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对于大多数速度场，地震波沿射线传播的初至波走时，可以用有限差分外推的方法在二维或三维数值网格上计算出来. 在保证精度的条件下，为提高计算效率和适应性，本文推导了基于任意矩形网格和局部平面波前近似的有限差分初至波走时计算方法. 另外，该方法对首波和散射波做了合适的处理，而且不会碰到传统射线法存在的阴影区和焦散区等问题. 简单模型和复杂的Marmousi模型试算的结果表明，该方法精度较高并适用于强纵、横向变速的复杂介质. 基于该方法的Kirchhoff叠前深度偏移, 在主要构造和目的层位置的成像效果上基本达到了波动方程法叠前深度偏移的位置成像效果. 由于未考虑续至波等有效能量，在成像的保幅性上不如波动方程法叠前深度偏移的效果，但其计算效率则明显高于全格林函数法和波动方程法. 相似文献
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近地表地层与人类生产生活密切相关,利用地震层析成像方法准确重建浅部地壳速度结构有助于开展高精度地震勘探、探查浅部矿产资源、规避潜在自然灾害,并利于城市地下空间建设.中国大陆地表条件复杂,尤其中西部盆岭结合带地形起伏剧烈,对浅部地壳精确速度建模构成严重挑战.本文系统论述了地震层析成像领域基于高频近似理论的走时成像方法和有限频层析成像方法,阐明两类方法的基本原理、存在问题和发展方向等.依据正演走时有无显式射线追踪,基于高频近似理论的走时成像方法分为传统走时层析成像方法和无射线路径的走时层析成像方法.基于射线追踪的传统走时层析成像方法,在浅层速度强烈变化时,因存在阴影区或多路径现象引起成像失真,严重影响成像效率;而无射线路径的层析成像方法通过程函方程走时场的正传和逆传直接计算敏感核,并利用伴随状态法获得目标函数的梯度,具有快速、稳健的优点.以上两种基于地震射线高频近似理论的走时成像方法由于未考虑地震波频率的带限性,存在波散射、波前愈合及反演约束差等问题.有限频层析成像方法克服了射线理论"无限高频"假设所带来的弊端,已成为重要的研究方向之一.该类方法主要分为射线有限频层析成像方法和基于波动方程的有限频层析成像方法.射线有限频层析成像方法能够提高成像的分辨率,但在方法本质上仍依赖于射线理论,较难处理较复杂的波现象问题;基于波动方程的有限频层析成像方法能准确处理复杂地质问题,提高成像可靠性并能以图像形式直观展示地球内部地震波的速度结构分布,但是该方法在实际应用中强烈依赖于数据中的低频信息及较精确的初始速度模型,其推广应用仍需进一步探索. 相似文献
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快速行进法(FMM)是一种求解程函方程数值解计算网格节点走时,然后向后处理进行射线追踪的方法.为了求取任意起伏界面下高精度多震相的地震走时与相应的射线路径,本文采用任意起伏地表条件下的的三维不等距上行差分公式结合分区多步计算技术实现了三维复杂层状起伏介质中多震相(透射、反射、转换波)地震走时的计算,利用上行有限差分公式逐次进行射线路径的追踪,并且通过与较为成熟的不规则最短路径法(ISPM)对比,验证了本算法的计算精度和有效性.数值模拟实例和对比结果表明该算法具有较高的计算精度,数值计算稳健,能灵活处理含任意三维起伏界面模型中多震相地震走时及相应射线路径的追踪问题. 相似文献
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最短路径射线追踪算法,用预先设置的网络节点的连线表示地震波传播路径,当网络节点稀疏时,获得的射线路径呈之字形,计算的走时比实际走时系统偏大. 本文在波前扩展和反向确定射线路径的过程中,在每个矩形单元内,通过对某边界上的已知走时节点的走时进行线性插值,并利用Fermat原理即时求出从该边界到达其他边界节点的最小走时及其子震源位置和射线路径,发展了相应的动态网络算法. 从而克服了最短路径射线追踪算法的缺陷,大大提高了最小走时和射线路径的计算精度. 相似文献
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提出一种对旅行时进行抛物线插值的地震射线追踪方法（简称PTI方法），它比基于旅行时线性插值方法（简称LTI方法）计算结果更准确.PTI和LTI方法都是基于2D网格单元模型，用于计算地震波的旅行时和射线路径.首先介绍了相关方法的一些基本概念.旅行时和射线路径都是在网格边界上进行计算的，因此，射线路径在同一恒速网格内是直线.其计算过程有两步.第一步，计算旅行时，第二步追踪射线路径.然后给出了LTI算法的基本公式.因为在炮点网格内可能存在折射波，文章也相应导出了其公式.最后详细推导了PTI 方法的公式.通过模型试算对比说明，用PTI方法较LTI算法更精确、更有效，PTI方法是一种很有发展前途的地震射线追踪算法. 相似文献
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An approach to calculate the accurate ray paths and traveltimes in multi-layered VTI media (transversely isotropic media with a vertical symmetry axis) is proposed. The expressions of phase velocity, group velocity and Snell’s law used for computation are all explicit and exact. The calculation of ray paths and traveltimes for a given ele-mentary wave is equivalent to that of a transmission problem which is much easier to be treated with the formulae proposed. In the section of numerical examples, the proce... 相似文献
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On anelliptic approximations for qP velocities in VTI media 总被引：5，自引：1，他引：5
Sergey Fomel 《Geophysical Prospecting》2004,52(3):247-259
A unified approach to approximating phase and group velocities of qP seismic waves in a transversely isotropic medium with vertical axis of symmetry (VTI) is developed. While the exact phase‐velocity expressions involve four independent parameters to characterize the elastic medium, the proposed approximate expressions use only three parameters. This makes them more convenient for use in surface seismic experiments, where the estimation of all four parameters is problematic. The three‐parameter phase‐velocity approximation coincides with the previously published ‘acoustic’ approximation of Alkhalifah. The group‐velocity approximation is new and noticeably more accurate than some of the previously published approximations. An application of the group‐velocity approximation for finite‐difference computation of traveltimes is shown. 相似文献
