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- Volume 14, Issue 2, 1966
Geophysical Prospecting - Volume 14, Issue 2, 1966
Volume 14, Issue 2, 1966
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RAPID COMPUTATION OF THE GRAVITATION ATTRACTION OF TOPOGRAPHY ON A SPHERICAL EARTH*
Authors MANOUTCHEHR TAKIN and MANIK TALWANIABSTRACTA brief review of the existing methods of gravity reduction is given and a new method suitable for use on high speed digital computers is described. The method is based on the formula for the gravitational attraction of a frustum of a cone. The topographic contours are represented by polygons and the x and y coordinates of corners of the polygons constitute the input to the computer. The vertical component of the gravitational attraction is calculated by evaluating the cone formula for a number of vertical sections of the topography. Each vertical section is simplified by adopting a procedure of grouping and averaging for the distant points of the section. The effect of the earth's sphericity is taken into account by lowering the distant points of the sections by amounts determined by the curvature. The computations include the area close to the point at which the attraction is required and may be limited to an area defined by a circle centered at this point. The method is therefore compatible with the conventional zone chart methods.
As an illustration of the method the gravitational attraction of Caryn Seamount in the Atlantic Ocean is computed. The total Bouguer correction and the Terrain correction are also computed for an area in northwestern South America and comparisons are made with hand computations by a zone chart method. As an example, for work at sea, the Bouguer corrections for an area near the Island of Mauritius in the Indian Ocean are computed and the effects of sphericity and three‐dimensionality are calculated.
The gravitational attraction of two‐dimensional bodies can be computed in a very similar manner. The attraction of the Puerto Rico Trench model is computed and the results are compared with other methods. The effects of sphericity and assumptions involved in extending the models to infinity are discussed.
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A SIMPLE METHOD OF MAGNETOTELLURIC INTERPRETATION *
By SUDHIR JAINABSTRACTA simple method of magnetotelluric interpretation is derived using the property that the earth currents flow in horizontal sheets. It is shown that when the depth is taken as two‐thirds of the Cagniard's depth of penetration (Cagniard, 1953), the mean resistivity‐over the depth is the same as the apparent resistivity of the medium. From a mean resistivity versus depth of penetration plot, resistivity can be easily computed at all depths of the sounding.
This method gives satisfactory results in a short time and makes it possible to interpret the soundings over media of several layers. However, the results are inaccurate near maximum and minimum points of the plot as well as in the zone of thin layers.
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AN EVALUATION METHOD FOR GEOMAGNETIC DEEP SOUNDING, ITS DERIVATION AND PRACTICAL USE*
More LessABSTRACTThe derivation and application of a new method of geomagnetic deep sounding, that is exploring for underground electrical conductivity anomalies by means of temporal variations of the earth's magnetic field, is presented.
The problem is restricted to two dimensions (horizontal and vertical) and for the case of a nearly homogeneous horizontal component of the disturbance vector as compared with the vertical over the area in question.
The basis of the method is a relationship between both components of the disturbance vector. The first step is a period analysis of the records and from this the construction of so called “characteristic functions”, one for each station, these functions being determined by the conductivity distribution of the earth's interior. The second step consists of a model interpretation of these functions.
The method is applied to simultaneous records from five stations (U. Schmucker, 1959) within the region of the conductivity‐anomaly of Northern Germany. A preliminary model of this anomaly is given.
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THEORETICAL ANALYSIS OF APPARENT RESISTIVITY OVER A DYKE OF ARBITRARY SHAPE*
More LessABSTRACTThis paper deals with the apparent resistivity as observed on the surface due to a dyke of arbitrary shape. In order to give a closed analytical solution it has been necessary to assume that the dyke is either perfectly conductive or resistive relative to the enclosing medium. Furthermore we have considered an infinite line source instead of a conventional point current source; however a simple integral transform is given to transform the point‐source‐data into the line‐source‐data. So the present study is equally useful where line sources are inconvenient to handle. Besides considering the conventional method of electrical surveying (bipole method) where the source and sink are separated by a finite distance, we have considered a new variation (unipole method) where the source and sink are separated by an infinite distance, and the source is split into two separate sources each of half strength. A series of apparent resistivity curves for both methods are presented for different parameters of the dyke. The usefulness of these curves lies mainly in the fact that they may provide the necessary guide‐lines for semi‐quantitative interpretation of the observed data.
