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  • 1
    Electronic Resource
    Electronic Resource
    PO Box 1354, 9600 Garsington Road , Oxford OX4 2XG , UK . : Blackwell Science Ltd
    Geophysical prospecting 53 (2005), S. 0 
    ISSN: 1365-2478
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
    Notes: 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.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Science Ltd
    Geophysical prospecting 50 (2002), S. 0 
    ISSN: 1365-2478
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
    Notes: 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 second-order 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 well-known 〈inlineGraphic alt="inline image" href="urn:x-wiley:00168025:GPR0285:GPR_0285_mu1" location="equation/GPR_0285_mu1.gif"/〉 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 5–6 times faster than the calculation of traveltime tables using a fast finite-difference eikonal solver.
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  • 3
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    ISSN: 1365-246X
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences
    Notes: A procedure to evaluate the geometrical properties of the slowness surface for arbitrary anisotropic media is presented. This allows us to use results for computing the displacement field from point sources in general anisotropic media utilizing the Gaussian curvature of the slowness surface of the considered waves. Since the formulae used are based on high frequency asymptotics the procedure gives reliable results as long as no parabolic points of the slowness surface are encountered. Radiation patterns of point sources for models representing rocks in the crust and upper mantle are presented and discussed. The radiation from point sources in anisotropic models is compared with the radiation from point sources in average isotropic models to emphasize the differences. Anisotropy is either caused by aligned cracks (crustal rocks) or by aligned olivine crystals (upper mantle rocks). Considering models of aligned cracks differing only in the physical parameters of the crack material (water or gas) significantly different radiation patterns are obtained. Models with wet cracks exhibit focusing of quasi S-wave energy for some directions whereas this effect is not observed for the corresponding model with dry cracks. The quasi S-wave radiation pattern from explosions are multilobed and the wet crack models exhibit more lobes than the dry crack models. The radiation of single forces in olivine shows strong energy focusing (wave tuning) of quasi S waves, however, for realistic compositions of upper mantle rocks with some 10 per cent of preferentially orientated olivine this wave tuning is less pronounced.
    Type of Medium: Electronic Resource
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