宽频双程走时计算方法及其波场照明分析
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摘要
为了准确模拟任意主频情况下的初至走时和照明,应用高阶交错网格有限差分法进行了时域双程波动方程正演数值模拟,拾取最大振幅能量节点位置对应的旅行时间作为初至走时。以均匀介质为例,对比研究了本文方法与解析走时和高频近似走时(基于程函方程)在不同主频情况下的双程走时结果,指出在主频较高时三者最为接近。以Marmousi模型为例,计算了不同主频对应的初至走时及其振幅能量。综合分析表明,低主频存在较大的旅行时计算误差,不同的主频可以照明不同尺度的介质变化,从而指导实际地震资料的数字处理。
In order to correctly determine the first arrivals and the illumination for arbitrary dominant frequency,we performed forward numerical simulation on time domain two way wave equation using high-order staggered grid finite difference scheme,and took the traveltime corresponding to the maximum amplitude energy as the first arrival time.We compared the two way traveltimes resulted from the proposed method,the analytic method,and the high frequency approximation method which is based on eikonal equation on isotropic medium for different dominant frequency,and concluded that the three methods yield similar results in high dominant frequency.On Marmousi model,we calculated first arrivals and illuminations for different dominant frequency.Large error of travel time occurs at low dominant frequency,and illumination varies with dominant frequency.
In order to correctly determine the first arrivals and the illumination for arbitrary dominant frequency,we performed forward numerical simulation on time domain two way wave equation using high-order staggered grid finite difference scheme,and took the traveltime corresponding to the maximum amplitude energy as the first arrival time.We compared the two way traveltimes resulted from the proposed method,the analytic method,and the high frequency approximation method which is based on eikonal equation on isotropic medium for different dominant frequency,and concluded that the three methods yield similar results in high dominant frequency.On Marmousi model,we calculated first arrivals and illuminations for different dominant frequency.Large error of travel time occurs at low dominant frequency,and illumination varies with dominant frequency.
引文
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14熊金良,李国发,王濮,等.地震波走时计算的逆风差分算法[J].物探化探计算技术,2004,26(4):295~298
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16赵爱华,丁志峰.宽角反射地震波走时模拟的双重网格法[J].地球物理学报,2005,48(5):1 141~1 147
17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
18王华忠,谢海兵,马在田.有限差分法地震波走时计算[J].同济大学学报,1997,25(3):318~321
19谢海兵,马在田,王燕琨.一种新程函方程差分法层析成像[J].石油地球物理勘探,1997,32(5):623~627
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21李振春,刘玉莲,张建磊,等.基于矩形网格的有限差分走时计算方法[J].地震学报,2004,26(6):644~650
22匡斌,王华忠,季玉新,等.任意复杂介质中主能量法地震波走时计算[J].地球物理学报,2005,48(2):394~398
23孙章庆,孙建国,韩复兴,等.波前快速推进法起伏地表地震波走时计算[J].勘探地球物理进展,2007,30(5):392~395
24 Nichols D E.Maxi mum energy travelti mes calculatedin the seismic frequency band[J].Geophysics,1996,61(1):253~263
25 Shin C S,Ko S W,Marfurt K,et al.Wave equation cal-culation of most energetic travelti mes and amplitudesfor Kirchhoff prestack migration[J].Geophysics,2003,68(6):2 040~2 042
26 Shin C,Ko S,Ki m W,et al.Travelti me calculationsfrom frequency-domain downward-continuation algo-rithms[J].Geophysics,2003,68(4):1 380~1 388
27 Shin S,Shin C,Ki m W.Travelti me calculation usingmonochromatic one-way wave equation[C].ExpandedAbstracts of 70thAnnual International SEG Meeting,2000,2 313~2 316
28秦义龙,张中杰,Shin Changsoo,等.利用单频双程波动方程计算初至走时及其振幅[J].地球物理学报,2005,48(2):423~428
29薛东川,王尚旭.波动方程有限元叠前逆时偏移[J].石油地球物理勘探,2008,43(1):17~21
30陈可洋.地震波旅行时计算方法及其模型试验分析[J].石油物探,2010,49(2):153~157
31陈可洋.标量声波波动方程高阶交错网格有限差分法[J].中国海上油气,2009,21(4):232~236
