共查询到20条相似文献，搜索用时 31 毫秒
1.
A fast and global two point low storage optimization technique for tracing rays in 2D and 3D isotropic media 总被引：1，自引：0，他引：1
We present the problem of tracing rays in 2D and 3D heterogeneous isotropic media as a set of optimization problems. Each optimization problem is obtained by applying Fermat's principle to an approximation of the travel time equation from a fixed source to a fixed receiver. We assume a piecewise linear ray path that simplifies the computations of the problem, in the same way Mao and Stuart suggested in a very recent paper. Here, instead, the reflector geometry and the velocity function are computed by using nonuniformly biharmonic splines. On the other hand, to solve the optimization problem we use the Global Spectral Gradient method. This recent developed optimization scheme is a low storage optimization technique that requires very few floating point operations. It only requires the gradient of the travel time function, and it is global because it converges independently of the initial guess, that is, it does not require a close initial ray path. These three properties of the optimization method and the assumption of piecewise linear rays make this ray tracing scheme a very fast, global and effective method when estimating velocities via tomography. Moreover, in a homogeneous stratified or dipped media, any solution of the optimization problem is the best solution, i.e., it is the global minimum, no matter what numerical approach is used. We present some numerical results that show the computational advantages and the performance of this ray tracing in homogeneous and heterogeneous media. 相似文献
2.
Common-ray tracing and dynamic ray tracing for S waves in a smooth elastic anisotropic medium 总被引：1，自引：0，他引：1
L. Klimeš 《Studia Geophysica et Geodaetica》2006,50(3):449-461
Anisotropic common S-wave rays are traced using the averaged Hamiltonian of both S-wave polarizations. They represent very
practical reference rays for calculating S waves by means of the coupling ray theory. They eliminate problems with anisotropic-ray-theory
ray tracing through some S-wave slowness-surface singularities and also considerably simplify the numerical algorithm of the
coupling ray theory for S waves.
The equations required for anisotropic-common-ray tracing for S waves in a smooth elastic anisotropic medium, and for corresponding
dynamic ray tracing in Cartesian or ray-centred coordinates, are presented. The equations, for the most part generally known,
are summarized in a form which represents a complete algorithm suitable for coding and numerical applications. 相似文献
3.
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
4.
射线追踪是地震波走时层析成像的基础,射线空间位置的准确性及射线走时的精度决定了层析成像的可靠性.本文根据哈密尔顿系统可以有效提高程函方程解稳定性的特性,采用辛几何算法（SAM-Symplectic Algorithm Method）及二维三次卷积插值技术进行地震波射线追踪.由于采用了SAM算法,保证了地震波波前精度,提高了射线空间位置的准确性.数值模拟结果表明SAM既能保证哈密尔顿系统的稳定性又具有运算速度快的特点,提高了射线追踪的计算精度. 相似文献
5.
Boundary-value problems (BVPs) for seismic rays generally have multiple solutions. In practical applications the number of solutions can be large. The algorithm presented below solves a one-parameter family of BVPs and makes it easy to obtain all the solutions of a BVP. 相似文献
6.
3D multivalued travel time and amplitude maps 总被引：2，自引：0，他引：2
An algorithm for computing multivalued maps for travel time, amplitude and any other ray related variable in 3D smooth velocity models is presented. It is based on the construction of successive isochrons by tracing a uniformly dense discrete set of rays by fixed travel-time steps. Ray tracing is based on Hamiltonian formulation and includes computation of paraxial matrices. A ray density criterion ensures uniform ray density along isochrons over the entire ray field including caustics. Applications to complex models are shown. 相似文献
7.
