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  • 1
    Electronic Resource
    Electronic Resource
    On anelliptic approximations for qP velocities in VTI 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
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
    Notes: A unified approach to approximating phase and group velocities of qP seismic waves in a transversely isotropic medium with vertical axis of symmetry (VTI) is developed. While the exact phase-velocity expressions involve four independent parameters to characterize the elastic medium, the proposed approximate expressions use only three parameters. This makes them more convenient for use in surface seismic experiments, where the estimation of all four parameters is problematic. The three-parameter phase-velocity approximation coincides with the previously published ‘acoustic’ approximation of Alkhalifah. The group-velocity approximation is new and noticeably more accurate than some of the previously published approximations. An application of the group-velocity approximation for finite-difference computation of traveltimes is shown.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1365-2478.2004.00413.x
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    The Wilson–Burg method of spectral factorization with application to helical filtering (2003)
    PO Box 1354, 9600 Garsington Road , Oxford OX4 2XG , UK . : Blackwell Publishing Ltd
    Geophysical prospecting 51 (2003), S. 0 
    Details
    ISSN: 1365-2478
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
    Notes: Spectral factorization is a computational procedure for constructing minimum-phase (stable inverse) filters required for recursive inverse filtering. We present a novel method of spectral factorization. The method iteratively constructs an approximation of the minimum-phase filter with the given autocorrelation by repeated forward and inverse filtering and rearranging of the terms. This procedure is especially efficient in the multidimensional case, where the inverse recursive filtering is enabled by the helix transform.To exemplify a practical application of the proposed method, we consider the problem of smooth two-dimensional data regularization. Splines in tension are smooth interpolation surfaces whose behaviour in unconstrained regions is controlled by the tension parameter. We show that such surfaces can be efficiently constructed with recursive filter preconditioning and we introduce a family of corresponding two-dimensional minimum-phase filters. The filters are created by spectral factorization on a helix.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1046/j.1365-2478.2003.00382.x
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  • 3
    Electronic Resource
    Electronic Resource
    Iterative resolution estimation in least-squares Kirchhoff migration (2002)
    Oxford, UK : Blackwell Science Ltd
    Geophysical prospecting 50 (2002), S. 0 
    Details
    ISSN: 1365-2478
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
    Notes: We apply iterative resolution estimation to least-squares Kirchhoff migration. Reviewing the theory of iterative optimization uncovers the common origin of different optimization methods. This allows us to reformulate the pseudo-inverse, model resolution and data resolution operators in terms of effective iterative estimates. When applied to Kirchhoff migration, plots of the diagonal of the model resolution matrix reveal low illumination areas on seismic images and provide information about image uncertainties. Synthetic and real data examples illustrate the proposed technique and confirm the theoretical expectations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1046/j.1365-2478.2002.00341.x
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  • 4
    Electronic Resource
    Electronic Resource
    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
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1046/j.1365-2478.2001.00245.x
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  • 5
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    Generalized nonelliptic moveout approximation in t-p domain (2012)
    Society of Exploration Geophysicists (SEG)
    Details
    Publication Date: 2012-03-01
    Description: We have derived a generalized nonelliptic moveout approximation in the t-p domain that is a companion to the generalized nonhyperbolic moveout approximation in the t-x domain. Approximation requires five parameters: three parameters that can be determined from the zero-slowness ray and two parameters that can be determined from one additional ray. We convert the generalized approximation from the t-p domain to the t-x domain and vice versa. The generalized nonelliptic moveout approximation in the t-p domain admits other moveout approximations as special cases. Several analytical and numerical tests showed a superior accuracy of the generalized nonelliptic moveout approximation.
    Print ISSN: 0016-8033
    Electronic ISSN: 1942-2156
    Topics: Geosciences , Physics
    Published by Society of Exploration Geophysicists (SEG)
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  • 6
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    Time-frequency analysis of seismic data using local attributes (2011)
    Society of Exploration Geophysicists (SEG)
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    Publication Date: 2011-11-01
    Description: Time-frequency analysis is an important technology in seismic data processing and interpretation. To localize frequency content in time, we have developed a novel method for computing a time-frequency map for nonstationary signals using an iterative inversion framework. We calculated time-varying Fourier coefficients by solving a least-squares problem that uses regularized nonstationary regression. We defined the time-frequency map as the norm of time-varying coefficients. Time-varying average frequency of the seismic data can also be estimated from the time-frequency map calculated by our method. We tested the method on benchmark synthetic signals and compared it with the well-known S-transform. Two field data examples showed applications of the proposed method for delineation of sand channels and for detection of low-frequency anomalies.
