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  • Articles  (23)
  • Articles: DFG German National Licenses  (23)
  • Blackwell Publishing Ltd.  (17)
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  • Geosciences  (23)
  • 1
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    PO Box 1354, 9600 Garsington Road , Oxford OX4 2XG , UK . : Blackwell Publishing Ltd.
    Geophysical prospecting 53 (2005), S. 0 
    ISSN: 1365-2478
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
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  • 2
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    PO Box 1354, 9600 Garsington Road , Oxford OX4 2XG , UK . : Blackwell Publishing Ltd.
    Geophysical prospecting 52 (2004), S. 0 
    ISSN: 1365-2478
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
    Notes: This paper is concerned with numerical tests of several rock physical relationships. The focus is on effective velocities and scattering attenuation in 3D fractured media. We apply the so-called rotated staggered finite-difference grid (RSG) technique for numerical experiments. Using this modified grid, it is possible to simulate the propagation of elastic waves in a 3D medium containing cracks, pores or free surfaces without applying explicit boundary conditions and without averaging the elastic moduli. We simulate the propagation of plane waves through a set of randomly cracked 3D media. In these numerical experiments we vary the number and the distribution of cracks. The synthetic results are compared with several (most popular) theories predicting the effective elastic properties of fractured materials. We find that, for randomly distributed and randomly orientated non-intersecting thin penny-shaped dry cracks, the numerical simulations of P- and S-wave velocities are in good agreement with the predictions of the self-consistent approximation. We observe similar results for fluid-filled cracks. The standard Gassmann equation cannot be applied to our 3D fractured media, although we have very low porosity in our models. This is explained by the absence of a connected porosity. There is only a slight difference in effective velocities between the cases of intersecting and non-intersecting cracks. This can be clearly demonstrated up to a crack density that is close to the connectivity percolation threshold. For crack densities beyond this threshold, we observe that the differential effective-medium (DEM) theory gives the best fit with numerical results for intersecting cracks. Additionally, it is shown that the scattering attenuation coefficient (of the mean field) predicted by the classical Hudson approach is in excellent agreement with our numerical results.
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  • 3
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    PO Box 1354, 9600 Garsington Road , Oxford OX4 2XG , UK . : Blackwell Publishing Ltd.
    Geophysical prospecting 52 (2004), S. 0 
    ISSN: 1365-2478
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
    Notes: An intuitive method is presented for extending Hale–McClellan migration operators to handle surveys binned and stacked with in-line and cross-line spacings unequal. This avoids re-interpolating the input to 3D migration, either externally or internally. The algorithm does not require an integer or rational ratio between the in-line and cross-line spacings in order to be applied nor does it deliberately introduce artificial aliasing by interleaving subsampled grids along the more finely sampled axis. Examples of its impulse response and application to the SEG–EAGE salt model are shown.
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  • 4
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    PO Box 1354, 9600 Garsington Road , Oxford OX4 2XG , UK . : Blackwell Publishing Ltd.
    Geophysical prospecting 52 (2004), S. 0 
    ISSN: 1365-2478
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
    Notes: Euler deconvolution and the analytic signal are both used for semi-automatic interpretation of magnetic data. They are used mostly to delineate contacts and obtain rapid source depth estimates. For Euler deconvolution, the quality of the depth estimation depends mainly on the choice of the proper structural index, which is a function of the geometry of the causative bodies. Euler deconvolution applies only to functions that are homogeneous. This is the case for the magnetic field due to contacts, thin dikes and poles. Fortunately, many complex geological structures can be approximated by these simple geometries. In practice, the Euler equation is also solved for a background regional field. For the analytic signal, the model used is generally a contact, although other models, such as a thin dike, can be considered. It can be shown that if a function is homogeneous, its analytic signal is also homogeneous. Deconvolution of the analytic signal is then equivalent to Euler deconvolution of the magnetic field with a background field. However, computation of the analytic signal effectively removes the background field from the data. Consequently, it is possible to solve for both the source location and structural index. Once these parameters are determined, the local dip and the susceptibility contrast can be determined from relationships between the analytic signal and the orthogonal gradients of the magnetic field. The major advantage of this technique is that it allows the automatic identification of the type of source. Implementation of this approach is demonstrated for recent high-resolution survey data from an Archean granite-greenstone terrane in northern Ontario, Canada.
