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- Volume 67, Issue 8, 2019
Geophysical Prospecting - Volume 67, Issue 8, 2019
Volume 67, Issue 8, 2019
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The kinematics of S waves in acoustic orthorhombic media
Authors Shibo Xu and Alexey StovasABSTRACTOrthorhombic models are often used in the seismic industry nowadays to describe azimuthal and polar anisotropy and reasonably realistic in capturing the features of the earth interior. It is challenging to handle so many model parameters in the seismic data processing. In order to reduce the number of the parameters for P wave, the acoustic orthorhombic medium is proposed by setting all on‐axis S wave velocities to zero. However, due to the coupled behaviour for P and S waves in the orthorhombic model, the ‘S wave artefacts’ are still remained in the acoustic orthorhombic model, which kinematics needs to be defined and analysed. In this paper, we analyse the behaviour of S wave in acoustic orthorhombic media. By analysis of the slowness surface in acoustic orthorhombic media, we define the S waves (or S wave artefacts) that are more complicated in shape comparing to the one propagating in an acoustic transversely isotropic medium with a vertical symmetry axis. The kinematic properties of these waves are defined and analysed in both phase and group domain. The caustics, amplitude and the multi‐layered case for S wave in acoustic orthorhombic model are also discussed. It is shown that there are two waves propagating in this acoustic orthorhombic medium. One of these waves is similar to the one propagating in acoustic vertical symmetry axis media, whereas another one has a very complicated shape consisting of two crossing surfaces.
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Some remarks on Q‐compensated sparse deconvolution without knowing the quality factor Q
Authors Xintao Chai, Ronghua Peng, Genyang Tang, Wei Chen and Jingnan LiABSTRACTThe subsurface media are not perfectly elastic, thus anelastic absorption, attenuation and dispersion (aka Q filtering) effects occur during wave propagation, diminishing seismic resolution. Compensating for anelastic effects is imperative for resolution enhancement. Q values are required for most of conventional Q‐compensation methods, and the source wavelet is additionally required for some of them. Based on the previous work of non‐stationary sparse reflectivity inversion, we evaluate a series of methods for Q‐compensation with/without knowing Q and with/without knowing wavelet. We demonstrate that if Q‐compensation takes the wavelet into account, it generates better results for the severely attenuated components, benefiting from the sparsity promotion. We then evaluate a two‐phase Q‐compensation method in the frequency domain to eliminate Q requirement. In phase 1, the observed seismogram is disintegrated into the least number of Q‐filtered wavelets chosen from a dictionary by optimizing a basis pursuit denoising problem, where the dictionary is composed of the known wavelet with different propagation times, each filtered with a range of possible values. The elements of the dictionary are weighted by the infinity norm of the corresponding column and further preconditioned to provide wavelets of different values and different propagation times equal probability to entry into the solution space. In phase 2, we derive analytic solutions for estimates of reflectivity and Q and solve an over‐determined equation to obtain the final reflectivity series and Q values, where both the amplitude and phase information are utilized to estimate the Q values. The evaluated inversion‐based Q estimation method handles the wave‐interference effects better than conventional spectral‐ratio‐based methods. For Q‐compensation, we investigate why sparsity promoting does matter. Numerical and field data experiments indicate the feasibility of the evaluated method of Q‐compensation without knowing Q but with wavelet given.
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Common‐offset common‐reflection‐surface attributes estimation with differential evolution
Authors Tiago Barros, Renato Lopes, Rafael Krummenauer and Hervé ChaurisABSTRACTCommon‐reflection surface is a method to describe the shape of seismic events, typically the slopes (dip) and curvature portions (traveltime). The most systematic approach to estimate the common‐reflection surface traveltime attributes is to employ a sequence of single‐variable search procedures, inheriting the advantage of a low computational cost, but also the disadvantage of a poor estimation quality. A search strategy where the common‐reflection surface attributes are globally estimated in a single stage may yield more accurate estimates. In this paper, we propose to use the bio‐inspired global optimization algorithm differential evolution to estimate all the two‐dimensional common‐offset common‐reflection surface attributes simultaneously. The differential evolution algorithm can provide accurate estimates for the common‐reflection surface traveltime attributes, with the benefit of having a small set of input parameters to be configured. We apply the differential evolution algorithm to estimate the two‐dimensional common‐reflection surface attributes in the synthetic Marmousi data set, contaminated by noise, and in a land field data with a small fold. By analysing the stacked and coherence sections, we could see that the differential evolution based common‐offset common‐reflection surface approach presented significant signal‐to‐noise ratio enhancement.
