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- Volume 54, Issue 5, 2006
Geophysical Prospecting - Volume 54, Issue 5, 2006
Volume 54, Issue 5, 2006
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Path‐integral seismic imaging
Authors E. Landa, S. Fomel and T.J. MoserABSTRACTA new type of seismic imaging, based on Feynman path integrals for waveform modelling, is capable of producing accurate subsurface images without any need for a reference velocity model. Instead of the usual optimization for traveltime curves with maximal signal semblance, a weighted summation over all representative curves avoids the need for velocity analysis, with its common difficulties of subjective and time‐consuming manual picking. The summation over all curves includes the stationary one that plays a preferential role in classical imaging schemes, but also multiple stationary curves when they exist. Moreover, the weighted summation over all curves also accounts for non‐uniqueness and uncertainty in the stacking/migration velocities. The path‐integral imaging can be applied to stacking to zero‐offset and to time and depth migration. In all these cases, a properly defined weighting function plays a vital role: to emphasize contributions from traveltime curves close to the optimal one and to suppress contributions from unrealistic curves. The path‐integral method is an authentic macromodel‐independent technique in the sense that there is strictly no parameter optimization or estimation involved. Development is still in its initial stage, and several conceptual and implementation issues are yet to be solved. However, application to synthetic and real data examples shows that it has the potential for becoming a fully automatic imaging technique.
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Wavefield Migration plus Monte Carlo Imaging of 3D Prestack Seismic Data
Authors Ernesto Bonomi, Leesa M. Brieger, Luca Cazzola and Francesco ZanolettiABSTRACTPrestack wave‐equation migration has proved to be a very accurate shot‐by‐shot imaging tool. However, 3D imaging with this technique of a large field acquisition, especially one with hundreds of thousands of shots, is prohibitively costly. Simply adapting the technique to migrate many superposed shot‐gathers simultaneously would render 3D wavefield prestack migration cost‐effective but it introduces uncontrolled non‐physical interference among the shot‐gathers, making the final image useless. However, it has been observed that multishot signal interference can be kept under some control by averaging over many such images, if each multishot migration is modified by a random phase encoding of the frequency spectra of the seismic traces.
In this article, we analyse this technique, giving a theoretical basis for its observed behaviour: that the error of the image produced by averaging over M phase encoded migrations decreases as M−1. Furthermore, we expand the technique and define a general class of Monte‐Carlo encoding methods for which the noise variance of the average imaging condition decreases as M−1; these methods thus all converge asymptotically to the correct reflectivity map, without generating prohibitive costs.
The theoretical asymptotic behaviour is illustrated for three such methods on a 2D test case. Numerical verification in 3D is then presented for one such method implemented with a 3D PSPI extrapolation kernel for two test cases: the SEG–EAGE salt model and a real test constructed from field data.
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Borehole‐guided AVO analysis of P‐P and P‐S reflections: Quantifying uncertainty on density estimates
Authors Hugues A. Djikpesse, Wael Meghirbi, Irina Nizkous and Di CaoABSTRACTSeismic properties of isotropic elastic formations are characterized by the three parameters: acoustic impedance, Poisson's ratio and density. Whilst the first two are usually well estimated by analysing the amplitude variation with angle (AVA) of reflected P‐P waves, density is known to be poorly resolved. However, density estimates would be useful in many situations encountered in oil and gas exploration, in particular, for minimizing risks in looking ahead while drilling. We design a borehole seismic experiment to investigate the reliability of AVA extracted density. Receivers are located downhole near the targeted reflectors and record reflected P‐P and converted P‐S waves. A non‐linear, wide‐angle‐based Bayesian inversion is then used to access the a posteriori probability distributions associated with the estimation of the three isotropic elastic parameters. The analysis of these distributions suggests that the angular variation of reflected P‐S amplitudes provides additional substantial information for estimating density, thus reducing the estimate uncertainty variance by more than one order of magnitude, compared to using only reflected P‐waves.