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  • 5
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    PO Box 1354, 9600 Garsington Road , Oxford OX4 2XG , UK . : Blackwell Publishing Ltd.
    Geophysical prospecting 52 (2004), S. 0 
    ISSN: 1365-2478
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
    Notes: We present an adaptation of the full multigrid algorithm in DC resistivity modelling in an effort to increase its accuracy. There is a great difficulty with conventional multigrid solvers in representing the physics of an arbitrary distribution of electrical conductivity on a very coarse grid. In general, conventional rectangular finite-difference or 5-point approximations of Poisson's equation cannot represent, at a coarse grid level, the effective anisotropy on a coarse scale which results from fine structure in the model. An exception to this generalization occurs when the principal axes of structural anisotropy are aligned with the coordinate axis. Additional and similarly generated problems arise when a coarse cell is obliged to represent fine structure containing very high conductivity contrasts. We have developed an adaptation of the usual resistive-network representation of the continuum, which avoids some of these problems, and have compared it with the traditional resistive network currently used. The network adaptation consists of replacing the usual 5-point Laplacian operator stencil used on the finite-difference grid with a 9-point stencil, and the conductivity scalar with a 6-parameter conductivity parametrization. This parametrization permits representation of arbitrarily orientated anisotropy as well as more complex behaviour related to high conductivity contrasts. The importance of multigrid solvers does not lie in their speed at forward modelling (which is comparable with other methods), but rather in their potential for inverse modelling. Inverse solvers which proceed by refinement of an initially very coarse solution can, in principle, take time only linearly proportional to the number of gridpoints in the final desired model.
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  • 6
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    PO Box 1354, 9600 Garsington Road , Oxford OX4 2XG , UK . : Blackwell Publishing Ltd.
    Geophysical prospecting 52 (2004), S. 0 
    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.
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  • 7
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    PO Box 1354, 9600 Garsington Road , Oxford OX4 2XG , UK . : Blackwell Publishing Ltd.
    Geophysical prospecting 52 (2004), S. 0 
    ISSN: 1365-2478
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
    Notes: Regularization is the most popular technique to overcome the null space of model parameters in geophysical inverse problems, and is implemented by including a constraint term as well as the data-misfit term in the objective function being minimized. The weighting of the constraint term relative to the data-fitting term is controlled by a regularization parameter, and its adjustment to obtain the best model has received much attention. The empirical Bayes approach discussed in this paper determines the optimum value of the regularization parameter from a given data set. The regularization term can be regarded as representing a priori information about the model parameters. The empirical Bayes approach and its more practical variant, Akaike's Bayesian Information Criterion, adjust the regularization parameter automatically in response to the level of data noise and to the suitability of the assumed a priori model information for the given data. When the noise level is high, the regularization parameter is made large, which means that the a priori information is emphasized. If the assumed a priori information is not suitable for the given data, the regularization parameter is made small. Both these behaviours are desirable characteristics for the regularized solutions of practical inverse problems. Four simple examples are presented to illustrate these characteristics for an underdetermined problem, a problem adopting an improper prior constraint and a problem having an unknown data variance, all frequently encountered geophysical inverse problems. Numerical experiments using Akaike's Bayesian Information Criterion for synthetic data provide results consistent with these characteristics. In addition, concerning the selection of an appropriate type of a priori model information, a comparison between four types of difference-operator model – the zeroth-, first-, second- and third-order difference-operator models – suggests that the automatic determination of the optimum regularization parameter becomes more difficult with increasing order of the difference operators. Accordingly, taking the effect of data noise into account, it is better to employ the lower-order difference-operator models for inversions of noisy data.
