复杂地表条件下快速推进法地震波走时计算
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摘要
为获得计算复杂地表条件下地震波走时的方法,对常规快速推进法(Fast marching method,简写为FMM)做了两点改进:①引入不等距差分格式,用于地表和界面处的局部走时计算;②增加新的网格节点类型,用于实现不规则边界条件下的窄带技术.通过对算法的计算精度、效率及实例的分析可得,算法计算精度高,其中反射波走时计算的精度高于初至波;不会因为处理不规则边界而引入过多额外的计算量;能灵活稳定地处理各种强起伏复杂地形、近地表及地下复杂介质等问题.计算结果满足复杂地表条件下地震波的传播规律.
Conventional fast marching method (FMM) is improved for traveltime computation. A non-equidistant difference scheme is used to carry local traveltime computation near surface and interface. New grid node type is used to realize narrow band technique under irregular boundary conditions. Analysis on accuracy, efficiency and numerical tests shows that the new method has high-accuracy and accuracy of the reflection wave is higher than that of the first-arrival wave. The new method does not need too more additional computing capacity in dealing with irregular boundaries. The new method can treat strong topographical change, near-surface and subsurface complex media effectively and flexibly. The results consist with laws of wave propagation under complex topographical conditions.
Conventional fast marching method (FMM) is improved for traveltime computation. A non-equidistant difference scheme is used to carry local traveltime computation near surface and interface. New grid node type is used to realize narrow band technique under irregular boundary conditions. Analysis on accuracy, efficiency and numerical tests shows that the new method has high-accuracy and accuracy of the reflection wave is higher than that of the first-arrival wave. The new method does not need too more additional computing capacity in dealing with irregular boundaries. The new method can treat strong topographical change, near-surface and subsurface complex media effectively and flexibly. The results consist with laws of wave propagation under complex topographical conditions.
引文
[1]Sun J.True-amplitude weight functions in3D limited-aperture migration revisited[J].Geophysics,2004,69(4):1025-1036.
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[8]Julian B R,Gubbins D.Three-dimensional seismic ray tracing[J].J Geophys,1977,43:95-113.
[9]Vinje V E A.3-D ray modeling by wavefront construction in open models[J].Geophys Prospect,1993,64:1912-1919.
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[11]Han F X,Sun J G,Yang H.Ray tracing by implementing C++language-based wavefront construction approach[J].Oil Geophysical Prospecting,2007,42(4):475-481.
[12]Vidale J E.Finite-difference calculations of traveltimes[J].Bull Seism Soc Am,1988,78:2062-2076.
[13]Asakawa E K T.Seismic ray tracing using linear traveltime interpolation[J].Geophysical Prospecting,1993,41(1):99-111.
[14]Moser T J.Shortest path calculation of seismic rays[J].Geophysics,1991,56:59-67.
[15]Chen J B,Qin M Z.Ray tracing、symplectic algorithms and wave field simulation[J].Chinese J Comput Phys,2001,18(6):481-486.
[16]Gao L,Li Y M,et al.An attempt to seismic ray tracing with symplectic algorithm[J].Chinese J Geophys,2000,43(3):402-409.
[17]Sun J G.Methods for numerical modeling of geophysical fields under complex topographical conditions:a critical review[J].Global Geology,2007,26(3):345-362.
[18]Leidenfrost A,Ettrich N,Gajewski D,Kosloff D.Comparison of six different methods for calculating traveltimes[J].Geophys Prospect,1999,47:269-297.
[19]Sethian J A.A fast marching level set method for monotonically advancing fronts[J].Proc Nat Acad Sci,1996,93:591-1595.
[20]Sun Z Q.Study on the traveltimes computation method under complex topographical condition[D].Changchun:Applied Geophysics Department of Jilin University,2008.
[21]Sethian J A,Popovici A M.3-D traveltime computation using the fast marching method[J].Geophysics,1999,64:516-523.
[22]Sethian J A.Evolution,implementation,and application of level set and fast marching methods for advancing fronts[J].J Comp Phys,2001,169:503-555.
[23]Yang H.Study on the fast computation technique of seismic traveltimes with finite-difference method[D].Changchun:Applied Geophysics Department of Jilin University,2007.
[2]Sun J.Limited-aperture migration[J].Geophysics,2000,65(3):584-595.
[3]Sun J.On the aperture effect in3D Kirchhoff-type migration[J].Geophysical Prospecting,1999,47(5):1045-1076.
[4]Sun J.On the limited aperture migration in two dimensions[J].Geophysics,1998,63(5):984-994.
[5]Chen S C,Ma Z T,Wu R S.Wave equation migration in angle domain[J].Chinese J Comput Phys,2007,24(2):211-216.
[6]Yang W C.Theory and methods of geophysical inversion[M].Beijing:Geological Press,1997.
[7]Song L P.Damped and weighted least-square solution for seismic traveltime tomography[J].Chinese J Comput Phys,1995,12(4):499-504.
[8]Julian B R,Gubbins D.Three-dimensional seismic ray tracing[J].J Geophys,1977,43:95-113.
[9]Vinje V E A.3-D ray modeling by wavefront construction in open models[J].Geophys Prospect,1993,64:1912-1919.
[10]Han F X,Sun J G,Yang H.Interpolation algorithms in wavefront construction[J].Chinese J Comput Phys,2008,25(2):197-202.
[11]Han F X,Sun J G,Yang H.Ray tracing by implementing C++language-based wavefront construction approach[J].Oil Geophysical Prospecting,2007,42(4):475-481.
[12]Vidale J E.Finite-difference calculations of traveltimes[J].Bull Seism Soc Am,1988,78:2062-2076.
[13]Asakawa E K T.Seismic ray tracing using linear traveltime interpolation[J].Geophysical Prospecting,1993,41(1):99-111.
[14]Moser T J.Shortest path calculation of seismic rays[J].Geophysics,1991,56:59-67.
[15]Chen J B,Qin M Z.Ray tracing、symplectic algorithms and wave field simulation[J].Chinese J Comput Phys,2001,18(6):481-486.
[16]Gao L,Li Y M,et al.An attempt to seismic ray tracing with symplectic algorithm[J].Chinese J Geophys,2000,43(3):402-409.
[17]Sun J G.Methods for numerical modeling of geophysical fields under complex topographical conditions:a critical review[J].Global Geology,2007,26(3):345-362.
[18]Leidenfrost A,Ettrich N,Gajewski D,Kosloff D.Comparison of six different methods for calculating traveltimes[J].Geophys Prospect,1999,47:269-297.
[19]Sethian J A.A fast marching level set method for monotonically advancing fronts[J].Proc Nat Acad Sci,1996,93:591-1595.
[20]Sun Z Q.Study on the traveltimes computation method under complex topographical condition[D].Changchun:Applied Geophysics Department of Jilin University,2008.
[21]Sethian J A,Popovici A M.3-D traveltime computation using the fast marching method[J].Geophysics,1999,64:516-523.
[22]Sethian J A.Evolution,implementation,and application of level set and fast marching methods for advancing fronts[J].J Comp Phys,2001,169:503-555.
[23]Yang H.Study on the fast computation technique of seismic traveltimes with finite-difference method[D].Changchun:Applied Geophysics Department of Jilin University,2007.
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