Traveltime computation by wavefront-orientated ray tracing 总被引：1，自引：0，他引：1
For multivalued traveltime computation on dense grids, we propose a wavefront‐orientated ray‐tracing (WRT) technique. At the source, we start with a few rays which are propagated stepwise through a smooth two‐dimensional (2D) velocity model. The ray field is examined at wavefronts and a new ray might be inserted between two adjacent rays if one of the following criteria is satisfied: (1) the distance between the two rays is larger than a predefined threshold; (2) the difference in wavefront curvature between the rays is larger than a predefined threshold; (3) the adjacent rays intersect. The last two criteria may lead to oversampling by rays in caustic regions. To avoid this oversampling, we do not insert a ray if the distance between adjacent rays is smaller than a predefined threshold. We insert the new ray by tracing it from the source. This approach leads to an improved accuracy compared with the insertion of a new ray by interpolation, which is the method usually applied in wavefront construction. The traveltimes computed along the rays are used for the estimation of traveltimes on a rectangular grid. This estimation is carried out within a region bounded by adjacent wavefronts and rays. As for the insertion criterion, we consider the wavefront curvature and extrapolate the traveltimes, up to the second order, from the intersection points between rays and wavefronts to a gridpoint. The extrapolated values are weighted with respect to the distances to wavefronts and rays. Because dynamic ray tracing is not applied, we approximate the wavefront curvature at a given point using the slowness vector at this point and an adjacent point on the same wavefront. The efficiency of the WRT technique is strongly dependent on the input parameters which control the wavefront and ray densities. On the basis of traveltimes computed in a smoothed Marmousi model, we analyse these dependences and suggest some rules for a correct choice of input parameters. With suitable input parameters, the WRT technique allows an accurate traveltime computation using a small number of rays and wavefronts. 相似文献
8.
Petr Bulant 《Pure and Applied Geophysics》1996,148(3-4):421-447
Algorithm for determination of all two-point rays of a given elementary wave by means of the shooting method is presented. The algorithm is designed for general 3-D models composed of inhomogeneous geological blocks separated by curved interfaces. It is independent of the initial conditions for rays and of the initial-value ray tracer. The algorithm described has been coded in Fortran 77, using subroutine packages MODEL and CRT for model specification and for initial-value ray tracing. 相似文献
9.
本文提出了在计算机上实现分块三维地壳模型及利用加权最小二乘拟合生成平缓光滑的三维速度函数的方法,给出了适用于分块、块内速度连续变化的三维模型中Cauchy射线追踪的新算法,简介了基于上述方法反射线的基本理论所编制的合成三维理论地震图的程序包RSSGTD.给出的两个盆地状模型的算例表明,所使用的模型生成方法具有模拟复杂地壳结构的能力;与三维样条函数方法比较,最小二乘拟合方法能给出更加适合射线方法合成地震图计算的速度函数,并且内存小、计算速度快;所给出的Cauchy射线追踪算法能够适合块状模型中任何体波射线的追踪. 相似文献
10.
Seismic ray path variations in a 3D global velocity model 总被引：2，自引：0，他引：2
A three-dimensional (3D) ray tracing technique is used to investigate ray path variations of P, PcP, pP and PP phases in a global tomographic model with P wave velocity changing in three dimensions and with lateral depth variations of the Moho, 410 and 660 km discontinuities. The results show that ray paths in the 3D velocity model deviate considerably from those in the average 1D model. For a PcP wave in Western Pacific to East Asia where the high-velocity (1-2%) Pacific slab is subducting beneath the Eurasian continent, the ray path change amounts to 27 km. For a PcP ray in South Pacific where very slow (−2%) velocity anomalies (the Pacific superplume) exist in the whole mantle, the maximum ray path deviation amounts to 77 km. Ray paths of other phases (P, pP, PP) are also displaced by tens of kilometers. Changes in travel time are as large as 3.9 s. These results suggest that although the maximal velocity anomalies of the global tomographic model are only 1-2%, rays passing through regions with strong lateral heterogeneity (in velocity and/or discontinuity topography) can have significant deviations from those in a 1D model because rays have very long trajectories in the global case. If the blocks or grid nodes adopted for inversion are relatively large (3-5°) and only a low-resolution 3D model is estimated, 1D ray tracing may be feasible. But if fine blocks or grid nodes are used to determine a high-resolution model, 3D ray tracing becomes necessary and important for the global tomography. 相似文献
11.
