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1.
振幅随偏移距变化是描述储层特征的重要方法之一,保幅偏移方法就是使偏移剖面能够反映出振幅随偏移距的变化.本论文中的保幅偏移是以走时为基础,主要的方法是采用走时的双曲线展开法,通过走时的二阶空间导数来确定波前曲率.该方法通过建立在大网格上的走时表来确定插值系数,将大网格插值成为较为精细的网格,这样就节省了数据的存储空间.对于相同的网格密度,通过插值来计算走时表比采用程函方程有限差分法直接计算走时要节省5至6倍的时间.走时的插值系数还可以用来计算几何扩散因子、权函数,不仅提高了成像质量,还大大节省了计算时间. 相似文献
2.
三维地震波走时计算技术是三维地震反演、层析成像、偏移成像等诸多地震数据处理技术中非常重要的正演计算工具.为了获得精度高且兼顾效率的三维走时计算方法:首先,在常规双线性插值公式推导过程中,充分利用平面波双线性假设的结论,获得了二元极小值超越方程的解析解,进而推导出了准确的局部走时计算公式,同时构造性地证明了该计算公式满足地震波的传播规律和Eikonal方程;其次,引入迎风差分的基本思想,提出迎风双线性插值的局部走时计算策略,该计算策略能简化算法、提高效率且保证无条件稳定性;然后,将上述计算公式和迎风双线性插值策略与常规快速推进法中的窄带技术结合,获得了一种新的基于快速推进迎风双线性插值法的三维地震波走时计算方法;最后,通过精度和效率分析检验了新算法的精度、效率和正确性,并通过计算实例验证了算法在面对复杂介质时的稳定性和有效性. 相似文献
3.
To carry out a 3D prestack migration of the Kirchhoff type is still a task of enormous computational effort. Its efficiency can be significantly enhanced by employing a fast traveltime interpolation algorithm. High accuracy can be achieved if secondorder spatial derivatives of traveltimes are included in order to account for the curvature of the wavefront. We suggest a hyperbolic traveltime interpolation scheme that permits the determination of the hyperbolic coefficients directly from traveltimes sampled on a coarse grid, thus reducing the requirements in data storage. This approach is closely related to the paraxial ray approximation and corresponds to an extension of the wellknown method to arbitrary heterogeneous and complex media in 3D. Application to various velocity models, including a 3D version of the Marmousi model, confirms the superiority of our method over the popular trilinear interpolation. This is especially true for regions with strong curvature of the local wavefront. In contrast to trilinear interpolation, our method also provides the possibility of interpolating source positions, and it is 56 times faster than the calculation of traveltime tables using a fast finitedifference eikonal solver. 相似文献
4.
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
5.
为了在复杂地表条件下实现地震波走时计算,提出了一种基于线性插值和窄带技术的走时计算新方法.其中,线性插值用于局部走时计算,窄带技术用于局部波前捕获和追踪.为了逼近起伏地表,采用三角网和矩形网相结合的方法对速度模型进行剖分.为了得到局部走时计算公式,利用费马（Fermat）原理和关于入射点位置的限定条件.有关编程实践和数值试验表明：新方法不仅可以有效、灵活地处理地表高程的剧烈变化,而且还具有很好的适应性和稳定性,得到的计算结果满足波前传播规律. 相似文献
6.
The performance of a 3D prestack migration of the Kirchhoff type can be significantly enhanced if the computation of the required stacking surface is replaced by an efficient and accurate method for the interpolation of diffraction traveltimes. Thus, input traveltimes need only be computed and stored on coarse grids, leading to considerable savings in CPU time and computer storage. However, interpolation methods based on a local approximation of the traveltime functions fail in the presence of triplications of the wavefront or later arrivals. This paper suggests a strategy to overcome this problem by employing the coefficients of a hyperbolic traveltime expansion to locate triplications and correct for the resulting errors in the interpolated traveltime tables of first and later arrivals. 相似文献
7.
