共查询到20条相似文献，搜索用时 109 毫秒
1.
Jaromír Janský Vlastislav Červený Reviewer J. Vaněk 《Studia Geophysica et Geodaetica》1981,25(3):288-292
Summary A new approximation of the velocity-depth distribution in radially symmetric media is suggested. This approximation guarantees the continuity of velocity and its first and second derivatives, and does not generate false low-velocity layers. It removes false anomalies from the amplitude-distance curve and considerably increases its stability. The evaluation of ray integrals and ray amplitudes using this velocity-depth approximation does not require the computation of any transcendental function and is, therefore, very fast. Numerical examples are presented. 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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Vlastislav Červený Věnceslava Pretlová Reviewer I. Pšenčik 《Studia Geophysica et Geodaetica》1977,21(3-4):248-255
Summary Standard methods of interpolating the velocity-depth distribution v=v(z) do not guarantee the continuity of the first and second derivatives of velocity and generate false interfaces of a higher order. These false interfaces cause anomalies in the amplitude-distance curves. It is suggested to apply the smoothed spline approximation to the depth-velocity distribution z=z(v). In this case, the ray integrals can be evaluated in a closed form. The amplitude-distance curves become quite smooth and stable. All necessary formulae and numerical examples are presented. 相似文献
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The common ray approximation considerably simplifies the numerical algorithm of the coupling ray theory for S waves, but may introduce errors in travel times due to the perturbation from the common reference ray. These travel-time errors can deteriorate the coupling-ray-theory solution at high frequencies. It is thus of principal importance for numerical applications to estimate the errors due to the common ray approximation.We derive the equations for estimating the travel-time errors due to the isotropic and anisotropic common ray approximations of the coupling ray theory. These equations represent the main result of the paper. The derivation is based on the general equations for the second-order perturbations of travel time. The accuracy of the anisotropic common ray approximation can be studied along the isotropic common rays, without tracing the anisotropic common rays.The derived equations are numerically tested in three 1-D models of differing degree of anisotropy. The first-order and second-order perturbation expansions of travel time from the isotropic common rays to anisotropic-ray-theory rays are compared with the anisotropic-ray-theory travel times. The errors due to the isotropic common ray approximation and due to the anisotropic common ray approximation are estimated. In the numerical example, the errors of the anisotropic common ray approximation are considerably smaller than the errors of the isotropic common ray approximation.The effect of the isotropic common ray approximation on the coupling-ray-theory synthetic seismograms is demonstrated graphically. For comparison, the effects of the quasi-isotropic projection of the Green tensor, of the quasi-isotropic approximation of the Christoffel matrix, and of the quasi-isotropic perturbation of travel times on the coupling-ray-theory synthetic seismograms are also shown. The projection of the travel-time errors on the relative errors of the time-harmonic Green tensor is briefly presented. 相似文献
5.
Summary A method of approximation, minimizing the number of knots and satisfying the smoothing and fitting properties of the cubic spline approximation, is suggested. Two modifications of the method are presented. The first approach is specified to provide an adequate simple approximation to the digitalized smooth curve (such as the velocity-depth function in seismology), while the second is more general and may be used to approximate geophysical measurements, which may include errors. 相似文献
6.
T. B. Yanovskaya 《Pure and Applied Geophysics》1996,148(1-2):319-336
A method of estimating the lateral velocity variations in the 2D case using the data on deviations of wave paths from straight lines (or great circle paths in the spherical case) is proposed. The method is designed for interpretation of azimuthal anomalies of surface waves which contain information on lateral variations of phase velocities supplementary to that obtained from travel-time data in traditional surface wave tomography. In the particular 2D case, when the starting velocity is constant (c 0) and velocity perturbations δc(x,y) are sufficiently smooth, a relationship between azimuthal anomaly δα and velocity perturbations δc(x,y) can be obtained by approximate integration of the ray tracing system, which leads to the following functional: $$\delta \alpha = \int_0^L {\frac{{s(\nabla m,n_0 )}}{L}} ds,$$ wherem(x,y)=δc(x,y)/c 0,L is the length of the ray,n 0 is a unit vector perpendicular to the ray in the starting model, integration being performed from the source to the receiver. This formula is valid for both plane and spherical cases. Numerical testing proves that for a velocity perturbation which does not exceed 10%, this approximation is fairly good. Lateral variations of surface wave velocities satisfy these assumptions. Therefore this functional may be used in surface wave tomography. For the determination ofm(x,y) from a set ofδα k corresponding to different wave paths, the solution is represented as a series in basis functions, which are constructed using the criterion of smoothness of the solution proposed byTarantola andNersessian (1984) for time-delay tomography problems. Numerical testing demonstrates the efficiency of the tomography method. The method is applied to the reconstruction of lateral variations of Rayleigh wave phase velocities in the Carpathian-Balkan region. The variations of phase velocities obtained from data on azimuthal anomalies are found to be correlated with group-velocity variations obtained from travel-time data. 相似文献
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井间地震射线层析成像 总被引：3，自引：0，他引：3
本文采用射线走时对井间介质的地震波速进行层析成像，反演出井间介质的异常分布和构造．作者用快速弯曲射线迫踪法求解初值问题，用两步法和插值逼近法结合求解两点问题，避免了复杂运算，提高了运算效率和精度．反问题的数值计算用ＬＳＱＲ法．为了求取速度任意分布、对比度大的较为复杂介质模型的槽确初至时，本文采用动态程序法。该法灵活不受地质界面条件约束，且对介质速度分布未加任何限制。本文给出了几个算例．文中层析成像试验结果表明，此种层析成像算法是成功和有效的。 相似文献
10.
