共查询到20条相似文献，搜索用时 46 毫秒
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给出了计算多层垂直对称轴横向各向同性（VTI）介质精确射线路径和走时的方法,所用的体波相速度公式、群速度公式和Snell定律都是严格的显式解析公式. 任意基本波的射线路径和走时计算问题都可以转化成一个等效的透射问题,再用文中的公式来计算,具体实现方法用一个多次波和一个首波的实例给出. 最后分别用精确公式和Thomsen近似公式计算了相同模型相同基本波的走时曲线. 比较两者计算结果可发现, 近似公式反复使用会使误差积累,同时揭示了近似公式适用范围的局限性,强调了使用近似公式需要注意其适用范围的重要性. 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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井间地震数据直达波走时层析成像 总被引：1，自引：0，他引：1
本文利用矢量射线追踪正演模拟技术计算地震波直达波传播的路径及走时,进而利用射线走时及路径的内插,发展了弯曲射线迭代反演技术.该方法可用来重建井间地层的速度图像.基于所发展的方法,我们对较为复杂的典型地质模型进行了井间速度重建.结果表明该方法是一项快速、高精度的走时层析成像技术. 相似文献
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Vlastislav Červený Antoine B. Frangié Reviewer J. Vaněk 《Studia Geophysica et Geodaetica》1982,26(3):238-253
Summary The effects of the causal absorption on seismic wave fields are discussed. Several computer programs for the evaluation of seismic wave fields have been modified to include the causal absorption. The programs are based mostly on matrix and ray methods. The main attention is paid to ray methods. A simple plane wave algorithm is described, which can be used along the ray to compute elementary seismograms in dissipative media. For a certain class of signals, commonly used in seismology, its application does not require any convolution or frequency-domain computations, and is only slightly slower than the evaluation of elementary seismograms in non-dissipative media. The derived algorithm even describes the velocity dispersion related to absorption and the decrease of the prevailing frequency of the signal well. Numerical examples are presented, both exact and approximate. 相似文献
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三维复杂地形近地表速度估算及地震层析静校正 总被引：18，自引：6，他引：18
在地表一致性模型的基础上提出一种可适用于宽线剖面、弯曲测线、传统的二维和目前广泛使用的三维地震观测.在地形及近地表低降速带地质结构复杂的探区，低降速带厚度及速度估算的精度是静校正处理的关键.本研究根据三维地震观测的初至走时数据，利用最小平方与QR分解相结合的算法，在三维空间重建近地表低降速带速度模型，根据重建速度模型实现了静校正长波长分量与短波长分量的同步计算.分析了复杂的近地表低降速带模型初至波的性质，在观测值的自动拾取以及理论值的计算中充分考虑了可能成为初至波的直达波、折射波和反射波的利用，提高了低降速带速度模型反演的精度.在初至走时观测数据的拾取中，本研究采用分形算法克服了初至波波形差异以及折射波相位反转导致的拾取误差，实现了三维初至拾取的大规模全自动化运算.在射线路径与初至波理论走时的计算中，本研究采用一种计算量与模型复杂程度无关的三维射线追踪方法，该方法以最小走时射线路径保证了与观测数据有同等意义的初至波的射线追踪及理论走时的计算.野外实际资料的处理结果表明了方法的有效性. 相似文献
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The 4 × 4 T -propagator matrix of a 3D central ray determines, among other important seismic quantities, second-order (parabolic or hyperbolic) two-point traveltime approximations of certain paraxial rays in the vicinity of the known central ray through a 3D medium consisting of inhomogeneous isotropic velocity layers. These rays result from perturbing the start and endpoints of the central ray on smoothly curved anterior and posterior surfaces. The perturbation of each ray endpoint is described only by a two-component vector. Here, we provide parabolic and hyperbolic paraxial two-point traveltime approximations using the T -propagator to feature a number of useful 3D seismic models, putting particular emphasis on expressing the traveltimes for paraxial primary reflected rays in terms of hyperbolic approximations. These are of use in solving several forward and inverse seismic problems. Our results simplify those in which the perturbation of the ray endpoints upon a curved interface is described by a three-component vector. In order to emphasize the importance of the hyperbolic expression, we show that the hyperbolic paraxial-ray traveltime (in terms of four independent variables) is exact for the case of a primary ray reflected from a planar dipping interface below a homogeneous velocity medium. 相似文献
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具有垂直对称轴的横向各向同性介质模型(VTI)是目前各向异性理论研究和多波多分量地震资料叠前成像处理中最常用的一种各向异性模型.VTI介质中反射 P波时距曲线一般不再是双曲线.基于不同的相速度近似公式会得到不同的时距关系式.文中对几种典型的非双曲时距曲线与射线追踪得到的准确时距曲线在不同各向异性强度下进行了对比，结果表明Muir等和Stovas等提出的非双曲时距公式由于过高地考虑了横波垂直速度的影响与精确的时距曲线有很大偏差；Tsvankin等提出的弱各向异性非双曲时距公式在ε-δ<0时误差增大；Alkhalifah等提出的非双曲时距公式在大炮检距任意各向异性强度下都具有较高的精度，适于在实际资料处理中应用. 相似文献
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Summary A new approximation of the velocity-depth distribution in a vertically inhomogeneous medium is suggested. This approximation guarantees the continuity of velocity and of its first and second derivatives and does not generate false low-velocity zones. It is very suitable for the computations of seismic wave fields in vertically inhomogeneous media by ray methods and its modifications, as it removes many false anomalies from the travel-time and amplitude-distance curves of seismic body waves. The ray integrals can be evaluated in a closed form; the resulting formulae for rays, travel times and geometrical spreading are very simple. They do not contain any transcendental functions (such asln (x) orsin
–1, (x)) like other approximations; only the evaluation of one square root and of certain simple arithmetic expressions for each layer is required. From a computational point of view, the evaluation of ray integrals and of geometrical spreading is only slightly slower than for a system of homogeneous parallel layers and even faster than for a piece-wise linear approximation. 相似文献
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Introduction The determination of the ray path between a source and a receiver is fundamental to many seismic problems such as earthquake location, travel time inversion, computation of synthetic seismograms, depth migration, and seismic tomography. The calculation of travel times and their derivatives depend on the determination of ray paths, which is the most time-consuming work in seismic tomography. Therefore, a fast and accurate ray tracing method is particularly important. Many ray-traci… 相似文献
