射线追踪方程与程函方程的初至旅行时层析对比
|
摘要
初至旅行时层析反演是目前应用最广泛的近地表建模方法。按照反演中正演算子的不同,可将基于射线理论的层析反演方法分为基于射线追踪方程与程函方程两类。本文分别从理论及数值测试上对两种方法在反演精度、计算效率等方面进行了系统的对比分析。结果表明:①两种方法可在统一的反演框架下推导得到,两者主要的差别均是由反演中正演算子的不同引起的;②两者具有相似的反演精度,由于后者的核函数是带限的,在复杂地区的层析反演中更加稳定;③前者的计算效率、内存占用等依赖于检波点个数,后者则依赖于模型大小,检波点稀疏时优选前者,否则优选后者;④前者具有射线密度等质控手段,后者缺少类似的质控手段。
The first-arrival traveltime tomographic inversion is the most widely used near-surface modeling method.According to the forward modeling operator in the inversion,the tomographic inversion based on the ray theory can be divided into two kinds of methods:based on the ray-tracing equation and based on the eikonal equation.In this paper,a detailed contrastive analysis of the two methods in terms of inversion accuracy and computational efficiency are carried out respectively in theory and numerical tests.The following observations are obtained:(1)The two methods can be deduced from the unified inversion framework.The main differences between the two methods are caused by the differences of the forward-modeling operators in the inversion;(2) The two methods have similar inversion accuracy.The kernel function of the second method is band-limited,so it is more stable in complex areas;(3)The computational efficiency of the first method depends on the number of receivers and the second method depends on the size of the model.So the first method is preferable when receivers are sparse.Otherwise,the second method is preferred;(4)The first method has lots of quality controls such as ray density,while the second method lacks similar quality controls.
The first-arrival traveltime tomographic inversion is the most widely used near-surface modeling method.According to the forward modeling operator in the inversion,the tomographic inversion based on the ray theory can be divided into two kinds of methods:based on the ray-tracing equation and based on the eikonal equation.In this paper,a detailed contrastive analysis of the two methods in terms of inversion accuracy and computational efficiency are carried out respectively in theory and numerical tests.The following observations are obtained:(1)The two methods can be deduced from the unified inversion framework.The main differences between the two methods are caused by the differences of the forward-modeling operators in the inversion;(2) The two methods have similar inversion accuracy.The kernel function of the second method is band-limited,so it is more stable in complex areas;(3)The computational efficiency of the first method depends on the number of receivers and the second method depends on the size of the model.So the first method is preferable when receivers are sparse.Otherwise,the second method is preferred;(4)The first method has lots of quality controls such as ray density,while the second method lacks similar quality controls.
引文
[1] 高秦,陈超群,王智茹,等.多方法静校正融合技术在鄂尔多斯盆地黄土塬区中的应用[J].石油地球物理勘探,2017,52(增刊2):38-44.GAO Qin,CHEN Chaoqun,WANG Zhiru,et al.Multiple statics fusion in loess tablelands,Ordos Basin[J].Oil Geophysical Prospecting,2017,52(S2):38-44.
[2] 李素闪,程元方,刘建红,等.火成岩发育区静校正技术与应用[J].石油地球物理勘探,2017,52(增刊2):45-49.LI Sushan,CHENG Yuanfang,LIU Jianhong,et al.Static corrections for igneous rock areas[J].Oil Geophysical Prospecting,2017,52(S2):45-49.
[3] Zhu X,Sixta D,Angstman B.Tomostatics:Turning-ray tomography+static corrections[J].The Leading Edge,1992,11(12):15-23.
[4] Carney B J.Building Velocity Models for Steep-dip Prestack Depth Migration through First Arrival Tra-veltime Tomography[D].Virginia Polytechnic Institute and State University,Blacksburg,2000.
[5] Stewart R R.Exploration Seismic Tomography:Fundamentals[M].SEG,1991.
[6] Bulant P.Two-point ray tracing in 3-D[J].Pure and Applied Geophysics,1996,148(3-4):421-447.
[7] Vidale J E.Finite-difference calculation of traveltimes in three dimensions[J].Geophysics,1990,55(5):521-526.
[8] Noble M,Gesret A,Belayouni N.Accurate 3-D finite difference computation of traveltimes in strongly he-terogeneous media[J].Geophysical Journal International,2014,199(3):1572-1585.
[9] Zhang J,Huang Y,Song L P,et al.Fast and accurate 3-D ray tracing using bilinear traveltime interpolation and the wave front group marching[J].Geophysical Journal International,2011,184(3):1327-1340.
[10] Zhang J,Toksoz M N.Nonlinear refraction traveltime tomography[J].Geophysics,1998,63(5):1726-1737.
[11] Zelt C A,Barton P J.Three-dimensional seismic re-fraction tomography:A comparison of two methods applied to data from the Faeroe Basin[J].Journal of Geophysical Research Atmospheres,1998,103(B4):7187-7210.