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Non‐monotone spectral projected gradient method applied to full waveform inversion
Authors Noam Zeev, Olga Savasta and Debora CoresABSTRACTThe seismic inversion problem is a highly non‐linear problem that can be reduced to the minimization of the least‐squares criterion between the observed and the modelled data. It has been solved using different classical optimization strategies that require a monotone descent of the objective function. We propose solving the full‐waveform inversion problem using the non‐monotone spectral projected gradient method: a low‐cost and low‐storage optimization technique that maintains the velocity values in a feasible convex region by frequently projecting them on this convex set. The new methodology uses the gradient direction with a particular spectral step length that allows the objective function to increase at some iterations, guarantees convergence to a stationary point starting from any initial iterate, and greatly speeds up the convergence of gradient methods. We combine the new optimization scheme as a solver of the full‐waveform inversion with a multiscale approach and apply it to a modified version of the Marmousi data set. The results of this application show that the proposed method performs better than the classical gradient method by reducing the number of function evaluations and the residual values.
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Non‐hyperbolic moveout inversion of wide‐azimuth P‐wave data for orthorhombic media
Authors Ivan Vasconcelos and Ilya TsvankinABSTRACTThe azimuthally varying non‐hyperbolic moveout of P‐waves in orthorhombic media can provide valuable information for characterization of fractured reservoirs and seismic processing. Here, we present a technique to invert long‐spread, wide‐azimuth P‐wave data for the orientation of the vertical symmetry planes and five key moveout parameters: the symmetry‐plane NMO velocities, V(1)nmo and V(2)nmo, and the anellipticity parameters, η(1), η(2) and η(3). The inversion algorithm is based on a coherence operator that computes the semblance for the full range of offsets and azimuths using a generalized version of the Alkhalifah–Tsvankin non‐hyperbolic moveout equation.
The moveout equation provides a close approximation to the reflection traveltimes in layered anisotropic media with a uniform orientation of the vertical symmetry planes. Numerical tests on noise‐contaminated data for a single orthorhombic layer show that the best‐constrained parameters are the azimuth ϕ of one of the symmetry planes and the velocities V(1)nmo and V(2)nmo, while the resolution in η(1) and η(2) is somewhat compromised by the trade‐off between the quadratic and quartic moveout terms. The largest uncertainty is observed in the parameter η(3), which influences only long‐spread moveout in off‐symmetry directions. For stratified orthorhombic models with depth‐dependent symmetry‐plane azimuths, the moveout equation has to be modified by allowing the orientation of the effective NMO ellipse to differ from the principal azimuthal direction of the effective quartic moveout term.
The algorithm was successfully tested on wide‐azimuth P‐wave reflections recorded at the Weyburn Field in Canada. Taking azimuthal anisotropy into account increased the semblance values for most long‐offset reflection events in the overburden, which indicates that fracturing is not limited to the reservoir level. The inverted symmetry‐plane directions are close to the azimuths of the off‐trend fracture sets determined from borehole data and shear‐wave splitting analysis. The effective moveout parameters estimated by our algorithm provide input for P‐wave time imaging and geometrical‐spreading correction in layered orthorhombic media.
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Observation of azimuthal anisotropy from the seismic reflectivity of a Tertiary turbidite sand
Authors Colin MacBeth and Asghar ShamsABSTRACTP‐wave data from a time‐lapse 3D OBC survey have been analysed to estimate and interpret azimuthal seismic anisotropy. This is achieved by careful processing to preserve the azimuthal signature. The survey images a major reservoir body in a channelized turbidite field in the Gulf of Mexico. Three distinct and significant anisotropy anomalies are discovered on or around this particular ‘4500‐ft sand’, all of which change intensity but not orientation with hydrocarbon production. These anomalies are distributed along the highest concentration of cumulative sand thickness, with their symmetry axes aligned with the main channel axis. We suspect that this time‐lapse anisotropy could be caused by the alignment of the depositional grain fabric. Theoretical calculation predicts that this mechanism, when combined with fluid‐saturation changes, can generate the observed pattern of behaviour. If further supported by other researchers, this result would indicate that appropriately designed seismic surveys could be a useful tool for palaeo‐direction studies in clastic reservoirs and also a useful constraint for directional permeability in the reservoir flow simulation model.