KLAUS HELBIG 《Geophysical Prospecting》1990,38(2):189-220
Wavefront charts in anisotropic gradient media are a useful tool in ray geometric constructions, particular in shear-wave exploration. They can be constructed by: (i) a family of wavefronts that contains a vertical plane as member - it is convenient to choose constant time increments; (ii) tracing one ray that makes everywhere the angle with the normal to the wavefront that is required by the anisotropy of the medium; (iii) scaling this ray to obtain a set of rays with different ray parameters; (iv) shifting these rays (with wavefront elements attached) so that they pass through a common source point; (v) interpolating the wavefronts between the elements. The construction is particularly simple in linear-gradient media, since here all members of the family of wavefronts are planes. Since the ray makes everywhere the angle prescribed by the anisotropy with the normal of the (plane) wavefronts, the ray has the shape of the slowness curve rotated by ?π/2. For isotropic media the slowness curve is a circle, and thus rays are circular arcs. The circles themselves intersect in the source point and in a second point above the surface of the earth. This provides a simple proof that wavefronts emanating from a point source in an isotropic linear-gradient medium are spheres: inversion of the set of circular rays with the source as centre maps the pencil of circular rays into a pencil of straight lines passing through a point. A pencil of concentric spheres around this point is perpendicular to the pencil of straight lines. On inverting back the pencil of spheres is mapped into another pencil of spheres that is perpendicular to the circular rays. 相似文献
12.
Paraxial ray methods for anisotropic inhomogeneous media 总被引：1，自引：0，他引：1
A new formalism of surface-to-surface paraxial matrices allows a very general and flexible formulation of the paraxial ray theory, equally valid in anisotropic and isotropic inhomogeneous layered media. The formalism is based on conventional dynamic ray tracing in Cartesian coordinates along a reference ray. At any user-selected pair of points of the reference ray, a pair of surfaces may be defined. These surfaces may be arbitrarily curved and oriented, and may represent structural interfaces, data recording surfaces, or merely formal surfaces. A newly obtained factorization of the interface propagator matrix allows to transform the conventional 6 × 6 propagator matrix in Cartesian coordinates into a 6 × 6 surface-to-surface paraxial matrix. This matrix defines the transformation of paraxial ray quantities from one surface to another. The redundant non-eikonal and ray-tangent solutions of the dynamic ray-tracing system in Cartesian coordinates can be easily eliminated from the 6 × 6 surface-to-surface paraxial matrix, and it can be reduced to 4 × 4 form. Both the 6 × 6 and 4 × 4 surface-to-surface paraxial matrices satisfy useful properties, particularly the symplecticity. In their 4 × 4 reduced form, they can be used to solve important boundary-value problems of a four-parametric system of paraxial rays, connecting the two surfaces, similarly as the well-known surface-to-surface matrices in isotropic media in ray-centred coordinates. Applications of such boundary-value problems include the two-point eikonal, relative geometrical spreading, Fresnel zones, the design of migration operators, and more. 相似文献
13.
The recursive nature of rays in blocky models can be exploited to solve some difficult problems in seismic modelling. Each segment of a ray travels from an initial point up to a reflecting interface, where it is split into reflected and transmitted ray segments, which each continue in a similar way. The tree structure that thus emanates is conveniently handled by a recursive scheme. Recursion allows an automatic generation of all phases on a seismogram, together with all information necessary to analyse or select them. By operating recursively with a ray cell, bounded by a pair of vicinal rays in 2D, or a triplet of vicinal rays in 3D, and two successive isochrons, the two-point ray-tracing problem is reduced to a simple interpolation. Also, the cellular approach allows for a stable and robust evaluation of dynamic ray quantities without any paraxial tracing, which is cumbersome in blocky models of realistic complexity. Geometric shadows are filled by recursively generated diffractions. The recursive ray tracer has found applications in the fast computation of Green's functions in target-oriented inversion and in phase identification in VSP. 相似文献
14.
立体层析成像是一种新的地震反射波层析成像方法,能为叠前深度偏移提供较为精确的宏观速度模型。本文研究了立体层析成像的实现方法,包括斜率与走时数据的拾取、离散速度模型构建和初始化、射线参数的确定、斜率和走时及射线计算以及反演问题解法等,建立立体层析成像的算法流程。并通过对Marmousi模型试验,对立体层析成像运行所需的主要参数,如初始速度模型、拾取数据量、离散网格尺寸、速度平滑权重等进行测试和分析,总结这些不同参数对立体层析反演结果的影响规律,用以指导生产实践。 相似文献
15.
