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- Volume 63, Issue 5, 2015
Geophysical Prospecting - Volume 63, Issue 5, 2015
Volume 63, Issue 5, 2015
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Point‐spread functions for interferometric imaging
Authors Joost van der Neut and Kees WapenaarABSTRACTInterferometric redatuming is a data‐driven method to transform seismic responses with sources at one level and receivers at a deeper level into virtual reflection data with both sources and receivers at the deeper level. Although this method has traditionally been applied by cross‐correlation, accurate redatuming through a heterogeneous overburden requires solving a multidimensional deconvolution problem. Input data can be obtained either by direct observation (for instance in a horizontal borehole), by modelling or by a novel iterative scheme that is currently being developed. The output of interferometric redatuming can be used for imaging below the redatuming level, resulting in a so‐called interferometric image. Internal multiples from above the redatuming level are eliminated during this process. In the past, we introduced point‐spread functions for interferometric redatuming by cross‐correlation. These point‐spread functions quantify distortions in the redatumed data, caused by internal multiple reflections in the overburden. In this paper, we define point‐spread functions for interferometric imaging to quantify these distortions in the image domain. These point‐spread functions are similar to conventional resolution functions for seismic migration but they contain additional information on the internal multiples in the overburden and they are partly data‐driven. We show how these point‐spread functions can be visualized to diagnose image defocusing and artefacts. Finally, we illustrate how point‐spread functions can also be defined for interferometric imaging with passive noise sources in the subsurface or with simultaneous‐source acquisition at the surface.
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Image‐warping waveform tomography
Authors Francesco Perrone and Paul SavaABSTRACTImaging the change in physical parameters in the subsurface requires an estimate of the long wavelength components of the same parameters in order to reconstruct the kinematics of the waves propagating in the subsurface. One can reconstruct the model by matching the recorded data with modeled waveforms extrapolated in a trial model of the medium. Alternatively, assuming a trial model, one can obtain a set of images of the reflectors from a number of seismic experiments and match the locations of the imaged interfaces. Apparent displacements between migrated images contain information about the velocity model and can be used for velocity analysis. A number of methods are available to characterize the displacement between images; in this paper, we compare shot‐domain differential semblance (image difference), penalized local correlations, and image‐warping. We show that the image‐warping vector field is a more reliable tool for estimating displacements between migrated images and leads to a more robust velocity analysis procedure. By using image‐warping, we can redefine the differential semblance optimization problem with an objective function that is more robust against cycle‐skipping than the direct image difference. We propose an approach that has straightforward implementation and reduced computational cost compared with the conventional adjoint‐state method calculations. We also discuss the weakness of migration velocity analysis in the migrated‐shot domain in the case of highly refractive media, when the Born modelling operator is far from being unitary and thus its adjoint (migration) operator poorly approximates the inverse.
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Monitoring viscosity changes from time‐lapse seismic attenuation: case study from a heavy oil reservoir
Authors Andrey H. Shabelansky, Alison Malcolm and Michael FehlerABSTRACTHeating heavy oil reservoirs is a common method for reducing the high viscosity of heavy oil and thus increasing the recovery factor. Monitoring of these viscosity changes in the reservoir is essential for delineating the heated region and controlling production. In this study, we present an approach for estimating viscosity changes in a heavy oil reservoir. The approach consists of three steps: measuring seismic wave attenuation between reflections from above and below the reservoir, constructing time‐lapse Q and Q−1 factor maps, and interpreting these maps using Kelvin–Voigt and Maxwell viscoelastic models. We use a 4D relative spectrum method to measure changes in attenuation. The method is tested with synthetic seismic data that are noise free and data with additive Gaussian noise to show the robustness and the accuracy of the estimates of the Q‐factor. The results of the application of the method to a field data set exhibit alignment of high attenuation zones along the steam‐injection wells, and indicate that temperature dependent viscosity changes in the heavy oil reservoir can be explained by the Kelvin–Voigt model.