We present a new method of three-dimensional (3-D) seismic ray tracing, based on an improvement to the linear traveltime interpolation (LTI) ray tracing algorithm. This new technique involves two separate steps. The first involves a forward calculation based on the LTI method and the dynamic successive partitioning scheme, which is applied to calculate traveltimes on cell boundaries and assumes a wavefront that expands from the source to all grid nodes in the computational domain. We locate several dynamic successive partition points on a cell's surface, the traveltimes of which can be calculated by linear interpolation between the vertices of the cell's boundary. The second is a backward step that uses Fermat's principle and the fact that the ray path is always perpendicular to the wavefront and follows the negative traveltime gradient. In this process, the first-arriving ray path can be traced from the receiver to the source along the negative traveltime gradient, which can be calculated by reconstructing the continuous traveltime field with cubic B-spline interpolation. This new 3-D ray tracing method is compared with the LTI method and the shortest path method (SPM) through a number of numerical experiments. These comparisons show obvious improvements to computed traveltimes and ray paths, both in precision and computational efficiency. 相似文献
8.
三维复杂山地条件下的各种地震波型的走时计算技术,可以直接用于复杂山地区域地震波运动学特性的分析、地震数据采集观测系统的设计以及直接基于三维复杂地表的地震数据处理技术的研发.为了在三维复杂地表条件下准确、灵活且稳定地计算各种地震波型的走时,提出一种多级次群推进迎风混合法.该算法利用不等距迎风差分法简洁稳定地处理三维复杂地表及附近的局部走时计算问题,利用计算精度不错的迎风双线性插值法处理绝大部分均匀正方体网格中的局部走时计算问题,利用群推进法模拟三维复杂地表条件下地震波前的扩展问题,利用多级次算法处理各种类型的地震波的走时计算问题.算法分析和计算实例表明:新方法具有很好的计算精度与效率,且能灵活稳定地处理三维复杂地表复杂介质条件下的多波型走时计算问题. 相似文献
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11.
Tariq Alkhalifah 《Geophysical Prospecting》2011,59(1):1-9
Kirchhoff 3D prestack migration, as part of its execution, usually requires repeated access to a large traveltime table data base. Access to this data base implies either a memory intensive or I/O bounded solution to the storage problem. Proper compression of the traveltime table allows efficient 3D prestack migration without relying on the usually slow access to the computer hard drive. Such compression also allows for faster access to desirable parts of the traveltime table. Compression is applied to the traveltime field for each source location on the surface on a regular grid using 3D Chebyshev polynomial or cosine transforms of the traveltime field represented in the spherical coordinates or the Celerity domain. We obtain practical compression levels up to and exceeding 20 to 1. In fact, because of the smaller size traveltime table, we obtain exceptional traveltime extraction speed during migration that exceeds conventional methods. Additional features of the compression include better interpolation of traveltime tables and more stable estimates of amplitudes from traveltime curvatures. Further compression is achieved using bit encoding, by representing compression parameters values with fewer bits. 相似文献
12.
Amplitude versus offset information is a key feature to seismic reservoir characterization. Therefore amplitude preserving migration was developed to obtain this information from seismic reflection data. For complex 3-D media, however, this process is computationally expensive. In this paper we present an efficient traveltime based strategy for amplitude preserving migration of the Kirchhoff type. Its foundations are the generation of traveltime tables using a wavefront-oriented ray-tracing technique, and a generalized moveout relation for 3-D heterogeneous media. All required quantities for the amplitude preserving migration are computed from coarsely gridded traveltime tables. The migration includes the interpolation from the coarsely gridded input traveltimes onto the fine migration grid, the computation of amplitude preserving weight functions, and, optionally, the evaluation of an optimized migration aperture. Since ray tracing is employed for the traveltime computation the input velocity model needs to be smooth, i.e. velocity variations of spatial dimensions below the wavelength of the considered reflection signals are removed. Numerical examples on simple generic models validate the technique and an application to the Marmousi model demonstrates its potential to complex media. The major advantage of the traveltime based strategy consists of its computational efficiency by maintaining sufficient accuracy. Considerable savings in storage space (105 and more for 3-D data with respect to no interpolation at all) can be achieved. The computational time for the stack can be substantially reduced (up to 90% in 3-D) with the optimized migration aperture since only those traces are stacked which really contribute to the image point under consideration. 相似文献
13.