We present a new ray bending approach, referred to as the Eigenray method, for solving two‐point boundary‐value kinematic and dynamic ray tracing problems in 3D smooth heterogeneous general anisotropic elastic media. The proposed Eigenray method is aimed to provide reliable stationary ray path solutions and their dynamic characteristics, in cases where conventional initial‐value ray shooting methods, followed by numerical convergence techniques, become challenging. The kinematic ray bending solution corresponds to the vanishing first traveltime variation, leading to a stationary path between two fixed endpoints (Fermat's principle), and is governed by the nonlinear second‐order Euler–Lagrange equation. The solution is based on a finite‐element approach, applying the weak formulation that reduces the Euler–Lagrange second‐order ordinary differential equation to the first‐order weighted‐residual nonlinear algebraic equation set. For the kinematic finite‐element problem, the degrees of freedom are discretized nodal locations and directions along the ray trajectory, where the values between the nodes are accurately and naturally defined with the Hermite polynomial interpolation. The target function to be minimized includes two essential penalty (constraint) terms, related to the distribution of the nodes along the path and to the normalization of the ray direction. We distinguish between two target functions triggered by the two possible types of stationary rays: a minimum traveltime and a saddle‐point solution (due to caustics). The minimization process involves the computation of the global (all‐node) traveltime gradient vector and the traveltime Hessian matrix. The traveltime Hessian is used for the minimization process, analysing the type of the stationary ray, and for computing the geometric spreading of the entire resolved stationary ray path. The latter, however, is not a replacement for the dynamic ray tracing solution, since it does not deliver the geometric spreading for intermediate points along the ray, nor the analysis of caustics. Finally, we demonstrate the efficiency and accuracy of the proposed method along three canonical examples. 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
17.
The numerical tracing of short ray segments and interpolation of new rays between these ray segments are central constituents of the wavefront construction method. In this paper the details of the ray tracing and ray-interpolation procedures are described. The ray-tracing procedure is based on classical ray theory (high-frequency approximation) and it is both accurate and efficient. It is able to compute both kinematic and dynamic parameters at the endpoint of the ray segments, given the same set of parameters at the starting point of the ray. Taylor series are used to approximate the raypath so that the kinematic parameters (new position and new ray tangent) may be found, while a staggered finite-difference approximation gives the dynamic parameters (geometrical spreading). When divergence occurs in some parts of the wavefront, new rays are interpolated. The interpolation procedure uses the kinematic and dynamic parameters of two parent rays to estimate the initial parameters of a new ray on the wavefront between the two rays. Third-order (cubic) interpolation is used for interpolation of position, ray tangent and take-off vector from the source) while linear interpolation is used for the geometrical spreading parameters. 相似文献
18.
A. Hanyga 《Pure and Applied Geophysics》2000,157(5):679-717
19.
针对线性走时插值算法(LTI)不能正确追踪逆向传播射线的问题, 目前已提出多种改进算法, 如扩张收缩LTI算法、 循环计算LTI算法、 动态网络最短路径射线追踪算法等, 但这些算法的计算效率普遍偏低. 在分析各种改进LTI算法的优劣后, 本文提出了改进动态网络最短路径射线追踪算法. 该改进算法依据波的传播规律以及LTI算法的基本方程, 排除动态网络最短路径射线追踪算法中大量冗余节点计算, 并采用传统的二叉树堆排序算法对波前阵列节点进行管理. 数值算例表明, 本文提出的改进算法具有较高的计算效率, 其计算效率是动态网络最短路径射线追踪算法的4.5—30倍, 是原始LTI算法的2—6.5倍; 当动态网络最短路径射线追踪算法采用堆排序算法时, 改进算法的计算效率是其3.5—15倍. 相似文献
20.
The coupling ray theory is usually applied to anisotropic common reference rays, but it is more accurate if it is applied to reference rays which are closer to the actual wave paths. If we know that a medium is close to uniaxial (transversely isotropic), it may be advantageous to trace reference rays which resemble the SH–wave and SV–wave rays. This paper is devoted to defining and tracing these SH and SV reference rays of elastic S waves in a heterogeneous generally anisotropic medium which is approximately uniaxial (approximately transversely isotropic), and to the corresponding equations of geodesic deviation (dynamic ray tracing). All presented equations are simultaneously applicable to ordinary and extraordinary reference rays of electromagnetic waves in a generally bianisotropic medium which is approximately uniaxially anisotropic. The improvement of the coupling–ray–theory seismograms calculated along the proposed SH and SV reference rays, compared to the coupling–ray–theory seismograms calculated along the anisotropic common reference rays, has already been numerically demonstrated by the authors in four approximately uniaxial velocity models. 相似文献