[12] 苗贺,孙建国,王蕤,等.基于Chebyshev多项式的三维射线追踪[J].石油地球物理勘探,2018,53(3):462-468.MIAO He,SUN Jianguo,WANG Rui,et al.3D tra-veltime ray tracing based on Chebyshev polynomials[J].Oil Geophysical Prospecting,2018,53(3):462-468.
[13] Hole J A.Nonlinear high-resolution three-dimensional seismic travel time tomography[J].Journal of Geophysical Research:Solid Earth,1992,97(B5):6553-6562.
[14] Yang Y,Qin K,Zhang D,et al.Improvement of SIRT algorithm in near-surface seismic tomography[J].Journal of Wuhan University,2009,55(2):201-205.
[15] Liu Z Y and Zhang J.Joint traveltime,waveform,and waveform envelope inversion for near-surface imaging[J].Geophysics,2017,82(4):R235-R244.
[16] Sun M,Zhang J,Zhang W,et al.Alternating traveltime tomography and waveform inversion for near-surface imaging[C].SEG Technical Program Expanded Abstracts,2017,36:2596-2600.
[17] Plessix R E.A review of the adjoint-state method for computing the gradient of a functional with geophysical applications[J].Geophysical Journal of the Royal Astronomical Society,2010,167(2):495-503.
[18] Sei A,Symes W W.Gradient calculation of the travel time cost function without ray-tracing[C].SEG Technical Program Expanded Abstracts,1994,13:1351-1354
[19] Leung S,Qian J.An adjoint state method for three-dimensional transmission traveltime tomography using first-arrivals[J].Communications in Mathematical Sciences,2006,4(1):249-266.
[20] Taillandier C,Noble M,Chauris H,et al.First-arrival traveltime tomography based on the adjoint-state method[J].Geophysics,2009,74(6):WCB1-WCB10.
[21] 谢春,刘玉柱,董良国,等.伴随状态法初至波走时层析[J].石油地球物理勘探,2014,49(5):877-883.XIE Chun,LIU Yuzhu,DONG Liangguo,et al.First arrival traveltime tomography based on the adjoint state method[J].Oil Geophysical Prospecting,2014,49(5):877-883.
[22] Huang J W,Bellefleur G.Joint transmission and reflection traveltime tomography using the fast swee-ping method and the adjoint-state technique[J].Geophysical Journal International,2012,188(2):570-582.
[23] Benaichouche A,Noble M,Gesret A.First arrival tra-veltime tomography using the fast marching method and the adjoint state technique[C].Extended Abstracts of 77th EAGE Conference & Exhibition,2015,Tu N102 09.
[24] 李勇德,董良国,刘玉柱.一种新的预条件伴随状态法初至波走时层析[J].地球物理学报,2017,60(10):3934-3941.LI Yongde,DONG Liangguo,LIU Yuzhu.First arrival traveltime tomography based on a new preconditioned adjoint-state method[J].Chinese Journal of Geophysics,2017,60(10):3934-3941.
[25] Waheed U B,Flagg G,Yarman C E.First-arrival tra-veltime tomography for anisotropic media using the adjoint-state method[J].Geophysics,2016,81(4):R147-R155.
[26] Sethian J A.A fast marching level set method for monotonically advancing fronts[J].Proceedings of the National Academy of Sciences of the United States of America,1996,93(4):1591-1595.
[27] 江燕,陈晓非.有限频与射线层析成像比较研究综述[J].地球物理学进展,2011,26(5):1566-1575.JIANG Yan,CHEN Xiaofei.Review on the comparative study between finite-frequency tomography and ray-theoretical tomography[J].Progress in Geophy-sics,2011,26(5):1566-1575.
[28] 刘小民,邬达理,梁硕博,等.潜水波胖射线走时层析速度反演及其在深度偏移速度建模中的应用[J].石油物探,2017,56(5):718-726.LIU Xiaomin,WU Dali,LIANG Shuobo,et al.Diving wave tomography velocity inversion using fat ray in prestack depth migration.Geophysical Prospecting for Petroleum,2017,56(5):718-726.
[2] 李素闪,程元方,刘建红,等.火成岩发育区静校正技术与应用[J].石油地球物理勘探,2017,52(增刊2):45-49.LI Sushan,CHENG Yuanfang,LIU Jianhong,et al.Static corrections for igneous rock areas[J].Oil Geophysical Prospecting,2017,52(S2):45-49.
[3] Zhu X,Sixta D,Angstman B.Tomostatics:Turning-ray tomography+static corrections[J].The Leading Edge,1992,11(12):15-23.
[4] Carney B J.Building Velocity Models for Steep-dip Prestack Depth Migration through First Arrival Tra-veltime Tomography[D].Virginia Polytechnic Institute and State University,Blacksburg,2000.
[5] Stewart R R.Exploration Seismic Tomography:Fundamentals[M].SEG,1991.
[6] Bulant P.Two-point ray tracing in 3-D[J].Pure and Applied Geophysics,1996,148(3-4):421-447.
