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- Volume 24, Issue 2, 1976
Geophysical Prospecting - Volume 24, Issue 2, 1976
Volume 24, Issue 2, 1976
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CALCUL DES COURBES DE, SONDAGES ÉLECTRIQUES À L'AIDE DES FONCTIONS D'ÉCHANTILLONNAGE*
By W. BARANOVAbstractRecently I had an opportunity to apply the theory of sampling functions to the functional transformations of gravity and magnetic anomalies (Baranov 1975). It would be interesting to examine if there is a possibility to use these functions in the electrical prospecting. It seems that the answer might be affirmative.
This paper is an attempt to compute the master curves for the electrical vertical sounding with the aid of sampling functions.
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PROGRESS IN THE DIRECT INTERPRETATION OF RESISTIVITY SOUNDINGS: AN ALGORITHM*
By O. KOEFOEDAbstractAn algorithm is presented for the direct interpretation of resistivity sounding data. The algorithm is based on the method of successive reductions to lower boundary plane of the resistivity transform function. A novel aspect of the algorithm is that error limits are assigned to the initial values of the resistivity transform, and these error limits are carried through in all the subsequent computations. The width of the error range is then used as the basis for assigning weight factors in the final computation of thicknesses and resistivities of the layers. The errors in the resistivity transform derived from the solution given by the algorithm are usually not more than twice as large as those in the original data.
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THE INDUCED POLARIZATION RESPONSE OF A THIN HIGHLY‐CONDUCTIVE ORE BODY*
Authors M. E. FISHER and D. G. HURLEYAbstractConsider a lamina of ore of thickness 2t whose electrical resistivity p2 is much smaller than the resistivity p1 of the surrounding host rock. The induced polarization response of such an ore body is investigated under the assumption that it arises from the variation of p2 with the frequency of measurement.
Let p2l and p2h be the resistivities of the ore‐body for the low and high frequencies of measurement and L a length of the order of the distance between the transmitting electrodes. A theory is developed under the assumptions that each of the quantities t/L, p2l/p1, p2h/p1, Lp2l/2tp1, and Lp2h/tp1 is small. The main conclusion is that the frequency effect parameter P is given approximately by P=cL(p2l − p2h)/2tp1, where the constant c is independent of t, p2l, p2h, and p1. Thus for a family of similar ore bodies having differing values of t, P will be the larger the smaller t.
Detailed results are given for a semi‐infinite submerged dipping dyke and the two dimensional Wenner array.
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ELECTROMAGNETIC RESPONSE OF A BROKEN ORE‐VEIN (MODEL STUDIES)*
Authors M. PODDAR, A. K. LAHIRI and B. K. DEBAbstractA broken ore‐vein is very common in nature. A small scale model of such a vein has been made by placing two thin metal sheets edge to edge with an air gap between them. The electromagnetic response of this model in a uniform oscillating magnetic field has been measured. The results show that (a) the response of the whole body is not the sum of responses of the constituent parts, (b) the response of the upper part is dominant by virtue of its proximity to the receiving coil and (c) the lower part has the effect of making the upper part appear nearer to the surface and poorer in conductance than it really is.
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ACCURATE DETERMINATION OF THE DIP ANGLE OF A GEOLOGICAL CONTACT USING THE GRAVITY METHOD*
By R. GREENAbstractFrom a gravity profile over a truncated horizontal plate, the horizontal derivative and, by means of the Hilbert Transform, the vertical derivative are obtained.
When the horizontal derivative is plotted against the vertical derivative, the axis of symmetry of the resulting curve is inclined at the angle of dip of the face of the truncated plate. The depths to the upper and lower surfaces of the plate can be obtained uniquely from the symmetrical figure. Because of the derivatives being used, the method avoids the difficulties which arise from other methods of interpretation which depend upon a knowledge of the position of the origin of the gravity field data. The entire procedure for interpretation can be accommodated on a programmable calculator. An illustrative example is given.