    Print ISSN: 0016-8033
    Electronic ISSN: 1942-2156
    Topics: Geosciences , Physics
    Published by Society of Exploration Geophysicists (SEG)
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  • 7
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    Seismic data interpolation beyond aliasing using regularized nonstationary autoregression (2011)
    Society of Exploration Geophysicists (SEG)
    Details
    Publication Date: 2011-09-01
    Description: Seismic data are often inadequately or irregularly sampled along spatial axes. Irregular sampling can produce artifacts in seismic imaging results. We have developed a new approach to interpolate aliased seismic data based on adaptive prediction-error filtering (PEF) and regularized nonstationary autoregression. Instead of cutting data into overlapping windows (patching), a popular method for handling nonstationarity, we obtain smoothly nonstationary PEF coefficients by solving a global regularized least-squares problem. We employ shaping regularization to control the smoothness of adaptive PEFs. Finding the interpolated traces can be treated as another linear least-squares problem, which solves for data values rather than filter coefficients. Compared with existing methods, the advantages of the proposed method include an intuitive selection of regularization parameters and fast iteration convergence. The technique was tested on benchmark synthetic and field data to prove it can successfully reconstruct data with decimated or missing traces.
    Print ISSN: 0016-8033
    Electronic ISSN: 1942-2156
    Topics: Geosciences , Physics
    Published by Society of Exploration Geophysicists (SEG)
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  • 8
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    Velocity-independent t-p moveout in a horizontally layered VTI medium (2011)
    Society of Exploration Geophysicists (SEG)
    Details
    Publication Date: 2011-07-01
    Description: Local slopes of seismic events carry complete information about the structure of the subsurface. This information is sufficient for accomplishing all time-domain imaging tasks, without the need to estimate or know the seismic velocity model. A velocity-independent t-p imaging approach has been developed to perform moveout correction in horizontally layered vertical-transverse-isotropy (VTI) media. The effective and interval anisotropic parameters are transformed into data attributes through the use of slopes and become directly mappable to the zero-slope traveltime. The t-p transform is the natural domain for anisotropy parameter estimation in layered media because the phase velocity is given explicitly in terms of p. Therefore, the t-p transform permits reflection-traveltime modeling and inversion that are simpler than traditional methods, which are based on Taylor-series expansions of traveltime in the t-x domain. Synthetic and field data tests demonstrate the practical effectiveness of the t-p method.
    Print ISSN: 0016-8033
    Electronic ISSN: 1942-2156
    Topics: Geosciences , Physics
    Published by Society of Exploration Geophysicists (SEG)
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  • 9
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    Fourier finite-difference wave propagation (2011)
    Society of Exploration Geophysicists (SEG)
    Details
    Publication Date: 2011-09-01
    Description: We introduce a novel technique for seismic wave extrapolation in time. The technique involves cascading a Fourier transform operator and a finite-difference operator to form a chain operator: Fourier finite differences (FFD). We derive the FFD operator from a pseudoanalytical solution of the acoustic wave equation. Two-dimensional synthetic examples demonstrate that the FFD operator can have high accuracy and stability in complex-velocity media. Applying the FFD method to the anisotropic case overcomes some disadvantages of other methods, such as the coupling of qP-waves and qSV-waves. The FFD method can be applied to enhance accuracy and stability of seismic imaging by reverse time migration.
    Print ISSN: 0016-8033
    Electronic ISSN: 1942-2156
    Topics: Geosciences , Physics
    Published by Society of Exploration Geophysicists (SEG)
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  • 10
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    Least-squares horizons with local slopes and multigrid correlations (2018)
    Society of Exploration Geophysicists
    Details
    Publication Date: 2018-04-27
    Print ISSN: 0016-8033
    Electronic ISSN: 1942-2156
    Topics: Geosciences , Physics
    Published by Society of Exploration Geophysicists
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