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  • 8
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    Geophysical prospecting 52 (2004), S. 0 
    ISSN: 1365-2478
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
    Notes: Most existing reservoir models are based on 2D outcrop studies; 3D aspects are inferred from correlation between wells, and so are inadequately constrained for reservoir simulations. To overcome these deficiencies, we have initiated a multidimensional characterization of reservoir analogues in the Cretaceous Ferron Sandstone in Utah. Detailed sedimentary facies maps of cliff faces define the geometry and distribution of reservoir flow units, barriers and baffles at the outcrop. High-resolution 2D and 3D ground-penetrating radar (GPR) images extend these reservoir characteristics into 3D to allow the development of realistic 3D reservoir models. Models use geometric information from mapping and the GPR data, combined with petrophysical data from surface and cliff-face outcrops, and laboratory analyses of outcrop and core samples.The site of the field work is Corbula Gulch, on the western flank of the San Rafael Swell, in east-central Utah. The outcrop consists of an 8–17 m thick sandstone body which contains various sedimentary structures, such as cross-bedding, inclined stratification and erosional surfaces, which range in scale from less than a metre to hundreds of metres. 3D depth migration of the common-offset GPR data produces data volumes within which the inclined surfaces and erosional surfaces are visible. Correlation between fluid permeability, clay content, instantaneous frequency and instantaneous amplitude of the GPR data provides estimates of the 3D distribution of fluid permeability and clay content.
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  • 9
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    9600 Garsington Road , Oxford OX4 2XG , UK . : Blackwell Publishing Ltd.
    Geophysical prospecting 51 (2003), S. 0 
    ISSN: 1365-2478
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
    Notes: We find errors in theory and application in the paper by van der Kolk et al. (Geophysical Prospecting49, 179–197 (2001)) that invalidate their arguments for the cause of the reduction in the velocity of the vertically propagating slower split shear-wave in the gas cap over the Natih field in Oman. We suggest that existing theories are adequate and can explain the anomaly.
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  • 10
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    Geophysical prospecting 51 (2003), S. 0 
    ISSN: 1365-2478
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
    Notes: We compare two geophysical survey measurements of the same type made at different times in order to characterize the change in the geological medium during the elapsed time. The aim of this study is to develop a strategy using a full non-linear inversion algorithm as the interpretation tool. In this way, not only the location and the form of the changes are recovered, but also the changes in the material parameters of the geological medium can be estimated. In order to solve this fully non-linear problem, the so-called ‘multiplicative regularized contrast source inversion’ (MR-CSI) method is employed. The unique property of this iterative method is that it does not solve the forward problem at each iterative step. This makes it possible to use the non-linear inversion algorithm for large-scale computation problems. The numerical results show that by taking into account the non-linear nature of the problem, interpretation of the time-lapse data can be significantly improved, compared with that obtained using linear inversion.
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  • 11
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    9600 Garsington Road , Oxford OX4 2XG , UK . : Blackwell Publishing Ltd.
    Geophysical prospecting 51 (2003), S. 0 
    ISSN: 1365-2478
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
    Notes: Transverse isotropy with a tilted axis of symmetry (TTI) causes image distortion if isotropic models are assumed during data processing. A simple anisotropic migration approach needs long computational times and is sensitive to the signal-to-noise ratio. This paper presents an efficient, general approach to common-depth-point (CDP) mapping to image the subsurface in TTI media from qP-wave seismic data by adding anisotropic and dip parameters to the velocity model. The method consists of three steps: (i) calculating traveltimes and positions of the CDP points; (ii) determining CDP trajectories; (iii) CDP imaging. A crucial step is the rapid computation of traveltimes and raypaths in the TTI media, which is achieved by the Fermat method, specially adapted for anisotropic layered media. The algorithm can image the subsurface of a given model quickly and accurately, and is suitable for application to a bending reflector. The effectiveness of the method is demonstrated by comparing the raypaths, the traveltimes and the results of CDP mapping, when assuming isotropic media, transversely isotropic media with a vertical axis of symmetry (TIV), and TTI media.
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  • 12
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    9600 Garsington Road , Oxford OX4 2XG , UK . : Blackwell Publishing Ltd.
