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- Volume 32, Issue 1, 1984
Geophysical Prospecting - Volume 32, Issue 1, 1984
Volume 32, Issue 1, 1984
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SHEAR WAVES BY AN EXPLOSIVE POINT‐SOURCE: THE EARTH SURFACE AS A GENERATOR OF CONVERTED P‐S WAVES*
By J. FERTIGAbstractThe most common source of seismic energy is an explosion at some depth in a borehole. The radiated waves are reflected not only at the subsurface layers but also at the free surface. The earth's surface acts as a generator of both P‐ and S‐waves.
If the source depth is much less than the dominant wavelength the reflected waves resemble closely the waves generated by a single force. Theoretical seismograms were computed with different methods to look for the relevance of the surface‐reflected waves. The numerical experiments show reflected shear waves even for small shotpoint—receiver distances. Due to their polarization these waves can be detected most easily on in‐line horizontal geophones. The existence of these waves was examined during a conventional survey in Northern Germany. Conventional data analysis shows a large variability in the νp/νs ratio. The method used here produced a shear‐wave section with a rather good signal‐to‐noise ratio down to 4 s S‐wave reflection time.
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A THREE‐DIMENSIONAL NUMERICAL BOTTOM‐HOLE TEMPERATURE STABILIZATION MODEL*
Authors F. W. JONES, M. RAHMAN and Y. LEBLANCAbstractThe heat flow equation in cylindrical coordinates is solved numerically for any general distribution of thermal diffusivity. The temperature stabilization of a borehole is considered, and solutions for the case where thermal diffusivity is a function of radial distance from the borehole are obtained and compared to solutions for uniform diffusivity. The results are discussed in terms of thermal diffusivities that are different for the well contents and for the surrounding material. It is found that the approach to formation temperature is affected by differences between well contents and the surrounding region.
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TWO STRUCTURAL MODELS FOR THE WESTERN FLANK OF THE BRABANT MASSIF*
By F. DE MEYERAbstractThis paper is concerned with an interpretation of the Bouguer anomaly on the Western flank of the Brabant Massif (Belgium). The position, shape, and density contrast of elementary bodies in the upper part of the earth's crust are determined in a purely numerical manner. A batholith‐like body and a basin‐type structure both adequately account for the observed surface field, at least from a one‐sided geophysical and mathematical point of view. Since seismological control is lacking the two models are representative of the ambiguity and indeterminacy of the definitions of the geologic cause of the anomalous features, if the data are restricted to gravity information alone.
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ON THE ORIGIN AND INTERPRETATION OF SELF‐POTENTIAL ANOMALIES*
By K. T. KILTYAbstractThe renewed interest in the self‐potential method of exploration for mineral deposits gives an understanding of the self‐potential mechanism new importance. The cause of SP anomalies in general lies in the interference between simultaneously occurring nonequilibrium phenomena. However, theories of the mechanism of mineral SP anomalies generally relate the SP anomaly to the equilibrium potential of the chemical reaction supposed to occur on the ore body surface. In this paper, I reformulate these equilibrium mechanisms in terms of nonequilibrium thermodynamics. The result is that the SP anomaly depends not on the equilibrium potential alone, but also on the potential resulting from current transferred across the ore body—electrolyte interface. It is not possible to calculate the overpotential theoretically because of the number of complicating factors, and experimental data are not available. This does not imply that SP data are uninterpretable quantitatively. SP data may be interpreted similarly to other potential field data.
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THE CLASSIFICATION OF PHYSICO‐GEOLOGICAL MODELS OF MINERAL DEPOSITS*
Authors G. S. VAKHROMEYEV and A. S. BARYSHEVAbstractWe describe the concept of physico‐geological models (PGMs) in geophysical exploration. They represent a “general model”, a spatial combination of a set of particular models (disturbing bodies). The modeling is called complete, incomplete or approximate, depending on the degree of characterization of the PGM by parameters such as dimension, shape and petrophysical property. Each of the three modeling types can be realized as a conceptual, and analytical, or a material PGM. Both deterministic and stochastic PGMs exist; deterministic models are mainly used to investigate the possibilities of a geophysical method, while stochastic models serve to substantiate complex geophysical interpretations.
Depending on the geological problem, PGMs are subdivided into multi‐alternative models (geological mapping, prediction, general prospecting) and double alternative models (specialized prospecting).
An exploration‐oriented classification of the PGMs of mineral deposits is discussed. According to this classification the variety of known genetic deposit types is reduced to a limited number of generalized PGM types. The development of typical PGMs is illustrated with examples of magnetitic deposits of Siberia.
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A METHOD FOR CALCULATING IP ANOMALIES FOR MODELS WITH SURFACE POLARIZATION*
Authors L. ESKOLA, E. ELORANTA and R. PURANENAbstractA numerical method is given for calculating resistivity and induced polarization anomalies produced by a surface polarization model. Surface polarization is generated when a purely electronic conductor is located in an electrolyte environment. The system that develops on the boundary between the conductor and the electrolyte is described macroscopically by a net surface charge distribution and an electric double layer. An integral equation is derived for the potential by assuming that the electronic conductor forms an equipotential system and that the polarization impedance across the boundary is linear. The integral equation is solved by means of the method of subsections. As an application some numerical modeling results are presented. The surface impedance values used in calculations are based on laboratory measurements that are briefly described. Implications of the results for scale modeling are discussed.