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Angle‐domain common‐image gathers in reverse‐time migration by combining the Poynting vector with local‐wavefield decomposition
Authors Wu Chengliang, Wang Huazhong, Zhou Yang and Hu JiangtaoABSTRACTAngle‐domain common‐image gathers are an important tool in the post‐processing of seismic images and for reservoir characterization. The generation of angle gathers is a very important issue when dealing with angle‐domain images. Efficiency and robustness are the main concerns in the generation of angle gathers. In this paper, we propose two methods for producing angle gathers based on the implementation of a reverse‐time migration. In the hybrid method, we adopt the local‐plane‐wave decomposition method to extract the local plane waves and obtain two possible opposite propagation directions in the time‐wavenumber domain. Then, Poynting vectors are used to determine the correct propagation direction. The hybrid method achieves a satisfactory balance between robustness and computational efficiency. Furthermore, in the improved hybrid method, additional computational acceleration is obtained by separating the overlapping and non‐overlapping wavefield areas. The hybrid method is only applied in these areas with overlapping wave fronts, and the Poynting‐vector‐based method is adopted in the other areas. The location of the overlapping events is determined using the eigenvalues of the structural tensor. Finally, the two‐dimensional synthetic and field examples demonstrate the effectiveness of both methods.
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Frequency‐domain double‐plane‐wave least‐squares reverse time migration
Authors Zeyu Zhao and Mrinal K. SenABSTRACTLeast‐squares reverse time migration is often formulated as an iterative updating process, where estimating the gradient of the misfit function is necessary. Traditional time domain shot‐profile least‐squares reverse time migration is computationally expensive because computing the gradient involves solving the two‐way wave equation several times in every iteration. To reduce the computational cost of least‐squares reverse time migration, we propose a double‐plane‐wave least‐squares reverse time migration method based on a misfit function for frequency‐domain double‐plane‐wave data. In double‐plane‐wave least‐squares reverse time migration, the gradient is computed by multiplying frequency‐domain plane‐wave Green's functions with the corresponding double‐plane‐wave data residual. Because the number of plane‐wave Green's functions used for migration is relatively small, they can be pre‐computed and stored in a computer's discs or memory. We can use the pre‐computed plane‐wave Green's functions to obtain the gradient without solving the two‐way wave equation in each iteration. Therefore, the migration efficiency is significantly improved. In addition, we study the effects of using sparse frequency sampling and sparse plane‐wave sampling on the proposed method. We can achieve images with correct reflector amplitudes and reasonable resolution using relatively sparse frequency sampling and plane‐wave sampling, which are larger than that determined by the Nyquist theorem. The well‐known wrap‐around artefacts and linear artefacts generated due to under‐sampling frequency and plane wave can be suppressed during iterations in cases where the sampling rates are not excessively large. Moreover, implementing the proposed method with sparse frequency sampling and sparse plane‐wave sampling further improves the computational efficiency. We test the proposed double‐plane‐wave least‐squares reverse time migration on synthetic models to show the practicality of the method.
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Source wavelet correction for practical Marchenko imaging: A sub‐salt field‐data example from the Gulf of Mexico
ABSTRACTImaging a target zone below a salt body can be challenging because large velocity contrasts in the overburden between the salt and surrounding sediments generate internal multiples, which interfere with primary reflections from the target level in the imaging process. This can lead to an erroneous interpretation of reflections in the sub‐salt area if multiples are misinterpreted as primaries. The Marchenko redatuming method may enable imaging of the sub‐salt target area where the effect of the multiply‐scattering overburden is removed. This is achieved by creating a redatumed reflection response where virtual sources and receivers are located below the overburden using a macromodel of the velocity field and the surface reflection data. The accuracy of the redatumed data and the associated internal multiple removal, however, depends on the accurate knowledge of the source wavelet of the acquired reflection data. For the first time, we propose a method which can accurately and reliably correct the amplitudes of the reflection response in field data as required by the Marchenko method. Our method operates by iteratively and automatically updating the source function so as to cancel the most artefact energy in the focusing functions, which are also generated by the Marchenko method.
We demonstrate the method on a synthetic dataset and successfully apply it to a field dataset acquired in a deep‐water salt environment in the Gulf of Mexico. After the successful source wavelet estimation for the field dataset, we create sub‐salt target‐oriented images with Marchenko redatumed data. Marchenko images using the proposed source wavelet estimation show clear improvements, such as increased continuity of reflectors, compared to surface‐based images and to conventional Marchenko images computed without the inverted source wavelet. Our improvements are corroborated by evidence in the literature and our own synthetic results.
