速度模型的光滑处理分析
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摘要
针对速度模型光滑处理对地震波走时、射线路径以及振幅信息的影响问题,从射线追踪方程组成立的前提条件、射线理论成立的高频近似理论以及菲涅尔带的角度着手,分析了速度模型光滑的理论基础。通过对同一模型光滑前后射线路径的计算表明,在不额外增加射线初始角度的前提下,模型的光滑处理可以有效地提高射线追踪的覆盖率;通过对不同速度模型光滑前后的走时计算及误差分析表明,选取合理的光滑次数,在保证射线追踪可行性和覆盖率的前提下,可以使走时的误差达到最小(横纵向各光滑50次时,Marmousi模型同一横坐标z方向上所有点的走时误差不超过5%;纵向光滑50次时,起伏层状模型同一横坐标z方向上所有点的走时误差不超过1%),而不影响偏移成像的质量。
In view of the impact of velocity model smoothing on wave traveltime,ray path and the amplitude information,we analyzed the theoretical basis of velocity model smoothing from prerequisite establishment of ray tracing equations,the ray theory of high-frequency approximation and Fresnel zone.Ray paths calculation before and after velocity smoothing for a same model showed that the smoothing of model can effectively improve the coverage of ray tracing without additional initial angle.Ray paths calculation and error analysis of before and after velocity smoothing for different model showed that selecting a reasonable number of smoothing under the premise of ensuring the viability of ray tracing and coverage,travel time can minimize errors(50 times smoothing in horizontal and vertical,the maximum relative error less than 5% on marmousi model and 50 times smoothing in vertical,the maximum relative error less than 1% on undulating layered model at the same abscissa of all points in z direction) without affecting the quality of migration.
In view of the impact of velocity model smoothing on wave traveltime,ray path and the amplitude information,we analyzed the theoretical basis of velocity model smoothing from prerequisite establishment of ray tracing equations,the ray theory of high-frequency approximation and Fresnel zone.Ray paths calculation before and after velocity smoothing for a same model showed that the smoothing of model can effectively improve the coverage of ray tracing without additional initial angle.Ray paths calculation and error analysis of before and after velocity smoothing for different model showed that selecting a reasonable number of smoothing under the premise of ensuring the viability of ray tracing and coverage,travel time can minimize errors(50 times smoothing in horizontal and vertical,the maximum relative error less than 5% on marmousi model and 50 times smoothing in vertical,the maximum relative error less than 1% on undulating layered model at the same abscissa of all points in z direction) without affecting the quality of migration.
引文
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[18]CervenV.Seismic ray theory[M].Cambridge:Cambridge University Press,2001.
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[20]谢里夫R E,吉尔达特L P.勘探地震学[M].初英,李承楚,王宏伟,等译.北京:石油工业出版社,1999:199-203.Sherif R E,Geldart L P.Exploration seismology[M].Translated by CHU Ying,LI Cheng-chu,WANG Hong-wei,et al.Beijing:Petroleum IndustryPress,1999:199-203.
[21]Sun J.The relationship between the first Fresnel zoneand the normalized geometrical spreading factor[J].Geophysical Prospecting,1996,44:351-374.
[22]Jesper S,Roel S.Tutorial:the Fresnel volume andseismic imaging[R].Stanford:Stanford University,2002:37-46.
[23]韩复兴,孙建国,杨昊.基于二维三次卷积的波前构建射线追踪[J].吉林大学学报:地球科学版,2008,38(2):336-340.HAN Fu-xing,SUN Jian-guo,YANG Hao.Ray-tracing of wavefront construction by bicubicinterpolation[J].Journal of Jilin University:EarthScience Edition,2008,38(2):336-340.
[24]Vinje V,Iversen E,Astebol K,et al.Estimation ofmultivalued arrivals in 3D models using wavefrontconstruction:Part I[J].Geophysical Prospecting,1996,44:819-842.
[25]Vinje V,Iversen E,Astebol K,et al.Estimation ofmultivalued arrivals in 3D models using wavefrontconstruction:Part II[J].Geophysical Prospecting,1996,44:843-858.
[26]Coman R,Gajewski D.3-D multivalued traveltimecomputation using a hybrid method[R].Calgary:Society of Exploration Geophysicists,2000:2309-2312.
[27]Vinje V,Iversen E,Astebol K,et al.3-D ray mode-ling by wavefront construction in open models[J].Geophysics,1999,64:1911-1919.
[28]Vinje V.A new interpolation criterion for controllingaccuracy in wavefront construction[R].Dallas:Society of Exploration Geophysicists,1997:1723-1726.
[29]Bjrn E.Computational high frequency wave pro-pagation[M].Cambridge:Cambridge UniversityPress,2003:181-266.
[2]何洋.基于波前构建的射线走时和振幅计算[D].长春:吉林大学,2005.HE Yang.Computation of traveltimes and amplitudesbased on wavefront construction ray tracing[D].Changchun:Jilin University,2005.
[3]韩复兴.论波前构建法中的几个计算问题[D].长春:吉林大学,2009.HAN Fu-xing.On some computational problems inwavefront construction method[D].Changchun:JilinUniversity,2009.
[4]Ettrich N,Gajewski D.Wavefront construction in sm-ooth media for prestack depth migration[J].Pageoph,1996,148:481-502.