Tariq Alkhalifah 《Geophysical Prospecting》2002,50(4):373-382
A linearized eikonal equation is developed for transversely isotropic (TI) media with a vertical symmetry axis (VTI). It is linear with respect to perturbations in the horizontal velocity or the anisotropy parameter η. An iterative linearization of the eikonal equation is used as the basis for an algorithm of finite-difference traveltime computations. A practical implementation of this iterative technique is to start with a background model that consists of an elliptically anisotropic, inhomogeneous medium, since traveltimes for this type of medium can be calculated efficiently using eikonal solvers, such as the fast marching method. This constrains the perturbation to changes in the anisotropy parameter η (the parameter most responsible for imaging improvements in anisotropic media). The iterative implementation includes repetitive calculation of η from traveltimes, which is then used to evaluate the perturbation needed for the next round of traveltime calculations using the linearized eikonal equation. Unlike isotropic media, interpolation is needed to estimate η in areas where the traveltime field is independent of η, such as areas where the wave propagates vertically.
Typically, two to three iterations can give sufficient accuracy in traveltimes for imaging applications. The cost of each iteration is slightly less than the cost of a typical eikonal solver. However, this method will ultimately provide traveltime solutions for VTI media. The main limitation of the method is that some smoothness of the medium is required for the iterative implementation to work, especially since we evaluate derivatives of the traveltime field as part of the iterative approach. If a single perturbation is sufficient for the traveltime calculation, which may be the case for weak anisotropy, no smoothness of the medium is necessary. Numerical tests demonstrate the robustness and efficiency of this approach. 相似文献
Typically, two to three iterations can give sufficient accuracy in traveltimes for imaging applications. The cost of each iteration is slightly less than the cost of a typical eikonal solver. However, this method will ultimately provide traveltime solutions for VTI media. The main limitation of the method is that some smoothness of the medium is required for the iterative implementation to work, especially since we evaluate derivatives of the traveltime field as part of the iterative approach. If a single perturbation is sufficient for the traveltime calculation, which may be the case for weak anisotropy, no smoothness of the medium is necessary. Numerical tests demonstrate the robustness and efficiency of this approach. 相似文献
14.
径向道变换(Radial Trace Transform)是将地震道集振幅值从偏移距一双程旅行时坐标系变换到视速度-双程旅行时坐标系,通过这种坐标系的变换,使相干噪声与有效信号在视速度和频率方面都有效分离.本文在介绍RT变换基本原理基础上,分析了RT变换中两种常用插值方法及其特点.并利用对模拟地震资料的处理,证明了RT域模拟-相减法较其带通滤波法在相干噪声压制与反射信号保持方面具有明显优势.最后,根据噪声特点,通过选择合理RT滤波参数,对实际地震资料进行处理试验,获得了较好的去噪效果,明显提高了资料信噪比,验证了研究方法的有效性. 相似文献
15.
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
16.
Alexey Stovas 《Geophysical Prospecting》2010,58(2):219-227
The factorized velocity model that incorporates both vertical heterogeneity and constant anisotropy is one of the complicated analytical models used in seismic data processing and interpretation. In this paper, I derive the analytic equations for offset, traveltime and relative geometrical spreading for the quasi‐compressional (qP‐) waves that can be used for modelling and inversion of the traveltime parameters. I show that the presence of anelliptic anisotropy usually dominates over the vertical heterogeneity with respect to the non‐hyperbolicity of the factorized velocity model. 相似文献
17.
