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- Volume 55, Issue 3, 2007
Geophysical Prospecting - Volume 55, Issue 3, 2007
Volume 55, Issue 3, 2007
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Elastic‐impedance analysis constrained by rock‐physics bounds†
Authors Futoshi Tsuneyama and Gary MavkoABSTRACTBy applying seismic inversion, we can derive rock impedance from seismic data. Since it is an interval property, impedance is valuable for reservoir characterization. Furthermore, the decomposition of the impedance into two fundamental properties, i.e. velocity and density, provides a link to the currently available rock‐physics applications to derive quantitative reservoir properties. However, the decomposition is a challenging task due to the strong influence of noise, especially for seismic data with a maximum offset angle of less than 30°. We present a method of impedance decomposition using three elastic impedance data derived from the seismic inversion of angle stacks, where the far‐stack angle is 23.5°. We discuss the effect of noise on the analysis as being the most significant cause of making the decomposition difficult. As the result, the offset‐consistent component of noise mostly affects the determination of density but not the velocities (P‐ and S‐wave), whereas the effect of the random component of noise occurs equally in the determination of the velocities and density. The effect is controlled by the noise enhancement factor 1/A, which is determined by a combination of stack angles. Based on the results of the analysis, we show an innovative method of decomposition incorporating rock‐physics bounds as constraints for the analysis. The method is applied to an actual data set from an offshore oilfield; we demonstrate the result of analysis for sandbody detection.
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Elastic behaviour of North Sea chalk: A well‐log study
Authors L. Gommesen, I.L. Fabricius, T. Mukerji, G. Mavko and J.M. PedersenABSTRACTWe present two different elastic models for, respectively, cemented and uncemented North Sea chalk well‐log data. We find that low Biot coefficients correlate with anomalously low cementation factors from resistivity measurements at low porosity and we interpret this as an indication of cementation. In contrast, higher Biot coefficients and correspondingly higher cementation factors characterize uncemented chalk for the same (low) porosity. Accordingly, the Poisson's ratio–porosity relationship for cemented chalk is different from that of uncemented chalk.
We have tested the application of the self‐consistent approximation, which here represents the unrelaxed scenario where the pore spaces of the rock are assumed to be isolated, and the Gassmann theory, which assumes that pore spaces are connected, as tools for predicting the effect of hydrocarbons from the elastic properties of brine‐saturated North Sea reservoir chalk. In the acoustic impedance–Poisson's ratio plane, we forecast variations in porosity and hydrocarbon saturation from their influence on the elastic behaviour of the chalk. The Gassmann model and the self‐consistent approximation give roughly similar predictions of the effect of fluid on acoustic impedance and Poisson's ratio, but we find that the high‐frequency self‐consistent approach gives a somewhat smaller predicted fluid‐saturation effect on Poisson's ratio than the low‐frequency Gassmann model. The Gassmann prediction for the near and potentially invaded zone corresponds more closely to logging data than the Gassmann prediction for the far, virgin zone. We thus conclude that the Gassmann approach predicts hydrocarbons accurately in chalk in the sonic‐frequency domain, but the fluid effects as recorded by the acoustic tool are significantly affected by invasion of mud filtrate.
The amplitude‐versus‐angle (AVA) response for the general North Sea sequence of shale overlying chalk is predicted as a function of porosity and pore‐fill. The AVA response of both cemented and uncemented chalk generally shows a declining reflectivity coefficient versus offset and a decreasing normal‐incidence reflectivity with increasing porosity. However, for the uncemented model, a phase reversal will appear at a relatively lower porosity compared to the cemented model.
