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- Volume 69, Issue 8, 2021
Geophysical Prospecting - Volume 69, Issue 8-9, 2021
Volume 69, Issue 8-9, 2021
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Point‐spread function convolution to simulate prestack depth migrated images: A validation study
Authors Kristian Jensen, Isabelle Lecomte, Leiv Jacob Gelius and Tina KaschwichABSTRACTSeismic migration commonly yields an incomplete reconstruction of the Earth model due to restricted survey aperture, band‐limited frequency content and propagation effects. This affects both illumination and resolution of the structures of interest. Through the application of spatial convolution operators commonly referred to as point‐spread functions, simulated prestack depth‐migrated images incorporating these effects may be obtained. Such simulated images are tailored for analysing distortion effects and enhance our understanding of seismic imaging and subsequent interpretation. Target‐oriented point‐spread functions may be obtained through a variety of waveform and ray‐based approaches. Waveform approaches are generally more robust, but the computational cost involved may be prohibitive. Ray‐based approaches, on the other hand, allow for efficient and flexible sensitivity studies at a low computational cost, but inherent limitations may lead to less accuracy. To yield more insight into the similarities and differences between point‐spread functions obtained via these two approaches, we first derive analytical expressions of both wave‐ and ray‐based point‐spread functions in homogeneous media. By considering single‐point scatterers embedded in a uniform velocity field, we demonstrate the conditions under which the derived equations diverge. The accuracy of wave‐based and ray‐based point‐spread functions is further assessed and validated at selected targets in a subsection of the complex BP Statics Benchmark model. We also compare our simulated prestack depth migrated images with the output obtained from an actual prestack depth migration (reverse time migration). Our results reveal that both the wave‐ and ray‐based approaches accurately model illumination, resolution and amplitude effects observed in the reverse time‐migrated image. Furthermore, although some minor deviations between the wave‐based and ray‐based approaches are observed, the overall results indicate that both approaches can be used also for complex models.
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Perturbation‐based traveltime approximation for two acoustic assumptions in the transversely isotropic media with a vertical symmetry axis
Authors Shibo Xu and Alexey StovasABSTRACTThe accuracy of an explicit traveltime‐offset approximation affects the results of the velocity analysis that plays a crucial role in the seismic data processing. Seismic anisotropy is important to account for large offset and azimuth since it can provide detailed information comparing with the isotropic assumption. For the perturbation‐based method, different traveltime approximation forms result in different accuracy. It is necessary to find the optimal traveltime approximation for specific signs and magnitudes of the anellipticity and different offset ranges. In this paper, a series of perturbation‐based traveltime approximations from different acoustic assumptions and parameterizations are specified. The perturbation coefficients are derived from the corresponding acoustic eikonal equations. We test the accuracy of the defined perturbation approximations in four homogeneous transversely isotropic medium with vertical symmetry axis (VTI) medium with a different set of anisotropy parameters and one multilayered transversely isotropic medium with vertical symmetry axis medium. The sensitivity in anellipticity for different approximations is also analysed. We find that different approximation achieves different accuracy under the circumstance of specific offset range and the value of anellipticity. Therefore, the optimal approximation form with higher accuracy can be selected based on different offset ranges and the magnitudes of anellipticity.
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Acquisition geometry analysis with point‐spread functions
Authors Billy Revelo‐Obando and Gerrit BlacquièreABSTRACTSeismic data are traditionally acquired based on spatial sampling requirements, noise properties and budgetary constraints. However, designing a survey without taking into account the complexity of the subsurface may result in an image without the expected quality. Also, the subsequent preprocessing and processing steps may exploit or misuse the acquired data. The design should therefore incorporate the complexity of the subsurface and the (pre)processing steps that will be followed. We propose an analysis method that evaluates if the proposed combination of survey design, preprocessing and processing for a specific subsurface model fulfils a pre‐defined quality criterion. With our method, we estimate a set of point‐spread functions that correspond to the chosen combination, and we analyse their resolution and illumination‐detection properties in the spatial and wavenumber domains, respectively. The estimated point‐spread functions include the scattering and propagation effects generated by the subsurface, including internal multiples. We show that in some cases, the use of internal multiples in imaging can improve amplitude and resolution compared with the use of primaries only. The proposed analysis method is also used to evaluate the effect of blending noise when blended acquisition is carried out.
