references.bib

@article{Benzanson2017,
  title={Julia: A fresh approach to numerical computing},
  author={Bezanson, Jeff and Edelman, Alan and Karpinski, Stefan and Shah, Viral B},
  journal={SIAM {R}eview},
  volume={59},
  number={1},
  pages={65--98},
  year={2017},
  publisher={SIAM},
  doi={10.1137/141000671},
  url={https://epubs.siam.org/doi/10.1137/141000671}
}

@book{Lauwens2018,
  author = {Lauwens, Ben and Downey, Allen},
  title = {Think Julia: How to Think Like a Computer Scientist},
  year = {2018},
  url = {https://benlauwens.github.io/ThinkJulia.jl/latest/book.html}
}

@software{Quinn2023,
  author       = {Jacob Quinn and
                  Bogumił Kamiński and
                  David Anthoff and
                  Milan Bouchet-Valat and
                  Tamas K. Papp and
                  Takafumi Arakaki and
                  Rafael Schouten and
                  Alex Arslan and
                  Anthony Blaom, PhD and
                  ExpandingMan and
                  Jarrett Revels and
                  Okon Samuel and
                  mathieu17g and
                  Nick Robinson and
                  Andy Ferris and
                  Andrey Oskin and
                  Arsh Sharma and
                  Ben Baumgold and
                  Carlo Lucibello and
                  Dilum Aluthge and
                  Eric Davies and
                  Eric Hanson and
                  Erjan Kalybek and
                  Hendrik Ranocha and
                  Iblis Lin and
                  Jack Dunn and
                  Jacob Adenbaum and
                  Jerry Ling and
                  Josh Day and
                  José Bayoán Santiago Calderón, PhD},
  title        = {JuliaData/Tables.jl: v1.10.1},
  month        = {mar},
  year         = {2023},
  publisher    = {Zenodo},
  version      = {v1.10.1},
  doi          = {10.5281/zenodo.7730968},
  url          = {https://doi.org/10.5281/zenodo.7730968}
}

@proceedings{Correia2015,
  author = {Correia, M..  and Hohendorff, J..  and Gaspar, A. T. and Schiozer, D.. },
  title = "{UNISIM-II-D: Benchmark Case Proposal Based on a Carbonate Reservoir}",
  volume = {Day 3 Fri, November 20, 2015},
  series = {SPE Latin America and Caribbean Petroleum Engineering Conference},
  pages = {D031S020R004},
  year = {2015},
  month = {11},
  abstract = "{Brazilian pre-salt reservoirs are mainly carbonate formations and they represent a great opportunity for research development. There is an increasing need of synthetic simulation models that reproduce these Pre-salt flow features for research development in reservoir simulation. This work presents a simulation benchmark model available as public domain data that represents Brazilian pre-salt trends and add a great opportunity to test new methodologies for reservoir development and management using numerical simulation.The work structure is divided in three steps: development of a reference model with known properties, development of a simulation model under uncertainties considering a specific date that represents the field development phase, and, elaboration of a benchmark proposal for studies related to the oil field development and production strategy selection. The reference model, treated as the real field, is a fine grid model in order to guarantee a high level of geologic details. The simulation model under uncertainties is a large scale model, a result of a development project considering an initial stage of field management.The benchmark model is based in a combination of Pre-salt characteristics and Ghawar field information given its diagenetic events and flow features close to Pre-salt. Based on the available information, several uncertainty attributes were considered in structural framework, facies, petrophysical properties, discrete fracture network. Economic and technical uncertainties were also considered. There is an increasing need of synthetic simulation models that reproduce these Pre-salt flow features for research development in reservoir simulation. This work presents a simulation benchmark model available as public domain data that represents Brazilian pre-salt trends and add a great opportunity to test new methodologies for reservoir development and management using numerical simulation. The main result of this project is achieved: the construction of a reference model and the construction of a simulation model under uncertainties assuming the well log information from three wells. This work provides a great contribution for further research development in reservoirs with geologic and dynamic pre-salt trends.}",
  doi = {10.2118/177140-MS},
  url = {https://doi.org/10.2118/177140-MS},
  eprint = {https://onepetro.org/SPELACP/proceedings-pdf/15LACP/3-15LACP/D031S020R004/1458256/spe-177140-ms.pdf},
}

@article{Hoffimann2021,
  author={Hoffimann, Júlio and Zortea, Maciel and de Carvalho, Breno and Zadrozny, Bianca},   
  title={Geostatistical Learning: Challenges and Opportunities},      
  journal={Frontiers in Applied Mathematics and Statistics},      
  volume={7},           
  year={2021},      
  url={https://www.frontiersin.org/articles/10.3389/fams.2021.689393},       
  doi={10.3389/fams.2021.689393},      
  issn={2297-4687},   
  abstract={Statistical learning theory provides the foundation to applied machine learning, and its various successful applications in computer vision, natural language processing and other scientific domains. The theory, however, does not take into account the unique challenges of performing statistical learning in geospatial settings. For instance, it is well known that model errors cannot be assumed to be independent and identically distributed in geospatial (a.k.a. regionalized) variables due to spatial correlation; and trends caused by geophysical processes lead to covariate shifts between the domain where the model was trained and the domain where it will be applied, which in turn harm the use of classical learning methodologies that rely on random samples of the data. In this work, we introduce the geostatistical (transfer) learning problem, and illustrate the challenges of learning from geospatial data by assessing widely-used methods for estimating generalization error of learning models, under covariate shift and spatial correlation. Experiments with synthetic Gaussian process data as well as with real data from geophysical surveys in New Zealand indicate that none of the methods are adequate for model selection in a geospatial context. We provide general guidelines regarding the choice of these methods in practice while new methods are being actively researched.}
}

