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- Volume 27, Issue 1, 1979
Geophysical Prospecting - Volume 27, Issue 1, 1979
Volume 27, Issue 1, 1979
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SEISMIC SIGNAL DETECTION AND PARAMETER ESTIMATION*
By B. URSINAbstractIn the mathematical theory of seismic signal detection and parameter estimation given, the seismic measurements are assumed to consist of a sum of signals corrupted by additive Gaussian white noise uncorrelated to the signals. Each signal is assumed to consist of a signal pulse multiplied by a space‐dependent amplitude function and with a space‐dependent arrival time. The signal pulse, amplitude, and arrival time are estimated by the method of maximum likelihood.
For this signal‐and‐noise model, the maximum likelihood method is equivalent to the method of least squares which will be shown to correspond to using the signal energy as coherency measure. The semblance coefficient is equal to the signal energy divided by the measurement energy. For this signal model we get a more general form of the semblance coefficient which reduces to the usual expression in the case of a constant signal amplitude function.
The signal pulse, amplitude, and arrival time can be estimated by a simple iterative algorithm. The effectiveness of the algorithm on seismic field data is demonstrated.
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SUPERSTACK—AN ITERATIVE STACKING ALGORITHM*
By O. E. NÆSSAbstractAn algorithm for separation of signals according to their coherency is proposed. The algorithm, called Superstack, is used on common depth point data after normal moveout corrections have been applied. The algorithm can be regarded as an iterative stacking procedure. After each stack, input values are changed depending on the consistency of the output of the previous stack.
The Superstack algorithm is able to provide better separation of signals showing a different degree of horizontal consistency (coherency) than the normal horizontal stack.
All noise signals in a CDP‐gather may be assumed to show less horizontal consistency than the primary reflections. On this basis the algorithm will give an improved primary/multiple and an improved primary/noise ratio.
The Superstack is very general, should not be especially expensive in terms of computer time, and can easily be implemented in routine processing.
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COHERENCY WEIGHTING—AN EFFECTIVE APPROACH TO THE SUPPRESSION OF LONG LEG MULTIPLES*
By B. BUTTKUSAbstractLong leg multiples can be suppressed by a method which provides an alternative to weighted common‐depth‐point stacking and multichannel stacking filtering. The suppression is achieved by coherency weighting whereby the time‐dependent weighting factor decreases as the semblance of the multiple reflections increases.
The algorithm of the method is described. Its efficiency is discussed in relation to the input data and results of its application to marine seismic data are presented.
For practical application, the stacking velocity of the multiples has to be known. As the process is based on stacking velocities, different types of multiples can be handled, for instance water‐bottom multiples or internal multiples. The parameter analysis shows that the degree of multiple suppression can easily be controlled by adapting the parameters of the procedure to the field conditions.
During the suppression of multiples, the primaries are saved according to the moveout differences between the two. The non‐linear behaviour of the process causes signal suppression and distortion effects, which have to be corrected by AGC normalization and low‐pass filtering.
Among the various applications available, only the suppression of long leg water‐bottom multiples is treated here. The results show that their suppression on the basis of moveout differences is efficient even when standard length streamers are used in regions with water depth of up to 1500 m and more, if the stacking velocity of the primaries is about 10 to 20% higher than that of the multiples. Even if those parts of the primaries which are masked by the multiples are suppressed in the individual common‐depth‐point gathers by the procedure, the remaining primaries in the AGV stacked section are largely uncovered by the multiple suppression.
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TIME‐VARYING PREDICTION FILTERING BY MEANS OF UPDATING*
Authors D. RISTOW and B. KOSBAHNAbstractIn contrast to the conventional deconvolution technique (Wiener‐Levinson), the spike‐, predictive‐, and gap‐deconvolution is realized with the help of an adaptive updating technique of the prediction operator. As the prediction operator will be updated from sample to sample, this procedure can be used for time variant deconvolution. Updating formulae discussed are the adaptive updating formula and the sequential algorithm for the sequential estimation technique. This updating technique is illustrated using both synthetic and real seismic data.
