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  • 1
    Digitale Medien
    Digitale Medien
    Residual dip moveout in VTI media (2005)
    PO Box 1354, 9600 Garsington Road , Oxford OX4 2XG , UK . : Blackwell Science Ltd
    Geophysical prospecting 53 (2005), S. 0 
    Details
    ISSN: 1365-2478
    Quelle: Blackwell Publishing Journal Backfiles 1879-2005
    Thema: Geologie und Paläontologie , Physik
    Notizen: Dip-moveout (DMO) correction is often applied to common-offset sections of seismic data using a homogeneous isotropic medium assumption, which results in a fast execution. Velocity-residual DMO is developed to correct for the medium-treatment limitation of the fast DMO. For reasonable-sized velocity perturbations, the residual DMO operator is small, and thus is an efficient means of applying a conventional Kirchhoff approach. However, the shape of the residual DMO operator is complicated and may form caustics. We use the Fourier domain for the operator development part of the residual DMO, while performing the convolution with common-offset data in the space–time domain. Since the application is based on an integral (Kirchhoff) method, this residual DMO preserves all the flexibility features of an integral DMO. An application to synthetic and real data demonstrates effectiveness of the velocity-residual DMO in data processing and velocity analysis.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1111/j.1365-2478.2005.00459.x
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  • 2
    Digitale Medien
    Digitale Medien
    Azimuth moveout correction for transversely isotropic media (2004)
    PO Box 1354, 9600 Garsington Road , Oxford OX4 2XG , UK . : Blackwell Publishing Ltd
    Geophysical prospecting 52 (2004), S. 0 
    Details
    ISSN: 1365-2478
    Quelle: Blackwell Publishing Journal Backfiles 1879-2005
    Thema: Geologie und Paläontologie , Physik
    Notizen: The azimuth moveout (AMO) operator in homogeneous transversely isotropic media with a vertical symmetry axis (VTI), as in isotropic media, has an overall skewed saddle shape. However, the AMO operator in anisotropic media is complicated; it includes, among other things, triplications at low angles. Even in weaker anisotropies, with the anisotropy parameter η= 0.1 (10% anisotropy), the AMO operator is considerably different from the isotropic operator, although free of triplications. The structure of the operator in VTI media (positive η) is stretched (has a wider aperture) compared with operators in isotropic media, with the amount of stretch being dependent on the strength of anisotropy. If the medium is both vertically inhomogeneous, i.e. the vertical velocity is a function of depth (v(z)), and anisotropic, which is a common combination in practical problems, the shape of the operator again differs from that for isotropic media. However, the difference in the AMO operator between the homogeneous and the v(z) cases, even for anisotropic media, is small. Stated simply, anisotropy influences the shape and aperture of the AMO operator far more than vertical inhomogeneity does.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1046/j.1365-2478.2004.00398.x
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  • 3
    Digitale Medien
    Digitale Medien
    Traveltime computation with the linearized eikonal equation for anisotropic media (2002)
    Oxford, UK : Blackwell Science Ltd
    Geophysical prospecting 50 (2002), S. 0 
    Details
    ISSN: 1365-2478
    Quelle: Blackwell Publishing Journal Backfiles 1879-2005
    Thema: Geologie und Paläontologie , Physik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1046/j.1365-2478.2002.00322.x
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  • 4
    Digitale Medien
    Digitale Medien
    Implementing the fast marching eikonal solver: spherical versus Cartesian coordinates (2001)
    Oxford, UK : Blackwell Science Ltd
    Geophysical prospecting 49 (2001), S. 0 
    Details
    ISSN: 1365-2478
    Quelle: Blackwell Publishing Journal Backfiles 1879-2005
    Thema: Geologie und Paläontologie , Physik
    Notizen: Spherical coordinates are a natural orthogonal system for describing wavefronts emanating from a point source. A regular grid distribution in the Cartesian-coordinate system tends to undersample the wavefront description near the source (at the highest wavefront curvature) and oversample it away from the source. Spherical coordinates, in general, provide a more balanced grid distribution for characterizing point-source wavefronts. Our numerical implementation confirms that the recently introduced fast marching algorithm is both a highly efficient and an unconditionally stable eikonal solver. However, its first-order approximation of traveltime derivatives can induce relatively large traveltime errors for waves propagating in a diagonal direction with respect to the coordinate system. Examples, including the IFP Marmousi and the SEG/EAGE 3D salt-dome models, show that a spherical-coordinate implementation of the method results in far fewer errors in traveltime calculation than the conventional Cartesian-coordinate implementation, and with practically no loss in computational advantages.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1046/j.1365-2478.2001.00245.x
