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  • 1
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical prospecting 41 (1993), S. 0 
    ISSN: 1365-2478
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
    Notes: A short convolutional differentiator (CD) for computing second spatial derivatives in the acoustic wave equation is presented. This differentiator is obtained by tapering the inverse Fourier transform of the band-limited Fourier spectrum of the second-derivative operator. This new filter has been applied to seismogram computations for inhomogeneous media and results are compared with the conventional high-order finite-difference (FD) and Fourier schemes. The operator can be progressively shortened at the model edges to reduce boundary artefacts. The CD method is superior to the conventional FD operator and comparable with the Fourier method in accuracy but faster to run. A strategy to reduce computation time by 20%, which exploits the localized nature of the operator, is given. The method is illustrated using simple 2D models.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical prospecting 29 (1981), S. 0 
    ISSN: 1365-2478
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
    Notes: Vertical velocity gradients can be readily accommodated in seismic refraction interpretations by using simple mathematical idealizations of curved raypaths entailed by certain analytic representations of these gradients. Computation procedures are formulated for velocity gradients in the overburden or an intermediate layer of a multilayer section. The former is demonstrated for an overburden velocity gradient manifest in published time-distance data.
    Type of Medium: Electronic Resource
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  • 3
    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 non-linear kinematic inversion of elastic anisotropy parameters and related investigations of the sensitivity of seismic data, the derivatives of the wavespeed (phase velocity and group velocity) with respect to the individual elastic moduli are required. This paper presents two analytic methods, called the eigenvalue and eigenvector methods, to compute the derivatives of the wavespeeds for wave propagation in a general anisotropic medium, which may be defined by up to 21 density-normalized elastic moduli. The first method employs a simple and compact form of the eigenvalue (phase velocity) and a general form of the group velocity, and directly yields general expressions of the derivatives for the three wave modes (qP, qS1, qS2). The second method applies simple eigenvector solutions of the three wave modes and leads to other general forms of the derivatives. These analytic formulae show that the derivatives are, in general, functions of the 21 elastic moduli as well as the wave propagation direction, and they reflect the sensitivity of the wavespeeds to the individual elastic moduli. Meanwhile, we give results of numerical investigations with some examples for particular simplified forms of anisotropy. They show that the eigenvalue method is suitable for the qP-, qS1- and qS2-wave computations and mitigates the singularity problem for the two quasi-shear waves. The eigenvector method is preferable to the eigenvalue method for the group velocity and the derivative of the phase velocity because it involves simpler expressions and independent computations, but for the derivative of the group velocity the derivative of the eigenvector is required. Both methods tackle the singularity problem and are applicable to any degree of seismic anisotropy for all three wave modes.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical prospecting 43 (1995), S. 0 
    ISSN: 1365-2478
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
    Notes: An accurate analytical expression for shot-gather dip-moveout (DMO) in the timespace log-stretch domain has until now not been published. We present a simpler, alternative derivation of the exact DMO relationships of Black et al. which correctly take account of the repositioning of the midpoint. A new computationally efficient frequency-wavenumber (F-K) DMO operator for shot profiles is then derived, based on these DMO relationships in the time-space log-stretch domain. The newly derived DMO operator is, unlike most other log-stretch DMO operators) accurate for the full range of reflector dips. Along with other schemes which are performed in the log-stretch domain, it offers considerable time savings over conventional DMO processing. We have compared numerically the impulse response of the new operator with those of a number of other shot-gather DMO operators, and found it to be superior and well match to the theoretical elliptical DMO response.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Science Ltd
    Geophysical prospecting 48 (2000), S. 0 
    ISSN: 1365-2478
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
    Notes: This paper investigates the relative merits and effectiveness of cross-hole resistivity tomography using different electrode configurations for four popular electrode arrays: pole–pole, pole–bipole, bipole–pole and bipole–bipole. By examination of two synthetic models (a dipping conductive strip and a dislocated fault), it is shown that besides the popular pole–pole array, some specified three- and four-electrode configurations, such as pole–bipole AM–N, bipole–pole AM–B and bipole–bipole AM–BN with their multispacing cross-hole profiling and scanning surveys, are useful for cross-hole resistivity tomography. These configurations, compared with the pole–pole array, may reduce or eliminate the effect of remote electrodes (systematic error) and yield satisfactory images with 20% noise-contaminated data. It is also shown that the configurations which have either both current electrodes or both potential electrodes in the same borehole, i.e. pole–bipole A–MN, bipole–pole AB–M and bipole–bipole AB–MN, have a singularity problem in data acquisition, namely low readings of the potential or potential difference in cross-hole surveying, so that the data are easily obscured by background noise and yield images inferior to those from other configurations.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Amsterdam : Elsevier
    Wave Motion 16 (1992), S. 307-322 
    ISSN: 0165-2125
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Geosciences , Physics
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    Amsterdam : Elsevier
    Physics of the Earth and Planetary Interiors 25 (1981), S. 372-389 
    ISSN: 0031-9201
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Geosciences , Physics
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    Amsterdam : Elsevier
    Physics of the Earth and Planetary Interiors 58 (1989), S. 323-343 
    ISSN: 0031-9201
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Geosciences , Physics
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    Amsterdam : Elsevier
    Physics of the Earth and Planetary Interiors 86 (1994), S. 277-299 
    ISSN: 0031-9201
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Geosciences , Physics
    Type of Medium: Electronic Resource
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