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ACOUSTICAL IMAGING OF SOURCE RECEIVER COINCIDENT PROFILES*
By M. J. KUHNAbstractThe first part of this paper examines a special case of acoustical imaging in which the source and the receiver coincide. The benefits of weighting and muting are studied in detail by means of computer modeling. The test model consists of a single planar interface z=z1, abruptly terminated at x= o. The amplitude and phase responses are computed in the plane z=z0= o for two separations of neighboring stations, Δx=λ/10 and Δx=λ/2. Six different weighting factors are used in the test. However, in this source‐receiver coincident case, three of the weighting factors produce identical responses, so that all six test factors may be represented by only four curves. It is found that when the spatial sampling at the aperture approaches the condition of critical sampling, i.e. Δx=λ/2, only the weighting factor which implicitly takes into account beam steering along the specular reflection path is acceptable. This factor alone keeps the amplitude and the phase curves undistorted until the difference 2 ·ΔR between two neighboring paths reaches approximately λ/2. If we set 2 ·ΔR=λ/2, we may construct a set of curves which we may call quite appropriately muting curves. These curves are physically interpretable only for station separation Δx > λ/4. The muting curves are symmetrical about the line x= 0 and their angular opening depends on spatial separation Δx, depth z, and wavelength λ (which may vary with depth).
The second part of this paper suggests how the weighting factor with implicit beam steering can be applied to reconstruction of two and three‐dimensional wavefields. Seismic migration of common depth point (CDP) stacked line data is also discussed. This is a hybrid case which presents certain theoretical difficulties. We shall also mention the velocity problem which is inherent to migration of CDP stacked data.
The third and final part concerns implementation of the migration of CDP stacked data. When the spatial sampling is between λ/4 and λ/2, the migration process will benefit from beam steering and from muting. The benefits are more subtle when the separation of the traces is less than λ/4. However, in that case the cost of data collection is considerable and often prohibitive. In either case the migration of seismic data can be expedited by use of precalculated tables of migration velocities, ray path distances, and weights (including muting).
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COMBISWEEP—A CONTRIBUTION TO SWEEP TECHNIQUES*
More LessAbstractNonlinear sweeps have often successfully been employed in the 1960s. However, this area of sweep technology has been neglected since the introduction of digital recording techniques in the Vibroseis system. Now the advent of computerized recording instruments yields a new economical possibility of forming approximately nonlinear sweeps by combining several linear sweeps with or without time gaps to a “Combisweep”. The total duration of a Combisweep may be as long as the maximum available recording time, for example 32 s.
Beside the attenuation of correlation noise, the new method has further merits, such as the weighting of predetermined frequency ranges, in order to effect a certain kind of optimum filtering on the emitter side, or in order to compensate to some degree for frequency dependent absorption.
In all these applications the Combisweep is considered as one signal in the correlation process. But by correlating with the individual sweeps or a partial combination of them and by applying automatic switching at predetermined times within the gaps between the individual sweeps additional possibilities arise, such as obtaining in one run with a twenty‐four channel recording unit twenty‐four traces with small distances between vibrators and geophones for shallow reflections and another twenty‐four traces with larger distances for deeper reflections. Various Combisweeps and their applications are presented.
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RESISTIVITY MODELLING FOR ARBITRARILY SHAPED TWO‐DIMENSIONAL STRUCTURES*
Authors A. DEY and H. F. MORRISONAbstractA numerical technique is developed to solve the three‐dimensional potential distribution about a point source of current located in or on the surface of a half‐space containing arbitrary two‐dimensional conductivity distribution. Finite difference equations are obtained for Poisson's equations by using point‐ as well as area‐discretization of the subsurface. Potential distributions at all points in the set defining the half‐space are simultaneously obtained for multiple point sources of current injection. The solution is obtained with direct explicit matrix inversion techniques. An empirical mixed boundary condition is used at the “infinitely distant” edges of the lower half‐space. Accurate solutions using area‐discretization method are obtained with significantly less attendant computational costs than with the relaxation, finite‐element, or network solution techniques for models of comparable dimensions.