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The well‐known asymptotic fractional four‐parameter traveltime approximation and the five‐parameter generalised traveltime approximation in stratified multi‐layer transversely isotropic elastic media with a vertical axis of symmetry have been widely used for pure‐mode and converted waves. The first three parameters of these traveltime expansions are zero‐offset traveltime, normal moveout velocity, and quartic coefficient, ensuring high accuracy of traveltimes at short offsets. The additional parameter within the four‐parameter approximation is an effective horizontal velocity accounting for large offsets, which is important to avoid traveltime divergence at large offsets. The two additional parameters in the above‐mentioned five‐parameter approximation ensure higher accuracy up to a given large finite offset with an exact match at this offset. In this paper, we propose two alternative five‐parameter traveltime approximations, which can be considered extensions of the four‐parameter approximation and an alternative to the five‐parameter approximation previously mentioned. The first three short‐offset parameters are the same as before, but the two additional long‐offset parameters are different and have specific physical meaning. One of them describes the propagation in the high‐velocity layer of the overburden (nearly horizontal propagation in the case of very large offsets), and the other characterises the intercept time corresponding to the critical slowness that includes contributions of the lower velocity layers only. Unlike the above‐mentioned approximations, both of the proposed traveltime approximations converge to the theoretical (asymptotic) linear traveltime at the limit case of very large (“infinite”) offsets. Their accuracy for moderate to very large offsets, for quasi‐compressional waves, converted waves, and shear waves polarised in the horizontal plane, is extremely high in cases where the overburden model contains at least one layer with a dominant higher velocity compared with the other layers. We consider the implementation of the proposed traveltime approximations in all classes of problems in which the above‐mentioned approximations are used, such as reflection and diffraction analysis and imaging. 相似文献
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Large-offset approximation to seismic reflection traveltimes 总被引：4，自引：0，他引：4
Conventional approximations of reflection traveltimes assume a small offset-to-depth ratio, and their accuracy decreases with increasing offset-to-depth ratio. Hence, they are not suitable for velocity analysis and stacking of long-offset reflection seismic data. Assuming that the offset is large, rather than small, we present a new traveltime approximation which is exact at infinite offset and has a decreasing accuracy with decreasing offset-to-depth ratio. This approximation has the form of a series containing powers of the offset from 1 to −∞. It is particularly accurate in the presence of a thin high-velocity layer above the reflector, i.e. in a situation where the accuracy of the Taner and Koehler series is poor. This new series can be used to gain insight into the velocity information contained in reflection traveltimes at large offsets, and possibly to improve velocity analysis and stacking of long-offset reflection seismic data. 相似文献
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Practical VTI approximations: a systematic anatomy 总被引：3，自引：0，他引：3
