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- Volume 65, Issue 4, 2017
Geophysical Prospecting - Volume 65, Issue 4, 2017
Volume 65, Issue 4, 2017
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Noise transfer in variable‐depth streamer deghosting
Authors Ralf Ferber and Dirk‐Jan van ManenABSTRACTSingle‐component towed‐streamer marine data acquisition records the pressure variations of the upgoing compressional waves followed by the polarity‐reversed pressure variations of downgoing waves, creating sea‐surface ghost events in the data. The sea‐surface ghost for constant‐depth towed‐streamer marine data acquisition is usually characterised by a ghost operator acting on the upgoing waves, which can be formulated as a filtering process in the frequency–wavenumber domain. The deghosting operation, usually via the application of the inverse Wiener filter related to the ghost operator, acts on the signal as well as the noise. The noise power transfer into the deghosted data is proportional to the power spectrum of the inverse Wiener filter and is amplifying the noise strongly at the notch wavenumbers and frequencies of the ghost operator. For variable‐depth streamer acquisition, the sea‐surface ghost cannot be described any longer as a wavenumber–frequency operator but as a linear relationship between the wavenumber–frequency representation of the upgoing waves at the sea surface and the data in the space–frequency domain. In this article, we investigate how the application of the inverse process acts on noise. It turns out that the noise magnification is less severe with variable‐depth streamer data, as opposed to constant depth, and is inversely proportional to the local slant of the streamer. We support this statement via application of the deghosting process to real and numerical random noise. We also propose a more general concept of a wavenumber–frequency ghost power transfer function, applicable for variable‐depth streamer acquisition, and demonstrate that the inverse of the proposed variable‐depth ghost power transfer function can be used to approximately quantify the action of the variable‐depth streamer deghosting process on noise.
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Arctangent function‐based third derivative attribute for characterisation of faults
More LessABSTRACTUsing seismic attributes such as coherence and curvature to characterise faults not only can improve the efficiency of seismic interpretation but also can expand the capability to detect faults. The coherence and curvature have been widely applied to characterising faults for years. These two methods detect faults based on the similarity of seismic waveforms and shapes of the reflectors, respectively, and they are complementary to each other and both have advantages and disadvantages in fault characterisation. A recent development in fault characterisation based on reflector shapes has been the use of the rate of change of curvature. Through an application to the seismic data from Western Tazhong of the Tarim Basin, China, it was demonstrated that the rate of change of curvature is more capable of detecting subtle faults having quite small throws and heaves. However, there often exist multiple extreme values indicating the same fault when applying the rate of change of curvature, which significantly degrades the signal‐to‐noise ratio of the computation result for multiple extrema interfering with each other. To resolve this problem, we propose the use of a linear combination of arctangent and proportional functions as the directrix of a cylindrical surface to fit the fault model and calculate its third derivative, which can then be used to characterise the fault. Through an application to the 3D seismic data from Western Tazhong of the Tarim Basin, the results show that the proposed method not only retains the same capability to detect subtle faults having small throws as the curvature change rate but also greatly improves the signal‐to‐noise ratio of the calculated result.
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A fast joint seismic data reconstruction by sparsity‐promoting inversion
Authors Lanshu Bai, Huiyi Lu, Yike Liu and Majid KhanABSTRACTSeismic field data are often irregularly or coarsely sampled in space due to acquisition limits. However, complete and regular data need to be acquired in most conventional seismic processing and imaging algorithms. We have developed a fast joint curvelet‐domain seismic data reconstruction method by sparsity‐promoting inversion based on compressive sensing. We have made an attempt to seek a sparse representation of incomplete seismic data by curvelet coefficients and solve sparsity‐promoting problems through an iterative thresholding process to reconstruct the missing data. In conventional iterative thresholding algorithms, the updated reconstruction result of each iteration is obtained by adding the gradient to the previous result and thresholding it. The algorithm is stable and accurate but always requires sufficient iterations. The linearised Bregman method can accelerate the convergence by replacing the previous result with that before thresholding, thus promoting the effective coefficients added to the result. The method is faster than conventional one, but it can cause artefacts near the missing traces while reconstructing small‐amplitude coefficients because some coefficients in the unthresholded results wrongly represent the residual of the data. The key process in the joint curvelet‐domain reconstruction method is that we use both the previous results of the conventional method and the linearised Bregman method to stabilise the reconstruction quality and accelerate the recovery for a while. The acceleration rate is controlled through weighting to adjust the contribution of the acceleration term and the stable term. A fierce acceleration could be performed for the recovery of comparatively small gaps, whereas a mild acceleration is more appropriate when the incomplete data has a large gap of high‐amplitude events. Finally, we carry out a fast and stable recovery using the trade‐off algorithm. Synthetic and field data tests verified that the joint curvelet‐domain reconstruction method can effectively and quickly reconstruct seismic data with missing traces.
