Finite-difference calculation of travel times[J].Bulletin of the Seismological Society of America,1988,78(6):2062-2076.
[3]熊彬,阮百尧.MATLAB在有限差分法中的应用[J].桂林工学院学报,2001,21(2):104-109.
[4]赵烽帆,马婷,徐涛.地震波初至走时的计算方法综述[J].地球物理学进展,2014,29(3):1102-1113.
[5]王华忠,方正茂,徐兆涛,等.地震波旅行时计算[J].石油地球物理勘探,1999,34(2):155-163.
[6]Qin F H,Luo Y,Olsen K B,et al.Finite-difference solution of the eikonal equation along expanding wavefronts[J].Geophysics,1992,57(3):478-487.
[7]李文杰,魏修成,宁俊瑞,等.一种改进的利用程函方程计算旅行时的方法[J].石油地球物理勘探,2008,43(5):589-594.
[8]Van Avendonk H J A,Harding A J,Orcutt J A,et al.Hybird shortest path and ray bending method for traveltime and raypath calculations[J].Geophysics,2001,66(2):648-653.
[9]张建中,陈世军,余大祥.最短路径射线追踪方法及其改进[J].地球物理学进展,2003,18(1):146-150.
[10]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[J].地球物理学报,2009,52(10):2635-2643.
[11]韩果花,李川,黄明曦,等.二维复杂速度结构中的射线追踪[J].桂林理工大学学报,2013,33(3):425-429.
[12]Qian J L,Zhang Y T,Zhao H K.Fast sweeping methods for Eikonal equations on triangular meshes[J].SIAM Journal on Numerical Analysis,2007,45(1):83-107.
[13]兰海强,张智,徐涛,等.地震波走时场模拟的快速推进法和快速扫描法比较研究[J].地球物理学进展,2012,27(5):1863-1870.
[14]杨昊,孙建国,韩复兴,等.基于完全三叉树堆排序的波前扩展有限差分地震波走时快速算法[J].吉林大学学报(地球科学版),2010,40(1):188-194.
[15]张智,刘有山,徐涛,等.弹性波逆时偏移中的稳定激发振幅成像条件[J].地球物理学报,2013,56(10):3523-3533.