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INTERPRETATION OF GRAVITV ANOMALIES BY MEANS OF LOCAL POWER SPECTRA*
Authors B. CIANCIARA and H. MARCAKAbstractA statistical model of the medium is introduced as source of a gravimetric anomaly. On the basis of this model the estimation of the parameters of the medium is proposed based on the statistically transformed power spectrum of the gravity anomaly. The method permits to associate the estimated depths to the disturbing limit with the profile points. Practical examples illustrate usefulness of this method to interpretation.
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DEPTH ESTIMATION OF MAGNETIC SOURCES BY MEANS OF FOURIER AMPLITUDE SPECTRA*
Authors A. HAHN, E. G. KIND and D. C. MISHRAAbstractThe Fourier transform of a square‐shaped section of a magnetic survey, digitized in a square grid, forms a rectangular matrix of coefficients which can be condensed to a series of average amplitudes dependent only on their frequency and no longer on the direction of the respective partial waves. These average amplitudes together represent a spectrum which–when plotted in a semilogarithmic coordinate system (log amplitude versus frequency)–often shows straight segments which decrease with increasing frequency. By continuing the given field downwards these straight segments become horizontal at a certain depth, the so‐called “white depth”. This white depth may be used as a first estimate for the depth of magnetic sources producing the respective part of the field. It is shown that the sources which correspond to such use of the white depth can be expected to be “randomly distributed with some positive autocorrelation”.
As an example for such a depth estimation the interpretation of the aeromagnetic survey of NW‐Germany by a relief in 8–16 km depth is given. The relief divides the subsurface in an upper nonmagnetic layer and a lower layer with magnetization M= 2 Am−1.
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THE NANOLOG, A NEW WAY TO LOG THE RESISTIVITY OF THE SEA FLOOR*
Authors H. BECKMANN and G. DEMIRAYAbstractA new device for resistivity logging has been developed with a doubly focussed system. It resembles a simplified double set of microlaterologs. The diagram of the log shows the formation resistivity factor of the sediments on the sea floor. The probe is trailed after the logging boat on a cable with at least two or four cores. The penetration of this log is better than 10 cm. The log is used for resistivity mapping, and it could be used for the exploration of heavy minerals and managese nodules.
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THE DETERMINATION OF DIGITAL WIENER FILTERS FROM AN ILL‐CONDITIONED SYSTEM OF NORMAL EQUATIONS*
Authors S. TREITEL and R. J. WANGAbstractThe system of normal equations associated with the discrete Wiener filter is sometimes ill‐conditioned. The purpose of this paper is to show that in such cases the solutions obtained vary drastically with the particular choice of an algorithm and of the computer used for its implementation.
A review of the basic mathematical theory behind an ill‐conditioned matrix is first presented. Numerical examples are then given to illustrate that the solutions of the normal equations are sensitive to the word length of a given computer. Finally, two possible remedies are described: (1) The well‐known method of prewhitening and (2) the use of the conjugate‐gradient algorithm for solving the normal equations.
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CALIBRATION OF MARINE SEISMIC SOURCES USING A HYDROPHONE OF UNKNOWN SENSITIVITY*
By M. H. SAFARAbstractThe absolute amplitude of the pressure pulse radiated by a marine seismic source is one of the prime criteria used in evaluating its performance. A technique for this measurement is proposed which is applicable to all sources which radiate a bubble pulse. The technique is described with reference to an air‐gun array in which the pulse radiated from a single gun is compared with that radiated by the full array. The advantage of the method is that absolute values of pressure are obtained without any need for a calibrated hydrophone. In theory this may seem a trivial advantage but in practice sensitivity factors for the hydrophone channel cannot always be relied upon. The proposed technique is illustrated by an example.