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We test the accuracy of the previously derived weak-anisotropy approximations of the P-wave phase and ray (group) velocities. The formulae are of varying accuracy, and are applicable to weak or moderate anisotropy of arbitrary symmetry and orientation. They have a form of expressions for squares of phase velocity depending on the phase-velocity direction and of ray velocity depending on the ray-velocity direction. Both velocities are expressed in terms of three elements of the rotated Christoffel matrix, which depend linearly on the parameters specifying the medium, the weak-anisotropy parameters. The least accurate formulae are fully independent of the choice of a reference isotropic medium and depend linearly on weak-anisotropy parameters. The most accurate formulae depend only slightly on the ratio of S- and P-wave velocities of a reference medium, their dependence on weak-anisotropy parameters being quadratic. We show that the accuracy of the formulae is quite high, in fact, in some cases, it is close to the accuracy of the socalled anelliptic approximations, very accurate approximations based on a perturbation of the elliptical anisotropy. 相似文献
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Determination of the ray vector (the unit vector specifying the direction of the group velocity vector) corresponding to a given wave normal (the unit vector parallel to the phase velocity vector or slowness vector) in an arbitrary anisotropic medium can be performed using the exact formula following from the ray tracing equations. The determination of the wave normal from the ray vector is, generally, a more complicated task, which is usually solved iteratively. We present a first-order perturbation formula for the approximate determination of the ray vector from a given wave normal and vice versa. The formula is applicable to qP as well as qS waves in directions, in which the waves can be dealt with separately (i.e. outside singular directions of qS waves). Performance of the approximate formulae is illustrated on models of transversely isotropic and orthorhombic symmetry. We show that the formula for the determination of the ray vector from the wave normal yields rather accurate results even for strong anisotropy. The formula for the determination of the wave normal from the ray vector works reasonably well in directions, in which the considered waves have convex slowness surfaces. Otherwise, it can yield, especially for stronger anisotropy, rather distorted results. 相似文献
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Einar Iversen 《Pure and Applied Geophysics》1996,148(1-2):287-317
The motivation for this paper is to provide expressions for first-order partial derivatives of reflection point coordinates, taken with respect to model parameters. Such derivatives are expected to be useful for processes dealing with the problem of estimating velocities for depth migration of seismic data.The subject of the paper is a particular aspect of ray perturbation theory, where observed parameters—two-way reflection time and horizontal components of slowness, are constraining the ray path when parameters of the reference velocity model are perturbed. The methodology described here is applicable to general rays in a 3D isotropic, heterogeneous medium. Each ray is divided into a shot ray and a receiver ray, i.e., the ray portions between the shot/receiver and the reflection point, respectively. Furthermore, by freezing the initial horizontal slowness of these subrays as the model is perturbed,elementary perturbation quantities may be obtained, comprising derivatives of ray hit positions within theisochrone tangent plane, as well as corresponding time derivatives. The elementary quantities may be estimated numerically, by use of ray perturbation theory, or in some cases, analytically. In particular, when the layer above the reflection point is homogeneous, explicit formulas can be derived. When the elementary quantities are known,reflection point derivatives can be obtained efficiently from a set of linear expressions.The method is applicable for a common shot, receiver or offset data sorting. For these gather types, reflection point perturbationlaterally with respect to the isochrone is essentially different. However, in theperpendicular direction, a first-order perturbation is shown to beindependent of gather type.To evaluate the theory, reflection point derivatives were estimated analytically and numerically. I also compared first-order approximations to true reflection point curves, obtained by retracing rays for a number of model perturbations. The results are promising, especially with respect to applications in sensitivity analysis for prestack depth migration and in velocity model updating. 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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A first-order perturbation theory for seismic isochrons is presented in a model independent form. Two ray concepts are fundamental in this theory, the isochron ray and the velocity ray, for which I obtain first-order approximations to position vectors and slowness vectors. Furthermore, isochron points are connected to a shot and receiver by conventional ray fields. Based on independent perturbation of the shot and receiver ray I obtain first-order approximations to velocity rays. The theory is applicable for 3D inhomogeneous anisotropic media, given that the shot and receiver rays, as well as their perturbations, can be generated with such model generality.
