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- Volume 54, Issue 2, 2006
Geophysical Prospecting - Volume 54, Issue 2, 2006
Volume 54, Issue 2, 2006
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Energy Group optimization for forward and inverse problems in nuclear engineering: application to downwell‐logging problems
ABSTRACTSimulating radiation transport of neutral particles (neutrons and γ‐ray photons) within subsurface formations has been an area of research in the nuclear well‐logging community since the 1960s, with many researchers exploiting existing computational tools already available within the nuclear reactor community. Deterministic codes became a popular tool, with the radiation transport equation being solved using a discretization of phase‐space of the problem (energy, angle, space and time). The energy discretization in such codes is based on the multigroup approximation, or equivalently the discrete finite‐difference energy approximation. One of the uncertainties, therefore, of simulating radiation transport problems, has become the multigroup energy structure. The nuclear reactor community has tackled the problem by optimizing existing nuclear cross‐sectional libraries using a variety of group‐collapsing codes, whilst the nuclear well‐logging community has relied, until now, on libraries used in the nuclear reactor community. However, although the utilization of such libraries has been extremely useful in the past, it has also become clear that a larger number of energy groups were available than was necessary for the well‐logging problems. It was obvious, therefore, that a multigroup energy structure specific to the needs of the nuclear well‐logging community needed to be established. This would have the benefit of reducing computational time (the ultimate aim of this work) for both the stochastic and deterministic calculations since computational time increases with the number of energy groups.
We, therefore, present in this study two methodologies that enable the optimization of any multigroup neutron–γ energy structure. Although we test our theoretical approaches on nuclear well‐logging synthetic data, the methodologies can be applied to other radiation transport problems that use the multigroup energy approximation. The first approach considers the effect of collapsing the neutron groups by solving the forward transport problem directly using the deterministic code EVENT, and obtaining neutron and γ‐ray fluxes deterministically for the different group‐collapsing options. The best collapsing option is chosen as the one which minimizes the effect on the γ‐ray spectrum. During this methodology, parallel processing is implemented to reduce computational times. The second approach uses the uncollapsed output from neural network simulations in order to estimate the new, collapsed fluxes for the different collapsing cases. Subsequently, an inversion technique is used which calculates the properties of the subsurface, based on the collapsed fluxes. The best collapsing option is chosen as the one that predicts the subsurface properties with a minimal error. The fundamental difference between the two methodologies relates to their effect on the generated γ‐rays. The first methodology takes the generation of γ‐rays fully into account by solving the transport equation directly. The second methodology assumes that the reduction of the neutron groups has no effect on the γ‐ray fluxes. It does, however, utilize an inversion scheme to predict the subsurface properties reliably, and it looks at the effect of collapsing the neutron groups on these predictions. Although the second procedure is favoured because of (a) the speed with which a solution can be obtained and (b) the application of an inversion scheme, its results need to be validated against a physically more stringent methodology. A comparison of the two methodologies is therefore given.
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2D data modelling by electrical resistivity tomography for complex subsurface geology
Authors E. Cardarelli and F. FischangerABSTRACTA new tool for two‐dimensional apparent‐resistivity data modelling and inversion is presented. The study is developed according to the idea that the best way to deal with ill‐posedness of geoelectrical inverse problems lies in constructing algorithms which allow a flexible control of the physical and mathematical elements involved in the resolution.
The forward problem is solved through a finite‐difference algorithm, whose main features are a versatile user‐defined discretization of the domain and a new approach to the solution of the inverse Fourier transform.
The inversion procedure is based on an iterative smoothness‐constrained least‐squares algorithm. As mentioned, the code is constructed to ensure flexibility in resolution. This is first achieved by starting the inversion from an arbitrarily defined model. In our approach, a Jacobian matrix is calculated at each iteration, using a generalization of Cohn's network sensitivity theorem. Another versatile feature is the issue of introducing a priori information about the solution. Regions of the domain can be constrained to vary between two limits (the lower and upper bounds) by using inequality constraints. A second possibility is to include the starting model in the objective function used to determine an improved estimate of the unknown parameters and to constrain the solution to the above model. Furthermore, the possibility either of defining a discretization of the domain that exactly fits the underground structures or of refining the mesh of the grid certainly leads to more accurate solutions. Control on the mathematical elements in the inversion algorithm is also allowed. The smoothness matrix can be modified in order to penalize roughness in any one direction. An empirical way of assigning the regularization parameter (damping) is defined, but the user can also decide to assign it manually at each iteration.
An appropriate tool was constructed with the purpose of handling the inversion results, for example to correct reconstructed models and to check the effects of such changes on the calculated apparent resistivity.
Tests on synthetic and real data, in particular in handling indeterminate cases, show that the flexible approach is a good way to build a detailed picture of the prospected area.