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Image‐domain wavefield tomography with extended common‐image‐point gathers
Authors Tongning Yang and Paul SavaABSTRACTWaveform inversion is a velocity‐model‐building technique based on full waveforms as the input and seismic wavefields as the information carrier. Conventional waveform inversion is implemented in the data domain. However, similar techniques referred to as image‐domain wavefield tomography can be formulated in the image domain and use a seismic image as the input and seismic wavefields as the information carrier. The objective function for the image‐domain approach is designed to optimize the coherency of reflections in extended common‐image gathers. The function applies a penalty operator to the gathers, thus highlighting image inaccuracies arising from the velocity model error. Minimizing the objective function optimizes the model and improves the image quality. The gradient of the objective function is computed using the adjoint state method in a way similar to that in the analogous data‐domain implementation. We propose an image‐domain velocity‐model building method using extended common‐image‐point space‐ and time‐lag gathers constructed sparsely at reflections in the image. The gathers are effective in reconstructing the velocity model in complex geologic environments and can be used as an economical replacement for conventional common‐image gathers in wave‐equation tomography. A test on the Marmousi model illustrates successful updating of the velocity model using common‐image‐point gathers and resulting improved image quality.
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Theory of equivalent staggered‐grid schemes: application to rotated and standard grids in anisotropic media
Authors Leandro Di Bartolo, Cleberson Dors and Webe J. MansurABSTRACTThe previous finite‐difference numerical schemes designed for direct application to second‐order elastic wave equations in terms of displacement components are strongly dependent on Poisson's ratio. This fact makes theses schemes useless for modelling in offshore regions or even in onshore regions where there is a high Poisson's ratio material. As is well known, the use of staggered‐grid formulations solves this drawback. The most common staggered‐grid algorithms apply central‐difference operators to the first‐order velocity–stress wave equations. They have been one of the most successfully applied numerical algorithms for seismic modelling, although these schemes require more computational memory than those mentioned based on second‐order wave equations. The goal of the present paper is to develop a general theory that enables one to formulate equivalent staggered‐grid schemes for direct application to hyperbolic second‐order wave equations. All the theory necessary to formulate these schemes is presented in detail, including issues regarding source application, providing a general method to construct staggered‐grid formulations to a wide range of cases. Afterwards, the equivalent staggered‐grid theory is applied to anisotropic elastic wave equations in terms of only velocity components (or similar displacements) for two important cases: general anisotropic media and vertical transverse isotropy media using, respectively, the rotated and the standard staggered‐grid configurations. For sake of simplicity, we present the schemes in terms of velocities in the second‐ and fourth‐order spatial approximations, with second‐order approximation in time for 2D media. However, the theory developed is general and can be applied to any set of second‐order equations (in terms of only displacement, velocity, or even stress components), using any staggered‐grid configuration with any spatial approximation order in 2D or 3D cases. Some of these equivalent staggered‐grid schemes require less computer memory than the corresponding standard staggered‐grid formulation, although the programming is more evolved. As will be shown in theory and practice, with numerical examples, the equivalent staggered‐grid schemes produce results equivalent to corresponding standard staggered‐grid schemes with computational advantages. Finally, it is important to emphasize that the equivalent staggered‐grid theory is general and can be applied to other modelling contexts, e.g., in electrodynamical and poroelastic wave propagation problems in a systematic and simple way.
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An efficient wave extrapolation method for anisotropic media with tilt
Authors Umair bin Waheed and Tariq AlkhalifahABSTRACTWavefield extrapolation operators for elliptically anisotropic media offer significant cost reduction compared with that for the transversely isotropic case, particularly when the axis of symmetry exhibits tilt (from the vertical). However, elliptical anisotropy does not provide accurate wavefield representation or imaging for transversely isotropic media. Therefore, we propose effective elliptically anisotropic models that correctly capture the kinematic behaviour of wavefields for transversely isotropic media. Specifically, we compute source‐dependent effective velocities for the elliptic medium using kinematic high‐frequency representation of the transversely isotropic wavefield. The effective model allows us to use cheaper elliptic wave extrapolation operators. Despite the fact that the effective models are obtained by matching kinematics using high‐frequency asymptotic, the resulting wavefield contains most of the critical wavefield components, including frequency dependency and caustics, if present, with reasonable accuracy. The methodology developed here offers a much better cost versus accuracy trade‐off for wavefield computations in transversely isotropic media, particularly for media of low to moderate complexity. In addition, the wavefield solution is free from shear‐wave artefacts as opposed to the conventional finite‐difference‐based transversely isotropic wave extrapolation scheme. We demonstrate these assertions through numerical tests on synthetic tilted transversely isotropic models.
