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- Volume 20, Issue 2, 1972
Geophysical Prospecting - Volume 20, Issue 2, 1972
Volume 20, Issue 2, 1972
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THE EFFECTS OF ANISOTROPY ON SQUARE ARRAY RESISTIVITY MEASUREMENTS*
More LessABSTRACTAn account is given of the use of the square array technique in investigating the surface effects of rotational anisotropy when the axes of anisotropy are inclined to the surface. It is shown that, as with other arrays, two anisotropy parameters and n can be derived by varying the array orientation.
On the basis of these considerations, the effects of such anisotropy on the values of the mean apparent resistivity and azimuthal inhomogeneity ratio normally obtained in square array measurements is reviewed.
Particular attention is paid to the variation of resistivity with orientation and it is noted that, in areas of moderate anisotropy, this variation is lower for the square than for the Schlumberger array.
In addition to this advantage, the azimuthal inhomogeneity ratio obtained from square array measurements may be used to indicate the severity of anisotropy in an area and two field examples of this use are given.
Where anisotropy is severe, gross variations of apparent resistivity with orientation are obtained with either square or collinear arrays. In these circumstances, the use of crossed measurements is considered and the particular stability of the crossed square array demonstrated.
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POTENTIAL FIELD CONTINUATION BETWEEN GENERAL SURFACES*
More LessAbstractThe theory of potential field continuation is studied with a view of extending it to include continuation between non‐linear surfaces. This theoretical extension is regarded as useful in reducing observed potential fields along one general surface to another general surface.
It is demonstrated that the continuation operators considered in past geophysical literature are special cases of the generalized operators. In view of the tremendous growth in the art of high‐speed computing it is possible to consider applications of the generalized operators. In worked examples upward continuation between a general surface and a datum is considered for the gravity field due to geometrically simple sources; this in order to test the accuracy of the digital applications. It is indicated that for observations on an undulating surface it is possible to account for considerable errors when, during interpretation, the observation locations are taken to be along a datum. For aids to profile interpretation in areas of considerable topographic relief some simple convolution operators for continuation between linear, non‐parallel surfaces are proposed.
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RESISTIVITY SOUNDING ON A THREE‐LAYER TRANSITIONAL MODEL*
By S. C. JAINAbstractThe expression for the potential due to a point source of current, placed on the surface of a horizontal three‐layer earth, has been derived when conductivity in the second layer varies linearly with depth and changes abruptly at the boundaries. Master curves for Wenner and Schlumberger configurations have been presented for an insulating basement and for one value of conductivity gradient in the second layer.
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CONDUCTING SPHERE IN ELECTROMAGNETIC INPUT FIELD*
By K. MALLICKAbstractA frequency‐domain analysis is outlined for a conducting sphere in a uniform Input field: inequispaced alternating half‐sine wave pulses. The Barringer Input air‐borne electromagnetic exploration system uses such source fields. Theoretical profiles of Hρ(t), the horizontal magnetic component over the sphere from different elevations and for various conductivity and geometrical factors are presented. Based on these results some useful features such as penetration and detectibility are discussed.
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ELECTRICAL SOUNDING ON THE WATER SURFACE AT KHOR KUNDI EL‐BAHARI IN EGYPT*
By F. K. BOULOSAbstractElectrical resistivity sounding was attempted with success in 1960 on the surface of the Nile water in Khor Kundi El‐Bahari, the starting place for the construction of the offset channel of the High Dam. The method was applied to determine the depth to the upper surface of the granite below the alluvium and Nile water. The success of the method conducted at two stations in the Khor is attributed to the favourable geological conditions of the section which consists of nearly homogeneous layers besides the good earthing conditions of electrodes dipped in water. The high resistivity contrast between water and granite facilitates interpretation of sounding curves. Factors interfering with the results of interpretation are mentioned.