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THE QUANTITATIVE ANALYSIS OF FREQUENCY‐DOMAIN INDUCED POLARIZATION SOUNDINGS OVER HORIZONTAL BEDS*
Authors D. PATELLA and D. SCHIAVONEAbstractFollowing up our recent study of an indirect procedure for the practical determination of the maximum frequency‐effect, defined as fe = 1 − pρ∞/ρdc with ρ∞ the resistivity at infinite frequency, we show at first how, through the Laplace transform theory, ρ∞ can be related to stationary field vectors in the simple form of Ohm's law. Then applying the equation of continuity for stationary currents with a suitable set of boundary conditions, we derive the integral expression of the apparent resistivity at infinite frequency ρ∞,a in the case of a horizontally layered earth. Finally, from the definition of the maximum apparent frequency‐effect, analytical expressions of feα are obtained for both Schlumberger and dipole arrays placed on the surface of the multi‐layered earth section in the most general situation of vertical changes in induced polarization together with dc resistivity variations not at the same interfaces. Direct interpretation procedures are suggested for obtaining the layering parameters directly from the analysis of the sounding curves.
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DIRECT APPLICATIONS OF THE DAR ZARROUK PARAMETERS IN GROUND WATER SURVEYS*
More LessAbstractThe combination of layer resistivity and thickness in the so‐called Dar Zarrouk parameters S and T may be of direct use in aquifer protection studies and for the evaluation of hydrologic properties of aquifers.
The protective capacity of a clayey aquifer overburden is proportional to its longitudinal unit conductance S which, in terms of aquifer protection, gets a dimension of time (e.g. infiltration time). Aquifer storage in fissured reservoirs may be determined from differential conductance measurements (ΔS). Combination of the expression for ΔS with an empirical expression for electric conduction in fissured media yields a simple formula for water content per unit surface area. Both principles and possible developments are illustrated for a set of carboniferous limestone basins.
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FAST AUTOMATIC PROCESSING OF RESISTIVITY SOUNDINGS*
Authors M. BICHARA and J. LAKSHMANANAbstractThe difficulty to use master curves as well as classical techniques for the determination of layer distribution (ei, ρi) from a resistivity sounding arises when the presumed number of layers exceeds five or six.
The principle of the method proposed here is based on the identification of the resistivity transform. This principle was recently underlined by many authors. The resistivity transform can be easily derived from the experimental data by the application of Ghosh's linear filter, and another method for deriving the filter coefficientes is suggested.
For a given theoretical resistivity transform corresponding to a given distribution of layers (thicknesses and resistivities) various criteria that measure the difference between this theoretical resistivity transform and an experimental one derived by the application of Ghosh's filter are given. A discussion of these criteria from a physical as well as a mathematical point of view follows.
The proposed method is then exposed; it is based on a gradient method. The type of gradient method used is defined and justified physically as well as with numerical examples of identified master curves. The practical use for the method and experimental confrontation of identified field curves with drill holes are given. The cost as well as memory occupation and time of execution of the program on CDC 7600 computer is estimated.
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COMBINED REFRACTION SEISMIC AND GRAVIMETRIC INVESTIGATIONS IN A PALEOGEOGRAPHICAL AND GEOLOGICAL RESEARCH PROGRAM*
More LessAbstractRefraction seismic and gravity investigations were executed to solve geological and hydrographical problems in recent strata: These loose sediments necessitated a special arrangement for the energy source in the seismic measurements, By the use of a falling weight the refracted wave could be registered from a depth of more than 30 m. Quaternary fluviatile sands are characterized by lower velocities than the Tertiary sediments. Even a marked velocity difference between different Tertiary formations could be observed. Sand‐filled valleys in Tertiary clays give relatively important variations in the gravity field caused by the small differences of densities. Thus buried channels in a clay subsoil can be found by accurate gravity measurements.
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THE WAVE EQUATION APPLIED TO MIGRATION*
Authors D. LOEWENTHAL, L. LU, R. ROBERSON and J. SHERWOODAbstractClaerbout's method has been implemented for the migration of stacked seismic data. A simplified description of the method is given together with an account of some of the practical programming problems and the types of inaccuracy encountered. Routine production results are considered to be comparable or superior to the results derived from alternative migration techniques. Particular advantages are 1) the possibility of using a detailed velocity model for the migration and 2) the preservation of the amplitude and character of the seismic events on the migrated time section.
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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)