共查询到20条相似文献，搜索用时 31 毫秒
1.
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
2.
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
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.
5.
Improving modelling and inversion in refraction seismics with a first-order Eikonal solver 总被引：1，自引：0，他引：1
Isabelle Lecomte Håvar Gjøystdal ers Dahle & Ole Christian Pedersen 《Geophysical Prospecting》2000,48(3):437-454
A first-order Eikonal solver is applied to modelling and inversion in refraction seismics. The method calculates the traveltime of the fastest wave at any point of a regular grid, including head waves as used in refraction. The efficiency, robustness and flexibility of the method give a very powerful modelling tool to find both traveltimes and raypaths. Comparisons with finite-difference data show the validity of the results. Any arbitrarily complex model can be studied, including the exact topography of the surface, thus avoiding static corrections. Later arrivals are also obtained by applying high-slowness masks over the high-velocity zones. Such an efficient modelling tool may be used interactively to invert for the model, but a better method is to apply the refractor-imaging principle of Hagedoorn to obtain the refractors from the picked traveltime curves. The application of this principle has already been tried successfully by previous authors, but they used a less well-adapted Eikonal solver. Some of their traveltimes were not correct in the presence of strong velocity variations, and the refractor-imaging principle was restricted to receiver lines along a plane surface. With the first-order Eikonal solver chosen, any topography of the receiving surface can be considered and there is no restriction on the velocity contrast. Based on synthetic examples, the Hagedoorn principle appears to be robust even in the case of first arrivals associated with waves diving under the refractor. The velocities below the refractor can also be easily estimated, parallel to the imaging process. In this way, the model can be built up successively layer by layer, the refractor-imaging and velocity-mapping processes being performed for each identified refractor at a time. The inverted model could then be used in tomographic inversions because the calculated traveltimes are very close to the observed traveltimes and the raypaths are available. 相似文献
6.
Geometrical spreading plays an important role for amplitude preserving migration, which is a very time-consuming process. In order to achieve efficiency in terms of computational time and, particularly, storage space, we propose a method to determine geometrical spreading from coarsely gridded traveltime tables. The method is based on a hyperbolic traveltime expansion and provides also a fast and accurate algorithm for the interpolation of traveltimes, including the interpolation of complete shots. Examples demonstrate the applicability of the method to isotropic and anisotropic media. 相似文献
7.
8.
A new ray-tracing method called linear traveltime interpolation (LTI) is proposed. This method computes traveltimes and raypaths in a 2D velocity structure more rapidly and accurately than other conventional methods. The LTI method is formulated for a 2D cell model, and calculations of traveltimes and raypaths are carried out only on cell boundaries. Therefore a raypath is considered to be always straight in a cell with uniform velocity. This approach is suitable to tomography analysis. The algorithm of LTI consists of two separate steps: step 1 calculates traveltimes on all cell boundaries; step 2 traces raypaths for all pairs of receivers and the shot. A traveltime at an arbitrary point on a cell boundary is assumed to be linearly interpolated between traveltimes at the adjacent discrete points at which we calculate traveltimes. Fermat's principle is used as the criterion for choosing the correct traveltimes and raypaths from several candidates routinely. The LTI method has been compared numerically with the shooting method and the finite-difference method (FDM) of the eikonal equation. The results show that the LTI method has great advantages of high speed and high accuracy in the calculation of both traveltimes and raypaths. The LTI method can be regarded as an advanced version of the conventional FDM of the eikonal equation because the formulae of FDM are independently derived from LTI. In the process of derivation, it is shown theoretically that LTI is more accurate than FDM. Moreover in the LTI method, we can avoid the numerical instability that occurs in Vidale's method where the velocity changes abruptly. 相似文献
9.
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
10.
11.
Field static corrections in general need be applied to all onshore seismic reflection data to eliminate the disturbing effects a weathering layer or near-surface low velocity zone has on the continuity of deep seismic reflections. The traveltimes of waves refracted at the bottom of the low velocity zone (or intermediate refracting interfaces) can often be observed as first breaks on shot records and used to develop a laterally inhomogeneous velocity model for this layer, from which the field static corrections can then be obtained. A simple method is described for computing accurate field statics from first breaks. It is based on a linearization principal for traveltimes and leads to the algorithms that are widely and successfully applied within the framework of seismic tomography. We refine an initial model for the low velocity layer (estimated by a standard traveltime inversion technique) by minimizing the errors between the observed first arrivals on field records and those computed by ray theory through an initial model of the low velocity layer. Thus, one can include more lateral velocity variations within the low velocity layers, which are important to obtain good field static corrections. Traditional first break traveltime inversion methods cannot, in general, provide such refined velocity values. The technique is successfully applied to seismic data from the Amazon Basin. It is based on a simple model for the low velocity layer that consists of an undulating earth surface and one planar horizontal refractor overlain by a laterally changing velocity field. 相似文献
12.
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
13.
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
14.