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Surface‐wave inversion for a P‐velocity profile with a constant depth gradient of the squared slowness
Authors A.V. Ponomarenko, B.M. Kashtan, V.N. Troyan and W.A. MulderABSTRACTSurface waves are often used to estimate a near‐surface shear‐velocity profile. The inverse problem is solved for the locally one‐dimensional problem of a set of homogeneous horizontal elastic layers. The result is a set of shear velocities, one for each layer. To obtain a P‐wave velocity profile, the P‐guided waves should be included in the inversion scheme. As an alternative to a multi‐layered model, we consider a simple smooth acoustic constant‐density velocity model, which has a negative constant vertical depth gradient of the squared P‐wave slowness and is bounded by a free surface at the top and a homogeneous half‐space at the bottom. The exact solution involves Airy functions and provides an analytical expression for the dispersion equation. If the ratio is sufficiently small, the dispersion curves can be picked from the seismic data and inverted for the continuous P‐wave velocity profile. The potential advantages of our model are its low computational cost and the fact that the result can serve as a smooth starting model for full‐waveform inversion. For the latter, a smooth initial model is often preferred over a rough one. We test the inversion approach on synthetic elastic data computed for a single‐layer P‐wave model and on field data, both with a small ratio. We find that a single‐layer model can recover either the shallow or deeper part of the profile but not both, when compared with the result of a multi‐layer inversion that we use as a reference. An extension of our analytic model to two layers above a homogeneous half‐space, each with a constant vertical gradient of the squared P‐wave slowness and connected in a continuous manner, improves the fit of the picked dispersion curves. The resulting profile resembles a smooth approximation of the multi‐layered one but contains, of course, less detail. As it turns out, our method does not degrade as gracefully as, for instance, diving‐wave tomography, and we can only hope to fit a subset of the dispersion curves. Therefore, the applicability of the method is limited to cases where the ratio is small and the profile is sufficiently simple. A further extension of the two‐layer model to more layers, each with a constant depth gradient of the squared slowness, might improve the fit of the modal structure but at an increased cost.
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Joint up/down decomposition and reconstruction using three‐component streamers with or without ghost model: the sampling theory
Authors Zijian Tang and Xander CampmanABSTRACTThis paper addresses two artefacts inherent to marine towed‐streamer surveys: 1) ghost reflections and 2) too sparse a sampling in the crossline direction. A ghost reflection is generated when an upcoming reflection bounces off the sea surface back into the sensors and can, in principle, be removed by decomposing the measured wavefield into its up‐ and downgoing constituents. This process requires a dense sampling of the wavefield in both directions along and perpendicular to the streamers. A dense sampling in the latter direction is, however, often impossible due to economical and operational constraints. Recent multi‐component streamers have been designed to record the spatial gradients on top of the pressure, which not only benefits the wavefield decomposition but also facilitates a lower‐than‐Nyquist sampling rate of the pressure. In this paper, wavefield reconstruction and deghosting are posed as a joint inverse problem. We present two approaches to establish a system matrix that embeds both a deghosting and an interpolation operator. The first approach is derived with a ghost model, whereas the second approach is derived without a ghost model. The embodiment of a ghost model leads to an even lower sampling rate but relies on a more restrictive assumption on the sea surface.
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Scanning anisotropy parameters in horizontal transversely isotropic media
Authors Nabil Masmoudi, Alexey Stovas and Tariq AlkhalifahABSTRACTThe horizontal transversely isotropic model, with arbitrary symmetry axis orientation, is the simplest effective representative that explains the azimuthal behaviour of seismic data. Estimating the anisotropy parameters of this model is important in reservoir characterisation, specifically in terms of fracture delineation. We propose a travel‐time‐based approach to estimate the anellipticity parameter η and the symmetry axis azimuth ϕ of a horizontal transversely isotropic medium, given an inhomogeneous elliptic background model (which might be obtained from velocity analysis and well velocities). This is accomplished through a Taylor's series expansion of the travel‐time solution (of the eikonal equation) as a function of parameter η and azimuth angle ϕ. The accuracy of the travel time expansion is enhanced by the use of Shanks transform. This results in an accurate approximation of the solution of the non‐linear eikonal equation and provides a mechanism to scan simultaneously for the best fitting effective parameters η and ϕ, without the need for repetitive modelling of travel times. The analysis of the travel time sensitivity to parameters η and ϕ reveals that travel times are more sensitive to η than to the symmetry axis azimuth ϕ. Thus, η is better constrained from travel times than the azimuth. Moreover, the two‐parameter scan in the homogeneous case shows that errors in the background model affect the estimation of η and ϕ differently. While a gradual increase in errors in the background model leads to increasing errors in η, inaccuracies in ϕ, on the other hand, depend on the background model errors. We also propose a layer‐stripping method valid for a stack of arbitrary oriented symmetry axis horizontal transversely isotropic layers to convert the effective parameters to the interval layer values.