Transverse isotropy (TI) with a vertical symmetry axis (VTI) often provides an appropriate earth model for prestack imaging of steep-dip reflection seismic data. Exact P-wave and SV-wave phase velocities in VTI media are described by complicated equations requiring four independent parameters. Estimating appropriate multiparameter earth models can be difficult and time-consuming, so it is often useful to replace the exact VTI equations with simpler approximations requiring fewer parameters. The accuracy limits of different previously published VTI approximations are not always clear, nor is it always obvious how these different approximations relate to each other. Here I present a systematic framework for deriving a variety of useful VTI approximations. I develop first a sequence of well-defined approximations to the exact P-wave and SV-wave phase velocities. In doing so, I show how the useful but physically questionable heuristic of setting shear velocities identically to zero can be replaced with a more precise and quantifiable approximation. The key here to deriving accurate approximations is to replace the stiffness a13 with an appropriate factorization in terms of velocity parameters. Two different specific parameter choices lead to the P-wave approximations of Alkhalifah (Geophysics 63 (1998) 623) and Schoenberg and de Hoop (Geophysics 65 (2000) 919), but there are actually an infinite number of reasonable parametrizations possible. Further approximations then lead to a variety of other useful phase velocity expressions, including those of Thomsen (Geophysics 51 (1986) 1954), Dellinger et al. (Journal of Seismic Exploration 2 (1993) 23), Harlan (Stanford Exploration Project Report 89 (1995) 145), and Stopin (Stopin, A., 2001. Comparison of v(θ) equations in TI medium. 9th International Workshop on Seismic Anisotropy). Each P-wave phase velocity approximation derived this way can be paired naturally with a corresponding SV-wave approximation. Each P-wave or SV-wave phase velocity approximation can then be converted into an equivalent dispersion relation in terms of horizontal and vertical slownesses. A simple heuristic substitution also allows each phase velocity approximation to be converted into an explicit group velocity approximation. From these, in turn, travel time or moveout approximations can also be derived. The group velocity and travel time approximations derived this way include ones previously used by Byun et al. (Geophysics 54 (1989) 1564), Dellinger et al. (Journal of Seismic Exploration 2 (1993) 23), Tsvankin and Thomsen (Geophysics 59 (1994) 1290), Harlan (89 (1995) 145), and Zhang and Uren (Zhang, F. and Uren, N., 2001. Approximate explicit ray velocity functions and travel times for P-waves in TI media. 71st Annual International Meeting, Society of Exploration Geophysicists, Expanded Abstracts, 106–109). 相似文献
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V.B. Piip 《Geophysical Prospecting》2001,49(4):461-482
A method using simple inversion of refraction traveltimes for the determination of 2D velocity and interface structure is presented. The method is applicable to data obtained from engineering seismics and from deep seismic investigations. The advantage of simple inversion, as opposed to ray‐tracing methods, is that it enables direct calculation of a 2D velocity distribution, including information about interfaces, thus eliminating the calculation of seismic rays at every step of the iteration process. The inversion method is based on a local approximation of the real velocity cross‐section by homogeneous functions of two coordinates. Homogeneous functions are very useful for the approximation of real geological media. Homogeneous velocity functions can include straight‐line seismic boundaries. The contour lines of homogeneous functions are arbitrary curves that are similar to one another. The traveltime