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Free‐surface implementation in a mesh‐free finite‐difference method for elastic wave propagation in the frequency domain
Authors Junichi Takekawa and Hitoshi MikadaABSTRACTWe present an original implementation of the free‐surface boundary condition in a mesh‐free finite‐difference method for simulating elastic wave propagation in the frequency domain. For elastic wave modelling in the frequency domain, the treatment of free surfaces is a key issue which requires special consideration. In the present study, the free‐surface boundary condition is directly implemented at node positions located on the free‐surface. Flexible nature of the mesh‐free method for nodal distribution enables us to introduce topography into numerical models in an efficient manner. We investigate the accuracy of the proposed implementation by comparing numerical results with an analytical solution. The results show that the proposed method can calculate surface wave propagation even for an inclined free surface with substantial accuracy. Next, we calculate surface wave propagation in a model with a topographic surface using our method, and compare the numerical result with that using the finite‐element method. The comparison shows the excellent agreement with each other. Finally, we apply our method to the SEG foothill model to investigate the effectiveness of the proposed method. Since the mesh‐free method has high flexibility of nodal distribution, the proposed implementation would deal with models of topographic surface with sufficient accuracy and efficiency.
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Estimation of groundwater storage from seismic data using deep learning
ABSTRACTConvolutional neural networks can provide a potential framework to characterize groundwater storage from seismic data. Estimation of key components, such as the amount of groundwater stored in an aquifer and delineate water table level, from active‐source seismic data are performed in this study. The data to train, validate and test the neural networks are obtained by solving wave propagation in a coupled poroviscoelastic–elastic media. A discontinuous Galerkin method is applied to model wave propagation, whereas a deep convolutional neural network is used for the parameter estimation problem. In the numerical experiment, the primary unknowns estimated are the amount of stored groundwater and water table level, while the remaining parameters, assumed to be of less of interest, are marginalized in the convolutional neural network‐based solution. Results, obtained through synthetic data, illustrate the potential of deep learning methods to extract additional aquifer information from seismic data, which otherwise would be impossible based on a set of reflection seismic sections or velocity tomograms.
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Acquisition design for direct reflectivity and velocity estimation from blended and irregularly sampled data
Authors Shotaro Nakayama, Gerrit Blacquière and Tomohide IshiyamaABSTRACTBlended acquisition along with efficient spatial sampling is capable of providing high‐quality seismic data in a cost‐effective and productive manner. While deblending and data reconstruction conventionally accompany this way of data acquisition, the recorded data can be processed directly to estimate subsurface properties. We establish a workflow to design survey parameters that account for the source blending as well as the spatial sampling of sources and detectors. The proposed method involves an iterative scheme to derive the survey design leading to optimum reflectivity and velocity estimation via joint migration inversion. In the workflow, we extend the standard implementation of joint migration inversion to cope with the data acquired in a blended fashion along with irregular detector and source geometries. This makes a direct estimation of reflectivity and velocity models feasible without the need of deblending or data reconstruction. During the iterations, the errors in reflectivity and velocity estimates are used to update the survey parameters by integrating a genetic algorithm and a convolutional neural network. Bio‐inspired operators enable the simultaneous update of the blending and sampling operators. To relate the choice of survey parameters to the performance of joint migration inversion, we utilize a convolutional neural network. The applied network architecture discards suboptimal solutions among newly generated ones. Conversely, it carries optimal ones to the subsequent step, which improves the efficiency of the proposed approach. The resultant acquisition scenario yields a notable enhancement in both reflectivity and velocity estimation attributable to the choice of survey parameters.
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Propagation of seismic waves in patchy‐saturated porous media: double‐porosity representation
By M.D. SharmaABSTRACTPropagation of harmonic plane waves is studied in a patchy‐saturated porous medium. Patchy distribution of the two immiscible fluids is considered in a porous frame with uniform skeletal properties. A composition of two types of patches, connected through continuous paths, constitutes a double‐porosity medium. Different compressibilities of pore‐fluids in two porous phases facilitate the wave‐induced fluid‐flow in this composite material. Constitutive relations are considered with frequency‐dependent complex elastic coefficients, which define the dissipative behaviour of porous aggregate due to the flow of viscous fluid in connected patches. Relevant equations of motion are solved to explain the propagation of three compressional waves and one shear wave in patchy‐saturated porous solids. A numerical example is solved to illustrate dispersion in phase velocity and quality factor of attenuated waves in patchy‐saturated porous materials. Role of fluid–solid inertial coupling in Darcy's law is emphasized to keep a check on the dispersion of wave velocities in the porous composite. Effects of patchy saturation on phase velocities and quality factors of attenuation are analysed using the double‐porosity formulation as well as the reduced single‐porosity equivalents.
