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- Volume 53, Issue 3, 2005
Geophysical Prospecting - Volume 53, Issue 3, 2005
Volume 53, Issue 3, 2005
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Broadband constant‐coefficient propagators
By Li‐Yun FuABSTRACTThe phase error between the real phase shift and the Gazdag background phase shift, due to lateral velocity variations about a reference velocity, can be decomposed into axial and paraxial phase errors. The axial phase error depends only on velocity perturbations and hence can be completely removed by the split‐step Fourier method. The paraxial phase error is a cross function of velocity perturbations and propagation angles. The cross function can be approximated with various differential operators by allowing the coefficients to vary with velocity perturbations and propagation angles. These variable‐coefficient operators require finite‐difference numerical implementation. Broadband constant‐coefficient operators may provide an efficient alternative that approximates the cross function within the split‐step framework and allows implementation using Fourier transforms alone. The resulting migration accuracy depends on the localization of the constant‐coefficient operators. A simple broadband constant‐coefficient operator has been designed and is tested with the SEG/EAEG salt model. Compared with the split‐step Fourier method that applies to either weak‐contrast media or at small propagation angles, this operator improves wavefield extrapolation for large to strong lateral heterogeneities, except within the weak‐contrast region. Incorporating the split‐step Fourier operator into a hybrid implementation can eliminate the poor performance of the broadband constant‐coefficient operator in the weak‐contrast region. This study may indicate a direction of improving the split‐step Fourier method, with little loss of efficiency, while allowing it to remain faster than more precise methods such as the Fourier finite‐difference method.
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A radiomagnetotelluric survey on an oil‐contaminated area near the Brazi Refinery, Romania
Authors B. Tezkan, P. Georgescu and U. FauziABSTRACTScalar radiomagnetotelluric measurements were carried out on a contaminated test area close to the Brazi Refinery in Romania in order to detect and to monitor a 1 m thick oil layer expected at 5 m depth. Radio transmitters broadcasting in a frequency range from 10 kHz to 300 kHz were selected to observe the apparent resistivity and the phase data associated with the E‐ and B‐polarizations. They were located parallel and perpendicular to the assumed strike direction of the contamination plume. The data were interpreted by a 2D inversion technique from which the conductivity structure of the area was derived. The 2D inversion models of all profiles on the contaminated area show a poor‐conductivity zone above the groundwater table which could be associated with the oil contamination.
A first attempt was also made to monitor the contaminated layer: the radiomagnetotelluric measurements were repeated on the same profiles a year later, but this time in a dry period, not in a rainy one. The 2D inversion results of the measurements in the dry period indicate that the high‐resistivity layer moved closer to the surface. Additional reference measurements were then carried out on a non‐contaminated area situated at a distance from the refinery, in the opposite direction to the flow of the groundwater. These reference measurements were used for the derivation of the unperturbed geology and they were also compared with the measurements of the contaminated test area. There is a significant difference in the frequency dependences of the apparent resistivities of the reference and contaminated areas, which could indicate a contamination at shallow depth. The 2D inversion results show the increase of resistivity at a depth of about 5 m beneath the contaminated area where the oil contamination is expected according to the information from the boreholes.
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A field test of imaging properties of rotational invariants of the magnetotelluric impedance tensor
Authors László Szarka, Antal Ádám and Michel MenvielleABSTRACTA part of the Békés Basin (an extensional sub‐basin of the Pannonian Basin, where the basement under thick Pannonian sediments is well known from deep boreholes and from seismic measurements, and where many magnetotelluric (MT) soundings have been carried out for frequencies ranging from 1 to 10−3 Hz) was selected as a test area to assess the imaging performances of various apparent‐resistivity definitions computed with rotational invariants of either the real part of the complex impedance tensor, or its imaginary part, or both. A comparison (based on earlier 3D numerical studies) has been made between the magnetotelluric images obtained in this way and the depths to the high‐resistivity basement, as known from boreholes and seismic investigations. The correlation coefficient between the series of basement depth values at 39 MT sites and the apparent‐resistivity values was found to be stronger and high correlation appeared at a shorter period when it was computed with apparent resistivities based on the real tensor rather than with apparent resistivities based on the imaginary tensor. In the light of our studies, ρReZ and the impedance phase seem to be more informative than any other combination of magnetotelluric interpretation parameters.
