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- Volume 23, Issue 1, 1975
Geophysical Prospecting - Volume 23, Issue 1, 1975
Volume 23, Issue 1, 1975
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CONTOURING AND THE CONTOUR MAP: A NEW PERSPECTIVE*
By A. E. WRENAbstractWith few exceptions, traditional approaches to contouring have been too subjective. Contouring and contour maps are too often discussed in terms more appropriate to art than to science. With hand contouring there is some justification for this attitude; with machine (i.e. programmed) contouring there is none.
Hand contouring is highly susceptible to interpretive judgement and the interpreter is not bound by rigid mathematical constraints. Hence, in allowing for the interpreter's “freedom of expression” it may be difficult to evaluate hand contouring in a totally analytical and objective manner. Machine contouring, however, is based upon mathematical formulation. It is therefore a consistent and objective procedure, ideally suited to objective definition and analysis.
It can be demonstrated that the combined process of sampling plus contouring constitutes a two‐dimensional filter. The contouring component is that part which introduces “distortion” or wavenumber discrimination. An ideal contour package is one that acts as an all‐pass filter where the distortion is zero.
The application of filter theory to the evaluation of a machine contour package and its performance permits description in the more convenient language and terminology of the wavenumber domain, rather than that of the space domain. A more important advantage is that the contour package can be subjected to the various standards of filter evaluation such as amplitude and phase response.
The practical application, as well as the benefit, of this approach is revealed through the comparison, in both the space and wavenumber domains, of contour maps generated from various machine contour packages.
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APPLICATION OF A HILBERT TRANSFORM METHOD TO THE INTERPRETATION OF SURFACE‐VEHICLE MAGNETIC DATA*
Authors R. GREEN and J. M. STANLEYAbstractThe development of an alkali vapour vehicle borne magnetometer providing very high resolution and a high sampling rate has called for reconsideration of interpretation procedures. With continuous profiling at ground level, the close proximity to near surface structures requires that the precise interpretation of geological boundaries be of paramount importance. Rapid digital recording also demands efficient data processing. Both these requirements can be met by the method described. Essentially the method reduces to a simple Hilbert transform of the magnetic profile. The calculation provides an extremely well defined position of the contact and accurate specification of the dip, strike, depth of overburden, and magnetic susceptibility parameters. Particular advantages are tolerance to high frequency noise, independence from a predetermined origin and baseline, and freedom from subjective judgements.
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THE USE OF FOURIER SERIES METHOD IN UPWARD CONTINUATION WITH NEW IMPROVEMENTS*
By L. J. TSAYAbstractThis paper shows how to reduce the errors near edges of potential field data that result from using Fourier series in the computation of upward continuation of potential field anomalies. This kind of error, if uncorrected, can lead to erroneous geological interpretation.
The errors that occur at both edges of potential field data after upward continuation originate from the representation of data by using Fourier series from which data becomes periodic with discontinuities or sharp changes between each period. In order to reduce this type of error, we propose, either 1) to use only the cosine series, or 2) to add a certain number of constant data to both edges of the original data before continuation. Using these new schemes, we have demonstrated the improvement on the accuracy near edges of continued anomalies with profiles of magnetic anomaly computed from an assumed model.
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GRAVITY COMPUTATIONS BY FLUX DENSITY SUMMATIONS*
More LessAbstractGravity profiles can be computed by summing flux lines uniformly radiating from source elements within a density distribution. Digital computations are performed efficiently, irregular density distributions modeled, and alterations easily made to the model to alter the profile by recomputation of only the altered elements. The concept applies to both two‐ and three‐dimensional models and the corresponding datum plane contours. Two‐dimensional computations are described and illustrated.
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INTER‐BOREHOLE ACOUSTIC MEASUREMENTS AND THEIR USE IN ENGINEERING GEOLOGY*
Authors D. M. McCANN, P. GRAINGER and C. McCANNAbstractWell–to‐well seismic measurements are adapted to civil engineering problems by use of a sparker as a source of seismic signals and an 80 kHz hydrophone as a receiver. For display a Tektronix 549 oscilloscope is used.
Field application shows that the delineation of interfaces between homogeneous strata and the detection and delineation of localized and irregular features is possible from inter‐well travel times. In‐situ measurement of the compressional wave velocity in a medium is often complicated by refraction and wave guide effects. The degree of fracturing cannot be estimated from travel time measurements alone in a tightly jointed, saturated, rock mass, but it may be possible to correlate variations in pulse shape and length with this parameter.
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BOUNDARY CONDITIONS FOR THIN IMPERFECT CONDUCTORS AND INSULATORS*
By D. G. HURLEYAbstractConsider a thin, plane, finite sheet of material of thickness 2t whose electrical resistivity is σ2. It is surrounded by a medium of resistivity σ1 in which there is an electric field whose length scale is L. We consider the limit t/L→ o with , or fixed. In the former case the sheet is an imperfect conductor and it is shown that it may be modelled by a surface on which the boundary condition is , where φ and Z are the (nondimensional) electrical potential and distance measured normal to the surface, and the subscripts + and − denote values on either side of the surface.
In the latter case the sheet is an imperfect insulator and the boundary condition is
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A NEW APPROXIMATE METHOD FOR DIRECTLY INTERPRETING GRAVITY ANOMALY PROFILES CAUSED BY SURFACE GEOLOGIC STRUCTURES*
Authors K. P. FOURNIER and S. F. KRUPICKAAbstractFor outcropping bodies an approximate direct interpretation of the associated gravity anomaly is generally obtained with the flat plate formula. Results can be significantly improved if the causative body is approximated by a bell shape instead of a flat plate. A set of parameter curves allows the conversion to depth data. The validity of the method is borne out by synthetic models and by field examples in a Nevada valley with Tertiary and in the Los Angeles Basin. The method provides structural definition more accurate than can be obtained with the flat plate formula, particularly in the case of narrow anomalies.
