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- Volume 40, Issue 3, 1992
Geophysical Prospecting - Volume 40, Issue 3, 1992
Volume 40, Issue 3, 1992
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TWO‐POINT RAY TRACING IN GENERAL 3D MEDIA1
By V. PEREYRAAbstractThe modelling of realistic 3D geology and wave‐propagation phenomena is an important aspect of exploration geophysics. Ongoing research on a new model representation in terms of strongly reflecting interfaces described by surface patches, and on two‐point (i.e. source‐receiver) non‐zero‐offset ray tracing in such models, is presented.
Examples are used to demonstrate how this model representation facilitates the description of geological unconformities such as pinched‐out layers, overhangs and reverse faults. Neither pseudo‐layers, nor ‘transparent’ or zero‐impedance extensions are needed for surfaces that do not naturally cover the geological window under study. These are therefore no longer layered models and consequently they require new ray‐tracing techniques which are described and exemplified.
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SOME FADS AND FALLACIES IN SEISMIC DATA ANALYSIS1
Authors A. T. WALDEN and R. E. WHITEAbstractIn many branches of science, techniques designed for use in one context are used in other contexts, often with the belief that results which hold in the former will also hold or be relevant in the latter. Practical limitations are frequently overlooked or ignored. Three techniques used in seismic data analysis are often misused or their limitations poorly understood: (1) maximum entropy spectral analysis; (2) the role of goodness‐of‐fit and the real meaning of a wavelet estimate; (3) the use of multiple confidence intervals.
It is demonstrated that in practice maximum entropy spectral estimates depend on a data‐dependent smoothing window with unpleasant properties, which can result in poor spectral estimates for seismic data.
Secondly, it is pointed out that the level of smoothing needed to give least errors in a wavelet estimate will not give rise to the best goodness‐of‐fit between the seismic trace and the wavelet estimate convolved with the broadband synthetic. Even if the smoothing used corresponds to near‐minimum errors in the wavelet, the actual noise realization on the seismic data can cause important perturbations in residual wavelets following wavelet deconvolution.
Finally the computation of multiple confidence intervals (e.g. at several spatial positions) is considered. Suppose a nominal, say 90%, confidence interval is calculated at each location. The confidence attaching to the simultaneous use of the confidence intervals is not then 90%. Methods do exist for working out suitable confidence levels. This is illustrated using porosity maps computed using conditional simulation.
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A THEORETICAL TREATMENT OF THE EFFECT OF MICROSCOPIC FLUID DISTRIBUTION ON THE DIELECTRIC PROPERTIES OF PARTIALLY SATURATED ROCKS1
Authors ANTHONY L. ENDRES and ROSEMARY KNIGHTAbstractMicroscopic fluid distribution can have a significant effect on the dielectric properties of partially saturated rocks. Evidence of this effect is found in the laboratory data presented by Knight and Nur in which different methods for controlling saturation produced very different results for the dependence of the dielectric response on water saturation. In this study, previously derived models for the dielectric response of a heterogeneous medium are generalized and the case of a pore space occupied by multiple pore fluids is considered. By using various geometrical distributions of water and gas, it is observed that both the pore geometry in which saturation conditions are changing and the gas–water geometry within a given pore space are critical factors in determining the effective dielectric response of a partially saturated rock.
As an example, data for a tight gas sandstone undergoing a cycle of imbibition and drying are analysed. Previous research has demonstrated that significantly different microscopic fluid distributions result from the application of these two techniques to control the level of water saturation. By approximating these microscopic fluid distributions using simple geometrical models, good agreement is found between experimental data and calculated dielectric properties.
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BURGER'S EQUATION AS A MODEL FOR THE IP PHENOMENON1
Authors J. WYLLER, N. WELLANDER, F. LARSSON and D. S. PARASNISAbstractThe dynamic response characterizing the induced‐polarization (IP) phenomenon is modelled by a non‐linear diffusion equation (Burger's equation) supplemented by relevant initial and boundary values. The analysis of the model yields a voltage step response and an impedance curve in the frequency domain which agree qualitatively with experimental measurements. Curve fits based on the model have been made in the case of electrochemical cell measurements. The diffusion coefficients estimated by means of these curves are of the same order of magnitude as those calculated using experimental measurements. The normalized transient with these diffusion coefficients agrees with observations, but probably has a shorter discharge time. We have also carried out a comparison with predictions obtained from a linear, finite diffusion layer model, thus showing that for most practical situations the nonlinear term modelling the migration effect can be neglected.
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PLANE‐WAVE CONSTRAINTS IN 2D FILTER DESIGN1
By D. WALTHAMAbstractA method is presented for developing and/or evaluating 2D filters applied to seismic data. The approach used is to express linear 2D filtering operations in the space‐frequency (x–ω) domain. Correction filters are then determined using plane‐wave constraints. For example, requiring a vertically propagating plane wave to be unaffected by migration necessitates application of a half‐derivative correction in Kirchhoff migration. The same approach allows determination of the region of time‐offset space where half‐derivative corrections are correct in x–t domain dip moveout. Finally, an x–ω domain dip filter is derived using the constraint that a plane wave be attenuated as its dip increases. This filter has the advantage that it is significantly faster than f–k domain dip filtering and can be used on irregularly spaced data. This latter property also allows the filter to be used for interpolation of irregular data onto a regular grid.
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WHEN LEAST‐SQUARES SQUARES LEAST1
More LessAbstractThere is a general lack of awareness among ‘lay’ professionals (geophysicists included) regarding the limitations in the use of least‐squares. Using a simple numerical model under simulated conditions of observational errors, the performance of least‐squares and other goodness‐of‐fit criteria under various error conditions are investigated. The results are presented in a simplified manner that can be readily understood by the lay earth scientist. It is shown that the use of least‐squares is, strictly, only valid either when the errors pertain to a normal probability distribution or under certain fortuitous conditions. The correct power to use (e.g. square, cube, square root, etc.) depends on the form of error distribution. In many fairly typical practical situations, least‐squares is one of the worst criteria to use. In such cases, data treatment, ‘robust statistics’ or similar processes provide an alternative approach.
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Volume 72 (2023 - 2024)
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Volume 46 (1998)
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Volume 44 (1996)
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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 27 (1979)
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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 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 14 (1966)
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Volume 13 (1965)
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Volume 12 (1964)
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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)