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Multi‐block finite‐difference method for 3D elastodynamic simulations in anisotropic subhorizontally layered media
Authors Ivan Sofronov, Nikolai Zaitsev and Leonid DovgilovichABSTRACTPrediction of elastic full wavefields is required for reverse time migration, full waveform inversion, borehole seismology, seismic modelling, etc. We propose a novel algorithm to solve the Navier wave equation, which is based on multi‐block methodology for high‐order finite‐difference schemes on curvilinear grids. In the current implementation, the blocks are subhorizontal layers. Smooth anisotropic heterogeneous media in each layer can have strong discontinuities at the interfaces. A curvilinear adaptive hexahedral grid in blocks is generated by mapping the original 3D physical domain onto a parametric cube with horizontal layers and interfaces. These interfaces correspond to the main curvilinear physical contrast interfaces of a subhorizontally layered formation. The top boundary of the parametric cube handles the land surface with smooth topography. Free‐surface and solid–solid transmission boundary conditions at interfaces are approximated with the second‐order accuracy. Smooth media in the layers are approximated up to sixth‐order spatial schemes. All expected properties of the developed algorithm are demonstrated in numerical tests using corresponding parallel message passing interface code.
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Statistical analysis of background noise in seismic prospecting
Authors Tie Zhong, Yue Li, Ning Wu, Pengfei Nie and Baojun YangABSTRACTFrom a conventional viewpoint, seismic‐prospecting background noise is usually regarded as the product of a stationary and Gaussian stochastic process. In this paper, we use statistical methods to investigate the properties of the land‐seismic‐prospecting background noise on stationarity, Gaussianity, power spectral density, and spatial correlation. We use and analyse the passive noise records collected by receiver arrays at different typical geological environments (desert, steppe, and mountainous regions). Differences exist in the statistical properties of the background noise from different geological environments, but we still find some common characteristics. It is shown that the background noise is not strictly stationary and has different stationary properties over different timescales. Most of the noise records appear to be a Gaussian process when examined over a period of about 20 s but are found to be non‐Gaussian when examined over shorter periods of about 1 s. The background noise is a kind of colored noise, and its energy mainly concentrates in the low‐frequency bands. We also find that the spatial correlation of the background noise is weak. The results of this paper provide a scientific understanding about the properties of seismic‐prospecting background noise.
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Imaging pre‐existing natural fractures using microseismic data
Authors Myungsun Kim, Heewon Tak and Joongmoo ByunABSTRACTIn hydraulic fracturing treatments, locating not only hydraulic fractures but also any pre‐existing natural fractures and faults in a subsurface reservoir is very important. Hydraulic fractures can be tracked by locating microseismic events, but to identify the locations of natural fractures, an additional technique is required. In this paper, we present a method to image pre‐existing fractures and faults near a borehole with virtual reverse vertical seismic profiling data or virtual single‐well profiling data (limited to seismic reflection data) created from microseismic monitoring using seismic interferometry. The virtual source data contain reflections from natural fractures and faults, and these features can be imaged by applying migration to the virtual source data. However, the imaging zone of fractures in the proposed method is strongly dependent on the geographic extent of the microseismic events and the location and direction of the fracture. To verify our method, we produced virtual reverse vertical seismic profiling and single‐well profiling data from synthetic microseismic data and compared them with data from real sources in the same relative position as the virtual sources. The results show that the reflection travel times from the fractures in the virtual source data agree well with travel times in the real‐source data. By applying pre‐stack depth migration to the virtual source data, images of the natural fractures were obtained with accurate locations. However, the migrated section of the single‐well profiling data with both real and virtual sources contained spurious fracture images on the opposite side of the borehole. In the case of virtual single‐well profiling data, we could produce correct migration images of fractures by adopting directional redatuming for which the occurrence region of microseismic events is divided into several subdivisions, and fractures located only on the opposite side of the borehole are imaged for each subdivision.