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A PRELIMINARY PROCESSING OF THE BOUGUER ANOMALY IN AREAS OF VERY COMPLICATED RELIEF*
Authors M. IANAS and C. S. SAVAAbstractStrictly speaking, the Bouguer anomaly is the difference between the gravity observed at some point and the gravity to be expected at the same point for a “normal” earth corresponding to the same level. If the points of observation are located on a surface deviating significantly from a plane, a reduction of the data to a common plane is necessary before interpretation; otherwise spurious anomalies might occur. The processing is based on the solution of the generalized Dirichlet problem. Application of the proposed procedure to a synthetic, but realistic, model bears out the validity of the approach.
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EXEMPLES D'APPLICATION DE LA METHODE MAGNETOTELLURIQUE DE PROSPECTION GEOPHYSIQUE A L'ETUDE DE STRUCTURES OU DE FORMATIONS GEOLOGIQUES SITUEES SOUS UN TRES FAIBLE RECOUVREMENT*
By B. GUINEAUAbstractMagneto‐telluric radio frequency measurements can be developped in shallow applications in civil engineering, mining exploration hydrogeology and even archeology.
In the V.L.F. and L.F. ranges the depths usually encountered range from 4 or 5 meters to nearly 50 meters.
Specially designed equipment allows rapid work—in some cases even continuous profiling.
Field data obtained over a fault, a cavity, and sedimentary ore deposits agree well with data from conventional electric surveys.
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FACTORS AFFECTING SEISMIC AMPLITUDES*
More LessAbstractThe amplitude of seismic energy varies over a tremendous range. Some of the factors responsible for such variation do not contain subsurface information; these include source strength and coupling, geophone sensitivity, array directivity, instrument balance, scattering in the near‐surface, for example. Others depend on subsurface factors but do not convey information about lithology or hydrocarbon accumulation in a form from which we are able to extract it; these include spherical divergence, ray‐path curvature, loss in transmission through intervening reflectors, peg‐leg multiples, reflector rugosity, and curvature. The amplitude‐governing factors we are primarily interested in are reflection coefficient, the interference of reflections from the top and base of a sand, and absorption.
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ELECTROMAGNETIC DEPTH SOUNDING USING A SOURCE ORIENTATION MODE*
By K. DUCKWORTHAbstractElectromagnetic depth sounding using source orientation as the sounding variable provides advantages in instrumental simplicity and operational flexibility when compared with conventional modes of electromagnetic sounding. The ease with which the technique may be simulated in a scale model permits its application to sounding over localized structures. The theoretical approach to interpretation is at present limited to structures which approximate a perfectly conducting half space. However, scale model tests suggest that the perfect conductor theory may be applicable to many localized structures.
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EFFECTS OF DATA ERRORS AND ACCURACY IN SECOND DERIVATIVE COMPUTATION BY RATIONAL APPROXIMATION*
Authors B. N. P. AGARWAL and J. SINGHAbstractThe effects of systematic (constant) and random errors in the observed data have been investigated analytically for rational approximation method of computing second derivative involving a summation of the products of the averages of the gravity field with the corresponding weight coefficients, both in numerator as well as in denominator. A theoretical gravity anomaly over three spheres has been analyzed to demonstrate the high accuracy in the approximation. Since the sums of the weight coefficients in numerator and denominator are zero and one respectively, the regional gravity anomaly, even though approximated by a constant value over the entire area under computation, can produce substantially large error in the calculated derivative value. This is happening because of the contribution of the regional field in the denominator. Thus, inspite of the high accuracy in rational approximation, the method has limited application to field cases where a combined gravity field consisting of regional and residual anomalies is usually used. Master curves are presented for the constant and random errors by which a rough estimate of the percentage of error in second derivative computation can be made provided one has some idea of the magnitudes of the regional field and random error.
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ITERATIVE GRAVITY MODELING BY USING CUBICAL BLOCKS*
By I. R. MUFTIAbstractApproximation formulas for a cube's gravity field yield results which, for all practical purposes, are as accurate as those obtained by using the lengthy expressions defining the exact field. This fact is utilized in the development of a new gravity modeling scheme which uses cubes as building blocks.
A geologically feasible shape of the anomalous body is assumed and filled with cubes. To start with the largest cube which can be accommodated is placed inside the body. After that, the sidelength of the cube is halved, and as many cubes of that size as possible are placed into the remaining space. This procedure is repeated until the system of cubes has approached the shape of the body. The total gravity field due to all cubes placed represents the field of the body.
The placement of cubes is governed by an arrangement which is symmetrical with respect to the center of the first cube. Consequently, the data calculated for one cube may be used repeatedly for other symmetrically located cubes; this approach greatly reduces the number of calculations actually carried out. By reducing the size of the first cube and making it sufficiently small so that its density may be treated as uniform, the method can be used for evaluating the gravity field of an irregularly shaped body whose density varies in an arbitrary fashion.
The accuracy of the method is investigated by computing the gravity field of a sphere constructed from cubical blocks and buried at a shallow depth. A comparison of results with the analytical data obtained for the corresponding perfect sphere shows that a very high precision, of the order of microgals, is reached even at the end of the second cycle; moreover, depending on the accuracy desired, the method is three to five times faster than the Talwani‐Ewing algorithm. The method may be applied to borehole gravimetry, where very high precision is required, as well as to problems of topographic correction, where speed is the most important consideration.
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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)