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- Volume 55, Issue 2, 2007
Geophysical Prospecting - Volume 55, Issue 2, 2007
Volume 55, Issue 2, 2007
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Constraints on velocity‐depth trends from rock physics models
Authors Peter Japsen, Tapan Mukerji and Gary MavkoABSTRACTEstimates of depth, overpressure and amount of exhumation based on sonic data for a sedimentary formation rely on identification of a normal velocity–depth trend for the formation. Such trends describe how sonic velocity increases with depth in relatively homogeneous, brine‐saturated sedimentary formations as porosity is reduced during normal compaction (mechanical and chemical). Compaction is ‘normal’ when the fluid pressure is hydrostatic and the thickness of the overburden has not been reduced by exhumation. We suggest that normal porosity at the surface for a given lithology should be constrained by its critical porosity, i.e. the porosity limit above which a particular sediment exists only as a suspension. Consequently, normal velocity at the surface of unconsolidated sediments saturated with brine approaches the velocity of the sediment in suspension. Furthermore, porosity must approach zero at infinite depth, so the velocity approaches the matrix velocity of the rock and the velocity–depth gradient approaches zero. For sediments with initially good grain contact (when porosity is just below the critical porosity), the velocity gradient decreases with depth. By contrast, initially compliant sediments may have a maximum velocity gradient at some depth if we assume that porosity decreases exponentially with depth. We have used published velocity–porosity–depth relationships to formulate normal velocity–depth trends for consolidated sandstone with varying clay content and for marine shale dominated by smectite/illite. The first relationship is based on a modified Voigt trend (porosity scaled by critical porosity) and the second is based on a modified time‐average equation. Baselines for sandstone and shale in the North Sea agree with the established constraints and the shale trend can be applied to predict overpressure. A normal velocity–depth trend for a formation cannot be expressed from an arbitrary choice of mathematical functions and regression parameters, but should be considered as a physical model linked to the velocity–porosity transforms developed in rock physics.
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The stress sensitivity of shaley sandstones
Authors Colin MacBeth and Christophe RibeiroABSTRACTThe link between the stress sensitivity of shaley sandstones and their porosity and clay content is investigated. This is achieved by firstly fitting a compliance‐based stress‐sensitivity law to laboratory measurements of ultrasonic velocity taken from four sets of reservoir sandstones, extracted from a variety of depositional settings. Correlations are then sought between the independent parameters of this law and the porosity or clay fraction of the rocks, which are then subsequently interpreted in terms of framework or pore‐space‐related microstructural clay models. The general conclusion drawn from the results is that both of the parameters defining the stress‐sensitivity law (the asymptotic modulus and the stress‐dependent excess compliance) clearly vary with porosity. However, only the asymptotic modulus shows a convincing trend with clay and there is little observed variation of the stress‐dependent compliance with clay. There is therefore a resultant variation of stress sensitivity with clay, but it is controlled only by the asymptotic modulus. The analysis also concludes that all four data sets fall into a framework‐related category of clay model.
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Quantitative detection of fluid distribution using time‐lapse seismic
Authors Futoshi Tsuneyama and Gary MavkoABSTRACTAlthough previous seismic monitoring studies have revealed several relationships between seismic responses and changes in reservoir rock properties, the quantitative evaluation of time‐lapse seismic data remains a challenge. In most cases of time‐lapse seismic analysis, fluid and/or pressure changes are detected qualitatively by changes in amplitude strength, traveltime and/or Poisson's ratio.
We present the steps for time‐lapse seismic analysis, considering the pressure effect and the saturation scale of fluids. We then demonstrate a deterministic workflow for computing the fluid saturation in a reservoir in order to evaluate time‐lapse seismic data. In this approach, we derive the physical properties of the water‐saturated sandstone reservoir, based on the following inputs: VP, VS, ρ and the shale volume from seismic analysis, the average properties of sand grains, and formation‐water properties. Next, by comparing the in‐situ fluid‐saturated properties with the 100% formation‐water‐saturated reservoir properties, we determine the bulk modulus and density of the in‐situ fluid. Solving three simultaneous equations (relating the saturations of water, oil and gas in terms of the bulk modulus, density and the total saturation), we compute the saturation of each fluid. We use a real time‐lapse seismic data set from an oilfield in the North Sea for a case study.
