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  • 1
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    In:  Geophys. Prosp., Warszawa, Elsevier, vol. 26, no. 1, pp. 750-772, pp. 2091, (ISBN: 0-12-018847-3)
    Publication Date: 1978
    Keywords: seismic Migration ; Two-dimensional ; Seismics (controlled source seismology)
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  • 2
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    In:  Geophys. Prospecting, Warszawa, Elsevier, vol. 30, no. 1, pp. 813-828, pp. 2091, (ISBN: 0-12-018847-3)
    Publication Date: 1982
    Keywords: Applied geophysics ; Seismics (controlled source seismology)
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  • 3
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical prospecting 25 (1977), S. 0 
    ISSN: 1365-2478
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
    Notes: The sampling theorem in two dimensions univocally defines a surface, provided that its values are known at points disposed on a regular lattice. If the data are irregularly spaced, the usual procedure is first to interpolate the surface on a regular grid and then to contour the interpolated data: however, the resulting surface will not necessarily assume the prescribed values on the irregular grid.One way to obtain this result is to introduce a transformation of the coordinates such that all the original data points are transferred into part of the nodes of a regular grid. The surface is then interpolated in the points correspondent to the other crosspoints of the regular grid; the contour lines are determined in the transformed plane and then, using the inverse coordinate transformation, are transferred back to the original plane where they will certainly be congruent with the original data points.Nonetheless, the resulting surface is very sensitive to the interpolation method used: two algorithms for that are analyzed. The first (harmonization) corresponds to the determination of the potential of an electrical field whose contour conditions are those defined by the data points. The second method consists in two dimensional statistical estimation (krigeing); in particular, the effects of different choices for the data auto-covariance function are discussed.The solutions are compared and some practical results are shown.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical prospecting 30 (1982), S. 0 
    ISSN: 1365-2478
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
    Notes: Geometrical acoustic and wave theory lead to a second-order partial differential equation that links seismic sections with different offsets. In this equation a time-shift term appears that corresponds to normal moveout; a second term, dependent on offset and time only, corrects the moveout of dipping events.The zero-offset stacked section can thus be obtained by continuing the section with maximum offset towards zero, and stacking along the way the other common-offset sections.Without the correction for dip moveout, the spatial resolution of the section is noticeably impaired, thus limiting the advantages that could be obtained with expensive migration procedures. Trade-offs exist between multiplicity of coverage, spatial resolution, and signal-to-noise; in some cases the spatial resolution on the surface can be doubled and the aliasing noise averaged out.Velocity analyses carried out on data continued to zero offset show a better resolution and improved discrimination against multiples. For instance, sea-floor multiples always appear at water velocity, so that their removal is simplified.This offset continuation can be carried out either in the time-space domain or in the time-wave number domain. The methods are applied both to synthetic and real data.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical prospecting 26 (1978), S. 0 
    ISSN: 1365-2478
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
    Notes: The problem of the propagation of acoustic waves in a two-dimensional layered medium can be easily solved in the frequency domain if the Dix approximation is used, i.e. when only the primary reflections are considered. The migrated data at a depth z are obtained by convolving the time section with a proper two-dimensional operator dependent on z. The same result can be obtained by multiplying their two-dimensional spectra and summing for all the values of the temporal frequency.The aspect of the operator in the time-space domain has the classic hyperbolic structure together with the prescribed temporal and spatial decay.The main advantages of the frequency domain approach consist in the noticeable computer time savings and in the better approximation. On the other hand lateral velocity variations are very difficult to be taken into account. This can be done if a space variant filter is used in the time-space domain.To reduce computer time, this filter has to be recursive; the problem has been solved by Claerbout by transforming the hyperbolic partial differential equation into a parabolic one, and using the latter to generate the recursion operator.In the presentation a method is given for the generation of recursive filters with a better phase characteristics that have a pulse response with the requested hyperbolic shape instead of the parabocli one. This allows a better migration of steeper dips.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical prospecting 32 (1984), S. 0 
    ISSN: 1365-2478
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
    Notes: Offset continuation is a technique that was recently proposed for the dip moveout correction. This correction can be carried out in the time-wavenumber domain using a proper partial differential equation that links sections with different offset.It has been shown that a single spike in a common-offset section—corresponds to a semi-elliptically shaped reflector with foci located at the source and receiver in the section migrated after dip moveout correction.The sections that result after offset continuation, stack, and migration are thus a superposition not only of semicircles, but also of semi-ellipses with different lengths of axes. This effect smears the migration alias-noise which, without offset continuation, would appear as migration circles not close enough together to interfere destructively.Offset continuation can improve the quality of seismic sections in several ways:—the velocity analyses are more readable, less dispersed and dip independent; diffraction tails arrive with the same normal moveout velocity as the apex and thus diffraction-noise can be “stacked out”;—noise produced by aliasing in the migrated section is reduced.In this paper we give a practical and conceptual interpretation of the offset continuation method, with a generalization to three-dimensional volumes of data. A critical examination of several synthetic and field data examples shows the actual possibilities and advantages of offset continuation.
    Type of Medium: Electronic Resource
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  • 7
    Publication Date: 1984-12-01
    Print ISSN: 0016-8025
    Electronic ISSN: 1365-2478
    Topics: Geosciences , Physics
    Published by Wiley
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  • 8
    Publication Date: 1978-12-01
    Print ISSN: 0016-8025
    Electronic ISSN: 1365-2478
    Topics: Geosciences , Physics
    Published by Wiley
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  • 9
    Publication Date: 1977-03-01
    Print ISSN: 0016-8025
    Electronic ISSN: 1365-2478
    Topics: Geosciences , Physics
    Published by Wiley
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  • 10
    Publication Date: 1982-12-01
    Print ISSN: 0016-8025
    Electronic ISSN: 1365-2478
    Topics: Geosciences , Physics
    Published by Wiley
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