The standard ray theory (RT) for inhomogeneous anisotropic media does not work properly or even fails when applied to S-wave
propagation in inhomogeneous weakly anisotropic media or in the vicinity of shear-wave singularities. In both cases, the two
shear waves propagate with similar phase velocities. The coupling ray theory was proposed to avoid this problem. In it, amplitudes
of the two S waves are computed by solving two coupled, frequency-dependent differential equations along a common S-wave ray.
In this paper, we test the recently developed approximation of coupling ray theory (CRT) based on the common S-wave rays obtained
by first-order ray tracing (FORT). As a reference, we use the Fourier pseudospectral method (FM), which does not suffer from
the limitations of the ray method and yields very accurate results. We study the behaviour of shear waves in weakly anisotropic
media as well as in the vicinity of intersection, kiss or conical singularities. By comparing CRT and RT results with results
of the FM, we demonstrate the clear superiority of CRT over RT in the mentioned regions as well as the dangers of using RT
there. 相似文献
11.
Emil Blias 《Geophysical Prospecting》2013,61(3):574-581
I introduce a new explicit form of vertical seismic profile (VSP) traveltime approximation for a 2D model with non‐horizontal boundaries and anisotropic layers. The goal of the new approximation is to dramatically decrease the cost of time calculations by reducing the number of calculated rays in a complex multi‐layered anisotropic model for VSP walkaway data with many sources. This traveltime approximation extends the generalized moveout approximation proposed by Fomel and Stovas. The new equation is designed for borehole seismic geometry where the receivers are placed in a well while the sources are on the surface. For this, the time‐offset function is presented as a sum of odd and even functions. Coefficients in this approximation are determined by calculating the traveltime and its first‐ and second‐order derivatives at five specific rays. Once these coefficients are determined, the traveltimes at other rays are calculated by this approximation. Testing this new approximation on a 2D anisotropic model with dipping boundaries shows its very high accuracy for offsets three times the reflector depths. The new approximation can be used for 2D anisotropic models with tilted symmetry axes for practical VSP geometry calculations. The new explicit approximation eliminates the need of massive ray tracing in a complicated velocity model for multi‐source VSP surveys. This method is designed not for NMO correction but for replacing conventional ray tracing for time calculations. 相似文献
12.
Kirchhoff-Helmholtz积分方法推广到远震转换波的合成地震图的计算,其优点是,能够计算复杂界面的地震波。通过与反射率法及动力学射线追踪的对比,表明KH积分方法能很好地模拟远震转换波震相,且精度较高。KH积分方法能够计算任意复杂界面的地震波,是一种研究地壳上地幔结构的有效方法。 相似文献
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I reformulate well-established systems for kinematic and dynamic ray tracing in 3D heterogeneous media with arbitrary anisotropy. Matrices of size 3 × 3, e.g. the Christoffel matrix, are substituted by six-component vectors, and the Christoffel matrix elements are expressed explicitly in terms of the elements of the 6 × 6 matrix of elastic coefficients, written in Voigt notation. Thereby, I find it easier to see the effects on the ray tracing systems of vanishing elastic coefficients and Christoffel matrix elements and of vanishing derivatives with respect to spatial coordinates and slowness vector components. The eigenvalue of the current wave and its derivatives with respect to the ray parameters are included explicitly, which may be favorable for ray tracing processes optimized with respect to speed. With the ANRAY program as a reference, I show that the new formulation requires less optimization than the conventional one. 相似文献
14.