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The stress dependent elastic properties of thermally induced microfractures in aeolian Rotliegend sandstone
Authors Colin MacBeth and Hartmut SchuettABSTRACTThe impact of thermally induced microfractures on the stress‐sensitive elastic wave properties of aeolian Rotliegend sandstone samples is analysed. It is found that to identify the effects of the microfracture contribution accurately, a correction must first be made to account for water loss (representing a mass loss of 4–6%) from the pore throats and clays due to the heating process, despite care being taken to ensure that the thermally fractured samples re‐adsorb room moisture. Both the original and thermally fractured rocks are stress‐sensitive at the ultrasonic wave frequencies of the laboratory. However, a distinct shift in the estimated distribution of internal rock compliance indicates that the population of thermal microfractures differs in nature from that caused solely by core‐plug extraction damage. In particular, the ratio of normal to tangential compliance is observed to be higher for the thermally generated microfractures than for the broken grain‐grain contacts created by extraction unloading. This can be explained by the intragranular thermal‐fracture surfaces being smoother when compared to the intergranular boundaries. Mechanical hysteresis is observed between the up‐ and downgoing test cycles for both the original and, to a greater extent, the thermally fractured rock. This indicates that there is compaction‐induced movement of the fractures in the samples during application of stress in the laboratory.
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Fluid‐dependent shear‐wave splitting in a poroelastic medium with conjugate fracture sets
Authors Robert J. Galvin, Boris Gurevich and Colin M. SayersABSTRACTThe dependence of shear‐wave splitting in fractured reservoirs on the properties of the filling fluid may provide a useful attribute for identifying reservoir fluids. If the direction of wave propagation is not perpendicular or parallel to the plane of fracturing, the wave polarized in the plane perpendicular to the fractures is a quasi‐shear mode, and therefore the shear‐wave splitting will be sensitive to the fluid bulk modulus. The magnitude of this sensitivity depends upon the extent to which fluid pressure can equilibrate between pores and fractures during the period of the deformation. In this paper, we use the anisotropic Gassmann equations and existing formulations for the excess compliance due to fracturing to estimate the splitting of vertically propagating shear waves as a function of the fluid modulus for a porous medium with a single set of dipping fractures and with two conjugate fracture sets, dipping with opposite dips to the vertical. This is achieved using two alternative approaches. In the first approach, it is assumed that the deformation taking place is quasi‐static: that is, the frequency of the elastic disturbance is low enough to allow enough time for fluid to flow between both the fractures and the pore space throughout the medium. In the second approach, we assume that the frequency is low enough to allow fluid flow between a fracture set and the surrounding pore space, but high enough so that there is not enough time during the period of the elastic disturbance for fluid flow between different fracture sets to occur. It is found that the second approach yields a much stronger dependence of shear‐wave splitting on the fluid modulus than the first approach. This is a consequence of the fact that at higher wave frequencies there is not enough time for fluid pressure to equilibrate and therefore the elastic properties of the fluid have a greater effect on the magnitude of the shear‐wave splitting.
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Converted‐wave imaging in anisotropic media: theory and case studies
Authors Xiang‐Yang Li, Hengchang Dai and Fabio ManciniABSTRACTCommon‐conversion‐point binning associated with converted‐wave (C‐wave) processing complicates the task of parameter estimation, especially in anisotropic media. To overcome this problem, we derive new expressions for converted‐wave prestack time migration (PSTM) in anisotropic media and illustrate their applications using both 2D and 3D data examples.
The converted‐wave kinematic response in inhomogeneous media with vertical transverse isotropy is separated into two parts: the response in horizontally layered vertical transverse isotrophy media and the response from a point‐scatterer. The former controls the stacking process and the latter controls the process of PSTM. The C‐wave traveltime in horizontally layered vertical transverse isotrophy media is determined by four parameters: the C‐wave stacking velocity VC2, the vertical and effective velocity ratios γ0 and γeff, and the C‐wave anisotropic parameter χeff. These four parameters are referred to as the C‐wave stacking velocity model. In contrast, the C‐wave diffraction time from a point‐scatterer is determined by five parameters: γ0, VP2, VS2, ηeff and ζeff, where ηeff and ζeff are, respectively, the P‐ and S‐wave anisotropic parameters, and VP2 and VS2 are the corresponding stacking velocities. VP2, VS2, ηeff and ζeff are referred to as the C‐wave PSTM velocity model. There is a one‐to‐one analytical link between the stacking velocity model and the PSTM velocity model. There is also a simple analytical link between the C‐wave stacking velocities VC2 and the migration velocity VCmig, which is in turn linked to VP2 and VS2.