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Assessing uncertainty in refraction seismic traveltime inversion using a global inversion strategy
Authors M. Rumpf and J. TronickeABSTRACTTo analyse and invert refraction seismic travel time data, different approaches and techniques have been proposed. One common approach is to invert first‐break travel times employing local optimization approaches. However, these approaches result in a single velocity model, and it is difficult to assess the quality and to quantify uncertainties and non‐uniqueness of the found solution. To address these problems, we propose an inversion strategy relying on a global optimization approach known as particle swarm optimization. With this approach we generate an ensemble of acceptable velocity models, i.e., models explaining our data equally well. We test and evaluate our approach using synthetic seismic travel times and field data collected across a creeping hillslope in the Austrian Alps. Our synthetic study mimics a layered near‐surface environment, including a sharp velocity increase with depth and complex refractor topography. Analysing the generated ensemble of acceptable solutions using different statistical measures demonstrates that our inversion strategy is able to reconstruct the input velocity model, including reasonable, quantitative estimates of uncertainty. Our field data set is inverted, employing the same strategy, and we further compare our results with the velocity model obtained by a standard local optimization approach and the information from a nearby borehole. This comparison shows that both inversion strategies result in geologically reasonable models (in agreement with the borehole information). However, analysing the model variability of the ensemble generated using our global approach indicates that the result of the local optimization approach is part of this model ensemble. Our results show the benefit of employing a global inversion strategy to generate near‐surface velocity models from refraction seismic data sets, especially in cases where no detailed a priori information regarding subsurface structures and velocity variations is available.
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Spatially non‐local model of inelastic deformations: applications for rock failure problem
Authors V. Dorovsky, Е. Romensky and А. SinevABSTRACTA spatially non‐local model for inelastic deformation of solids is proposed and studied. The non‐locality of deformation is taken into account by the additional parameter of state beyond the classical parameters such as stress and strain tensors. This additional parameter is the curvature tensor expressed in terms of the metric strain tensor, and it is called the failure parameter. In the case of small deformation, it is equivalent to the Saint‐Venant incompatibility tensor. Thermodynamic properties of the model are studied, and governing differential equations for spatially non‐local model are formulated, which are composed by the elasticity equations and parabolic equation for the failure parameter. The model can be applied to the study of the rock failure problem, and as an example, the one‐dimensional problem for the deformation of half‐plane loaded by the normal surface stress is studied. Stationary and non‐stationary formulations of the problem are considered, and qualitative agreement with available experimental data is observed.
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Utilizing spectral decomposition to determine the distribution of injected CO2 at the Snøhvit Field
Authors James C. White, Gareth A. Williams, Sissel Grude and R. Andrew ChadwickABSTRACTTime‐lapse 3D seismic reflection data, covering the CO2 storage operation at the Snøhvit gas field in the Barents Sea, show clear amplitude and time‐delay differences following injection. The nature and extent of these changes suggest that increased pore fluid pressure contributes to the observed seismic response, in addition to a saturation effect.
Spectral decomposition using the smoothed pseudo‐Wigner–Ville distribution has been used to derive discrete‐frequency reflection amplitudes from around the base of the CO2 storage reservoir. These are utilized to determine the lateral variation in peak tuning frequency across the seismic anomaly as this provides a direct proxy for the thickness of the causative feature.