A. Hanyga 《Pure and Applied Geophysics》2000,157(5):679-717
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Tomography is the inversion of boundary projections to reconstruct the internal characteristics of the medium between the source and detector boreholes. Tomography is used to image the structure of geological formations and localized inhomogenieties. This imaging technique may be applied to either seismic or electromagnetic data, typically recorded as transmission measurements between two or more boreholes. Algebraic algorithms are error-driven solutions where the goal is to minimize the error between measured and predicted projections. The purpose of this study is to assess the effect of the ray propagation model, the measurement errors, and the error functions on the resolving ability of algebraic algorithms. The problem under consideration is the identification of a two-dimensional circular anomaly surveyed using crosshole measurements. The results show that: (1) convergence to the position of the circular anomaly in depth between vertical boreholes is significantly better than for convergence in the horizontal direction; (2) error surfaces may not be convex, even in the absence of measurement and model errors; (3) the distribution of information content significantly affects the convexity of averaging error functions; (4) measurement noise and model inaccuracy manifest in increased residuals and in reduced convergence gradients near optimum convergence; (5) the maximum ray error function increases convergence gradients compared with the average error function, and is unaffected by the distribution of information content; however, it has higher probability of local minima. Therefore, inversions based on the minimization of the maximum ray error may be advantageous in crosshole tomography but it requires smooth projections. These results are applicable to both electromagnetic and seismic data for wavelengths significantly smaller than the size of anomalies. 相似文献
16.
The common-ray approximation eliminates problems with ray tracing through S-wave singularities and also considerably simplifies
the numerical algorithm of the coupling ray theory for S waves, but may introduce errors in travel times due to the perturbation
from the common reference ray. These travel-time errors can deteriorate the coupling-ray-theory solution at high frequencies.
It is thus of principal importance for numerical applications to estimate the errors due to the common-ray approximation applied.
The anisotropic-common-ray approximation of the coupling ray theory is more accurate than the isotropic-common-ray approximation.
We derive the equations for estimating the travel-time errors due to the anisotropic-common-ray (and also isotropic-common-ray)
approximation of the coupling ray theory. The errors of the common-ray approximations are calculated along the anisotropic
common rays in smooth velocity models without interfaces. The derivation is based on the general equations for the second-order
perturbations of travel time. 相似文献
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对于微地震正演模拟,本文以射线追踪的原理为基础,对两点间的射线追踪问题进行了研究,应用二分算法、改进二分算法和微变网格算法对水平层状匀速模型、弯曲层状匀速模型和复杂地质模型进行射线追踪,使得计算效率和适用范围都得到了很大的改善.文中对每种算法误差范围和计算效率进行了对比验证,对于不同的地质模型,选用合适的算法才能在计算速度和精度上得到双重保证,最后正演模拟了多波三分量记录.在模型建立上引入了超薄层概念,并在前人模拟的直达波、透射波、反射波基础上拟了折射波,使正演模拟的多波场信息更丰富.文中的应用实例及模型结果表明:与二分法相比,改进二分法能够对弯曲界面进行射线追踪,并能保证结果的精度.弯曲层状模型中,改进二分法与微变网格法相比计算速度有显著提高,能够应用到资料的反演中. 相似文献
19.
Common midpoint data are now being collected with ever increasing source-receiver offsets. For wide aperture seismic data classical methods of interpretation fail, since velocity analyses and signal-to-noise enhancement methods based on hyperbolic traveltime curves are no longer appropriate. Therefore, the goals of increased velocity resolution and signal enhancement, which motivate the increase in offset, are not achieved. Approximate methods, involving higher order traveltime curves or extrapolations, have been developed for velocity analysis but these are ineffective in the presence of refracted arrivals, and lack a physical basis. These problems can be minimized by transforming the observational data to the domain of intercept or vertical delay time τ and horizontal ray parameter p. In this domain headwave refractions are collapsed into points and both near vertical and wide angle reflections can be analyzed simultaneously to derive velocity-depth information, even in the presence of velocity gradients or low velocity zones. 相似文献
20.
The objective is to provide, in one single paper, a complete collection of equations governing kinematic and dynamic ray tracing related to a symmetry plane of an anisotropic medium. Well known systems for kinematic ray tracing and in-plane dynamic ray tracing are reformulated for the purpose of clarity, by taking advantage of a vector representation of the Christoffel matrix elements and related quantities. A generalized formula is derived for the integrand in out-of-plane dynamic ray tracing, pertaining to a monoclinic medium. Integrands corresponding to non-tilted orthorhombic and transversely isotropic media are obtained as special cases. 相似文献