The theory has applications in sensitivity analysis of prestack depth migration and in velocity model updating. Numerical examples of isochron and velocity rays are shown for a 2D homogeneous VTI model. The general impression is that the first-order approximation is, with some exceptions, sufficiently accurate for practical applications using an anisotropic velocity model. 相似文献
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Part II of this paper is a direct continuation of Part I, where we consider the same types of orthorhombic layered media and the same types of pure-mode and converted waves. Like in Part I, the approximations for the slowness-domain kinematical characteristics are obtained by combining power series coefficients in the vicinity of both the normal-incidence ray and an additional wide-angle ray. In Part I, the wide-angle ray was set to be the critical ray (‘critical slowness match’), whereas in Part II we consider a finite long offset associated with a given pre-critical ray (‘pre-critical slowness match’). Unlike the critical slowness match, the approximations in the pre-critical slowness match are valid only within the bounded slowness range; however, the accuracy within the defined range is higher. Moreover, for the pre-critical slowness match, there is no need to distinguish between the high-velocity layer and the other, low-velocity layers. The form of the approximations in both critical and pre-critical slowness matches is the same, where only the wide-angle power series coefficients are different. Comparing the approximated kinematical characteristics with those obtained by exact numerical ray tracing, we demonstrate high accuracy. Furthermore, we show that for all wave types, the accuracy of the pre-critical slowness match is essentially higher than that of the critical slowness match, even for matching slowness values close to the critical slowness. Both approaches can be valuable for implementation, depending on the target offset range and the nature of the subsurface model. The pre-critical slowness match is more accurate for simulating reflection data with conventional offsets. The critical slowness match can be attractive for models with a dominant high-velocity layer, for simulating, for example, refraction events with very long offsets. 相似文献
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槽波地震勘探利用槽波的频散特性反演煤层的结构特征，故理论频散曲线的计算是一个重要方面.使用水平层状模型假设下的面波频散曲线计算方法能够计算煤层厚度恒定模型地震槽波频散曲线；但当煤层厚度变化时该方法不再适用.基于前人水平层状均匀介质模型的面波理论频散曲线计算方法，对于含煤三层模型，本文发展了煤层厚度变化情况下的地震槽波理论频散曲线计算方法，并使用该方法计算分析了不同厚度函数模型的频散曲线形态特征.研究表明：与稳定厚度煤层相比，煤层厚度变化使得地震槽波群速度成为与频率及传播射线在水平面投影路径相关的二元函数；射线路径上煤层厚度的变化使得频散曲线在群速度方向上压缩，群速度变化范围变小，且使处于最小值位置的埃里相群速度增大；而煤层厚度的线性变化模型频散曲线只与射线首、尾处的煤层厚度有关，与煤层厚度恒定模型相比，曲线形态不发生改变；煤层厚度呈非线性变化时，频散曲线形态上可能发生改变. 相似文献
19.
Time horizons can be depth-migrated when interval velocities are known; on the other hand, the velocity distribution can be found when traveltimes and NMO velocities at zero offset are known (wavefront curvatures; Shah 1973). Using these concepts, exact recursive inversion formulae for the calculation of interval velocities are given. The assumption of rectilinear raypath propagation within each layer is made; interval velocities and curvatures of the interfaces between layers can be found if traveltimes together with their gradients and curvatures and very precise VNMO velocities at zero offset are known. However, the available stacking velocity is a numerical quantity which has no direct physical significance; its deviation from zero offset NMO velocity is examined in terms of horizon curvatures, cable length and lateral velocity inhomogeneities. A method has been derived to estimate the geological depth model by searching, iteratively, for the best solution that minimizes the difference between stacking velocities from the real data and from the structural model. Results show the limits and capabilities of the approach; perhaps, owing to the low resolution of conventional velocity analyses, a simplified version of the given formulae would be more robust. 相似文献
20.
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