Fei Li Tao Xu Minghui Zhang Zhenbo Wu Chenglong Wu Zhongjie Zhang Jiwen Teng 《地震科学（英文版）》2014,27(2):127-136
Seismic traveltime tomographic inversion has played an important role in detecting the internal structure of the solid earth. We use a set of blocks to approximate geologically complex media that cannot be well described by layered models or cells. The geological body is described as an aggregate of arbitrarily shaped blocks, which are separated by triangulated interfaces. We can describe the media as homogenous or heterogeneous in each block. We define the velocities at the given rectangle grid points for each block, and the heterogeneous velocities in each block can be calculated by a linear interpolation algorithm. The parameters of the velocity grid positions are independent of the model parameterization, which is advantageous in the joint inversion of the velocities and the node depths of an interface. We implement a segmentally iterative ray tracer to calculate traveltimes in the 3D heterogeneous block models. The damped least squares method is employed in seismic traveltime inversion, which includes the partial derivatives of traveltime with respect to the depths of nodes in the triangulated interfaces and velocities defined in rectangular grids. The numerical tests indicate that the node depths of a triangulated interface and homogeneous velocity distributions can be well inverted in a stratified model. 相似文献
18.
E. BRÜCKL 《Geophysical Prospecting》1987,35(9):973-992
We consider multiply covered traveltimes of first or later arrivals which are gathered along a refraction seismic profile. The two-dimensional distribution of these traveltimes above a coordinate frame generated by the shotpoint axis and the geophone axis or by the common midpoint axis and the offset axis is named a traveltime field. The application of the principle of reciprocity to the traveltime field implies that for each traveltime value with a negative offset there is a corresponding equal value with positive offset. In appendix A procedures are demonstrated which minimize the observational errors of traveltimes inherent in particular traveltime branches or complete common shotpoint sections. The application of the principle of parallelism to an area of the traveltime field associated with a particular refractor can be formulated as a partial differential equation corresponding to the type of the vibrating string. The solution of this equation signifies that the two-dimensional distribution of these traveltimes may be generated by the sum of two one-dimensional functions which depend on the shotpoint coordinate and the geophone coordinate. Physically, these two functions may be interpreted as the mean traveltime branches of the reverse and the normal shot. In appendix B procedures are described which compute these two functions from real traveltime observations by a least-squares fit. The application of these regressed traveltime field data to known time-to-depth conversion methods is straightforward and more accurate and flexible than the use of individual traveltime branches. The wavefront method, the plus-minus method, the generalized reciprocal method and a ray tracing method are considered in detail. A field example demonstrates the adjustment of regressed traveltime fields to observed traveltime data. A time-to-depth conversion is also demonstrated applying a ray tracing method. 相似文献
19.
B. URSIN 《Geophysical Prospecting》1986,34(8):1213-1218
The one-dimensional seismic inverse problem consists of recovering the acoustic impedance (or reflectivity function) as a function of traveltime from the reflection response of a horizontally layered medium excited by a plane-wave impulsive source. Most seismic sources behave like point sources, and the data must be corrected for geometrical spreading before the inversion procedure is applied. This correction is usually not exact because the geometrical spreading is different for primary and multiple reflections. An improved algorithm is proposed which takes the geometrical spreading from a point source into account. The zero-offset reflection response from a stack of homogeneous layers of variable thickness is used to compute the thickness, velocity and density of each layer. This is possible because the geometrical spreading contains additional information about the velocities. 相似文献
20.
对复杂山地介质的非均质性以及介质中地震波运动学特征进行深入研究,对于提高复杂山地区域地震勘探的效果有着重要的理论意义和实际价值.为了研究复杂山地非均质性和该介质中地震波的一些运动特性,提出了一种复杂山地随机介质的建模方法和一种新的射线追踪算法.与常规算法相比,复杂山地随机介质的生成方法采用更贴近实际介质特点的梯度介质作为背景介质,并在模型生成过程中加入地形修正步骤;新提出的GMM-ULTI射线追踪算法,充分融合群推进法、迎风思想、走时插值法的优势,采用先计算走时后追踪射线路径的两步策略完成射线追踪.算法分析与计算实例表明:复杂山地随机介质的生成方法能灵活、精细且更贴近实际地刻画复杂山地介质的非均质特点;新射线追踪算法兼顾精度和效率、能无条件稳定且灵活地适应复杂山地随机介质的特点;同时基于对几个模型试算结果的分析也得出了复杂山地随机介质中的地震波的一些传播规律. 相似文献