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Numerical study of seismic scattering and waveguide excitation in faulted coal seams
Authors S.A. Greenhalgh, B. Zhou, D.R. Pant and A. GreenABSTRACTFinite‐difference P‐SV simulations of seismic scattering characteristics of faulted coal‐seam models have been undertaken for near‐surface P‐ and S‐wave sources in an attempt to understand the efficiency of body‐wave to channel‐wave mode conversion and how it depends on the elastic parameters of the structure. The synthetic seismograms clearly show the groups of channel waves generated at the fault: one by the downgoing P‐wave and the other by the downgoing S‐wave. These modes travel horizontally in the seam at velocities less than the S‐wavespeed of the rock. A strong Airy phase is generated for the fundamental mode.
The velocity contrast between the coal and the host rock is a more important parameter than the density contrast in controlling the amplitude of the channel waves. The optimal coupling from body‐wave energy to channel‐wave energy occurs at a velocity contrast of 1.5. Strong guided waves are produced by the incident S‐sources for source angles of 75° to 90° (close to the near‐side face of the fault). As the fault throw increases, the amplitude of the channel wave also increases. The presence of a lower‐velocity clay layer within the coal‐seam sequence affects the waveguiding characteristics. The displacement amplitude distribution is shifted more towards the lower‐wavespeed layer. The presence of a ‘washout’ zone or a brecciated zone surrounding the fault also results in greater forward scattering and channel‐wave capture by the coal seam.
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Fourier reconstruction with sparse inversion
Authors P. Zwartjes and A. GisolfABSTRACTThe problem of seismic data reconstruction is posed as an inverse problem where the objective is to obtain the Fourier coefficients that synthesize the signal. Once the coefficients have been found, they are used to reconstruct the data on a uniformly spaced grid. A non‐quadratic model weight function is included to stabilize the inversion and to provide the additional information required to interpolate through gaps. In the reconstruction of a non‐uniformly sampled trace, an image and a marine 3D VSP shot‐record, the method shows improved reconstruction in large gaps and is less sensitive to the spatial bandwidth used in the inversion compared to Fourier reconstruction without the non‐quadratic model weight function.
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Non‐minimum phase wavelet estimation by non‐linear optimization of all‐pass operators
Authors Somanath Misra and Mauricio D. SacchiABSTRACTConvolution of a minimum‐phase wavelet with an all‐pass wavelet provides a means of varying the phase of the minimum‐phase wavelet without affecting its amplitude spectrum. This observation leads to a parametrization of a mixed‐phase wavelet being obtained in terms of a minimum‐phase wavelet and an all‐pass operator. The Wiener–Levinson algorithm allows the minimum‐phase wavelet to be estimated from the data. It is known that the fourth‐order cumulant preserves the phase information of the wavelet, provided that the underlying reflectivity sequence is a non‐Gaussian, independent and identically distributed process. This property is used to estimate the all‐pass operator from the data that have been whitened by the deconvolution of the estimated minimum‐phase wavelet. Wavelet estimation based on a cumulant‐matching technique is dependent on the bandwidth‐to‐central‐frequency ratio of the data. For the cumulants to be sensitive to the phase signatures, it is imperative that the ratio of bandwidth to central frequency is at least greater than one, and preferably close to two. Pre‐whitening of the data with the estimated minimum‐phase wavelet helps to increase the bandwidth, resulting in a more favourable bandwidth‐to‐central‐frequency ratio. The proposed technique makes use of this property to estimate the all‐pass wavelet from the prewhitened data. The paper also compares the results obtained from both prewhitened and non‐whitened data. The results show that the use of prewhitened data leads to a significant improvement in the estimation of the mixed‐phase wavelet when the data are severely band‐limited. The proposed algorithm was further tested on real data, followed by a test involving the introduction of a 90°‐phase‐rotated wavelet and then recovery of the wavelet. The test was successful.
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Estimation of the apertures of water‐saturated fractures by nuclear magnetic resonance well logging
Authors Yoshito Nakashima and Tsuneo KikuchiABSTRACTFracture aperture is an important transport property in subsurface hydrology because it influences well productivity and the volume of the water resource. Nuclear magnetic resonance (NMR) well logging measures the hydrogen‐bearing fluid molecules in porous or fractured strata, and the NMR signal intensity increases with the amount of fluid in the sensed region of the NMR sonde. Fluid confined in a large fracture of >>0.2 mm in aperture has T2 (i.e. spin‐spin relaxation time) values as long as those of the bulk fluid. The bulk‐fluid porosity (i.e. porosity calculated using this long T2 component in a T2 histogram data) increases linearly with aperture. Therefore, NMR logging enables quantitative estimation of fracture apertures of >>0.2 mm using the bulk‐fluid porosity data if the calibration of the NMR sonde is performed adequately. We applied NMR logging to a borehole in a Holocene andesite lava at Sumikawa, Japan, to estimate the aperture of open fractures within the lava. A test well of 100 m depth and 20 cm diameter, filled with bentonite drilling mud, was scanned with an NMR sonde to obtain a profile of the porosity and the T2 histogram of the andesite. The bulk‐fluid porosity was calculated from the T2 histogram data, as the porosity at which the T2 value is larger than or equal to a threshold T2 of bulk bentonite mud. The bulk‐fluid porosity of a specific inclined fracture responsible for the total loss of circulation at 61.2 m depth during drilling was calculated assuming a threshold or T2 cut‐off of 33 ms, and again for a cut‐off of 100 ms. Calibration of the NMR sensor in a laboratory and measurement of the fracture dip angle by electrical microimaging logging enabled us to estimate the fracture aperture as 1.7 cm, assuming a T2 cut‐off of 33 ms, or 1.6 cm for a T2 cut‐off of 100 ms. The method of aperture determination described in this study is independent of fluid species and lithology, and is applicable to various hydrogen‐bearing borehole fluids (clean water, mud and oil) and geological settings.
