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- Volume 48, Issue 5, 2000
Geophysical Prospecting - Volume 48, Issue 5, 2000
Volume 48, Issue 5, 2000
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Selection of the wavenumbers k using an optimization method for the inverse Fourier transform in 2.5D electrical modelling
Authors Shi‐zhe Xu, Ben‐chun Duan and Da‐hai ZhangAbstractAn optimization method is used to select the wavenumbers k for the inverse Fourier transform in 2.5D electrical modelling. The model tests show that with the wavenumbers k selected in this way the inverse Fourier transform performs with satisfactory accuracy.
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Depth of detection of highly conducting and volume polarizable targets using induced polarization
Authors A. Apparao, G.S. Srinivas, V. Subrahmanya Sarma, P.J. Thomas, M.S. Joshi and P. Rajendra PrasadAbstractWe define the apparent frequency effect in induced polarization (IP) as the relative difference between apparent resistivities measured using DC excitation on the one hand and high‐frequency excitation (when the IP effect vanishes) on the other. Assuming a given threshold for the minimum detectable anomaly in the apparent frequency effect, the depth of detection of a target by IP can be defined as that depth below which the target response is lower than the threshold for a given electrode array. Physical modelling shows that for the various arrays, the depth of detection of a highly conducting and volume polarizable target agrees closely with the depth of detection of an infinitely conducting and non‐polarized body of the same shape and size. The greatest depth of detection is obtained with a two‐electrode array, followed by a three‐electrode array, while the smallest depth of detection is obtained with a Wenner array when the array spread is in‐line (i.e. perpendicular to the strike direction). The depth of detection with a Wenner array improves considerably and is almost equal to that of a two‐electrode array when the array spread is broadside (i.e. along the strike direction).
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A brief study of applications of the generalized reciprocal method and of some limitations of the method
More LessAbstractAn analysis of the generalized reciprocal method (GRM), developed by Palmer for the interpretation of seismic refraction investigations, has been carried out. The aim of the present study is to evaluate the usefulness of the method for geotechnical investigations in connection with engineering projects. Practical application of the GRM is the main object of this study rather than the theoretical/mathematical aspects of the method.
The studies are partly based on the models and field examples presented by Palmer. For comparison, some other refraction interpretation methods and techniques have been employed, namely the ABC method, the ABEM correction method, the mean‐minus‐T method and Hales' method. The comparisons showed that the results, i.e. the depths and velocities determined by Palmer, are partly incorrect due to some errors and misinterpretations when analysing the data from field examples.
Due to the limitations of the GRM, some of which are mentioned here, stated by Palmer in his various publications, and other shortcomings of the method (e.g. the erasing of valuable information), the GRM must be regarded as being of limited use for detailed and accurate interpretations of refraction seismics for engineering purposes.
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Three‐dimensional structure of the Laguna Salada Basin and its thermal regime
Authors R.E. Chávez, E.L. Flores, J.O. Campos, M. Ladrón de Guevara, M.C. Fernández‐Puga and J. HerreraAbstractA comprehensive reinterpretation of the available gravity, magnetic, geothermal, geological and borehole information has been made of the Laguna Salada Basin to establish a 3D model of the basement and sedimentary infill. According to statistical spectral analysis, the residual gravity anomaly is due to sources with a mean regional depth of 2.8 km. The topography of the basement was obtained from a three‐dimensional inversion carried out in the wavenumber domain using an iterative scheme. The maximum density contrast of −300 kg/m3 estimated from previous studies and the mean depth of 2.5 km finally constrained this inversion. The resulting model indicated that the sedimentary infill is up to 4.2 km thick at its deepest point. According to the gravity‐derived basement topography, the basin presents an asymmetry (i.e. it is of the half‐graben type). It is deeper to the east, where it is delimited from the Sierra Cucapah by a step fault. By contrast, the limit with the Sierra de Juarez is a gently sloping fault (i.e. a listric fault). The basement is not even, but it comprises a series of structural highs and lows. N–S to NW–SE and E–W to NE–SW faults delimit these structural units.
The magnetic modelling was constrained by (i) the gravity‐derived basement topography; (ii) a Curie isotherm assumed to be between 7 km and 10 km; (iii) assuming induced magnetization only; (iv) the available geological and borehole information. The magnetic anomalies were interpreted successfully using the gravity‐derived basement/sedimentary interface as the top of the magnetic bodies (i.e. the magnetic modelling supports the gravity basement topography). An elongated N–S to NW–SE trending highly magnetized body running from south to north along the basin is observed to the west of the basin. This magnetic anomaly has no gravity signature. Such a feature can be interpreted as an intrusive body emplaced along a fault running through the Laguna Salada Basin. Treatment of the gravity and magnetic information (and of their horizontal gradients) with satellite image processing techniques highlighted lineaments on the basement gravity topography correlating with mapped faults. Based on all this information, we derived detailed geological models along four selected profiles to simulate numerically the heat and fluid flow in the basin. We used a finite‐difference scheme to solve the coupled Darcy and Fourier differential equations. According to our results, we have fluid flow in the sedimentary layers and a redistribution of heat flow from the basin axis toward its rims (Sierra de Juárez and Sierra Cucapah). Our model temperatures agree within an error of 4% with the observed temperature profiles measured at boreholes. Our heat‐flow determinations agree within an error of ±15% with extrapolated observations. The numerical and chemical analyses support the hypothesis of fluid circulation between the clay–lutite layer and the fractured granitic basement. Thermal modelling shows low heat‐flow values along the Laguna Salada Basin. Deep fluid circulation patterns were observed that redistribute such flow at depth. Two patterns were distinguished. One displays the heat flow increasing from the basin axis towards its borders (temperature increase of 20°C). The second pattern shows an increasing heat flow from south to north of the basin. Such behaviour is confirmed by the temperature measurements in the thermometric boreholes.