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A pattern‐based approach for multiple removal applied to a 3D Gulf of Mexico data set
More LessABSTRACTSurface‐related multiples are attenuated for one sail line and one streamer of a 3D data set (courtesy of Compagnie Générale de Géophysique). The survey was carried out in the Gulf of Mexico in the Green Canyon area where salt intrusions close to the water‐bottom are present. Because of the complexity of the subsurface, a wavefield method incorporating the full 3D volume of the data for multiple removal is necessary. This method comprises modelling of the multiples, where the data are used as a prediction operator, and a subtraction step, where the model of the multiples is adaptively removed from the data with matching filters. The accuracy of the multiple model depends on the source/receiver coverage at the surface. When this coverage is not dense enough, the multiple model contains errors that make successful subtraction more difficult. In these circumstances, one can either (1) improve the modelling step by interpolating the missing traces, (2) improve the subtraction step by designing methods that are less sensitive to modelling errors, or (3) both. For this data set, the second option is investigated by predicting the multiples in a 2D sense (as opposed to 3D) and performing the subtraction with a pattern‐based approach. Because some traces and shots are missing for the 2D prediction, the data are interpolated in the in‐line direction using a hyperbolic Radon transform with and without sparseness constraints. The interpolation with a sparseness constraint yields the best multiple model. For the subtraction, the pattern‐based technique is compared with a more standard, adaptive‐subtraction scheme. The pattern‐based approach is based on the estimation of 3D prediction‐error filters for the primaries and the multiples, followed by a least‐squares estimation of the primaries. Both methods are compared before and after prestack depth migration. These results suggest that, when the multiple model is not accurate, the pattern‐based method is more effective than adaptive subtraction at removing surface‐related multiples while preserving the primaries.
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Inversion of elongated magnetic anomalies using magnitude transforms
More LessABSTRACTThe calculable magnitudes of the anomalous magnetic field from simple 2D sources and their gradients and Laplacians appear as ratios that can be synthesized in functional forms, corresponding to the different source shapes. Field components and first‐order derivatives are involved in the inversion procedures presented. The structural index and source depth are estimated independently of each other. The applied functions allow magnetic profiles and magnetic maps to be shape‐ and depth‐converted with immediate imaging of the inversion results. The contours of these functions outline elongated loops around the 2.5D anomaly axis on magnetic maps. The width of the loops reflects the depth and structural index N of the source in the scale units of the inverted map. Model and field tests illustrate the effectiveness of this approach for fast automatic inversion of large sets of magnetic data for depth, shape, length and location of simple sources.
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Second‐order interpolation of later‐arrival traveltimes
Authors Claudia Vanelle, Jan Dettmer and Dirk GajewskiABSTRACTThe performance of a 3D prestack migration of the Kirchhoff type can be significantly enhanced if the computation of the required stacking surface is replaced by an efficient and accurate method for the interpolation of diffraction traveltimes. Thus, input traveltimes need only be computed and stored on coarse grids, leading to considerable savings in CPU time and computer storage. However, interpolation methods based on a local approximation of the traveltime functions fail in the presence of triplications of the wavefront or later arrivals. This paper suggests a strategy to overcome this problem by employing the coefficients of a hyperbolic traveltime expansion to locate triplications and correct for the resulting errors in the interpolated traveltime tables of first and later arrivals.
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Explicit use of the Biot coefficient in predicting shear‐wave velocity of water‐saturated sediments
By Myung W. LeeABSTRACTPredicting the shear‐wave (S‐wave) velocity is important in seismic modelling, amplitude analysis with offset, and other exploration and engineering applications. Under the low‐frequency approximation, the classical Biot–Gassmann theory relates the Biot coefficient to the bulk modulus of water‐saturated sediments. If the Biot coefficient under in situ conditions can be estimated, the shear modulus or the S‐wave velocity can be calculated. The Biot coefficient derived from the compressional‐wave (P‐wave) velocity of water‐saturated sediments often differs from and is less than that estimated from the S‐wave velocity, owing to the interactions between the pore fluid and the grain contacts. By correcting the Biot coefficients derived from P‐wave velocities of water‐saturated sediments measured at various differential pressures, an accurate method of predicting S‐wave velocities is proposed. Numerical results indicate that the predicted S‐wave velocities for consolidated and unconsolidated sediments agree well with measured velocities.