    Geophysical prospecting 51 (2003), S. 0 
    ISSN: 1365-2478
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
    Notes: Migration velocity analysis is carried out by analysing the residual moveout and amplitude variations in common image point gathers (CIGs) parametrized by scattering angle and azimuth. The misfit criterion in the analysis is of the differential-semblance type. By using angles to parametrize the imaging we are able to handle and exploit data with multiple arrivals, although artefacts may occur in the CIGs and need to be suppressed.The CIGs are generated by angle migration, an approach based on the generalized Radon transform (GRT) inversion, and they provide multiple images of reflectors in the subsurface for a range of scattering angles and azimuths. Within the differential semblance applied to these CIGs, we compensate for amplitude versus angle (AVA) effects. Thus, using a correct background velocity model, the CIGs should have no residual moveout nor amplitude variation with angles, and the differential semblance should vanish. If the velocity model is incorrect, however, the events in the CIGs will appear at different depths for different angles and the amplitude along the events will be non-uniform. A standard, gradient-based optimization scheme is employed to develop a velocity updating procedure. The model update is formed by backprojecting the differential semblance misfits through ray perturbation kernels, within a GRT inverse. The GRT inverse acts on the data, subject to a shift in accordance with ray perturbation theory.The performance of our algorithm is demonstrated with two synthetic data examples using isotropic elastic models. The first one allows velocity variation with depth only. In the second one, we reconstruct a low-velocity lens in the model that gives rise to multipathing. The velocity model parametrization is based upon the eigentensor decomposition of the stiffness tensor and makes use of B-splines.
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  • 13
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    9600 Garsington Road , Oxford OX4 2XG , UK . : Blackwell Publishing Ltd.
    Geophysical prospecting 51 (2003), S. 0 
    ISSN: 1365-2478
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
    Notes: This paper presents a method for velocity analysis in tilted transversely isotropic (TTI) media by combining CDP mapping with a genetic algorithm. CDP mapping is a velocity analysis method for determining anisotropic velocity but has difficulties due to the following factors: (i) it involves a non-linear and multimodal objective function; (ii) it is prohibitively expensive in the evaluation of candidate solutions, which often involves the calculation of images in the depth domain; (iii) there is often a very large parameter space. Recognizing the global and multimodal nature of the problem, a genetic algorithm is employed to search for the optimal velocity model. The efficiency of the method contributes to two critical processes: rapid model evaluation, achieved by generating CDP mapping only in the neighbourhood of specific reflectors, and fast computation, based on Fermat's principle, of the CDP points and traveltimes in TTI media. The method produces subsurface structure images in the depth domain, and can also solve for Thomsen's anisotropic parameters (ɛ and δ), the vertical velocity and the dip of the symmetry axis in the model space, simultaneously.
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  • 14
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    Geophysical prospecting 51 (2003), S. 0 
    ISSN: 1365-2478
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
    Notes: The problem of removing directional trends frequently occurs in the processing of magnetic data and also in the subsequent steps of data interpretation. The so-called corrugations are typical directional trends occurring in levelled data, which may be removed in several ways. Classical techniques are based on high-pass filtering of the data and successively filtering these transformed data with directional cosine filters. Other linear features are due to real sources, such as pipelines in shallow surveys or dike swarms in regional surveys. They should, nevertheless, be considered as noise, due to the fact that their effect is strong and tends to hide the field features related to structures of more interest. We deal with both kinds of problem, presenting the results of a study in an archaeological area of southern Italy. Decorrugation of magnetic field anomalies is performed using a method based on the excellent space–frequency localization properties of wavelet bases, allowing a very sharp filtering of the field along a selected direction. We compare this technique with the classical one in a synthetic case and find that the wavelet decorrugation is simpler and produces low distortion maps. Besides the field decorrugation, the wavelet approach was also shown to be useful in the subsequent enhancement of the measured field. In fact, we show that the wavelet analysis offers a unique framework where various filtering problems (directional, isotropic, global or local as well) may be easily solved. As regards the archaeological case, strong noisy effects from elongated sources (pipelines) were successfully removed in a sharp and local way.