The first-order perturbation theory is used for fast 3D computation of quasi-compressional (qP)-wave traveltimes in arbitrarily anisotropic media. For efficiency we implement the perturbation approach using a finite-difference (FD) eikonal solver. Traveltimes in the unperturbed reference medium are computed with an FD eikonal solver, while perturbed traveltimes are obtained by adding a traveltime correction to the traveltimes of the reference medium. The traveltime correction must be computed along the raypath in the reference medium. Since the raypath is not determined in FD eikonal solvers, we approximate rays by linear segments corresponding to the direction of the phase normal of plane wavefronts in each cell. An isotropic medium as a reference medium works well for weak anisotropy. Using a medium with ellipsoidal anisotropy as a background medium in the perturbation approach allows us to consider stronger anisotropy without losing computational speed. The traveltime computation in media with ellipsoidal anisotropy using an FD eikonal solver is fast and accurate. The relative error is below 0.5% for the models investigated in this study. Numerical examples show that the reference model with ellipsoidal anisotropy allows us to compute the traveltime for models with strong anisotropy with an improved accuracy compared with the isotropic reference medium. 相似文献
15.
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
16.
The presence of triplications (caustics) can be a serious problem in seismic data processing and analysis. The traveltime curve becomes multi‐valued and the geometrical spreading correction factor tends to zero due to energy focusing. We analyse the conditions for the qSV‐wave triplications in a homogeneous transversely isotropic medium with vertical symmetry axis. The proposed technique can easily be extended to the case of horizontally layered vertical symmetry axis medium. We show that the triplications of the qSV‐wave in a multilayered medium imply certain algebra. We illustrate this algebra on a two‐layer vertical symmetry axis model. 相似文献
17.
Chao-ying Bai Tao Wang Shang-bei Yang Xing-wang Li Guo-jiao Huang 《Journal of Seismology》2016,20(2):475-494
Traditional traveltime inversion for anisotropic medium is, in general, based on a “weak” assumption in the anisotropic property, which simplifies both the forward part (ray tracing is performed once only) and the inversion part (a linear inversion solver is possible). But for some real applications, a general (both “weak” and “strong”) anisotropic medium should be considered. In such cases, one has to develop a ray tracing algorithm to handle with the general (including “strong”) anisotropic medium and also to design a non-linear inversion solver for later tomography. Meanwhile, it is constructive to investigate how much the tomographic resolution can be improved by introducing the later arrivals. For this motivation, we incorporated our newly developed ray tracing algorithm (multistage irregular shortest-path method) for general anisotropic media with a non-linear inversion solver (a damped minimum norm, constrained least squares problem with a conjugate gradient approach) to formulate a non-linear inversion solver for anisotropic medium. This anisotropic traveltime inversion procedure is able to combine the later (reflected) arrival times. Both 2-D/3-D synthetic inversion experiments and comparison tests show that (1) the proposed anisotropic traveltime inversion scheme is able to recover the high contrast anomalies and (2) it is possible to improve the tomographic resolution by introducing the later (reflected) arrivals, but not as expected in the isotropic medium, because the different velocity (qP, qSV and qSH) sensitivities (or derivatives) respective to the different elastic parameters are not the same but are also dependent on the inclination angle. 相似文献
18.
We describe two practicable approaches for an efficient computation of seismic traveltimes and amplitudes. The first approach is based on a combined finite‐difference solution of the eikonal equation and the transport equation (the ‘FD approach’). These equations are formulated as hyperbolic conservation laws; the eikonal equation is solved numerically by a third‐order ENO–Godunov scheme for the traveltimes whereas the transport equation is solved by a first‐order upwind scheme for the amplitudes. The schemes are implemented in 2D using polar coordinates. The results are first‐arrival traveltimes and the corresponding amplitudes. The second approach uses ray tracing (the ‘ray approach’) and employs a wavefront construction (WFC) method to calculate the traveltimes. Geometrical spreading factors are then computed from these traveltimes via the ray propagator without the need for dynamic ray tracing or numerical differentiation. With this procedure it is also possible to obtain multivalued traveltimes and the corresponding geometrical spreading factors. Both methods are compared using the Marmousi model. The results show that the FD eikonal traveltimes are highly accurate and perfectly match the WFC traveltimes. The resulting FD amplitudes are smooth and consistent with the geometrical spreading factors obtained from the ray approach. Hence, both approaches can be used for fast and reliable computation of seismic first‐arrival traveltimes and amplitudes in complex models. In addition, the capabilities of the ray approach for computing traveltimes and spreading factors of later arrivals are demonstrated with the help of the Shell benchmark model. 相似文献
19.
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
20.
Introduction The calculation of seismic wave traveltimes is a basic and the most important step in tomo-graphy, seismic wave forward modeling and Kirchhoff prestack depth migration. Limitations withtraditional ray tracing fall into four categories. a) Analytical methods can only realize ray tracingfor simply varying velocity fields, so they have relative small applied-range; b) Shooting methodsof ray tracing can cause shadow zones. When the shadow zones exist the method will invalid; c)… 相似文献