curves recorded at the surface of media with homogeneous velocity functions are also similar to one another. This is true for both refraction and reflection traveltime curves. For two reverse traveltime curves, non‐linear transformations exist which continuously convert the direct traveltime curve to the reverse one and vice versa. This fact has enabled us to develop an automatic procedure for the identification of waves refracted at different seismic boundaries using reverse traveltime curves. Homogeneous functions of two coordinates can describe media where the velocity depends significantly on two coordinates. However, the rays and the traveltime fields corresponding to these velocity functions can be transformed to those for media where the velocity depends on one coordinate. The 2D inverse kinematic problem, i.e. the computation of an approximate homogeneous velocity function using the data from two reverse traveltime curves of the refracted first arrival, is thus resolved. Since the solution algorithm is stable, in the case of complex shooting geometry, the common‐velocity cross‐section can be constructed by applying a local approximation. This method enables the reconstruction of practically any arbitrary velocity function of two coordinates. The computer program, known as godograf , which is based on this theory, is a universal program for the interpretation of any system of refraction traveltime curves for any refraction method for both shallow and deep seismic studies of crust and mantle. Examples using synthetic data demonstrate the accuracy of the algorithm and its sensitivity to realistic noise levels. Inversions of the refraction traveltimes from the Salair ore deposit, the Moscow region and the Kamchatka volcano seismic profiles illustrate the methodology, practical considerations and capability of seismic imaging with the inversion method. 相似文献
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随机介质表征的地球介质自组织性,体现了地球内部复杂介质的统计性特征,对理解地球内部构造和动力学演化有重要的意义.波前愈合效应是自组织介质散射效应的体现,会导致高频近似射线理论的计算走时和真实波场到时有一定的差异.为了研究射线理论在自组织介质中的适应性范围,本文选取高斯型和指数型自相关函数来描述自组织介质,采用非均匀化多尺度方法进行大尺度地球模型的波场模拟.利用互相关方法求取背景速度场与附加自组织介质速度场之间的波场走时差,并与由射线理论得到的走时差进行比较.结果表明,非均匀化多尺度方法在节省计算时间的同时,又可保持计算精度.介质相关长度越小、波长越长且传播距离越远时,波前愈合效应越强.当相关长度a、波长λ以及传播距离L之间满足a/(λL)1/2≤0.5时,波前愈合效应显著,且随着比值减小两者差异增大,波前愈合效应在增加,在该范围内射线理论计算走时的误差较大. 相似文献
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CDP mapping in tilted transversely isotropic (TTI) media. Part I: Method and effectiveness 总被引：1，自引：0，他引：1
Transverse isotropy with a tilted axis of symmetry (TTI) causes image distortion if isotropic models are assumed during data processing. A simple anisotropic migration approach needs long computational times and is sensitive to the signal-to-noise ratio. This paper presents an efficient, general approach to common-depth-point (CDP) mapping to image the subsurface in TTI media from qP-wave seismic data by adding anisotropic and dip parameters to the velocity model. The method consists of three steps: (i) calculating traveltimes and positions of the CDP points; (ii) determining CDP trajectories; (iii) CDP imaging. A crucial step is the rapid computation of traveltimes and raypaths in the TTI media, which is achieved by the Fermat method, specially adapted for anisotropic layered media. The algorithm can image the subsurface of a given model quickly and accurately, and is suitable for application to a bending reflector. The effectiveness of the method is demonstrated by comparing the raypaths, the traveltimes and the results of CDP mapping, when assuming isotropic media, transversely isotropic media with a vertical axis of symmetry (TIV), and TTI media. 相似文献
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