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Multi‐refractor imaging with stacked refraction convolution section
More LessABSTRACTMulti‐refractor imaging is a technique for constructing a single two‐dimensional image of a number of refractors by stacking multiple convolved and cross‐correlated reversed shot records. The method is most effective with high‐fold data that have been obtained with roll‐along acquisition programs because the stacking process significantly improves the signal‐to‐noise ratios. The major advantage of the multi‐refractor imaging method is that all the data can be stacked to maximize the signal‐to‐noise ratios before the measurement of any traveltimes. However, the signal‐to‐noise ratios can be further increased if only those traces that have arrivals from the same refractor are used, and if the correct reciprocal times or traces are employed.
A field case study shows that multi‐refractor imaging can produce a cross‐section similar to the familiar reflection cross‐section with substantially higher signal‐to‐noise ratios for the equivalent interfaces.
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Velocity–porosity relationships: Predictive velocity model for cemented sands composed of multiple mineral phases
Authors Mark A. Knackstedt, Christoph H. Arns and W. Val PinczewskiABSTRACTComputer simulations are used to calculate the elastic properties of model cemented sandstones composed of two or more mineral phases. Two idealized models are considered – a grain‐overlap clay/quartz mix and a pore‐lining clay/quartz mix. Unlike experimental data, the numerical data exhibit little noise yet cover a wide range of quartz/cement ratios and porosities. The results of the computations are in good agreement with experimental data for clay‐bearing consolidated sandstones.
The effective modulus of solid mineral mixtures is found to be relatively insensitive to microstructural detail. It is shown that the Hashin–Shtrikman average is a good estimate for the modulus of the solid mineral mixtures. The distribution of the cement phase is found to have little effect on the computed modulus–porosity relationships. Numerical data for dry and saturated states confirm that Gassmann's equations remain valid for porous materials composed of multiple solid constituents. As noted previously, the Krief relationship successfully describes the porosity dependence of the dry shear modulus, and a recent empirical relationship provides a good estimate for the dry‐rock Poisson's ratio.
From the numerical computations, a new empirical model, which requires only a knowledge of system mineralogy, is proposed for the modulus–porosity relationship of isotropic dry or fluid‐saturated porous materials composed of multiple solid constituents. Comparisons with experimental data for clean and shaly sandstones and computations for more complex, three‐mineral (quartz/dolomite/clay) systems show good agreement with the proposed model over a very wide range of porosities.
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Numerical modelling of interface scattering of seismic wavefield from a random rough interface in an acoustic medium: comparison between 2D and 3D cases
Authors Wasiu Makinde, Nathalie Favretto‐Cristini and Eric De BazelaireABSTRACTSeismic wavefield scattering from a statistically randomly rough interface in a multilayered piecewise homogeneous medium is studied in 3D. The influence of the surface roughness on the scattered wavefield is analysed numerically by using a finite‐difference operator in the acoustic domain. Since interface scattering in the real practical sense is a 3D physical phenomenon, we show in this work that the scattering response of a randomly rough interface is not the same in 3D situations as in the 2D cases described in some earlier works. For a given interface roughness height in 3D, an interface roughness height at least three times greater is required to produce an equivalent phase scattering effect in 2D situations, for a given correlation length of the interface roughness scale. Based on observations from spectral analysis, we show that scattering results principally in de‐phasing and frequency band‐limiting of the incident wavefront, the frequency band‐limiting properties being comparable to cases reported in the literature for absorption and thin‐layer filtering. The interface scattering phenomenon should be critically considered when using amplitude and phase information from seismic signal during inversion processes.
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Depth determination from a non‐stationary magnetic profile for scaling geology
Authors A.R. Bansal and V.P. DimriABSTRACTThe conventional spectral analysis method for interpretation of magnetic data assumes stationary spatial series and a white‐noise source distribution. However, long magnetic profiles may not be stationary in nature and source distributions are not white. Long non‐stationary magnetic profiles can be divided into stationary subprofiles following Wiener filter theory. A least‐squares inverse method is used to calculate the scaling exponents and depth values of magnetic interfaces from the power spectrum. The applicability of this approach is demonstrated on non‐stationary synthetic and field magnetic data collected along the Nagaur–Jhalawar transect, western India. The stationarity of the whole profile and the subprofiles of the synthetic and field data is tested. The variation of the mean and standard deviations of the subprofiles is significantly reduced compared with the whole profile. The depth values found from the synthetic model are in close agreement with the assumed depth values, whereas for the field data these are in close agreement with estimates from seismic, magnetotelluric and gravity data.