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TIME‐DOMAIN ELECTROMAGNETIC SOUNDING—COMPUTATION OF MULTI‐LAYER RESPONSE AND THE PROBLEM OF EQUIVALENCE IN INTERPRETATION*
Authors K. MALLICK and R. K. VERMAAbstractComputations of the time‐domain electromagnetic response of a multi‐layered earth have been carried out for different source‐receiver coil systems. The primary excitation is a train of half‐sinusoidal waveforms of alternating polarity. The conversion into the time‐domain involves Fourier series summation of the matched complex mutual coupling ratios of the layered earth models computed by a digital linear filter method. As an example, the response of a perpendicular coil system on the ground surface for two source‐receiver separations has been presented for a five‐layer earth model. This has been compared with the responses of homogeneous, two‐layer, three‐layer, and four‐layer models.
Next, the investigations have been extended to study the problems of equivalence of three‐layer models, the intermediate layer of which is either conductive or resistive. For an intermediate conductive layer (H‐type), the studies show that in the early portion of the signal the interpretation of a true three‐layer earth is possible to some extent, whereas the ambiguity due to equivalence persists in the late samples. On the other hand, for an intermediate resistive layer (K‐type), the three‐layer earth and its equivalent model cannot be distinguished from each other over the entire sampling period.
On the basis of a computational approach, equivalence has been empirically established as √h/ρ=constant for H‐type earth‐sections, and as h2ρ=constant for K‐type earth sections, where h and ρ are respectively the thickness and resistivity of the intermediate layer.
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ON WIENER FILTER AND MAXIMUM ENTROPY METHOD FOR MULTICHANNEL COMPLEX SYSTEMS*
Authors J. G. NEGI and V. P. DIMRIAbstractThe Wiener filtering scheme is obtained for a multichannel complex system utilizing the “block‐Toeplitz” property of autocorrelation matrix. A numerical example is given to elucidate the application of the filter design. The study also outlines Burg's maximum entropy method to include the multi‐channel complex realm.
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SEISMIC DISCRIMINANTS OF STRATIGRAPHY DERIVED FROM MONTE CARLO SIMULATION OF SEDIMENTARY FORMATIONS*
Authors K. KHATTRI, A. SINVHAL and A. K. AWASTHIAbstractThe impulse response of models of subsurface formations are statistically analyzed for abstracting seismic parameters which could be characteristic of the stratigraphy and lithology of the formations. Two types of formations have been considered, consisting either of sand‐shale sequences or of coal‐shale sequences. Models of the formations are generated using the Monte Carlo method. It is found that three features in the power spectrum of the impulse response, namely the frequency fe at which the spectrum can be divided into a zone of high energy from a zone of low energy, the lowest frequency fp where there is a significant energy peak, and the frequency fm at which there is a maximum energy, can be used statistically to distinguish between the formations consisting of sand‐shale sequences and the formations made up of coal‐shale sequences. Three additional parameters A2/A1, A2/A0, and A1/A0, where A denotes the autocorrelation function of the impulse response and the subscripts denote the lags, are also statistically significant discriminators between the sand‐shale formations and the coal‐shale formations. The discrimination between the two subgroups of each model consisting of more (or less) than fifty percent of one lithology is also feasible, although there are fewer discriminants available.
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STEEP DIP FINITE‐DIFFERENCE MIGRATION*
More LessAbstractA method is presented to derive approximate versions of the wave equation which allow finite‐difference migration for very steep dips (> 50°). It is shown that for conventional finite‐difference schemes, in addition to the dip limitation, the maximum acceptable frequency should be specified. A finite‐difference migration technique is proposed in the frequency domain. It is derived that finite‐difference wave field extrapolation in the frequency domain consists of a space‐variant convolution procedure for each frequency component, the space‐variance being defined by the lateral variation in the velocity.
Finally it is shown that with finite‐difference migration, particle velocity data can be easily obtained from pressure data.