32陈可洋.声波完全匹配层吸收边界条件的改进算法[J].石油物探,2009,41(1):76~79
33陈可洋.边界吸收中镶边法的评价[J].中国科学院研究生院学报,2010,27(2):170~175
34陈可洋.基于高阶有限差分的波动方程叠前逆时偏移方法[J].石油物探,2009,48(5):475~478
2 Julian B R,Gubbins D.Three-di mensional seismic raytracing[J].J Geophysics,1977,43(1):95~114
3 LambaréG,Lucio P S,Hanyga A.Two-di mensionalmultivalued travelti me and amplitude maps by uniformsampling of a ray field[J].Geophys J Int,1996,125(2):584~598
4 Schneider W A,Ranzinger K A,Balch A H,et al.Adynamic programming approach to first arrival travel-ti me computation in media with arbitrarily distributedvelocities[J].Geophysics,1992,57(1):39~50
5 Moser TJ.Shortest path calculation of travel ti me[J].Geophysics,1991,56(1):59~67
6赵爱华,张中杰,王光杰,等.非均匀介质中地震波走时与射线路径快速计算技术[J].地震学报,2000,22(2):151~157
7 Vidale J.Finite-difference calculation of travelti mes[J].Bulletin of the Seismiclogical Society of America,1988,78(6):2 062~2 076
8 Podvin P,Lecomte I.Finite-difference computation oftravelti mes in very contrasted velocity models:a mas-sively paralled approach and its associated tools[J].Geophys J Internat,1991,105(1):271~284
9 Qin F,Luo Y,Olsen K B,et al.Finite-difference solu-tion of the eikonal equation along expanding wavefro-nts[J].Geophysics,1992,57(3):478~487
10 Hole J A,Zelt B C.3-D finite-difference reflectiontravelti me[J].Geophysical Journal International,1995,121(2):427~434
11 Afni mar Koketsu K.Finite difference travelti me calcu-lationfor head waves traveling along anirregular inter-face[J].Geophysical Journal International,2000,143(3):729~734
12 Sethian J A,Popovici A M.3-Dtravelti me computationusing the fast marching method[J].Geophysics,1999,64(3):516~523
13 Qin F,Luo Y,Olsen K B,et al.Finite difference solu-tion of the eikonal equation along expanding wavefro-nts[J].Geophysics,1992,57(3):478~487
14熊金良,李国发,王濮,等.地震波走时计算的逆风差分算法[J].物探化探计算技术,2004,26(4):295~298
15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):1 762~1 769
16赵爱华,丁志峰.宽角反射地震波走时模拟的双重网格法[J].地球物理学报,2005,48(5):1 141~1 147
17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
18王华忠,谢海兵,马在田.有限差分法地震波走时计算[J].同济大学学报,1997,25(3):318~321
19谢海兵,马在田,王燕琨.一种新程函方程差分法层析成像[J].石油地球物理勘探,1997,32(5):623~627
20杨昊,孙建国,韩复兴.波前扩展有限差分地震波走时算法的C++语言描述[J].吉林大学学报(地球科学版),2007,37(3):615~619
21李振春,刘玉莲,张建磊,等.基于矩形网格的有限差分走时计算方法[J].地震学报,2004,26(6):644~650
22匡斌,王华忠,季玉新,等.任意复杂介质中主能量法地震波走时计算[J].地球物理学报,2005,48(2):394~398
23孙章庆,孙建国,韩复兴,等.波前快速推进法起伏地表地震波走时计算[J].勘探地球物理进展,2007,30(5):392~395
24 Nichols D E.Maxi mum energy travelti mes calculatedin the seismic frequency band[J].Geophysics,1996,61(1):253~263
25 Shin C S,Ko S W,Marfurt K,et al.Wave equation cal-culation of most energetic travelti mes and amplitudesfor Kirchhoff prestack migration[J].Geophysics,2003,68(6):2 040~2 042
26 Shin C,Ko S,Ki m W,et al.Travelti me calculationsfrom frequency-domain downward-continuation algo-rithms[J].Geophysics,2003,68(4):1 380~1 388
27 Shin S,Shin C,Ki m W.Travelti me calculation usingmonochromatic one-way wave equation[C].ExpandedAbstracts of 70thAnnual International SEG Meeting,2000,2 313~2 316
28秦义龙,张中杰,Shin Changsoo,等.利用单频双程波动方程计算初至走时及其振幅[J].地球物理学报,2005,48(2):423~428
29薛东川,王尚旭.波动方程有限元叠前逆时偏移[J].石油地球物理勘探,2008,43(1):17~21
30陈可洋.地震波旅行时计算方法及其模型试验分析[J].石油物探,2010,49(2):153~157
31陈可洋.标量声波波动方程高阶交错网格有限差分法[J].中国海上油气,2009,21(4):232~236
32陈可洋.声波完全匹配层吸收边界条件的改进算法[J].石油物探,2009,41(1):76~79
33陈可洋.边界吸收中镶边法的评价[J].中国科学院研究生院学报,2010,27(2):170~175
34陈可洋.基于高阶有限差分的波动方程叠前逆时偏移方法[J].石油物探,2009,48(5):475~478
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