Under the assumption that the lateral and vertical extents of the respective saturation and pressure changes following CO2 injection will be significantly different, discrete spectral amplitudes are used to distinguish between the two effects. A clear spatial separation is observed in the distribution of low‐ and high‐frequency tuning. This is used to discriminate between direct fluid substitution of CO2, as a thin layer, and pressure changes that are distributed across a greater thickness of the storage reservoir. The results reveal a striking correlation with findings derived from pressure and saturation discrimination algorithms based on amplitude versus offset analysis.
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Geomechanical property estimation of unconventional reservoirs using seismic data and rock physics
Authors Michael E. Glinsky, Andrea Cortis, Jinsong Chen, Doug Sassen and Howard RaelABSTRACTAn extension of a previously developed rock physics model is made that quantifies the relationship between the ductile fraction of a brittle/ductile binary mixture and the isotropic seismic reflection response. By making a weak scattering (Born) approximation and plane wave (eikonal) approximation, with a subsequent ordering according to the angles of incidence, singular value decomposition analyses are performed to understand the stack weightings, number of stacks, and the type of stacks that will optimally estimate two fundamental rock physics parameters – the ductile fraction and the compaction and/or diagenesis. It is concluded that the full PP stack, i.e., sum of all PP offset traces, and the “full” PS stack, i.e., linear weighted sum of PS offset traces, are the two optimal stacks needed to estimate the two rock physics parameters. They dominate over both the second‐order amplitude variation offset “gradient” stack, which is a quadratically weighted sum of PP offset traces that is effectively the far offset traces minus the near offset traces, and the higher order fourth order PP stack (even at large angles of incidence). Using this result and model‐based Bayesian inversion, the seismic detectability of the ductile fraction (shown by others to be the important rock property for the geomechanical response of unconventional reservoir fracking) is demonstrated on a model characteristic of the Marcellus shale play.
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Stratigraphic coordinates: a coordinate system tailored to seismic interpretation
Authors Parvaneh Karimi and Sergey FomelABSTRACTIn certain seismic data processing and interpretation tasks such as spiking deconvolution, tuning analysis, impedance inversion, and spectral decomposition, it is commonly assumed that the vertical direction is normal to reflectors. This assumption is false in the case of dipping layers and may therefore lead to inaccurate results. To overcome this limitation, we propose a coordinate system in which geometry follows the shape of each reflector and the vertical direction corresponds to normal reflectivity. We call this coordinate system stratigraphic coordinates. We develop a constructive algorithm that transfers seismic images into the stratigraphic coordinate system. The algorithm consists of two steps. First, local slopes of seismic events are estimated by plane‐wave destruction; then structural information is spread along the estimated local slopes, and horizons are picked everywhere in the seismic volume by the predictive‐painting algorithm. These picked horizons represent level sets of the first axis of the stratigraphic coordinate system. Next, an upwind finite‐difference scheme is used to find the two other axes, which are perpendicular to the first axis, by solving the appropriate gradient equations. After seismic data are transformed into stratigraphic coordinates, seismic horizons should appear flat, and seismic traces should represent the direction normal to the reflectors. Immediate applications of the stratigraphic coordinate system are in seismic image flattening and spectral decomposition. Synthetic and real data examples demonstrate the effectiveness of stratigraphic coordinates.
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Gravimetric monitoring of the first field‐wide steam injection in a fractured carbonate field in Oman – a feasibility study
Authors Marcin Glegola, Pavel Ditmar, Femke Vossepoel, Rob Arts, Fahad Al‐Kindy and Roland KleesABSTRACTGas‐Oil Gravity Drainage is to be enhanced by steam injection in a highly fractured, low permeability carbonate field in Oman. Following a successful pilot, field‐wide steam injection is being implemented, first of this type in the world. A dedicated monitoring program has been designed to track changes in the reservoir. Various observations are to be acquired, including, surface deformation, temperature measurements, microseismic, well logs, pressure and saturation measurements to monitor the reservoir. Because significant changes in the reservoir density are expected, time‐lapse gravimetry is also being considered. In this paper we investigate the feasibility of gravimetric monitoring of the thermally enhanced gravity drainage process at the carbonate field in Oman. For this purpose, forward gravity modelling is performed. Based on field groundwater measurements, the estimates of the hydrological signal are considered and it is investigated under what conditions the groundwater influences can be minimized. Using regularized inversion of synthetic gravity data, we analyse the achievable accuracy of heat‐front position estimates. In case of large groundwater variations at the field, the gravity observations can be significantly affected and, consequently, the accuracy of heat‐front monitoring can be deteriorated. We show that, by applying gravity corrections based on local observations of groundwater, the hydrological influences can to a large extent be reduced and the accuracy of estimates can be improved. We conclude that gravimetric monitoring of the heat‐front evolution has a great potential.