Based on the above, we have developed an interactive processing scheme to build the stacking and PSTM velocity models and to perform 2D and 3D C‐wave anisotropic PSTM. Real data applications show that the PSTM scheme substantially improves the quality of C‐wave imaging compared with the dip‐moveout scheme, and these improvements have been confirmed by drilling.
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Overburden complexity and repeatability of seismic data: Impacts of positioning errors at the Oseberg field, North Sea
Authors Ali Misaghi, Martin Landrø and Steen A. PetersenABSTRACTRepeatability of seismic data plays a crucial role in time‐lapse seismic analysis. There are several factors that can decrease the repeatability, such as positioning errors, varying tide, source variations, velocity changes in the water layer (marine data) and undesired effects of various processing steps. In this work, the complexity of overburden structure, as an inherent parameter that can affect the repeatability, is studied. A multi‐azimuth three‐dimensional vertical‐seismic‐profiling data set with 10 000 shots is used to study the relationship between overburden structure and repeatability of seismic data. In most repeatability studies, two data sets are compared, but here a single data set has been used because a significant proportion of the 10 000 shots are so close to each other that a repeatability versus positioning error is possible. We find that the repeatability decreases by a factor of approximately 2 under an overburden lens. Furthermore, we find that the X‐ and Y‐components have approximately the same sensitivity to positioning errors as the Z‐component (for the same events) in this three‐dimensional vertical‐seismic‐profiling experiment. This indicates that in an area with complex overburden, positioning errors between monitor and base seismic surveys are significantly more critical than outside such an area. This study is based on a three‐dimensional three‐component vertical‐seismic‐profiling data set from a North Sea reservoir and care should be taken when extrapolating these observations into a general four‐dimensional framework.
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On the retrieval of moment tensors from borehole data
More LessABSTRACTThe complete moment tensors of seismic sources in homogeneous or vertically inhomogeneous isotropic structures cannot be retrieved using receivers deployed in one vertical borehole. The complete moment tensors can be retrieved from amplitudes of P‐waves, provided that receivers are deployed in at least three boreholes. Using amplitudes of P‐ and S‐waves, two boreholes are, in principle, sufficient. Similar rules also apply to transversely isotropic media with a vertical axis of symmetry.
In the case of limited observations, the inversion can be stabilized by imposing the zero‐trace constraint on the moment tensors. However, this constraint is valid only if applied to observations of shear faulting on planar faults in isotropic media, which produces double‐couple mechanisms. For shear faulting on non‐planar faults, for tensile faulting, and for shear faulting in anisotropic media, the zero‐trace constraint is no longer valid and can distort the retrieved moment tensor and bias the fault‐plane solution.
Numerical modelling simulating the inversion of the double‐couple mechanism from real data reveals that the errors in the double‐couple and non‐double‐couple percentages of the moment tensors rapidly decrease with increase in the number of boreholes used. For noisy P‐ and S‐wave amplitudes with noise of 15% of the top amplitude at each channel and for a velocity model biased by 10%, the errors in the double‐couple percentage attain 25, 13 and 6% when inverting for the double‐couple mechanism from one, two and three boreholes.