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Spatial behaviour of Rayleigh waves in layered half‐spaces under active surface sources
Authors Hua‐You Chai, Tian‐Bin Li, Kok‐Kwang Phoon, Elton J. Chen and Dian‐Ji ZhangABSTRACTIn the free state, Rayleigh waves are assumed to travel in the form of planar wavefronts. Under such an assumption, the propagation behaviour of the modes of Rayleigh waves in layered half‐spaces is only frequency dependent. The frequency behaviour, which is often termed as dispersion, is determined by the shear wave velocity profile of layered soils within the depth related to wavelength (or frequency). According to this characteristic, the shear wave velocity profile can be back‐analysed from the dispersion. The technique is widely used in the surface wave testing. However, the wavefronts of Rayleigh waves activated by the surface sources are non‐planar. The geometric discrepancy could result in Rayleigh waves manifesting distance‐dependent behaviour, which is referred to as spatial behaviour in this paper. Conventional analysis ignoring this spatial behaviour could introduce unexpected errors. In order to take the effects of sources on the propagation behaviour into account, a new mathematical model is established for Rayleigh waves in layered elastic media under vertical disc‐like surface sources using the thin‐layer method. The spatial behaviour of the activated modes and the apparent phase velocity, which is the propagation velocity of Rayleigh waves superposed by the multiple modes, are then analysed. Aspects of the spatial behaviour investigated in this paper include the equilibrium path, the particle orbit, and the geometric attenuation of the activated Rayleigh waves. The results presented in this paper can provide some guidelines for developing new inverse mathematical models and algorithms.
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Analysis of different parameterisations of waveform inversion of compressional body waves in an elastic transverse isotropic Earth with a vertical axis of symmetry
Authors Weiguang He and René‐Édouard PlessixABSTRACTIn a multi‐parameter waveform inversion, the choice of the parameterisation influences the results and their interpretations because leakages and the tradeoff between parameters can cause artefacts. We review the parameterisation selection when the inversion focuses on the recovery of the intermediate‐to‐long wavenumbers of the compressional velocities from the compressional body (P) waves. Assuming a transverse isotropic medium with a vertical axis of symmetry and weak anisotropy, analytical formulas for the radiation patterns are developed to quantify the tradeoff between the shear velocity and the anisotropic parameters and the effects of setting to zero the shear velocity in the acoustic approach. Because, in an anisotropic medium, the radiation patterns depend on the angle of the incident wave with respect to the vertical axis, two particular patterns are discussed: a transmission pattern when the ingoing and outgoing slowness vectors are parallel and a reflection pattern when the ingoing and outgoing slowness vectors satisfy Snell's law. When the inversion aims at recovering the long‐to‐intermediate wavenumbers of the compressional velocities from the P‐waves, we propose to base the parameterisation choice on the transmission patterns. Since the P‐wave events in surface seismic data do not constrain the background (smooth) vertical velocity due to the velocity/depth ambiguity, the preferred parameterisation contains a parameter that has a transmission pattern concentrated along the vertical axis. This parameter can be fixed during the inversion which reduces the size of the model space. The review of several parameterisations shows that the vertical velocity, the Thomsen parameter δ, or the Thomsen parameter ε have a transmission pattern along the vertical axis depending on the parameterisation choice. The review of the reflection patterns of those selected parameterisations should be done in the elastic context. Indeed, when reflection data are also inverted, there are potential leakages of the shear parameter at intermediate angles when we carry out acoustic inversion.
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Micro X‐Ray computed tomography imaging and ultrasonic velocity measurements in tetrahydrofuran‐hydrate‐bearing sediments
Authors Mandy Schindler, Michael L. Batzle and Manika PrasadABSTRACTNaturally occurring gas hydrates contain significant amounts of natural gas that might be produced as an energy resource in the foreseeable future. Thus, it is necessary to understand the pore‐space characteristics of hydrate reservoirs, particularly the pore‐scale distribution of the hydrate and its interaction with the sediment. Four end‐member models for hydrate distribution in the pore space are pore filling, sediment‐frame component, envelope cementing, and contact cementing. The goal of this study is to compare the models with pore‐scale hydrate distributions obtained in laboratory‐formed hydrates. Our results verify hydrate pore‐scale distributions by direct, visual observations that were previously implied by indirect, elastic property measurements.