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GEOLOGICAL INFORMATION FROM FLUCTUATING EARTH‐CURRENTS*
More LessAbstractInvestigation of fluctuating earth‐currents has led to a simple method of eliminating the noise superimposed on the signal in geoelectrical resistivity surveys. The similarity of the potential fluctuations, simultaneously measured at different locations, is used to calculate the direction and magnitude of the potential gradient. Contour maps of equipotential lines were made, both from disjointed gradient measurements using a numerical approximation method and from a network of measured potential differences. These contour maps were compared with potential fields calculated for simple homogeneous models. A good fit was obtained with the field of a conducting plate. When this is subtracted from the measured field, the result is a map that shows anomalies that can be correlated with geological structures.
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COMPARISON BETWEEN SCHLUMBERGER ELECTRODE ARRANGEMENT AND SOME FOCUSED ELECTRODE ARRANGEMENTS IN RESISTIVITY PROFILES*
Authors E. BRIZZOLARI and M. BERNABINIAbstractThe Mining Geophysics Institute of the University of Rome has tested focused electrode arrangements. These have been used both in the field for resistivity profiles in investigations for buried cavities and in the laboratory for model tests in an electrolytic tank with cylindrical and parallelepipedal bodies.
Anomalous potentials due to superficial noise, assumed to be a hemisphere having an equatorial plane coinciding with the earth surface, have been calculated for focused current electrode arrangements. Similar anomalies have also been calculated for the Schlumberger arrangement.
Model tests in an electrolytic tank have also been carried out for a Schlumberger arrangement and parallelepipedal buried bodies.
It is interesting to know whether the focused current arrangements give better results than the Schlumberger arrangement. Since it is not possible to compare directly the results of the two arrangements, the comparison is made by considering the ratio of the anomalies to the superficial noise (considered as hemisphere) for Schlumberger and focused arrangements. The results of the comparison show that, generally, the focused arrangements give better results even in the presence of superficial noise.
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DETERMINATION OF RESISTIVITY SOUNDING FILTERS BY THE WIENER‐HOPF LEAST‐SQUARES METHOD*
Authors O. KOEFOED and F. J. H. DIRKSAbstractIt has been found that the Wiener‐Hopf least‐squares method is a very successful tool for the determination of resistivity sounding filters. The values of the individual filter coefficients differ quite appreciably from those obtained by the Ghosh procedure. These differences in the filter coefficients, however, have only a negligible effect on the output of the filter. It seems that these differences in the coefficients correspond to a filter function of a rather narrow frequency band around the Nyquist frequency, which is only very weakly present in the input and output functions.
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GEOPHYSICAL ANOMALY INTERPRETATION OF POTENTIAL FIELDS BY MEANS OF SINGULAR POINTS METHOD AND FILTERING*
Authors B. CIANCIARA and H. MARCAKAbstractThe calculation of potential field anomalies on different levels below the measuring level permits to localize the singular points related to the sources of anomalies.
It is possible to achieve considerable improvement of the resolution of this method
- 1) filtering of analytical downward continuation,
- 2) the use of the magnitude of the gravitational vector,
- 3) calculation of physe changes.
The numerical examples confirm these assumptions.
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MIGRATION IN TERMS OF SPATIAL DECONVOLUTION*
Authors A. J. BERKHOUT and D. W. VAN WULFFTEN PALTHEAbstractThe relationship between two finite‐difference schemes (15° and 40°) and the Kirchhoff summation approach is discussed by using closed form solutions of Claerbout's approximate versions of the wave equation. Forward extrapolation is presented as a spatial convolution procedure for each frequency component. It is shown that downward extrapolation can be considered as a wavelet deconvolution procedure, the spatial wavelet being given by the wave theory. Using this concept, a three‐dimensional model for seismic data is proposed.
The advantages of downward extrapolation in the space‐frequency domain are discussed.
Finally, it is derived that spatial sampling imposes an upper limit on the aperture and a lower limit on the extrapolation step.
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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)