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GEOPHYSICAL CATEGORIZATION OF THE PRECAMBRIAN IN SOUTH INDIA*
By D. VOGELSANGAbstractThe ground follow‐up of a magnetic and radiometric air survey had to cope with the usual dilemma to check a great number of anomalies within a short time. A limited aggregate of magnetic anomalies, expected to correspond to magnetite quartzites was statistically selected for ground identification by this method: the ratios length/width times amplitude were listed for all coherent contours and the calculation of the standard deviation per unit area resulted in different key‐numbers for a new lithological “Salem Unit” and for the charnockitic or gneissic environment. The ground work thus directed and reduced by 85% yielded a substantial potential of iron ore. This was supported by by abundant determinations of the magnetic susceptibilities, confirming the sources of anomalies and revealing the amenabilities of iron ores for the magnetic separation process.
The lines of truncation of anomalies were found to represent a system of local and regional faults and shear zones, which segregated the area into different tectonic blocks. These sutures have also provided the ways of intrusion for alkaline and basic magmae in the style of a “Rift” structure, housing several carbonatites and impregnations of metal sulphides.
The airborne radiometrics obtained many uranium indications by gamma ray spectrometry. However, they led only to disseminated uranium‐silicates, associated with syenites, granites and pegmatites, each emanating a characteristic photon energy spectrum. But in general the radiation of thorium prevails, marking northern Madras as a “Thorium Province”.
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DEPTH OF INVESTIGATION IN WENNER, THREE‐ELECTRODE AND DIPOLE‐DIPOLE DC RESISTIVITY METHODS*
By A. ROYAbstractUsing a method and definition given earlier (Roy and Apparao, 1971), this paper computes the depths of investigation in homogeneous ground for (a) the Wenner α, β and γ configurations, (b) the three electrode system and (c) the dipole‐dipole arrangements when the dipole lengths are not infinitesimally small. The results for (a) and (b) have been summarised in a table, while those for (c) are shown as contour diagrams. In all the dipolar arrangements examined in this paper, except the equatorial, the depth of investigation decreases (and the vertical resolution increases) with increase in any or both of the dipole lengths. For the equatorial set up, this decrease (or increase) is very small.
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RESISTIVITY MEASUREMENTS IN VALLEYS WITH ELLIPTIC CROSS‐SECTION*
Authors E. MUNDRY and J. HOMILIUSAbstractIn this paper an idealized valley of a semi‐elliptic cross‐section is considered. For a Schlumberger configuration on the axis, sets of master curves are calculated for the ratio of semi‐axis a/b= 1, 2, 3, 4, 5 in corresponding to various resistivity ratios of surrounding rocks and valley sediments. For small resistivity ratios, these model curves have the shape of three‐layer curves for horizontal bedding and are often equivalent to them within the accuracy of measurements. The axial ratio a/b considerably affects the depth determination of valley sediments. In the special case of a circular cross‐section (a/b= 1) the influence of the position of the electrodes on the sounding curve is studied in more detail.
The application of the master curves in practice shows that the influence of the specific shape of the valley on soundings should not be neglected. In general, the valleys have a greater “true” depth than can be seen from the interpretation of a sounding by master curves corresponding to the horizontal bedding.
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A TWO‐AND THREE‐DIMENSIONAL GRAVITY DOT CHART*
Authors N. A. MORGAN and C. W. FAESSLERAbstractThis paper presents a dot chart for calculating gravity effects from two‐dimensional bodies with the addition of a supplementary set of curves which can be used to determine the “end corrections” to modify the calculated effects when the length of the body is not relatively long with respect to the horizontal dimensions of the cross‐section. The use of the chart is demonstrated by different examples. The results of theoretical cases amenable to mathematical treatment and computer results both compare favorably to those computed using the present chart.
A fundamental incentive of constructing this chart, in a final form ready to use, is to make it available to gravity interpreters for utilization. Future effort in chart construction is thereby avoided.