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Beam propagation of the 15‐degree equation and prestack depth migration in tilted transversely isotropic media using a ray‐centred coordinate system
Authors Bohan Zhang, Huazhong Wang and Xiaowen WangABSTRACTSeismic wave imaging in complex media requires an accurate wavefield simulation method that can accurately describethe wave propagation in realistic media. Reverse time‐depth migration is the preferred method for seismic wave imaging in complex media. Although it is relatively expensive, its imaging accuracy is usually better than migrations based on the ray method. Migration of primary reflection data requires a wave propagation simulation method that can accurately describe primary reflected/scattered wave energy and incorporate anisotropy. Accordingly, we propose the simulation of wave propagation in tilted transversely isotropic media using a 15° one‐way wave equation in a ray‐centred coordinate system, combining the flexibility of ray theory and the accuracy of wave theory. We use this equation to describe the propagation of body waves in a single ray tube, a ‘beam’. The wavefield along the beam, guided by its central raypath, has an angle limit defined only by the ray angle; therefore, wave propagation in complex and steeply dipping media can be simulated with a 15° one‐way wave equation. Numerical experiments show that the simulation results for beam propagation using the 15° equation in the ray‐centred coordinate system have good accuracy. For prestack depth migration in tilted transversely isotropic media, we built a beam imaging method using this propagator, and this migration method yielded accurate images with greater efficiency than reverse time‐depth migration.
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Multiscale phase inversion for vertical transverse isotropic media
Authors Shihang Feng, Lei Fu, Zongcai Feng and Gerard T. SchusterABSTRACTInanisotropy full waveform inversion, the pseudo‐acoustic approximation is widely used to reduce the computation cost. However, artefacts and inaccurate predictions of amplitudes by the pseudo‐acoustic approximation often result in slow convergence in the full waveform inversion iterations and inaccurate tomograms. To solve this problem, multiscale phase inversion methodology is extended to vertical transverse isotropic media. In multiscale phase inversion, the amplitude spectra of the predicted data are replaced by those of the recorded data to mitigate the amplitude mismatch problem. Moreover, multiscale phase inversion tends to avoid the local minimum problem of full waveform inversion by temporally integrating the traces several times. Numerical tests on synthetic data and field data demonstrate the superiority of this method compared to conventional multiscale full waveform inversion for vertical transverse isotropic media.
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Facies‐based full‐waveform inversion for anisotropic media: a North Sea case study
Authors Sagar Singh, Ilya Tsvankin and Ehsan Zabihi NaeiniABSTRACTElastic full‐waveform inversion can increase the resolution of reservoir characterization using seismic data. However, full‐waveform inversion for realistic anisotropic media suffers from the trade‐offs between the medium parameters and strongly relies on the accuracy of the initial model. Here, we employ a regularization methodology that utilizes geologically consistent information to reduce the inversion non‐linearity and crosstalk between the parameters. The geologic constraints are obtained from well logs and interpolated along major horizons in the migrated image. The algorithm, designed for transversely isotropic media with a tilted symmetry axis, is applied to ocean‐bottom data acquired at Volve field in the North Sea. The facies‐based constraints help build high‐resolution velocity fields and accurately image the reservoir region. In particular, the developed algorithm increases the resolution of the P‐ and S‐wave symmetry‐direction velocities and other parameters at the reservoir level. The facies‐based inversion also provides robust estimates of density, which is inverted simultaneously with the velocity fields. Overall, even relatively sparse prior information proves to be sufficient for the proposed methodology to achieve a much higher spatial resolution than the unconstrained full‐waveform inversion.