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Hybrid genetic algorithms in view of the evolution theories with application for the electrical sounding method
Authors Ahmet T. Başokur, Irfan Akça and Nedal W.A. SiyamABSTRACTThe classical genetic algorithm is a stochastic process which operates by natural selection. Although the algorithm may localize a point around the global minimum of the misfit function, it is not efficient at finding the precise solution. This paper suggests some hybrid genetic algorithms, derived from evolution theories, to overcome this problem. Firstly, sexual selection has been incorporated in the classical genetic algorithm to obtain a full representation of the Darwinist evolution concept. The simulation of sexual selection is performed by assigning a higher probability of surviving to some parameters that satisfy some algebraic relationships. This method is called the ‘marked constraints’ algorithm since it permits us to insert geological and geophysical constraints into the problem. The algorithm implementation is realized by progressively shrinking the parameter search space through successive generations. In this way, the genetic algorithm gains some degree of determinism. Secondly, since the evolution theory of Lamarck postulates that the acquired traits are passed on to the next generation, a hybrid use of the damped least‐squares method and the genetic algorithm is called Lamarckian inversion. Lamarckian inversion involves some improvement procedures that simulate the reduction of the misfit with the help of a derivative‐based method between two generations. Finally, although there is no correspondence in nature, Lamarckian and Darwinist evolution concepts are combined to strengthen the deterministic part of the solution algorithm. This is called the Lamarckian‐marked‐constraint algorithm. The merits and behaviours of the suggested algorithms are discussed using two examples. The first is a hypothetical example affected by a multiminima problem. The second examines the equivalence problem using vertical electrical sounding data.
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Improved seawater depth determination using corrected helicopter time‐domain electromagnetic data
Authors Julian Vrbancich and Peter K. FullagarABSTRACTTwo areas within Sydney Harbour were surveyed in 2002 with a helicopter‐borne time‐domain electromagnetic system to test its potential for bathymetric mapping in shallow seawater. As delivered, the data were improperly calibrated. Therefore a re‐calibration was performed to reconcile the measured data with ‘ground truth’. Synthetic electromagnetic transients were computed for two‐layer models representing the seawater and the sediment overlying bedrock at a number of locations within the survey area. The seawater depth in the models varied between 3 m and 70 m. The measured and calculated data were compared at each delay time, and were found to be linearly related. The slope and intercept of the line of best fit were used to correct all the measured data. Inversion of the corrected time‐domain electromagnetic data generally resolved the bathymetry to submetre accuracy down to depths of about 55 m.
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Localized cultural denoising of high‐resolution aeromagnetic data
Authors V. Paoletti, M. Fedi, G. Florio and A. RapollaABSTRACTWe show how a denoising technique based on the wavelet transform can be used to deal with localized noise related to DC electrified railway lines. This method, which performs localized and sharp filtering of cultural noise, was applied to high‐resolution aeromagnetic data acquired in the Phlegrean volcanic area, southern Italy, in 1999 and 2001. The helicopter‐borne survey was aimed at giving new detailed insights into the distribution of the magnetization of the area and, therefore, into the volcanological characteristics of the region. The surveyed area is characterized by the presence of towns, buildings and DC electrified railway lines whose magnetic effects influenced the measurements and were responsible for some of the measured anomalies. This cultural noise has, therefore, to be minimized as much as possible in order to allow the data to be interpreted accurately. Due to the excellent space‐scale localization properties of the discrete wavelet transform, the cultural disturbance was removed very precisely, leaving the field in the adjacent areas unchanged.
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A new least‐squares minimization approach to depth and shape determination from magnetic data
ABSTRACTWe have developed a least‐squares minimization approach to depth determination using numerical second horizontal derivative anomalies obtained from magnetic data with filters of successive window lengths (graticule spacings). The problem of depth determination from second‐derivative magnetic anomalies has been transformed into finding a solution to a non‐linear equation of the form, f(z) = 0. Formulae have been derived for a sphere, a horizontal cylinder, a dike and a geological contact. Procedures are also formulated to estimate the magnetic angle and the amplitude coefficient.
We have also developed a simple method to define simultaneously the shape (shape factor) and the depth of a buried structure from magnetic data. The method is based on computing the variance of depths determined from all second‐derivative anomaly profiles using the above method. The variance is considered a criterion for determining the correct shape and depth of the buried structure. When the correct shape factor is used, the variance of depths is less than the variances computed using incorrect shape factors.
The method is applied to synthetic data with and without random errors, complicated regionals, and interference from neighbouring magnetic rocks. Finally, the method is tested on a field example from India. In all the cases examined, the depth and the shape parameters are found to be in good agreement with the actual parameters.
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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)