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A derivative‐based interpretation approach to estimating source parameters of simple 2D magnetic sources from Euler deconvolution, the analytic‐signal method and analytical expressions of the anomalies
Authors Wen‐Bin Doo, Shu‐Kun Hsu and Yi‐Ching YehABSTRACTThe major advantage of using either the analytic‐signal or the Euler‐deconvolution technique is that we can determine magnetic‐source locations and depths independently of the ambient earth magnetic parameters. In this study, we propose adopting a joint analysis of the analytic signal and Euler deconvolution to estimate the parameters of 2D magnetic sources. The results can avoid solution bias from an inappropriate magnetic datum level and can determine the horizontal locations, depths, structural types (indices), magnetization contrasts and/or structural dips. We have demonstrated the feasibility of the proposed method on 2D synthetic models, such as magnetic contacts (faults), thin dikes and cylinders. However, the method fails to solve the parameters of magnetic sources if there is severe interference between the anomalies of two adjacent magnetic sources.
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Estimation of clay content in soil based on resistivity modelling and laboratory measurements
Authors Vladimir Shevnin, Aleksandr Mousatov, Albert Ryjov and Omar Delgado‐RodriquezABSTRACTThe determination of clay content in near‐surface formations is crucial for geotechnical, hydrogeological and oil‐contamination studies. We have developed a technique for estimating clay content that consists of the minimization of the difference between the theoretically calculated and measured soil resistivities as a function of water salinity. To calculate the resistivity, we used a model that takes into account the electrochemical processes in the clay micropores. The experimental measurements of soil resistivity were performed on soil samples, completely saturated by brines at different concentrations of NaCl salt in the range 0.6–100 g/l, to obtain the resistivity versus salinity curve. The parameters obtained with this curve inversion are the clay content, the total porosity and the cation exchange capacity. To verify the new technique, we determined clay concentrations of artificial mixtures of calibrated sand and clay. The relative mean error in the clay content does not exceed 20% for a 5% fitting error of the resistivity versus salinity curves. Such evaluations allow the correct separation of the main lithological groups (sand, sandy loam, loam, and light, medium and heavy clay).
We applied this technique to estimate the petrophysical parameters of soils (clay content, porosity and cation exchange capacity) at various sites in Mexico. The results improved the interpretation of the vertical electrical soundings, the lithological soil characterization and the delineation of oil‐contaminated areas.
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3D magnetotelluric modelling including surface topography
Authors Myung Jin Nam, Hee Joon Kim, Yoonho Song, Tae Jong Lee, Jeong‐Sul Son and Jung Hee SuhABSTRACTAn edge finite‐element method has been applied to compute magnetotelluric (MT) responses to three‐dimensional (3D) earth topography. The finite‐element algorithm uses a single edge shape function at each edge of hexahedral elements, guaranteeing the continuity of the tangential electric field while conserving the continuity of magnetic flux at boundaries. We solve the resulting system of equations using the biconjugate gradient method with a Jacobian preconditioner. The solution gives electric fields parallel to the slope of a surface relief that is often encountered in MT surveys. The algorithm is successfully verified by comparison with other numerical solutions for a 3D‐2 model for comparison of modelling methods for EM induction and a ridge model. We use a 3D trapezoidal‐hill model to investigate 3D topographic effects, which are caused mainly by galvanic effects, not only in the Zxy mode but also in the Zyx mode. If a 3D topography were approximated by a two‐dimensional topography therefore errors occurring in the transverse electric mode would be more serious than those in the transverse magnetic mode.
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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 63 (2015)
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Volume 55 (2007)
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Volume 53 (2005)
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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 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 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)