Laboratory measurements were conducted using tetrahydrofuran as a guest molecule since tetrahydrofuran hydrate can be used as a proxy for naturally occurring hydrates. We performed micro X‐ray computed tomography to obtain information about the distribution of hydrate in the pore space of synthetic sediment (glass beads). We also made ultrasonic velocity measurements on the same samples. Micro X‐ray computed tomography images and ultrasonic velocity measurements both indicate that the tetrahydrofuran hydrate forms in the pore space with a part of the hydrate bridging the grains without touching the grain surfaces. These hydrate‐bearing sediments appear to follow a pore‐filling model with a portion of the hydrate becoming a load‐bearing part of the sediment frame.
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Interaction of multiple courses of wave‐induced fluid flow in layered porous media
Authors Chenghao Cao, Hongbing Zhang and Yixin PanABSTRACTDifferent theoretical and laboratory studies on the propagation of elastic waves in layered hydrocarbon reservoir have shown characteristic velocity dispersion and attenuation of seismic waves. The wave‐induced fluid flow between mesoscopic‐scale heterogeneities (larger than the pore size but smaller than the predominant wavelengths) is the most important cause of attenuation for frequencies below 1 kHz. Most studies on mesoscopic wave‐induced fluid flow in the seismic frequency band are based on the representative elementary volume, which does not consider interaction of fluid flow due to the symmetrical structure of representative elementary volume. However, in strongly heterogeneous media with unsymmetrical structures, different courses of wave‐induced fluid flow may lead to the interaction of the fluid flux in the seismic band; this has not yet been explored. This paper analyses the interaction of different courses of wave‐induced fluid flow in layered porous media. We apply a one‐dimensional finite‐element numerical creep test based on Biot's theory of consolidation to obtain the fluid flux in the frequency domain. The characteristic frequency of the fluid flux and the strain rate tensor are introduced to characterise the interaction of different courses of fluid flux. We also compare the behaviours of characteristic frequencies and the strain rate tensor on two scales: the local scale and the global scale. It is shown that, at the local scale, the interaction between different courses of fluid flux is a dynamic process, and the weak fluid flux and corresponding characteristic frequencies contain detailed information about the interaction of the fluid flux. At the global scale, the averaged strain rate tensor can facilitate the identification of the interaction degree of the fluid flux for the porous medium with a random distribution of mesoscopic heterogeneities, and the characteristic frequency of the fluid flux is potentially related to that of the peak attenuation. The results are helpful for the prediction of the distribution of oil–gas patches based on the statistical properties of phase velocities and attenuation in layered porous media with random disorder.
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Effects of fluid displacement pattern on complex electrical impedance in Berea sandstone over frequency range 104–106 Hz
Authors Yi Zhang, Hyuck Park, Osamu Nishizawa, Tamotsu Kiyama, Yu Liu, Kwangseok Chae and Ziqiu XueABSTRACTTo better understand the effect of fluid distribution on the electric response of rocks saturated with oil and brine, we conducted experimental studies on the complex electrical impedance in a Berea sandstone, together with in situ acquisitions of oil distribution images employing a high‐resolution medical X‐ray computed tomography. We performed two tests of brine displacement by oil under high (10 MPa) and low (5 MPa) pressures, which were accompanied by fingering and stable displacement patterns, respectively. The measured complex impedance data were fitted to the Cole model to obtain the resistance, capacitance, peak frequency of the imaginary impedance, and the exponent α of the rock–fluid system. With increasing oil saturation, the resistance showed an increasing trend, whereas the other three parameters decreased. The fingering displacement exhibited lower resistance and capacitance than the stable displacement. The analysis of the resistance changes using a simple parallel connection model indicates that there are more components of residual brine in parallel connections in the fingering pattern than in the stable displacement pattern at the same saturation. We also interpreted the normalised changes in the capacitance (or apparent dielectric constant) with respect to the oil saturation via an analysis of the shape factor of fluid distribution based on the Maxwell–Wagner–Brugermann–Hanai model. The changes in the shape factor suggest that the pinch‐off of the brine in parallel connection by the oil is a dominant mechanism reducing the capacitance. In the stable displacement, most of the connections in the brine phase are immediately pinched off by oil displacement front at a local oil saturation of 65%. Conversely, in the fingering displacement, there is a transition from the bulk or layered brine to the pinched‐off at a local oil saturation below 60%. The analyses indicate that the difference in the fluid distribution under different fluid conditions is responsible for the non‐Archie behaviour.
