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- Volume 52, Issue 3, 2004
Geophysical Prospecting - Volume 52, Issue 3, 2004
Volume 52, Issue 3, 2004
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3D imaging of a reservoir analogue in point bar deposits in the Ferron Sandstone, Utah, using ground‐penetrating radar
ABSTRACTMost 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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Euler deconvolution of the analytic signal and its application to magnetic interpretation
Authors P. Keating and M. PilkingtonABSTRACTEuler 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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Effective elastic properties of randomly fractured soils: 3D numerical experiments
Authors Erik H. Saenger, Oliver S. Krüger and Serge A. ShapiroABSTRACTThis 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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An accurate and robust multigrid algorithm for 2D forward resistivity modelling
Authors Robert Moucha and Richard C. BaileyABSTRACTWe 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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Adjustment of regularization in ill‐posed linear inverse problems by the empirical Bayes approach
More LessABSTRACTRegularization 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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Δx≠Δy in 3D depth migration via McClellan transformations
More LessABSTRACTAn 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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On anelliptic approximations for qP velocities in VTI media
By Sergey FomelABSTRACTA 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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Volumes & issues
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Volume 72 (2023 - 2024)
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Volume 71 (2022 - 2023)
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Volume 70 (2021 - 2022)
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Volume 69 (2021)
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Volume 68 (2020)
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Volume 67 (2019)
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Volume 66 (2018)
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Volume 65 (2017)
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Volume 64 (2015 - 2016)
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Volume 63 (2015)
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Volume 62 (2014)
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Volume 61 (2013)
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Volume 60 (2012)
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Volume 59 (2011)
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Volume 58 (2010)
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Volume 57 (2009)
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Volume 56 (2008)
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Volume 55 (2007)
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Volume 54 (2006)
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Volume 53 (2005)
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Volume 52 (2004)
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Volume 51 (2003)
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Volume 50 (2002)
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Volume 49 (2001)
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Volume 48 (2000)
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Volume 47 (1999)
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Volume 46 (1998)
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Volume 45 (1997)
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Volume 44 (1996)
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Volume 43 (1995)
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Volume 42 (1994)
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Volume 41 (1993)
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Volume 40 (1992)
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Volume 39 (1991)
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Volume 38 (1990)
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Volume 37 (1989)
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Volume 36 (1988)
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Volume 35 (1987)
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Volume 34 (1986)
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Volume 33 (1985)
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Volume 32 (1984)
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Volume 31 (1983)
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Volume 30 (1982)
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Volume 29 (1981)
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Volume 28 (1980)
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Volume 27 (1979)
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Volume 26 (1978)
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Volume 25 (1977)
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Volume 24 (1976)
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Volume 23 (1975)
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Volume 22 (1974)
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Volume 21 (1973)
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Volume 20 (1972)
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Volume 19 (1971)
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Volume 18 (1970)
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Volume 17 (1969)
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Volume 16 (1968)
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Volume 15 (1967)
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Volume 14 (1966)
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Volume 13 (1965)
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Volume 12 (1964)
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Volume 11 (1963)
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Volume 10 (1962)
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Volume 9 (1961)
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Volume 8 (1960)
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Volume 7 (1959)
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Volume 6 (1958)
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Volume 5 (1957)
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Volume 4 (1956)
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Volume 3 (1955)
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Volume 2 (1954)
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Volume 1 (1953)