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Influence of pore pressure on velocity in low‐porosity sandstone: Implications for time‐lapse feasibility and pore‐pressure study
Authors Xiaoxia Xu, Ronny Hofmann, Michael Batzle and Tashi TsheringABSTRACTAs seismic data quality improves, time‐lapse seismic data is increasingly being called upon to interpret and predict changes during reservoir development and production. Since pressure change is a major component of reservoir change during production, a thorough understanding of the influence of pore pressure on seismic velocity is critical. Laboratory measurements show that differential pressure (overburden minus fluid pressure) does not adequately determine the actual reservoir conditions. Changes in fluid pressure are found to have an additional effect on the physical properties of rocks. The effective‐stress coefficient n is used to quantify the effect of pore pressure compared to confining pressure on rock properties. However, the current practice in time‐lapse feasibility studies, reservoir‐pressure inversion and pore‐pressure prediction is to assume that n= 1. Laboratory measurements, reported in both this and previous research show that n can be significantly less than unity for low‐porosity rocks and that it varies with porosity, rock texture and wave type.
We report the results of ultrasonic experiments to estimate n for low‐porosity sandstones with and without microcracks. Our results show that, for P‐waves, n is as low as 0.4 at a differential pressure of 20 MPa (about 3000 psi) for a low‐porosity sandstone. Thus, in pore‐pressure inversion, an assumption of n= 1 would lead to a 150% underestimation of the pore pressure. Comparison of the effective‐stress coefficient for fractured and unfractured samples suggests that the presence of microfractures increases the sensitivity of P‐wave velocity to pore pressure, and therefore the effective‐stress coefficient. Our results show that the effective‐stress coefficient decreases with the differential pressure, with a higher differential pressure resulting in a lower effective‐stress coefficient. While the effective‐stress coefficient for P‐wave velocity can be significantly less than unity, it is close to one for S‐waves.
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Anisotropic migration velocity analysis: Application to a data set from West Africa
Authors Debashish Sarkar and Ilya TsvankinABSTRACTAlthough it is widely recognized that anisotropy can have a significant influence on the focusing and positioning of migrated reflection events, conventional depth imaging methods still operate with isotropic velocity fields. Here, we present an application of a 2D migration velocity analysis (MVA) algorithm, designed for factorized v(x, z) VTI (transversely isotropic with a vertical symmetry axis) media, to an offshore data set from West Africa. By approximating the subsurface with factorized VTI blocks, it is possible to decouple the spatial variations in the vertical velocity from the anisotropic parameters with minimal a priori information.
Since our method accounts for lateral velocity variation, it produces more accurate estimates of the anisotropic parameters than those previously obtained with time‐domain techniques. The values of the anellipticity parameter η found for the massive shales exceed 0.2, which confirms that ignoring anisotropy in the study area can lead to substantial imaging distortions, such as mis‐stacking and mispositioning of dipping events. While some of these distortions can be removed by using anisotropic time processing, further marked improvement in image quality is achieved by prestack depth migration with the estimated factorized VTI model. In particular, many fault planes, including antithetic faults in the shallow part of the section, are better focused by the anisotropic depth‐migration algorithm and appear more continuous. Anisotropic depth migration facilitates structural interpretation by eliminating false dips at the bottom of the section and improving the images of a number of gently dipping features.
One of the main difficulties in anisotropic MVA is the need to use a priori information for constraining the vertical velocity. In this case study, we successfully reconstructed the time–depth curve from reflection data by assuming that the vertical velocity is a continuous function of depth and estimating the vertical and lateral velocity gradients in each factorized block. If the subsurface contains strong boundaries with jumps in velocity, knowledge of the vertical velocity at a single point in a layer is sufficient for our algorithm to determine all relevant layer parameters.