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SEISMIC REFRACTION AND SCREENING BY THIN HIGH‐VELOCITY LAYERS *
Authors J. Ph. POLEY and J. J. NOOTEBOOMAbstractThe screening effect of thin, relatively shallow high‐velocity layers often presents considerable problems in seismic exploration. Such layers prevent the greater part of the seismic energy from travelling to greater depths and introduce additional refraction arrivals, confusing the seismogram still further.
In order to investigate both the screening and refractive properties of high‐velocity layers, scale‐model experiments have been made over a wide range of layer‐thickness/ wavelength ratios (0.05 < d/λ < 2) for suitably chosen material contrasts. The results may be summarised as follows.
Refraction arrivals from thin layers in the field may be recognised by their relatively rapid amplitude decay. Furthermore, the “echeloning”‐effect observed for refraction first arrivals may be due to the presence of a (thin) layered structure. Since the apparent refraction velocity varies with d/λ when d/λ < 1, differences between vertical well‐log velocities and velocities observed along the surface may be expected, making time/depth conversion using surface velocity data inaccurate.
Transmission of elastic energy may be expected, if anywhere, only near the shotpoint, at small geophone offset, and for relatively thin screens (d/λ < 0.1). The transmitted signal shape is then independent of the layer thickness. This transmitted energy may be registered either in a reflection set‐up with geophones near the shotpoint, or in long‐distance refraction work.
Three possibilities are offered for overcoming the screening effect of thin high‐velocity layers: Use longer‐wavelength signals
Apply short‐spread reflection shooting
Apply long‐distance refraction shooting
The experimental results obtained in scale‐model arrangements of such set‐ups confirm the potentialities of these methods.
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POISSON'S CONSTANT WITH DRY SEDIMENTS AND WITH PACKINGS OF SPHERES*
By H. WACHHOLZABSTRACTIn order to find a relation between Poisson's constant of dry sediments and the porosity, it is necessary to consider the elastic behavior of the sediment's initial state and the final state during the process of consolidation. Sand and other loose materials of more or less granular substances represent the initial state. As substitute for this zone, elastic constants of simple cubic and hexagonal packing are examined. Supposed is the adhesion for the planes of contact. Besides of Hertz's formula for the contact area of spheres, an elastic function of displacement due to a tangential force for the contact area of the spheres is used. This function has been derived. With the aid of these two. elements, the constants of the mentioned packing are calculated. Poisson's constant will then be calculated from the formula being valid for isotropic solids for three different directions of the sound. The mean value is lying at .
With the known equation of Poisson's constant of rock having a small porosity, a third‐degree polynomial is formed. This polynomial agrees well with the average values of known measurements, and therefore can serve as a guide for the calculation of Poisson's constant of water‐saturated sediments.
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BOOK REVIEWS
K. Jung, Schwerkraftverfahren in der angewandten Geophysik (Gravity Methods in Applied Geophysics), Akademische Verlagsgesellschaft Geest & Portig KG., Leipzig, 1961, 348 pp., price: 48,– DM.
R. Meinhold, Geophysikalische Meβverfahren in Bohrungen, Geophysikalische Monographien Bd. 4, Akademische Verlagsgesellschaft Geest & Portig KG., Leipzig, 1965, 237 pp., 125 figs., 13 tables, size 8°, price: 55,– MDN.
George B. Clark, International Symposium, on Mining Research, Proceedings of a Symposium held at the University of Missouri (2 Volumes), Pergamon Press Ltd., Oxford, London, New York, 1962, 859 pages, price: γ 10 per set.
I. D. Savinskii, Probability Tables for Locating Elliptical Underground Masses with a Rectangular Grid, explanatory text translated from Russian, Consultants Bureau Enterprises Inc., New York, 1965, price: $ 15.
The World of Geology, edited by L. Donleet and Florence J. Leet, McGraw‐Hill Publishing Comp. Ltd., London, 1961, price: 21s 6d.
H. G. F. Winkler, Die Genese der metamorphen Gesteine. Springer‐Verlag, Berlin, Heidelberg, New York, 1965, 40 Figs., VIII, 218 pages, size 8°, price: 19,80. DM
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Volumes & issues
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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)