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MAGNETIC SUSCEPTIBILITY ANISOTROPY OF VARIOUS ROCK TYPES AND ITS SIGNIFICANCE FOR GEOPHYSICS AND GEOLOGY*
By F. JANÁKAbstractIn the interpretation of magnetic anomalies and in paleomagnetism, the anisotropy of magnetic susceptibility is commonly neglected. Nevertheless, this property has basic significance, because, owing to susceptibility anisotropy, the directions of the vectors of induced and remanent magnetization are deflected from the direction of the Earth's magnetic field. Almost all rock types investigated possess higher or lower degree of the susceptibility anisotropy. Effusive and sedimentary rocks have the lowest degree of anisotropy. For the latter, the “masking effect” of the paramagnetic mineral components has some influence on the anisotropy degree due to the low mean susceptibility of sedimentary rocks. Metamorphic and plutonic rocks usually exhibit a considerable degree of anisotropy. The highest degree of anisotropy has been found in the rocks containing ferromagnetic minerals with mimetic fabric.
The dependence of the degree of the susceptibility anisotropy on the degree of metamorphism proved to be very complicated; of the rock sequence from slates to gneisses, the transient rocks (roofing slates and mica‐schist‐gneisses) showed the highest degree of anisotropy. This result can be used in geology for reliable determination of these rock types.
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A GENERALIZED METHOD OF COMPUTING SECOND DERIVATIVE OF GRAVITY FIELD*
Authors B. N. P. AGARWAL and T. LALAbstractThe unsuitability of a particular method of computation of second derivative to varying types of field problems evinces the need of a method by which it may be possible to obtain a wide range of filters. This requirement is achieved by incorporating a mathematical smoothing operator, e‐λρ2, λ and ρ being the smoothing parameter and radial frequency respectively, in the theoretical frequency response of second derivative operation. A few sets of weights for various smoothing parameters, are presented. The analysis of Bouguer gravity anomaly map of Los Angeles Basin, California, U.S.A., is carried out by Elkins's (1951) and Rosenbach's (1953) methods and the sets of weights given in this paper which clearly establishes their filtering equivalence.
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A NOTE ON SIGNAL DISTORTION DUE TO DYNAMIC (NMO) CORRECTIONS*
By H. BUCHHOLTZAbstractBy applying dynamic corrections a seismic trace recorded at a distance x from the energy source should be varied in such a way as to obtain a trace which would be recorded at zero‐distance, i.e. at the source itself. Only such a zero‐offset‐trace contains the correct sequence of reflection coefficients (reflectivity function), whilst all other traces contain a distorted reflectivity function. In the simplest case, the reflectivity function is compressed over a shorter time whereas in more complicated cases a partial inversion of the reflectivity function results. This happens when some of the reflection hyperbolae intersect one another.
The reconstruction of the true zero‐offset reflectivity function by the application of dynamic corrections can only be an approximative process. In the first case mentioned we must expect a decrease in accuracy of the corrected trace in comparison with a zero‐offset‐trace. In the second case, where intersections of the hyperbolae occur, accurate reconstruction is clearly impossible.
The problems are discussed with the help of theoretical and practical examples.
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A NOTE ON THE LINEAR FILTER METHOD OF INTERPRETING RESISTIVITY SOUNDING DATA*
By O. KOEFOEDAbstractIn the linear filter method of interpreting resistivity sounding data, as developed by Ghosh (1971), it appears that the filter function in the x‐domain approaches an oscillating function for both large positive and large negative abscissa values. In the present note the reason for this oscillating behaviour is derived, and a possible practical application is indicated.
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COMPUTATION OF TYPE CURVES FOR ELECTROMAGNETIC DEPTH SOUNDING WITH A HORIZONTAL TRANSMITTING COIL BY MEANS OF A DIGITAL LINEAR FILTER*
Authors O. KOEFOED, D. P. GHOSH and G. J. POLMANAbstractThe computation method described in this paper is based on the existence of a linear relationship between the mutual coupling ratio and the kernel function in the integral expression for it. Accordingly, the mutual coupling ratio can be determined by first computing sample values of the kernel function and then subjecting these to a digital linear filter. In the present paper the appropriate sampling distance is determined and the values of the digital filter coefficients are computed, both for electromagnetic sounding with horizontal coils and for electromagnetic sounding with perpendicular coils.