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An approximate analytical approach to compute geoelectric dipole–dipole responses due to a small buried cube
Authors Sándor Szalai and László SzarkaA simple analytical solution is presented for computing direct current (DC) electric field distortion due to a small cube in a homogeneous half‐space, measured with a dipole–dipole array on the surface. Both the transmitter and the receiver may have any orientation; furthermore their position on the horizontal surface and the depth of the cube can be freely selected. It is shown that a simple approximate analytical method may replace more complicated 3D numerical modelling algorithms.
The approximation lies in the linearization of the problem: the secondary source (i.e. the cube) is considered as a system of three perpendicular electric dipoles. In spite of this first‐order approximation, in the case of realistic depths z (zR≈0.1–0.5, where R is the transmitter–receiver distance), this approximate solution fits very well with true 3D numerical modelling results, and with analogue modelling results if aR≤0.1, where a is the length of the side of the cube. Due to its simplicity, this method could be used for computing DC field distortion effects, estimating parameter‐sensitivities, or even determining some initial models for further inversions.
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Cross‐hole resistivity tomography using different electrode configurations
Authors Zhou Bing and S.A. GreenhalghThis paper investigates the relative merits and effectiveness of cross‐hole resistivity tomography using different electrode configurations for four popular electrode arrays: pole–pole, pole–bipole, bipole–pole and bipole–bipole. By examination of two synthetic models (a dipping conductive strip and a dislocated fault), it is shown that besides the popular pole–pole array, some specified three‐ and four‐electrode configurations, such as pole–bipole AM–N, bipole–pole AM–B and bipole–bipole AM–BN with their multispacing cross‐hole profiling and scanning surveys, are useful for cross‐hole resistivity tomography. These configurations, compared with the pole–pole array, may reduce or eliminate the effect of remote electrodes (systematic error) and yield satisfactory images with 20% noise‐contaminated data. It is also shown that the configurations which have either both current electrodes or both potential electrodes in the same borehole, i.e. pole–bipole A–MN, bipole–pole AB–M and bipole–bipole AB–MN, have a singularity problem in data acquisition, namely low readings of the potential or potential difference in cross‐hole surveying, so that the data are easily obscured by background noise and yield images inferior to those from other configurations.
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Automatic cross‐well tomography by semblance and differential semblance optimization: theory and gradient computation
Authors R.‐E. Plessix, W.A. Mulder and A.P.E. ten KroodeA technique for automatic cross‐well tomography based on semblance and differential semblance optimization is presented. Given a background velocity, the recorded seismic data traces are back‐propagated towards the source, i.e. shifted towards time zero using the modelled traveltime between the source and the receiver and corrected for the geometrical spreading. Therefore each back‐propagated trace should be a pulse, close to time zero. The mismatches between the back‐propagated traces indicate an error in the velocity model. This error can be measured by stacking the back‐propagated traces (semblance optimization) or by computing the norm of the difference between adjacent traces (differential semblance optimization).
It is known from surface seismic reflection tomography that both the semblance and differential semblance functional have good convexity properties, although the differential semblance functional is believed to have a larger basin of attraction (region of convergence) around the true velocity model. In the case of the cross‐well transmission tomography described in this paper, similar properties are found for these functionals.
The implementation of this automatic method for cross‐well tomography is based on the high‐frequency approximation to wave propagation. The wavefronts are constructed using a ray‐tracing algorithm. The gradient of the cost function is computed by the adjoint‐state technique, which has the same complexity as the computation of the functional. This provides an efficient algorithm to invert cross‐well data. The method is applied to a synthetic data set to demonstrate its efficacy.
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Automatic cross‐well tomography: an application of the differential semblance optimization to two real examples
More LessAn automatic tomography algorithm, based on differential semblance optimization (DSO), has been used to invert real cross‐well seismic data for the background velocity. The method relies on the first‐arrival transmitted waves. Given a background velocity model, the traveltimes between the sources and the receivers are computed, then semblance panels are created by back‐propagating the data traces. If the velocity model is correct all the first‐arrival transmitted waves will be aligned in the semblance panels. The DSO method consists of finding the background velocity by minimizing the L2‐norm of the difference between adjacent back‐propagated traces. Thanks to the good behaviour of this DSO cost function about the solution, a local (gradient) optimization can be performed. This provides a relatively fast algorithm when ray tracing and analytic computation of the gradient are used.
Unfortunately the method fails in the presence of caustics in the data. However, this difficulty can be circumvented by applying suitable masks to the data. This approach is first applied to a synthetic example then to two real data sets: the McElroy data set recorded in West Texas and the NIMR data set recorded in Oman. The results are quite encouraging and similar to those obtained with classical tomography.
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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)