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  • 5
    Digitale Medien
    Digitale Medien
    τ-migration and velocity analysis: application to data from the Red Sea (2005)
    PO Box 1354, 9600 Garsington Road , Oxford OX4 2XG , UK . : Blackwell Science Ltd
    Geophysical prospecting 53 (2005), S. 0 
    Details
    ISSN: 1365-2478
    Quelle: Blackwell Publishing Journal Backfiles 1879-2005
    Thema: Geologie und Paläontologie , Physik
    Notizen: Imaging pre-salt reflections for data acquired from the coastal region of the Red Sea is a task that requires prestack migration velocity analysis. Conventional post-stack time processing lacks the lateral inhomogeneity capability, necessary for such a problem. Prestack migration velocity analysis in the vertical time domain reduces the velocity–depth ambiguity that usually hampers the performance of prestack depth-migration velocity analysis. In prestack τ-migration velocity analysis, the interval velocity model and the output images are defined in τ (i.e. vertical time). As a result, we avoid placing reflectors at erroneous depths during the velocity analysis process and thus avoid inaccurately altering the shape of the velocity model, which in turn speeds up the convergence to the true model. Using a 1D velocity update scheme, the prestack τ-migration velocity analysis produces good images of data from the Midyan region of the Red Sea. For the first seismic line from this region, only three prestack τ-migration velocity analysis iterations were required to focus pre-salt reflections in τ. However, the second line, which crosses the first line, is slightly more complicated and thus required five iterations to reach the final, reasonably focused, τ-image. After mapping the images for the two crossing lines to depth, using the final velocity models, the placements of reflectors in the two 2D lines were consistent at their crossing point. Some errors occurred due to the influence of out-of-plane reflections on 2D imaging. However, such errors are identifiable and are generally small.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1111/j.1365-2478.2005.00493.x
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  • 6
    Digitale Medien
    Digitale Medien
    Reflection moveout inversion in azimuthally anisotropic media: accuracy, limitations and acquisition [Paper pres] (1999)
    Oxford BSL : Blackwell Science Ltd
    Geophysical prospecting 47 (1999), S. 0 
    Details
    ISSN: 1365-2478
    Quelle: Blackwell Publishing Journal Backfiles 1879-2005
    Thema: Geologie und Paläontologie , Physik
    Notizen: Parameter estimation from the elliptical variations in the normal-moveout (NMO) velocity in azimuthally anisotropic media is sensitive to the angular separation between the survey lines in 2D, or equivalently, the source-to-receiver azimuth in 3D, and to the set of azimuths used in the inversion procedure. The accuracy in estimating the orientation of an NMO ellipse, in particular the parameter α, is also sensitive to the magnitude of anisotropy. On the other hand, the accuracy in estimating the semi-axes of the NMO-velocity ellipse is about the same for any magnitude of anisotropy.  To invert for the NMO ellipse parameters at least three NMO-velocity measurements along distinct azimuth directions are needed. In order to maximize the accuracy and stability in parameter estimation, it is best to have the azimuths for the three source-to-receiver directions 60° apart. Having more than three distinct source-to-receiver azimuths (e.g. full azimuthal coverage) provides a useful data redundancy that enhances the quality of the estimates.  In order to maximize quality in the inversion process, it is recommended to design the seismic data acquisition such that it contains small sectors (≤10°) with adequate fold and offset distribution.  Using three NMO-velocity measurements, 60° apart, an azimuthally anisotropic layer overlain by an azimuthally isotropic overburden (as might occur for fractured reservoirs) should have a relative thickness (in time) with respect to the total thickness at least equal to the ratio of the error in the NMO (stacking) velocity to the interval anisotropy of the fractured layer. Coverage along more than three azimuths, however, improves this limitation, which is imposed by Dix differentiation, by at most 50%, depending on the number of observations (NMO velocities) that enter the inversion procedure.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1046/j.1365-2478.1999.00140.x
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