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  • 15
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    9600 Garsington Road , Oxford OX4 2XG , UK . : Blackwell Publishing Ltd.
    Geophysical prospecting 51 (2003), S. 0 
    ISSN: 1365-2478
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
    Notes: A 3D F–K dip-moveout (DMO) is developed, which is applicable to data acquired in an elementary single-fold cross-spread. The key idea is that a 3D log-stretch transform and the inherent regularity of the cross-spread geometry make it possible to transform 3D Fourier DMO. The derived theory generalizes the 2D Fourier shot-gather DMO in the log-stretch domain; 2D turns out to be a special case. Similarly to 2D, the cross-spread DMO becomes convolutional after multidimensional logarithmic stretch. The proposed method works for orthogonal and slanted acquisition geometries; the cross-spread DMO relationships are found to be independent of the intersection angle of the shot and receiver lines. In contrast to integral (Kirchhoff-style) methods, the cross-spread F–K DMO does not degrade from the inevitable irregularity in 3D sampling of offsets in a CMP gather. The newly derived F–K DMO operator can be approximated by finite-difference (FD) schemes; the low-order FD cross-spread DMO equation is shown to be the 3D extension of the Bolondi and Rocca offset continuation. It is shown that F–K and low-order FD operators are effective in a synthetic case.
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  • 16
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    Geophysical prospecting 51 (2003), S. 0 
    ISSN: 1365-2478
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
    Notes: Shear waves recorded at or near the sea-bed, i.e. a water–sediment interface, may suffer from unwanted phase change, which is detrimental to velocity analysis and processing and degrades the quality of the final stacked or migrated image. In this study, this phenomenon is analysed for P-SV converted waves recorded at the sea-bed. Theoretical analysis shows that phase change does not occur if the converted shear waves always maintain raypaths that lie within the critical angle, provided the subsurface layering is horizontal. A phase change that is asymmetric with offset can readily be explained as being due to dipping layers at targets or the dipping sea-bed. This analysis is extended to multiple layers and anisotropic media and shows that the same conclusions hold. The analysis performed on two sets of ocean-bottom-cable seismic data shows that the majority of observations show little evidence of phase change, and occasionally display the asymmetric phase change with offset. This finding underlines the robustness of converted shear waves for imaging the horizontal subsurfaces and sea-bed as all of the offset information may be used.
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  • 17
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    Geophysical prospecting 51 (2003), S. 0 
    ISSN: 1365-2478
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
    Notes: Direct-current (DC) resistivity tomography has been applied to different mountain permafrost regions. Despite problems with the very high resistivities of the frozen material, plausible results were obtained. Inversions with synthetic data revealed that an appropriate choice of regularization constraints was important, and that a joint analysis of several tomograms computed with different constraints was required to judge the reliability of individual features. The theoretical results were verified with three field experiments conducted in the Swiss and the Italian Alps. At the first site, near Zermatt, Switzerland, the location and the approximate lateral and vertical extent of an ice core within a moraine could be delineated. On the Murtel rock glacier, eastern Swiss Alps, a steeply dipping boundary at its frontal part was observed, and extremely high resistivities of several MΩ indicated a high ice content. The base of the rock glacier remained unresolved by the DC resistivity measurements, but it could be constrained with transient EM soundings. On another rock glacier near the Stelvio Pass, eastern Italian Alps, DC resistivity tomography allowed delineation of the rock glacier base, and the only moderately high resistivities within the rock glacier body indicated that the ice content must be lower compared with the Murtel rock glacier.