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Deep resistivity structure of the Dikili‐Bergama region, west Anatolia, revealed by two‐ dimensional inversion of vertical electrical sounding data
Authors Gülçin Özürlan, M. Emin Candansayar and M. Hüdavendigar ŞahinABSTRACTWithin the framework of the National Marine Geological and Geophysical Program, we re‐examined deep vertical electrical sounding (VES) data. The data, measured in 1968 by the General Directorate of Mineral Research and Exploration (MTA) of Turkey with the aim of exploring the deep resistivity structure of the Dikili–Bergama region, focus on the geothermal potential. The geoelectrical resistivity survey was conducted using a Schlumberger array with a maximum electrode half‐spacing of 4.5 km. The two‐dimensional (2D) inversion was utilized to interpret the VES data that were collected along 15‐ to 30‐km profiles. The 2D resistivity–depth cross‐sections obtained show very low resistivity values near the Dikili and Kaynarca hot springs. The 2D inversion results also indicate the presence of fault zones striking nearly N–S and E–W, and fault‐bounded graben‐horst structures that show promising potential for geothermal field resources. The 2D gravity model, which is in good agreement with the density variation of the region, supports the resistivity structure revealed by 2D inversion. The lithology information obtained from the borehole near Kaynarca also confirms the results of the resistivity interpretation and the density model.
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2D and 3D potential‐field upward continuation using splines
By Bingzhu WangABSTRACTThe dominant upward‐continuation technique used in the potential‐field geophysics industry is the fast Fourier transform (FFT) technique. However, the spline‐based upward‐continuation technique presented in this paper has some advantages over the FFT technique. The spline technique can be used to carry out level‐to‐uneven surface 2D and 3D potential‐field upward continuation. An example of level‐to‐uneven surface upward continuation of 3D magnetic data using the spline technique is shown, and it is evident that the continued anomalies are very close to the theoretical values. The spacing can be irregular. Synthetic examples using the spline technique to continue noise‐contaminated gravity and magnetic data upward to an altitude of 15 km on irregular grids are shown. Gaussian noise with a zero mean and a standard deviation of 1% does not cause much error and can readily be tolerated. Through comparison with the FFT technique, it is found that for low‐altitude gravity and magnetic upward continuation, both the FFT technique and the spline technique are suitable; for high‐altitude upward continuation, the FFT technique is inaccurate, whereas the spline technique works very well. Also, upward continuation by the spline technique has a smaller edge effect than upward continuation by the FFT technique. The spline‐based upward continuation technique works fairly well even when the periphery of a grid is not quiet: it is rather robust in general. A real example shows that the spline technique can be employed to perform upward continuation of total‐field magnetic data and to de‐emphasize near‐surface noise.
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The origin and nature of seismic reflections of sharp‐based shoreface deposits (upper Jurassic Siliciclastics, northern France)
Authors H. Braaksma, G.G. Drijkoningen, N. Filippidou, J.A.M. Kenter and J.N. ProustABSTRACTIn order to advance understanding of the relationship between geological properties and their physical expression in reflection images, this study has focused expertise in reflection geophysics, petrophysics and sedimentology on the same geological object, in this case a succession of Upper Jurassic sharp‐based shoreface deposits embedded in offshore marine shales in northern France. This integrated approach to determine firstly the origin and nature of seismic reflections (calibration) and secondly to provide a means of extracting geological information from seismic imagery (inverse calibration) was built on the following analytical steps.
Firstly, detailed and extensive petrophysical analyses of outcrop (plug) samples, continuous core and sonic well logs, in combination with a quantification of mineralogical and textural properties, allowed a direct conversion of acoustic properties (impedance) into sedimentological properties, resulting in a quantitative physical sequence stratigraphic model.
Secondly, the integration of scale‐dependent acoustic measurements, ranging from 0.01 m and 320 kHz on cores up to the wavelength of field seismic data was established using an averaging algorithm (an effective‐medium‐theory type) as an upscaling approach. This alternative to a VSP or check shot allows an optimized depth–time conversion and hence determination of the origin of the seismic reflections with previously unattainable accuracy.
Finally, the shape and scale dependence of impedance contrasts were integrated into so‐called singularity parameters that directly link depositional changes with information from seismic reflections: depositional changes in the shallow‐water domain are generally characterized by step functions, whereas those in more distal depositional environments are represented by spiky functions. This approach allows the recognition of the associated reflection events and, vice versa, it provides a unique opportunity to extract the character of impedance changes, and thus changes in depositional environment, from seismic reflection records in general.
This integrated and multiscale characterization of sharp‐based shoreface deposits calibrates the typical reflection patterns for such sedimentary units. These include continuous high‐amplitude smooth and flat tops, discontinuous sharp basal reflections with variable amplitude, and complex sigmoidal high‐amplitude reflections within the compound shoreface deposits. In addition, the results of this study, by detailing the effects of scale and frequency on impedance changes, improve the identification of similar deposits in subsurface seismic data and the extraction of maximum amounts of geological information beyond seismic resolution.
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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 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 59 (2011)
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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 50 (2002)
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Volume 47 (1999)
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Volume 37 (1989)
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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 10 (1962)
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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)