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Definitive superparamagnetic source identification through spatial, temporal, and amplitude analysis of airborne electromagnetic data
By James MacnaeABSTRACTThe aim of this paper is to add confidence to existing methods using decay shape analysis to detect superparamagnetic responses in airborne electromagnetic data. While expensive to acquire, vertical spatial gradient measurements of the electromagnetic signals can discriminate near‐surface superparamagnetic sources. This research investigated the use of horizontal spatial gradients and amplitude information as further indicators of superparamagnetic. High horizontal gradients were shown both theoretically and in field data to help discriminate superparamagnetic from deep mineral targets. Further, superparamagnetic responses have characteristically small amplitudes inconsistent with realistic mineral exploration targets at shallow depths.
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Slopes of an airborne electromagnetic resistivity model interpolated jointly with borehole data for 3D geological modelling
Authors P.‐A. Reninger, G. Martelet, J. Perrin, J. Deparis and Y. ChenABSTRACTWe investigate a novel way to introduce resistivity models deriving from airborne electromagnetic surveys into regional geological modelling. Standard geometrical geological modelling can be strengthened using geophysical data. Here, we propose to extract information contained in a resistivity model in the form of local slopes that constrain the modelling of geological interfaces. The proposed method is illustrated on an airborne electromagnetic survey conducted in the region of Courtenay in France. First, a resistivity contrast corresponding to the clay/chalk interface was interpreted confronting the electromagnetic soundings to boreholes. Slopes were then sampled on this geophysical model and jointly interpolated with the clay/chalk interface documented in boreholes using an implicit 3D potential‐field method. In order to evaluate this new joint geophysical–geological model, its accuracy was compared with that of both pure geological and pure geophysical models for various borehole configurations. The proposed joint modelling yields the most accurate clay/chalk interface whatever the number and location of boreholes taken into account for modelling and validation. Compared with standard geological modelling, the approach introduces in between boreholes geometrical information derived from geophysical results. Compared with conventional resistivity interpretation of the geophysical model, it reduces drift effects and honours the boreholes. The method therefore improves what is commonly obtained with geological or geophysical data separately, making it very attractive for robust 3D geological modelling of the subsurface.
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Experimental quantification of the seismoelectric transfer function and its dependence on conductivity and saturation in loose sand
Authors J. Holzhauer, D. Brito, C. Bordes, Y. Brun and B. GuatarbesABSTRACTUnder certain circumstances, seismic propagation within porous media may be associated to the conversion of mechanical energy to electromagnetic energy, which is known as a seismo‐electromagnetic phenomenon. The propagation of fast compressional P‐waves is more specifically associated to the manifestations of a seismoelectric field linked to the fluid flows within the pores. The analysis of seismoelectric phenomena, which requires the combination of the theory of electrokinetics and Biot's theory of poroelasticity, provides us with transfer function that links the coseismic seismoelectric field E to the seismic acceleration . To measure the transfer function, we have developed an experimental setup enabling seismoelectric laboratory observation in unconsolidated quartz sand within the kilohertz range. The investigation focused on the impact of fluid conductivity and water saturation over the coseismic seismoelectric field. During the experiment, special attention was given to the accuracy of electric field measurements. We concluded that, to obtain a reliable estimate of the electric field amplitude, the dipole from which the potential differences are measured should be of much smaller length than the wavelength of the propagating seismic field. Time‐lapse monitoring of the seismic velocities and seismoelectric transfer functions were performed during imbibition and drainage experiments. In all cases, the quantitative analysis of the seismoelectric transfer function was in good agreement with theoretical predictions. While investigating saturation variations from full to residual water saturation, we showed that the ratio undergoes a switch in polarity at a particular saturation , which also implies a sign change of the filtration, traducing a reversal of the relative fluid displacement with respect to the frame. This sign change at critical saturation stresses a particular behaviour of the poroelastic medium: the dropping of the coseismic electric field to zero traduces the absence of relative pore/fluid displacements representative of a Biot dynamically compatible medium. We concluded from our experimental study in loose sand that the measurements of the coseismic seismoelectric coupling may provide information on fluid distribution within the pores and that the reversal of the seismoelectric field may be used as an indicator of the dynamically compatible state of the medium.
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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 42 (1994)
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Volume 40 (1992)
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Volume 39 (1991)
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Volume 37 (1989)
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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 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 15 (1967)
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Volume 6 (1958)
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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)