[7] Vidale J E.Finite-difference calculation of traveltimes in three dimensions[J].Geophysics,1990,55(5):521-526.
[8] Noble M,Gesret A,Belayouni N.Accurate 3-D finite difference computation of traveltimes in strongly he-terogeneous media[J].Geophysical Journal International,2014,199(3):1572-1585.
[9] Zhang J,Huang Y,Song L P,et al.Fast and accurate 3-D ray tracing using bilinear traveltime interpolation and the wave front group marching[J].Geophysical Journal International,2011,184(3):1327-1340.
[10] Zhang J,Toksoz M N.Nonlinear refraction traveltime tomography[J].Geophysics,1998,63(5):1726-1737.
[11] Zelt C A,Barton P J.Three-dimensional seismic re-fraction tomography:A comparison of two methods applied to data from the Faeroe Basin[J].Journal of Geophysical Research Atmospheres,1998,103(B4):7187-7210.
[12] 苗贺,孙建国,王蕤,等.基于Chebyshev多项式的三维射线追踪[J].石油地球物理勘探,2018,53(3):462-468.MIAO He,SUN Jianguo,WANG Rui,et al.3D tra-veltime ray tracing based on Chebyshev polynomials[J].Oil Geophysical Prospecting,2018,53(3):462-468.
[13] Hole J A.Nonlinear high-resolution three-dimensional seismic travel time tomography[J].Journal of Geophysical Research:Solid Earth,1992,97(B5):6553-6562.
[14] Yang Y,Qin K,Zhang D,et al.Improvement of SIRT algorithm in near-surface seismic tomography[J].Journal of Wuhan University,2009,55(2):201-205.
[15] Liu Z Y and Zhang J.Joint traveltime,waveform,and waveform envelope inversion for near-surface imaging[J].Geophysics,2017,82(4):R235-R244.
[16] Sun M,Zhang J,Zhang W,et al.Alternating traveltime tomography and waveform inversion for near-surface imaging[C].SEG Technical Program Expanded Abstracts,2017,36:2596-2600.
[17] Plessix R E.A review of the adjoint-state method for computing the gradient of a functional with geophysical applications[J].Geophysical Journal of the Royal Astronomical Society,2010,167(2):495-503.
[18] Sei A,Symes W W.Gradient calculation of the travel time cost function without ray-tracing[C].SEG Technical Program Expanded Abstracts,1994,13:1351-1354
[19] Leung S,Qian J.An adjoint state method for three-dimensional transmission traveltime tomography using first-arrivals[J].Communications in Mathematical Sciences,2006,4(1):249-266.
[20] Taillandier C,Noble M,Chauris H,et al.First-arrival traveltime tomography based on the adjoint-state method[J].Geophysics,2009,74(6):WCB1-WCB10.
[21] 谢春,刘玉柱,董良国,等.伴随状态法初至波走时层析[J].石油地球物理勘探,2014,49(5):877-883.XIE Chun,LIU Yuzhu,DONG Liangguo,et al.First arrival traveltime tomography based on the adjoint state method[J].Oil Geophysical Prospecting,2014,49(5):877-883.
[22] Huang J W,Bellefleur G.Joint transmission and reflection traveltime tomography using the fast swee-ping method and the adjoint-state technique[J].Geophysical Journal International,2012,188(2):570-582.
[23] Benaichouche A,Noble M,Gesret A.First arrival tra-veltime tomography using the fast marching method and the adjoint state technique[C].Extended Abstracts of 77th EAGE Conference & Exhibition,2015,Tu N102 09.
[24] 李勇德,董良国,刘玉柱.一种新的预条件伴随状态法初至波走时层析[J].地球物理学报,2017,60(10):3934-3941.LI Yongde,DONG Liangguo,LIU Yuzhu.First arrival traveltime tomography based on a new preconditioned adjoint-state method[J].Chinese Journal of Geophysics,2017,60(10):3934-3941.
[25] Waheed U B,Flagg G,Yarman C E.First-arrival tra-veltime tomography for anisotropic media using the adjoint-state method[J].Geophysics,2016,81(4):R147-R155.
[26] Sethian J A.A fast marching level set method for monotonically advancing fronts[J].Proceedings of the National Academy of Sciences of the United States of America,1996,93(4):1591-1595.
[27] 江燕,陈晓非.有限频与射线层析成像比较研究综述[J].地球物理学进展,2011,26(5):1566-1575.JIANG Yan,CHEN Xiaofei.Review on the comparative study between finite-frequency tomography and ray-theoretical tomography[J].Progress in Geophy-sics,2011,26(5):1566-1575.
[28] 刘小民,邬达理,梁硕博,等.潜水波胖射线走时层析速度反演及其在深度偏移速度建模中的应用[J].石油物探,2017,56(5):718-726.LIU Xiaomin,WU Dali,LIANG Shuobo,et al.Diving wave tomography velocity inversion using fat ray in prestack depth migration.Geophysical Prospecting for Petroleum,2017,56(5):718-726.