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Processing of multi‐well offset vertical seismic profile data acquired with distributed acoustic sensors and surface orbital vibrators: Stage 3 of the CO2CRC Otway Project case study
ABSTRACTTime‐lapse seismic reservoir monitoring is used as a way to gain insight into subsurface processes. Yet, the application of standard 4D technology onshore faces challenges, such as high cost, significant environmental footprint and, consequently, relatively infrequent surveys. As part of the Otway Project Stage 3 CO2 injection study, continuous automated borehole‐based monitoring using distributed acoustic sensing has been paired with permanently deployed surface sources, referred to as surface orbital vibrators, as a way to monitor the spreading CO2 plume. The injection of 15,000 tonnes of CO2 in a saline reservoir at a depth of 1550 m is monitored using five boreholes instrumented with enhanced sensitivity fibre optic cables and nine surface orbital vibrators, creating an array of 45 well–source pairs. The data are processed with an offset vertical seismic profiling processing workflow developed to address key challenges of the continuous distributed acoustic sensing acquisition using surface orbital vibrators. The processing flow includes deconvolution with a source sweep recorded by a pilot geophone installed below the surface orbital vibrators. A second deconvolution with a wavelet estimated from direct arrivals compensates for the difference between distributed acoustic sensing measurements and the pilot geophone as well as near‐surface variations. Image quality is noted to be best for short offsets and decreases with increasing offsets and well deviations. As surface orbital vibrators generate unique sweeps in two rotation directions, further processing is applied to stack these rotation signals together, which further improves the images. The resulting 2D transects of each well–source pair visually provide good illumination of the subsurface, suggesting continuous monitoring of the spreading CO2 plume should be possible with some further tuning of the processing workflow for time‐lapse repeatability.
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Reflection coefficients of P‐waves in partially saturated fractured media
Authors Kang Wang, Suping Peng, Yongxu Lu and Xiaoqin CuiABSTRACTWave‐induced fluid flow, an important mechanism in seismic wave attenuation, is considered in the amplitude variation with the offset technique. In a fractured marine carbonate reservoir, fractures and pores develop simultaneously, such that wave‐induced flow is an important mechanism in attenuation caused by the fluid flow between pores as well as between pores and fractures. However, these two types of attenuation are typically investigated separately or studies assume that the pores and fractures are dry or saturated by the same fluid. Rock pores are usually saturated by a mixture of two or more fluids, such that the fracture and pore filling fluids may be different. During variation with offset reservoir prediction and fluid identification, the influence that the porosity, fracture, and fluid have on the P‐wave reflection coefficient should be considered. The patchy saturation model can describe the seismic wave dissipation caused by the wave‐induced flow between pore fluids, whereas the Norris model can describe seismic wave dissipation caused by the fluid flow between fractures and pores. This study considers both the patchy saturation model and Norris model to calculate the amplitude variation with the offset P‐wave reflection coefficient under different conditions. Combining the saturation and Norris models forms a new model, which is regarded as a transversely isotropic medium with a vertical symmetric axis, and can be extended to any incident angle through the relaxation function and the high‐ and low‐frequency elastic limits of the stiffness tensor, where the complete effective stiffness tensor of the new model can be obtained. Finally, the amplitude variation with offset reservoir technology is used to determine the influence of model parameters on the reflection coefficient of P‐waves under different angles and frequencies, including fracture weakness, fluid saturation and pore fluid saturation.
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Application of adaptive parameterized S‐transform to delta sandstone reservoir identification
Authors Yuxia Fang, Hui Chen, Ying Hu, Rui Li and Jun LiABSTRACTTime–frequency analysis plays an important role in seismic interpretation and reservoir identification because it reveals the variation of seismic frequency contents over time. The S‐transform is recognized as an efficient method for seismic time–frequency analysis, but its frequency distribution biases the actual Fourier spectrum due to the linear frequency‐dependent term in the analytical window. In this paper, an improved S‐transform, named adaptive parameterized S‐transform, is proposed for identifying delta sandstone reservoirs. In the proposed method, three parameters are introduced into the S‐transform to better adjust the time–frequency resolution in different frequency bands. Then these parameters are selected adaptively by using the concentration measure to provide a highly energy‐concentrated time–frequency representation for seismic signals. Two synthetic examples validate the effectiveness of the proposed method. Analysis of field seismic data illustrates that it can provide a better reservoir interpretation with a high resolution. Comparisons between the wavelet transform, S‐transform, and modified S‐transform prove the superiority of the proposed method in describing reservoir distribution and decreasing the uncertainty of reservoir detection. This paper presents a complementary approach to current methods for reservoir detection and identification.