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  • 18
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    Geophysical prospecting 46 (1998), S. 0 
    ISSN: 1365-2478
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
    Notes: Following previous work on bounds for complex dielectrics, bounds on the complex conductivity of a mixture of two isotropic components can be developed which are independent of any special assumption concerning the geometry of the mixture. If certain broad restrictions are assumed, such as isotropy of the mixture, then the bounds can be made more restrictive. These bounds reveal the range of the induced polarization response which can be caused by a mixture of two materials of known complex conductivity. The bounds can also be generalized for spectral responses. The bounds are conservative lithologically in the sense that many of the special models corresponding to boundary responses have lithological counterparts.The chief use for the given bounds is to gain insight into the nature of the induced polarization response. It is also possible to use the bounds to estimate the volume fractions of the components. We illustrate how this is done for the case of a general anisotropic medium.
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  • 19
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    Geophysical prospecting 46 (1998), S. 0 
    ISSN: 1365-2478
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
    Notes: An experimental multicomponent three-dimensional (3D) seismic survey has been carried out over the Natih field in Oman. This paper describes the small-scale two-dimensional experiment carried out beforehand, and how the results obtained from this pilot were used to assess the feasibility of a nine-component three-dimensional (9C3D) operation as well as to determine the field parameters for the field-scale 3D survey. It also describes the two VSPs and a wireline shear log, acquired in conjunction with the pilot experiment, and the importance of such borehole data for establishing the correct time-to-depth relationship for the seismic data and for providing an independent check on the seismic interpretation. The observation of cusps in the offset VSP indicated the strong anisotropy of the Fiqa shales overlying the Natih reservoir.
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  • 20
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    Geophysical prospecting 46 (1998), S. 0 
    ISSN: 1365-2478
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
    Notes: Tuning caused by closely spaced impedance boundaries affects seismic amplitudes. At zero-offset the shape of the composite reflected signal approaches the time-derivative of the original pulse as the layer thickness decreases. For layers thinner than half of the tuning thickness, the reflected amplitude is modified by a factor equal to twice the time-thickness of the thin layer. Offset-dependent tuning can be approximated by the time differences between primary reflections. For high-velocity contrasts locally converted waves will also affect the total reflected seismic response. The contribution from intrabed multiples can, in most cases, be ignored. Correction for offset-dependent tuning should be considered before conventional AVO analysis.
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  • 21
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    Geophysical prospecting 46 (1998), S. 0 
    ISSN: 1365-2478
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
    Notes: The magnetic anomaly ΔF due to a long horizontal cylinder yields three points related to its extrema. A nomogram is presented for the determination of some source parameters of the causative body.
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  • 22
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    Geophysical prospecting 46 (1998), S. 0 
    ISSN: 1365-2478
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
    Notes: Conventional finite-difference modelling algorithms for seismic forward modelling are based on a time-stepping scheme with a constant (global) time step. Large contrasts in the velocity model or in the spatial sampling rate cause oversampling in time for some regions of the model. The use of locally adjustable time steps can save large amounts of computation time for certain modelling configurations.  The computation of spatial derivatives across the transition zone between regions of the model with different temporal sampling requires the definition of the wavefield at corresponding time levels on both sides of the transition zone. This condition can be obtained by extrapolation in time, which is inaccurate, or by multiple time integration in the transition zone. The error in the latter solution is of the same order as the conventional time-stepping scheme because both methods are based on the same iteration formula. The technique of multiple time integration simply requires the use of different sizes of time step. It is applicable only for certain factors of variation of the time step.
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  • 23
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    Geophysical prospecting 46 (1998), S. 0 
    ISSN: 1365-2478
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
    Notes: The galvanic problem is frequently solved by a Fredholm integral equation of the second kind based on a single layer source formulation. At higher conductivity contrasts between the model and its surroundings the homogeneous part of the integral equation approaches an eigenvalue equation. With infinite contrast the solution of this limiting integral equation is non-unique, but in the subspace of zero total charge the solution is unique. This mathematical property of the integral equation is reflected in its numerical solution with the result that large numerical errors may appear and convergence of the solution becomes very slow. Errors are, for the most part, related to the computed excess charge generated in the numerical solution. The effect is studied by comparing the results computed from the solution of the integral equation alone with those computed from a particular solution where the requirement of zero total charge is used as a constraint. The model examples clearly show that the use of the constraint condition significantly improves the accuracy of the results.
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