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Refraction traveltime and amplitude corrections for very near‐ surface inhomogeneities
More LessABSTRACTThe performance of refraction inversion methods that employ the principle of refraction migration, whereby traveltimes are laterally migrated by the offset distance (which is the horizontal separation between the point of refraction and the point of detection on the surface), can be adversely affected by very near‐surface inhomogeneities. Even inhomogeneities at single receivers can limit the lateral resolution of detailed seismic velocities in the refractor.
The generalized reciprocal method ‘statics’ smoothing method (GRM SSM) is a smoothing rather than a deterministic method for correcting very near‐surface inhomogeneities of limited lateral extent. It is based on the observation that there are only relatively minor differences in the time‐depths to the target refractor computed for a range of XY distances, which is the separation between the reverse and forward traveltimes used to compute the time‐depth. However, any traveltime anomalies, which originate in the near‐surface, migrate laterally with increasing XY distance. Therefore, an average of the time‐depths over a range of XY values preserves the architecture of the refractor, but significantly minimizes the traveltime anomalies originating in the near‐surface. The GRM statics smoothing corrections are obtained by subtracting the average time‐depth values from those computed with a zero XY value. In turn, the corrections are subtracted from the traveltimes, and the GRM algorithms are then re‐applied to the corrected data. Although a single application is generally adequate for most sets of field data, model studies have indicated that several applications of the GRM SSM can be required with severe topographic features, such as escarpments.
In addition, very near‐surface inhomogeneities produce anomalous head‐wave amplitudes. An analogous process, using geometric means, can largely correct amplitude anomalies. Furthermore, the coincidence of traveltime and amplitude anomalies indicates that variations in the near‐surface geology, rather than variations in the coupling of the receivers, are a more likely source of the anomalies.
The application of the GRM SSM, together with the averaging of the refractor velocity analysis function over a range of XY values, significantly minimizes the generation of artefacts, and facilitates the computation of detailed seismic velocities in the refractor at each receiver. These detailed seismic velocities, together with the GRM SSM‐corrected amplitude products, can facilitate the computation of the ratio of the density in the bedrock to that in the weathered layer. The accuracy of the computed density ratio improves where lateral variations in the seismic velocities in the weathered layer are known.
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Integrated geological and geophysical exploration for concealed ores beneath cover in the Chaihulanzi goldfield, northern China
Authors Hongtao Liu, Jianming Liu, Changming Yu, Jie Ye and Qingdong ZengABSTRACTAn integrated geological and geophysical investigation was carried out in the near‐mine areas of the Chaihulanzi gold‐field, Inner Mongolia, northern China, to determine the south‐eastern strike extension of the principal mineralized shear system, in the search for new resources. In this case study, surface geophysical surveys played an important role in defining the mineralized structures beneath cover. A re‐investigation of the mine geology by observing the underground exposures of mineralization and its hosting structures, coupled with re‐evaluation and re‐examination of previous exploration data, revealed that the mineralization style at the Chaihulanzi gold‐field is not the skarn‐type as previously assumed, but is structurally controlled by an oblique‐sinistral shear structure. Moreover, a south‐eastward shallow‐plunging mineralized corridor within the principal mineralized shear system was also identified, implying that the ore‐forming fluid‐flow might move through the mineralizing system, from the south‐east at depth to the north‐west. These new geological findings imply that the mineralized shear system should extend much farther south‐eastwards along strike beneath cover, and thus a conceptual target area was proposed. A detailed geophysical survey program, involving the application of VLF‐EM, Stratagem EH4, CSAMT and gradient IP measurements, was carried out to test the validity of the conceptual target. Orientation surveys on the geologically known Line‐18 traverse revealed that VLF‐EM and Stratagem EH4 were the most effective methods of detecting the unseen mineralized system, whereas CSAMT could only provide low‐resolution data, and IP proved to be unsuitable in this environment due to the ubiquitous presence of graphite‐bearing schists in and around the mineralized system. A follow‐up systematic VLF‐EM survey highlighted the principal mineralized shear system as a linear conductive belt, tracing the principal mineralized system for a further 750 m of strike length beneath cover from the previous exploration limit (Line 18). Stratagem EH4 soundings over six parallel traverses perpendicular to the mineralized trend revealed that the principal mineralized shear structure extends for more than 500 m in the dip direction, a strong indication of the presence of potential deep mineralization under the surveyed area. Detailed modelling of the Stratagem EH4 sounding images provided well‐defined targets for test drilling. Subsequent test drilling on some of these targets returned encouraging results as several core‐intercepts of economic gold mineralization were encountered. This led to a more extensive drilling and underground prospecting program, focusing on deep mineralization south‐eastwards along the mineralized trend.