[5]王雪秋,孙建国,张文志.复杂地表地质条件下地震波数值模拟综述[J].吉林大学学报:地球科学版,2005,35(增刊),12-18.WANG Xue-qiu,SUN Jian-guo,ZHANG Wen-zhi.The state-of the-art in numerical modeling includingsurface topography[J].Journal of Jilin University:Earth Science Edition,2005,35(Sup.):12-18.
[6]赵爱华,张美根,丁志峰.横向各向同性介质中地震波走时模拟[J].地球物理学报,2006,49(6):1762-1769.ZHAO Ai-hua,ZHANG Mei-gen,DING Zhi-feng.Seismic traveltime computation for transverselyisotropic media[J].Chinese Journal of Geophysics,2006,49(6):1762-1769.
[7]董良国.复杂地表条件下地震波传播数值模拟[J].勘探地球物理进展,2005,28(3):187-194.DONG Liang-guo.Numerical simulation of seismicwave propagation under complex near surfaceconditions[J].Progress in Exploration Geophysics,2005,28(3):187-194.
[8]孙建国,何洋.基于波前构建的射线追踪:一种Java实现[J].吉林大学学报:地球科学版,2007,37(4):814-820.SUN Jian-guo,HE Yang.Ray-tracing based onwavefront construction:a Java implementation[J].Journal of Jilin University:Earth Science Edition,2007,37(4):814-820.
[9]吴振利,李家彪,阮爱国.地震层析成像及其国内研究进展[J].东海海洋,2003,21(3):54-64.WU Zhen-li,LI Jia-biao,RUAN Ai-guo.Seismictomography and its development in China[J].DonghaiMarine Science,2003,21(3):54-64.
[10]成谷,马在田,耿建华,等.地震层析成像发展回顾[J].勘探地球物理进展,2002,25(3):6-12.CHENG Gu,MA Zai-tian,GENG Jian-hua,et al.Areview on the growth of seismic tomography[J].Progress in Exploration Geophysics,2002,25(3):6-12.
[11]Sena A G,Toksz M N.Kirchhoff migration andvelocity analysis for converted and nonconvertedwaves in anisotropic media[J].Geophysics,1993,58:265-276.
[12]Schleicher J,Tygel M,Hubral P.3Dtrue-amplitudefinite-offset migration[J].Geophysics,1993,58:1112-1126.
[13]Gray S H,May W P.Kirchhoff migration usingeikonal equation traveltimes[J].Geophysics,1994,59:810-817.
[14]Moser T J.Migration using the shortest-path method[J].Geophysics,1994,59(7):1110-1120.
[15]Epili D,McMechan G A.Implementation of 3-Dprestack Kirchhoff migration,with application todata from the ouachita frontal thrust zone[J].Geophysics,1996,61:1400-1411.
[16]Sun Y,Clapp R G,Biondi B.Three dimensionaldynamic ray tracing in complex geological structures[R].Stanford:Stanford University,1997:63-75.
[17]ervenV,Mototkov I A,Psencik I.Ray method inseismology[M].Prague:Prague Charkes UniversityPress,1977:15-18.
[18]CervenV.Seismic ray theory[M].Cambridge:Cambridge University Press,2001.
[19]杨文采.地球物理反演和地震层析成像[M].北京:地质出版社,1989:155-156.YANG Wen-cai.Geophysical inversion and seismictomography[M].Beijing:Geological PublishingHouse,1989:155-156.
[20]谢里夫R E,吉尔达特L P.勘探地震学[M].初英,李承楚,王宏伟,等译.北京:石油工业出版社,1999:199-203.Sherif R E,Geldart L P.Exploration seismology[M].Translated by CHU Ying,LI Cheng-chu,WANG Hong-wei,et al.Beijing:Petroleum IndustryPress,1999:199-203.
[21]Sun J.The relationship between the first Fresnel zoneand the normalized geometrical spreading factor[J].Geophysical Prospecting,1996,44:351-374.
[22]Jesper S,Roel S.Tutorial:the Fresnel volume andseismic imaging[R].Stanford:Stanford University,2002:37-46.
[23]韩复兴,孙建国,杨昊.基于二维三次卷积的波前构建射线追踪[J].吉林大学学报:地球科学版,2008,38(2):336-340.HAN Fu-xing,SUN Jian-guo,YANG Hao.Ray-tracing of wavefront construction by bicubicinterpolation[J].Journal of Jilin University:EarthScience Edition,2008,38(2):336-340.
[24]Vinje V,Iversen E,Astebol K,et al.Estimation ofmultivalued arrivals in 3D models using wavefrontconstruction:Part I[J].Geophysical Prospecting,1996,44:819-842.
[25]Vinje V,Iversen E,Astebol K,et al.Estimation ofmultivalued arrivals in 3D models using wavefrontconstruction:Part II[J].Geophysical Prospecting,1996,44:843-858.
[26]Coman R,Gajewski D.3-D multivalued traveltimecomputation using a hybrid method[R].Calgary:Society of Exploration Geophysicists,2000:2309-2312.
[27]Vinje V,Iversen E,Astebol K,et al.3-D ray mode-ling by wavefront construction in open models[J].Geophysics,1999,64:1911-1919.
[28]Vinje V.A new interpolation criterion for controllingaccuracy in wavefront construction[R].Dallas:Society of Exploration Geophysicists,1997:1723-1726.
[29]Bjrn E.Computational high frequency wave pro-pagation[M].Cambridge:Cambridge UniversityPress,2003:181-266.
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