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On the electrical reflectivity tensor in d.c. electric field modelling
By J. SunABSTRACTWe use the integral equation for a d.c. electric field, published in the literature, to introduce the concept of the electrical reflectivity tensor into d.c. electric field modelling. It is shown that in d.c. electric field modelling, the electric reflectivity tensor can be obtained in exactly the same way as in electromagnetic modelling. As a result, for a d.c. electric field, the quasi‐linear and the quasi‐analytical approximations, as well as the quasi‐analytical series, can be constructed in exactly the same way as in electromagnetic modelling. If the primary field is uniform, and if the anomalous body is a uniform circular cylinder or a uniform sphere, the reflectivity tensor is zero order (constant), relating to the free surface charge density. Thus, for some homogeneous bodies that have simple shapes and are embedded in a uniform primary field, the electrical reflectivity tensor is not only a mathematical mechanism for obtaining approximate solutions, but also a physical reality. Indeed, the free surface charge density is defined as the change of the electric displacement vector across the boundary surface under consideration. If the primary field is caused by a point source, and if the anomalous body is a uniform sphere, the reflectivity tensor is second order, varying slowly within the sphere. The relationship to the free surface charge density can be established only when both the reflectivity tensor and the free surface charge density are approximated by the first terms of their series solutions. If the point source is far from the centre of the sphere, the corresponding reflectivity tensor reduces to zero order, and is independent of the observation position within the sphere, i.e. it is a constant. Therefore, the basic idea of the quasi‐analytical approximation, i.e. taking the reflectivity tensor outside the integral operator, is justified in the case considered here.
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Coherence methods in mapping AVO anomalies and predicting P‐wave and S‐wave impedances
Authors A.‐S. Barnola and R.E. WhiteABSTRACTFilters for migrated offset substacks are designed by partial coherence analysis to predict ‘normal’ amplitude variation with offset (AVO) in an anomaly free area. The same prediction filters generate localized prediction errors when applied in an AVO‐anomalous interval. These prediction errors are quantitatively related to the AVO gradient anomalies in a background that is related to the minimum AVO anomaly detectable from the data. The prediction‐error section is thus used to define a reliability threshold for the identification of AVO anomalies. Coherence analysis also enables quality control of AVO analysis and inversion. For example, predictions that are non‐localized and/or do not show structural conformity may indicate spatial variations in amplitude–offset scaling, seismic wavelet or signal‐to‐noise (S/N) ratio content. Scaling and waveform variations can be identified from inspection of the prediction filters and their frequency responses. S/N ratios can be estimated via multiple coherence analysis.
AVO inversion of seismic data is unstable if not constrained. However, the use of a constraint on the estimated parameters has the undesirable effect of introducing biases into the inverted results: an additional bias‐correction step is then needed to retrieve unbiased results. An alternative form of AVO inversion that avoids additional corrections is proposed. This inversion is also fast as it inverts only AVO anomalies. A spectral coherence matching technique is employed to transform a zero‐offset extrapolation or near‐offset substack into P‐wave impedance. The same technique is applied to the prediction‐error section obtained by means of partial coherence, in order to estimate S‐wave velocity to P‐wave velocity (VS/VP) ratios. Both techniques assume that accurate well ties, reliable density measurements and P‐wave and S‐wave velocity logs are available, and that impedance contrasts are not too strong. A full Zoeppritz inversion is required when impedance contrasts that are too high are encountered. An added assumption is made for the inversion to the VS/VP ratio, i.e. the Gassmann fluid‐substitution theory is valid within the reservoir area. One synthetic example and one real North Sea in‐line survey illustrate the application of the two coherence methods.
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Anisotropy from full waveform inversion of multicomponent seismic data using a hybrid optimization method
Authors Ying Ji and Satish C. SinghABSTRACTSeismic waveforms contain valuable information about the media, but the waveform inversion is a non‐linear problem. We present a waveform inversion method that combines a local optimization method with a genetic algorithm to determine the anisotropic parameters of a horizontally stratified medium. Synthetic seismograms for a horizontally stratified anisotropic medium are calculated using the reflectivity technique. In the initial stage of the inversion, the global space‐sampling properties of the genetic algorithm are used to direct the search to the region close to the global solution. This solution is then further improved using a conjugate‐gradient method. The numerical experiments performed with noisy synthetic data show that our hybrid optimization method satisfactorily reconstructs the anisotropic parameters at a reasonable computing cost while the range of slowness is adequate. We found that (i) for small‐angle data neither single‐ nor multiple‐component data are sufficient to determine the anisotropic parameters uniquely; (ii) for medium‐angle data the multiple‐component data are sufficient to determine the anisotropic parameters exactly whereas the single‐component data are not sufficient; and (iii) for wide‐angle data, either single‐ or multiple‐component data are sufficient to determine the anisotropic parameters accurately.
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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)