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A time‐domain induced‐polarization method for estimating permeability in a shaly sand reservoir
Authors Maosong Tong, Li Li, Weinan Wang and Yizhong JiangABSTRACTIt is known that the time‐domain induced‐polarization decay curve for a shaly sand reservoir depends on the pore structure of the reservoir, and this curve can be used to estimate permeability, which is a determining factor in making production decisions in the petroleum industry. Compared with NMR logging tools, induced polarization has several advantages, such as a deep depth of investigation and a high signal‐to‐noise ratio. The purpose of this paper is to establish an appropriate model using induced polarization to estimate the permeability. The curve can be modelled as a weighted superposition of exponential relaxations. The plot of weight versus the relaxation time constant is defined as the relaxation time spectrum.
Induced‐polarization decay‐curve measurements were performed on 123 samples from the Daqing oilfield using a four‐electrode technique. A singular‐value decomposition method was used to transform the induced‐polarization decay data into a spectrum. Different models to estimate the permeability were discussed. The results of the research indicate that the induced‐polarization measurements greatly improve the statistical significance of permeability correlations. Compared with the traditional forms, AφC and AFC, the forms, ATBφC and ATBFC, have lower error factors, where T, Φ and F are the geometric mean time constant of the induced‐polarization relaxation time spectrum, the porosity and the resistivity formation factor, respectively, and A, B and C are constants. The mean time constant is the decisive parameter in the permeability estimation and it is not completely independent of the resistivity formation factor. The additional use of the porosity and the resistivity formation factor leads to an appreciable improvement. It is concluded that this new model will make it possible to estimate the permeability of a shaly sand reservoir downhole.
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A multigrid solver for 3D electromagnetic diffusion
By W.A. MulderABSTRACTThe performance of a multigrid solver for the time‐harmonic electromagnetic problem in geophysical settings is investigated. The frequencies are sufficiently small for waves travelling at the speed of light to be negligible, so that a diffusive problem remains. The discretization of the governing equations is obtained by the finite‐integration technique, which can be viewed as a finite‐volume generalization of Yee's staggered grid scheme. The resulting set of discrete equations is solved by a multigrid method.
The convergence rate of the multigrid method decreased when the grid was stretched. The slower convergence rate of the multigrid method can be compensated by using bicgstab2, a conjugate‐gradient‐type method for non‐symmetric problems. In that case, the multigrid solver acts as a preconditioner. However, whereas the multigrid method provides excellent convergence with constant grid spacings, it performs less than satisfactorily when substantial grid stretching is used.
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Analytical solution for the electric potential in arbitrary anisotropic layered media applying the set of Hankel transforms of integer order
Authors E. Pervago, A. Mousatov and V. ShevninABSTRACTThe analytical solution and algorithm for simulating the electric potential in an arbitrarily anisotropic multilayered medium produced by a point DC source is here proposed. The solution is presented as a combination of Hankel transforms of integer order and Fourier transforms based on the analytical recurrent equations obtained for the potential spectrum. For the conversion of the potential spectrum into the space domain, we have applied the algorithm of the Fast Fourier Transform for logarithmically spaced points. A comparison of the modelling results with the power‐series solution for two‐layered anisotropic structures demonstrated the high accuracy and computing‐time efficiency of the method proposed.
The results of the apparent‐resistivity calculation for both traditional pole‐pole and tensor arrays above three‐layered sequence with an azimuthally anisotropic second layer are presented. The numerical simulations show that both arrays have the same sensitivity to the anisotropy parameters. This sensitivity depends significantly on the resistivity ratio between anisotropic and adjacent layers and increases for the models with a conductive second layer.
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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)