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Non‐invasive lab test in the monitoring of vadose zone contaminated by light non‐aqueous phase liquid
Authors Beatrice Alesse, Luciana Orlando and Lucia PalladiniABSTRACTWe discuss a strategy capable of a quantitative long‐term monitoring of water saturation and volume variation of light non‐aqueous phase liquids in the soil. The goal was reached monitoring a controlled sand cell contaminated with classical gasoline over 124 days, using geophysical methods such as electrical resistivity tomography, induced polarization and ground penetrating radar. We show that empirical relations, linking the water saturation to the physical parameters measured as resistivity from electrical resistivity tomography and travel time from georadar with advanced processing, are good tools for this purpose. The consistence of the proposed process is validated by both good overlap of results carried out from electrical resistivity tomography and georadar and theoretical models simulating the actual experiment.
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Hydrogeophysical modelling of Hisarcik (Kütahya) geothermal field, western Turkey
Authors Serkan Üner, Gülçin Özürlan Ağaçgözgü and Doğa Düşünür DoğanABSTRACTWestern Anatolia hosts many low‐to‐moderate and high‐temperature geothermal sources in which active faults play a dominant role to control the recharge and the discharge of geothermal fluid. In this study, we used the two‐dimensional geoelectric structure of Kütahya Hisarcık geothermal field, and created a conceptual hydrogeophysical model that includes faults, real topographical variations and geological units. The temperature distribution and fluid flow pattern are also investigated. The depth extension of Hisarcık Fault, electrical basement and low resistivity anomalies related to the presence of geothermal fluid are determined by using resistivity studies in the area. Numerical simulations suggest that Hisarcık fault functioning as a fluid conduit primarily enables hot fluid to be transported from depth to the surface. It is shown that the locations of predicted outflow vents coincide with those of hot springs in the area.
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Numerically quantifying energy loss caused by squirt flow
Authors Beatriz Quintal, Eva Caspari, Klaus Holliger and Holger SteebABSTRACTIn interconnected microcracks, or in microcracks connected to spherical pores, the deformation associated with the passage of mechanical waves can induce fluid flow parallel to the crack walls, which is known as squirt flow. This phenomenon can also occur at larger scales in hydraulically interconnected mesoscopic cracks or fractures. The associated viscous friction causes the waves to experience attenuation and velocity dispersion. We present a simple hydromechanical numerical scheme, based on the interface‐coupled Lamé–Navier and Navier–Stokes equations, to simulate squirt flow in the frequency domain. The linearized, quasi‐static Navier–Stokes equations describe the laminar flow of a compressible viscous fluid in conduits embedded in a linear elastic solid background described by the quasi‐static Lamé–Navier equations. Assuming that the heterogeneous model behaves effectively like a homogeneous viscoelastic medium at a larger spatial scale, the resulting attenuation and stiffness modulus dispersion are computed from spatial averages of the complex‐valued, frequency‐dependent stress and strain fields. An energy‐based approach is implemented to calculate the local contributions to attenuation that, when integrated over the entire model, yield results that are identical to those based on the viscoelastic assumption. In addition to thus validating this assumption, the energy‐based approach allows for analyses of the spatial dissipation patterns in squirt flow models. We perform simulations for a series of numerical models to illustrate the viability and versatility of the proposed method. For a 3D model consisting of a spherical crack embedded in a solid background, the characteristic frequency of the resulting P‐wave attenuation agrees with that of a corresponding analytical solution, indicating that the dissipative viscous flow problem is appropriately handled in our numerical solution of the linearized, quasi‐static Navier–Stokes equations. For 2D models containing either interconnected cracks or cracks connected to a circular pore, the results are compared with those based on Biot's poroelastic equations of consolidation, which are solved through an equivalent approach. Overall, our numerical simulations and the associated analyses demonstrate the suitability of the coupled Lamé–Navier and Navier–Stokes equations and of Biot's equations for quantifying attenuation and dispersion for a range of squirt flow scenarios. These analyses also allow for delineating numerical and physical limitations associated with each set of equations.