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Diagnosing of clay distribution in argillaceous sandstone by a rock physics template
Authors Junguang Nie, Zhipeng Qu, Yuanfeng Cheng, Xingmou Wang, Jianbing Zhu, Shuai Sun, Luanxiao Zhao and Jianhua GengABSTRACTThe elastic properties of argillaceous sandstones are significantly controlled, however, by the perplexing distribution of dispersed, cemented and matrix (including structural and layered) clay. The corresponding rock physics models are established to investigate the influence of different clay distribution on the elastic properties of sandstone. The rock physics modelling and laboratory experimental results exhibit that the higher the content of the matrix clay, the lower the elastic wave velocity. The dispersed and cemented clay increases the sandstone's velocity by reducing the porosity; the increase of dispersed clay only causes a slight increase in the elastic wave velocity in sandstone. In contrast, a small amount of cemented clay can significantly increase the velocity in sandstone. Based on these understandings, we construct a cross‐plot of P‐wave velocity and clay content as a template to diagnose clay distribution. Based on the rock physics model and empirical knowledge, we divide the template into four zones, namely, matrix, dispersed, cemented and mixed clay distribution zones. Then, we use the published experimental data and numerical modelling data to validate the template. Based on diagnosing the clay distribution, we introduce how to use the diagnostic results of the template to select a suitable rock physics model for argillaceous sandstone in Shengli Oil Field, East China. The selected rock physics model, guided by diagnosing the clay distribution, predicts P‐ and S‐wave velocity very well. The proposed rock physics template for diagnosing clay distribution also has potential application in well‐logging data interpretation, rock physics modelling and reservoir characterization.
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Frequency‐dependent seismic properties in layered and fractured rocks with partial saturation
Authors Denghui Xu, Tongcheng Han and Li‐Yun FuABSTRACTSeismic waves propagating in a fractured porous rock with fluids can be greatly attenuated due to the wave‐induced fluid flow, including the macroscopic Biot flow, the mesoscopic interlayer fluid flow and the microscopic squirt flow. However, the comprehensive effects of the above wave‐induced fluid flows on the frequency‐dependent seismic properties in layered and fractured rocks with partial saturation are still poorly understood. To obtain such knowledge, we present a superposition approach accounting for the dispersion and attenuation induced by the multi‐scale wave‐induced fluid flows in the above‐mentioned target rocks, and study the influences of the water saturation, layer thickness ratio and fracture properties (i.e. fracture density and fracture aspect ratio) on the frequency‐dependent vertical P‐wave velocity (VP0). The results demonstrate that the increasing water saturation enhances the dispersion and attenuation of VP0 in the full frequency band, and the varying layer thickness ratio not only affects the dispersion and attenuation induced by the interlayer fluid flow, but also influences those caused by the Biot flow and squirt flow. The fracture properties are also found to significantly impact the seismic properties of the target rock. In addition to its effects on the squirt flow, the increasing fracture density is shown to weaken the dispersion and attenuation induced by the Biot flow, and enhance those caused by the interlayer fluid flow. The obtained results provide new insights into the frequency‐dependent seismic properties in the partially saturated layered rocks with fractures, and the knowledge gained from these results has important practical applications for the successful interpretation of fluid and fracture properties applying the seismic exploration data acquired in fractured reservoirs.
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Porosity variation of elastic wave velocities in clean sandstones
Authors Colin M. Sayers and Lennert D. den BoerABSTRACTThe mechanical properties of sandstones, including porosity, density and elastic moduli, can be estimated non‐destructively through elastic wave‐velocity measurements. Here, the variation of elastic wave velocity with porosity in sandstones is modelled using Maxwell's effective field theory, extended to the elasticity of heterogeneous media by Sevostianov and coworkers. Comparing measured and predicted elastic wave velocities shows that on deposition, pores in sandstones are less stiff than spherical pores, but that their stiffness increases as porosity decreases. This suggests that concavity of pores in sandstone decreases with decreasing porosity. This interpretation is confirmed by the simple model of Sevostianov and Giraud in which concave pores are represented as superspherical pores, defined by a shape parameter that allows the effect of pore concavity on elastic wave velocities to be investigated. Inversion of measured velocities for this parameter indicates that pore concavity decreases with decreasing porosity. Moreover, values of the shape parameter obtained by inverting measured P‐velocities alone are found to give a good prediction of both P‐ and S‐wave velocities, confirming the applicability of the model.