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SIGNAL ENHANCEMENT OF VIBRATORY SOURCE DATA IN THE PRESENCE OF ATTENUATION*
By B. M. GURBUZAbstractAmplitude spectra of input FM signals used in the vibratory source method of seismic exploration often show undesirable oscillations near the initial and terminal frequencies. These oscillations have an effect on the correlation background and distort the output signal. Considerable improvement in reducing the amplitude of these oscillations is obtained using a proper taper fuction. Attention is given to the relation between the tapering time and bandwidth of the spectrum.
Analyses of the spectra of the received data from vibratory sources show considerable attenuation in comparison with the original field sweep. Since the matched filtering process will result in a series of waveforms which have the shape of the autocorrelation of the input signal, consideration is given to the autocorrelation function and its zero‐lag coefficient of the FM signal in the presence of attenuation. A method has been developed which compensates for the attenuation and recovers the distortion of waveforms when the received data is correlated.
The design of a waveform shaping filter for vibratory source data is given to reduce the influence of phase distortion on the received waveforms as well as to increase S/N ratio resolution. Parameters used for this filter are based on the properties of the FM signal and its autocorrelation function.
Several examples from field data are presented to illustrate the methods. The results indicate that the use of the above techniques yields sections with good frequency resolution and improved S/N ratio.
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AN ITERATIVE METHOD FOR THE SOLUTION OF ANON‐LINEAR INVERSE PROBLEM IN MAGNETIC INTERPRETATION*
More LessAbstractA method is presented for determining the lower surface of a two‐dimensional body producing a magnetic anomaly when its upper surface and the intensity of magnetization are given. The magnetization vector is assumed to lie along a specified direction but the sense of magnetization may be different in different vertical sections of the body and may be regarded as unknown. The method is illustrated using the computed anomalies of some theoretical models.
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CALCULATION OF THE VERTICAL GRADIENT OF THE GRAVITY FIELD USING THE FOURIER TRANSFORM*
Authors B. N. P. AGARWAL and T. LALAbstractFourier transform techniques have been used to calculate the theoretical filter (amplitude) response function of Nth order vertical derivative continuation operation. The amplitude response functions of the vertical gradient and its continuation follow from the same. These response functions are subsequently used to calculate the weighting coefficients suitable for two dimensional equispaced data. A shortening operator has been incorporated to limit the extent of the operator. For comparative study, some of the developed coefficient sets and the one presented in this paper are analysed in the frequency domain and their merits and demerits are discussed.
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INTERPRETATION QUANTITATIVE EN GRAVIMETRIE OU MAGNETISME A PARTIR DE CARTES TRANSFORMEES DE GRADIENT VERTICAL*
Authors A. GERARD and P. GRIVEAUAbstractA discussion is given of the requirements, the advantages and the methods to be considered in attempting the quantitative interpretation of gravity or magnetic fields from computed maps of the vertically derived field.
The transform which is used here is the first vertical derivative (or vertical gradient) with or without downward continuation, but the computed maps are in fact obtained by a controllable Fourier method in which two kinds of operations can be simultaneously performed in complete independance: on one hand the separation of any part of the data by frequency cut‐off, and on the other hand the transformation by vertical derivation or continuation of the part which is retained.
Taking as raw data either actual surveys or artificially constructed maps, it is first shown how separated and transformed maps of this type can be efficiently obtained under quite flexible conditions, using a special computer program. It is further seen that for correctly controlled filterings the accuracy of the computed maps actually permits to take them as the basis for quantitative interpretation.
To effect this, any one of the conventional methods which make use of equivalent model computations may in the first place be adapted to the interpretation of gradients, with the benefits, however, of an enhanced lateral separation of the anomalies and of a large attenuation of the regional effects.
Particularly, the delineation of horizontal contours for even fairly complex models can often be made directly in a sufficiently safe way on the anomalies as they show on the vertical gradient maps. This greatly accelerates the process of determining equivalent model bodies.
More special methods of interpretation can also be designed by taking into account first the fact that the vertical derivation of the field amounts to an operation of separation on the field's sources themselves, and in addition the availability of the frequency form of the information as a result of using a Fourier method of transform computation.
Trial utilisations of various such interpretation processes of either the conventional or the less conventional type, are presented especially in connection with an interpretation study on transformed maps of parts of an offshore aeromagnetic survey (English Channel).
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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)