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Forward plane‐wave electromagnetic model in three dimensions using hybrid finite volume–integral equation scheme
Authors Musa A. Bello, Rongwen Guo and Jianxin LiuABSTRACTWe present a concept of the hybrid finite volume–integral equation technique for solving Maxwell's equation in a quasi‐static form. The divergence correction was incorporated to improve the convergence and stability of the governing linear system equations which pose a challenge on the discretization of the curl–curl Helmholtz equation. A staggered finite volume approach is applied for discretizing the system of equations on a structured mesh and solved in a secondary field technique. The bi‐conjugate gradient stabilizer was utilized with block incomplete lower‐upper factorization preconditioner to solve the system of equation. To obtain the electric and magnetic fields at the receivers, we use the integral Green tensor scheme. We verify the strength of our hybrid technique with benchmark models relative to other numerical algorithms. Importantly, from the tested models, our scheme was in close agreement with the semi‐analytical solution. It also revealed that the use of a quasi‐analytical boundary condition helps to minimize the runtime for the linear system equation. Furthermore, the integral Green tensor approach to compute at the receivers demonstrates better accuracy compared with the conventional interpolation method. This adopted technique can be applied efficiently to the inversion procedure.
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Elongated horizontal and vertical receivers in three‐dimensional electromagnetic modelling and inversion
Authors Cedric Patzer, Kristina Tietze and Oliver RitterABSTRACTElectromagnetic geophysical methods often rely on measurements of naturally occurring or artificially impressed electric fields. It is technically impossible, however, to measure the electric field directly. Instead, the electric field is approximated by recording the voltage difference between two electrodes and dividing the obtained voltage by the distance between the electrodes. Typically, modelling and inversion algorithms assume that the electric fields are obtained over infinitely short point‐dipoles and thus measured fields are assigned to a single point between the electrodes. Such procedures imply several assumptions: (1) The electric field between the two electrodes is regarded as constant or being a potential field and (2) the receiver dimensions are negligible compared to the dimensions of the underlying modelling grid. While these conditions are often fulfilled for horizontal electric fields, borehole sensors for recordings of the vertical electric field have dimensions in the order of ≈100 m and span several modelling grid cells. Observations from such elongated borehole sensors can therefore only be interpreted properly if true receiver dimensions and variations of electrical conductivity along the receiver are considered. Here, we introduce a numerical solution to include the true receiver geometry into electromagnetic modelling schemes, which does not rely on such simplifying assumptions. The algorithm is flexible, independent of the chosen numerical method to solve Maxwell's equations and can easily be implemented in other electromagnetic modelling and inversion codes. We present conceptual modelling results for land‐based controlled source electromagnetic scenarios and discuss consideration of true receiver geometries for a series of examples of horizontal and vertical electric field measurements. Comparison with Ez data measured in an observation borehole in a producing oil field shows the importance of both considering the true length of the receiver and also its orientation. We show that misalignment from the vertical axis as small as 0.1° may seriously distort the measured signal, as horizontal electric field components are mapped into the desired vertical component. Adequate inclusion of elongated receivers in modelling and inversion can also help reducing effects of static shift when interpreting (natural source) magnetotelluric data.
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How natural remanent magnetization of basaltic units can dominate the reduced to pole magnetic value: A case study from the Faroe Islands
Authors Heri Ziska, Paul Williamson and Óluva Reginsdóttir EidesgaardABSTRACTEarly attempts to utilize magnetic data to understand the volcanic and subvolcanic succession on the Faroese Continental Shelf have shown that conventional interpretation and modelling of magnetic data from this area leads to ambiguous results. Interpretation of the aeromagnetic data on the Faroese Continental Shelf shows that some previously identified basement highs coincide with reduced‐to‐pole magnetic highs, whereas others coincide with negative or mixed magnetic features. Similarly, igneous centres are characterized by different polarity magnetic anomalies. Palaeomagnetic analysis of the onshore volcanic succession has demonstrated that the thermoremanent magnetization of the basaltic lavas is stronger than the induced magnetism, and both reversely and normally magnetized units are present. We have tested this with 2½D profile modelling using the palaeomagnetic information to correlate high‐amplitude magnetic anomalies with basalt successions containing changes in magnetic polarity. This approach has enabled us to map the termination of the differently magnetized units offshore and thereby extend the mapping of the Faroe Island Basalt Group on the Faroese Platform and into adjacent areas.
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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 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 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 37 (1989)
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Volume 35 (1987)
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Volume 34 (1986)
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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)