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DETECTABILITY OF AN INTERMEDIATE LAYER BY PERPENDICULAR AND VERTICAL COPLANAR ELECTROMAGNETIC SOUNDING SYSTEMS EMPLOYING DIFFERENT PRIMARY EXCITATIONS*
Authors R. K. VERMA and K. MALLICKAbstractThe detectability of an intermediate layer in a three‐layer earth model in the time domain has been investigated. The calculations were made for the perpendicular loop (designated system II) and vertical‐coplanar (designated system III) electromagnetic (EM) sounding systems. The primary excitation employed is a train of half‐sinusoidal and square waveforms of alternating polarity. The time‐domain response has been determined by Fourier transformation of the matched complex mutual coupling ratios into the time domain and by linear digital filtering. Top and bottom layers have equal resistivity. EM responses have been computed for conductive and resistive intermediate layer with a wide range of thickness and for two values (500 m and 1000 m) of loop‐separation. For the detectability analyses, the root mean square (rms) difference between three‐layer and homogeneous‐earth responses is adapted. The threshold value for detectability is defined as an rms difference of 10% and the measurement error is arbitrarily assumed to be of the order of 3%. It is observed that the perpendicular‐loop system is better than the vertical‐coplanar system in detecting thin intermediate layers (either conductive or resistive). For a loop separation of 1000 m and half‐sinusoidal pulse excitation, the detectable thickness ratio (h2/h1) is 0.10 by system II for the conducting middle layers; for square pulse excitation the corresponding thickness ratios are 0.06 for system II and 0.12 for system III. For a loop separation of 1000 m and half‐sinusoidal pulse excitation in detecting the resistive intermediate layers, the corresponding thickness ratios are 0.9 for system II and 2.25 for system III; while for square pulse excitation the thickness ratios are 0.55 for system II and 1.55 for system III.
Results in the frequency domain and time domain (for half‐sinusoidal and square pulsed field) have also been presented for systems II and III for detecting conducting layers by considering an earth model where p1≠ p3 and p3 > p1 (p is the resistivity). The loop separa‐ tion used is 1000 m. Direct comparisons between the frequency domain and time‐domain results clearly demonstrate the superiority of frequency‐domain systems for detecting con‐ ducting intermediate layers.
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A DIGITAL LINEAR FILTER FOR RESISTIVITY SOUNDING WITH A GENERALIZED ELECTRODE ARRAY*
Authors D. J. O'NEILL and N. P. MERRICKAbstractThis paper presents a digital linear filter which maps composite resistivity transforms to apparent resistivities for any four—electrode array over a horizontally layered earth. A filter is provided for each of three sampling rates; the choice of filter will depend on resistivity contrasts and computational facilities.
Two methods of filter design are compared. The Wiener‐Hopf least‐squares method is preferable for low sampling rate filters. The Fourier transform method is more successful in producing a filter with a high sampling rate which can handle resistivity contrasts of 100 000: 1.
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GEOELECTRICAL MODEL CALCULATIONS FOR TWO‐DIMENSIONAL RESISTIVITY DISTRIBUTIONS*
By E. MUNDRYAbstractFor the calculation of geoelectrical model curves for a two‐dimensional resistivity distribution, the potential equation is transformed by means of a Fourier cosine transform into a two‐dimensional Helmholtz equation containing the separation parameter λ.
The numerical solution of this equation for different values of λ for an irregular grid is obtained using the method of finite differences combined with the method of overrelaxation. The method by which derivatives are replaced by finite differences turned out to be very important, especially for high resistivity contrasts. After testing several methods designed to deal with any type of resistivity distribution, a method of discretization similar to that used by Brewitt—Taylor and Weaver (1976) for magnetotelluric modeling for H polarization was found the best.
Examples are given of model curves for Schlumberger soundings over a vertical fault covered by overburden. The incorrect use of horizontal‐layer models leads to erroneous interpretations that are more complex than the real subsurface situations.
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THE USE OF TWO‐ELECTRODE AND SCHLUMBERGER FILTERS FOR COMPUTING RESISTIVITY AND EM SOUNDING CURVES*
More LessAbstractDifferent sets of filter coefficients for the linear filter technique for the computations of resistivity and EM sounding curves are evaluated for several electrode and coil configurations. Instead of this procedure, the two‐electrode filter can be used for computations of Wenner, Schlumberger, and dipole—dipole apparent resistivity model curves by defining convolutional expressions which contain the new input functions in terms of the resistivity transform function. Similarly, the Schlumberger filter performs the computations of dipole—dipole apparent resistivity model curves. The Wenner, Schlumberger, and dipole—dipole filter functions are defined in terms of the two‐electrode filter using the new convolutional expressions. A relationship between the Schlumberger and dipole—dipole filter functions is given.
The above arguments are adopted for the computations of EM sounding curves. It is shown that the EM filter for the horizontal coplanar loop system (which is identical to the two‐electrode filter) performs the computations of the mutual coupling ratios for perpendicular, vertical coplanar, and vertical coaxial loop systems. In the same way, the Schlumberger filter can be used to compute vertical coaxial sounding curves. The corresponding input functions are defined in terms of the EM kernel for all convolutional expressions presented.
After these considerations, integral expressions of the mutual coupling ratios involving zero‐order Bessel function are derived. The mutual coupling ratio for the vertical coaxial loop system is given in the same form as the mutual coupling ratio for the vertical coplanar loop system.
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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)