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A computational review of the line integral analytical formulation of the polyhedral gravity signal
Authors Dimitrios Tsoulis and Georgia GavriilidouABSTRACTThe generally shaped polyhedron is a widely used model in gravity field modelling and interpretation. Its induced gravity signal – gravitational potential and its derivatives up to second order – has been studied extensively in the geophysical literature. The class of solutions with special interest is the one which leads to closed analytical expressions, as these offer an exact representation of the gravity signal of finite three‐dimensional distributions while being at the same time linked to a flexible means of geometric modelling. Of the several mathematical algorithms available, the line integral approach involves no approximations and is, however, connected with certain singularities, occurring for specific relative positions of the computation point with respect to the polyhedral source. The present contribution analyses the algorithmic details of the polyhedral line integral approach focusing on its geometric and computational aspects. Following the definitions of the individual coordinate systems and the two‐step application of the Gauss divergence theorem for each face and polygonal boundary of the source, the geometric insight of the algorithm is presented, which permits a deeper understanding of the significance of the involved numerical singular terms. An overview of the line integral analytical approach for the polyhedral gravity signal is presented with emphasis on its geometric and computational aspects. Matlab code and results for the two considered case studies, a prismatic source and asteroid Eros, are provided as electronic supplement.
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Convolutional neural network inversion of airborne transient electromagnetic data
Authors Sihong Wu, Qinghua Huang and Li ZhaoABSTRACTAs an efficient geophysical exploration technique, airborne transient electromagnetics shows strong adaptability to complex terrains and can provide subsurface resistivity information rapidly with a dense spatial coverage. However, the huge volume of airborne transient electromagnetic data obtained from a large number of spatial locations presents a great challenge to real‐time airborne transient electromagnetic interpretation due to the high computational cost. Moreover, the inherent non‐uniqueness of the inverse problem also limits our ability to constrain the underground resistivity structure. In this study, we develop an entirely data‐driven convolutional neural network to solve the airborne transient electromagnetic inverse problem. Synthetic tests show that the convolutional neural network is computationally efficient and yields robust results. Compared with the Gauss–Newton method, convolutional neural network inversion does not depend on the choices of an initial model and the regularization parameters and is less prone to getting trapped in a local minimum. We also demonstrate the general applicability of the convolutional neural network to three‐dimensional synthetic airborne transient electromagnetic responses and the field observations acquired from Leach Lake Basin, Fort Irwin, California. The efficient convolutional neural network inversion framework can support real‐time resistivity imaging of subsurface structures from airborne transient electromagnetic observations, providing a powerful tool for field explorations.
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Electrical resistivity tomography with smooth sparse regularization
Authors Shichao Zhong, Yibo Wang, Yikang Zheng, Shaojiang Wu, Xu Chang and Wei ZhuABSTRACTElectrical resistivity tomography employs L2 norm regularization in many applications. We developed the boundary‐sharping inversion method based on the finite element methods and irregular grid approach, in which the contact areas of elements are used to weight the model parameters. Similar approaches have previously only been used for structured grids. We also designed an electrical resistivity tomography system in the laboratory to conduct experimental data tests. Focusing on the imaging of small‐scale targets, we further compared the behaviour of various regularization schemes, including L2, L1 and L0 norm stabilizers. Different control parameters were tested and analysed for approximated L1 and L0 norm stabilizers. Three‐dimensional conductivity models were reconstructed from synthetic and experimental data. We found that reconstructed images obtained from smooth sparse regularization, such as L1, and L0 norm regularization are superior to L2 norm regularization for high‐contrast aquifer and block models. The synthetic and experimental data show that electrical resistivity tomography with smooth sparse regularization has the potential to improve the imaging of small‐scale targets with sharp contours.
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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 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 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 39 (1991)
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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)