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Evidence for a new regional NW–SE fault and crustal structure in Tunisia derived from gravity data
Authors Mohamed Arfaoui, Alan Reid and Mohamed Hedi InoubliABSTRACTA new Tunisian gravity map interpretation based on the Gaussian filtered residual anomaly, total horizontal gradient, and Moho discontinuity morphology established from gravity data exhibit a new regional northwest–southeast fault extending from Eastern Kairouan to Ghardimaou (Algeria–Tunisia Boundary). It presents a horizontal gradient maximum lineament that terminates the north–south Jurassic structures in the Kairouan plain. Further, this interpretation reveals other known fault systems and crustal structures in Tunisia. The new regional northwest–southeast fault constitutes with the north–south axis and Gafsa–Jefara faults the deepest faults coinciding with the Moho flexures, which had an important role in their initiation. They constitute the border intra‐continental crust faults of the Mesozoic rift. The newly recognized deep fault has critical implications for mineral and petroleum perspectives.
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Field test of sub‐basalt hydrocarbon exploration with marine controlled source electromagnetic and magnetotelluric data
Authors G. Michael Hoversten, David Myer, Kerry Key, David Alumbaugh, Oliver Hermann and Randall HobbetABSTRACTThe recent use of marine electromagnetic technology for exploration geophysics has primarily focused on applying the controlled source electromagnetic method for hydrocarbon mapping. However, this technology also has potential for structural mapping applications, particularly when the relative higher frequency controlled source electromagnetic data are combined with the lower frequencies of naturally occurring magnetotelluric data. This paper reports on an extensive test using data from 84 marine controlled source electromagnetic and magnetotelluric stations for imaging volcanic sections and underlying sediments on a 128‐km‐long profile. The profile extends across the trough between the Faroe and Shetland Islands in the North Sea. Here, we focus on how 2.5D inversion can best recover the volcanic and sedimentary sections. A synthetic test carried out with 3D anisotropic model responses shows that vertically transverse isotropy 2.5D inversion using controlled source electromagnetic and magnetotelluric data provides the most accurate prediction of the resistivity in both volcanic and sedimentary sections. We find the 2.5D inversion works well despite moderate 3D structure in the synthetic model. Triaxial inversion using the combination of controlled source electromagnetic and magnetotelluric data provided a constant resistivity contour that most closely matched the true base of the volcanic flows. For the field survey data, triaxial inversion of controlled source electromagnetic and magnetotelluric data provides the best overall tie to well logs with vertically transverse isotropy inversion of controlled source electromagnetic and magnetotelluric data a close second. Vertical transverse isotropy inversion of controlled source electromagnetic and magnetotelluric data provided the best interpreted base of the volcanic horizon when compared with our best seismic interpretation. The structural boundaries estimated by the 20‐Ω·m contour of the vertical resistivity obtained by vertical transverse isotropy inversion of controlled source electromagnetic and magnetotelluric data gives a maximum geometric location error of 11% with a mean error of 1.2% compared with the interpreted base of the volcanic horizon. Both the model study and field data interpretation indicate that marine electromagnetic technology has the potential to discriminate between low‐resistivity prospective siliciclastic sediments and higher resistivity non‐prospective volcaniclastic sediments beneath the volcanic section.
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Volumes & issues
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Volume 72 (2023 - 2024)
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