@article{Bogumil2023,
  title={DataFrames.jl: Flexible and Fast Tabular Data in Julia},
  volume={107},
  url={https://www.jstatsoft.org/index.php/jss/article/view/v107i04},
  doi={10.18637/jss.v107.i04},
  abstract={DataFrames.jl is a package written for and in the Julia language offering flexible and efficient handling of tabular data sets in memory. Thanks to Julia’s unique strengths, it provides an appealing set of features: Rich support for standard data processing tasks and excellent flexibility and efficiency for more advanced and non-standard operations. We present the fundamental design of the package and how it compares with implementations of data frames in other languages, its main features, performance, and possible extensions. We conclude with a practical illustration of typical data processing operations.},
  number={4},
  journal={Journal of Statistical Software},
  author={Bouchet-Valat, Milan and Kamiński, Bogumił},
  year={2023},
  pages={1--32}
}

@software{Koolen2023,
  author       = {Twan Koolen and
                  Yuto Horikawa and
                  Andy Ferris and
                  Claire Foster and
                  awbsmith and
                  ryanelandt and
                  Jan Weidner and
                  Tim Holy and
                  Brian Jackson and
                  Alex Arslan and
                  Daniel Matz and
                  Miguel Raz Guzmán Macedo and
                  Andrew Gibb and
                  Christof Stocker and
                  Elliot Saba and
                  Hendrik Ranocha and
                  Julia TagBot and
                  Kenta Sato and
                  Kristoffer Carlsson and
                  N5N3 and
                  Oliver Evans and
                  pbouffard and
                  Robin Deits and
                  Seth Axen and
                  Silvio Traversaro and
                  Simon Byrne and
                  Steve Kelly and
                  Tony Kelman},
  title        = {JuliaGeometry/Rotations.jl: v1.6.0},
  month        = {sep},
  year         = {2023},
  publisher    = {Zenodo},
  version      = {v1.6.0},
  doi          = {10.5281/zenodo.8366010},
  url          = {https://doi.org/10.5281/zenodo.8366010}
}

@inproceedings{Floriani2007,
  booktitle = {Eurographics 2007 - State of the Art Reports},
  editor = {Dieter Schmalstieg and Jiri Bittner},
  title = {{Shape Representations Based on Simplicial and Cell Complexes}},
  author = {Floriani, L. De and Hui, A.},
  year = {2007},
  publisher = {The Eurographics Association},
  DOI = {10.2312/egst.20071055}
}

@article{Danisch2021,
  doi = {10.21105/joss.03349},
  url = {https://doi.org/10.21105/joss.03349},
  year = {2021},
  publisher = {The Open Journal},
  volume = {6},
  number = {65},
  pages = {3349},
  author = {Simon Danisch and Julius Krumbiegel},
  title = {Makie.jl: Flexible high-performance data visualization for Julia},
  journal = {Journal of Open Source Software}
}

@software{Breloff2023,
  author       = {Tom Breloff},
  title        = {Plots.jl},
  month        = {jul},
  year         = {2023},
  publisher    = {Zenodo},
  version      = {v1.38.17},
  doi          = {10.5281/zenodo.8183938},
  url          = {https://doi.org/10.5281/zenodo.8183938}
}

@misc{Thompson2023,
  author = {William Thompson},
  title = {{PairPlots.jl} Beautiful and flexible visualizations of high dimensional data},
  year = {2023},
  howpublished = {\url{https://sefffal.github.io/PairPlots.jl/dev}},
}

@software{Lin2023,
  author       = {Dahua Lin and
                  David Widmann and
                  Simon Byrne and
                  John Myles White and
                  Andreas Noack and
                  Mathieu Besançon and
                  Douglas Bates and
                  John Pearson and
                  John Zito and
                  Alex Arslan and
                  Moritz Schauer and
                  Kevin Squire and
                  David Anthoff and
                  Theodore Papamarkou and
                  Jan Drugowitsch and
                  Benjamin Deonovic and
                  Avik Sengupta and
                  Giuseppe Ragusa and
                  Glenn Moynihan and
                  Brian J Smith and
                  Martin O'Leary and
                  Michael and
                  Mohamed Tarek and
                  Mike J Innes and
                  Christoph Dann and
                  Gustavo Lacerda and
                  Iain Dunning and
                  Jan Weidner and
                  Jiahao Chen},
  title        = {JuliaStats/Distributions.jl: v0.25.100},
  month        = {aug},
  year         = {2023},
  publisher    = {Zenodo},
  version      = {v0.25.100},
  doi          = {10.5281/zenodo.8224988},
  url          = {https://doi.org/10.5281/zenodo.8224988}
}

@article{Hoffimann2019,
  title = {Efficient variography with partition variograms},
  journal = {Computers & Geosciences},
  volume = {131},
  pages = {52-59},
  year = {2019},
  issn = {0098-3004},
  doi = {https://doi.org/10.1016/j.cageo.2019.06.013},
  url = {https://www.sciencedirect.com/science/article/pii/S0098300419302936},
  author = {Júlio Hoffimann and Bianca Zadrozny},
  keywords = {Variography, Geostatistics, Partition variogram, Parallel algorithm, Exploratory data analysis, Spatial correlation},
  abstract = {Directional variograms were introduced in geostatistics as a tool for revealing major directions of correlation in spatial data. However, their estimation presents some practical challenges, particularly in the case of large irregularly-sampled data sets where efficient spectral-based estimation methods are not applicable. In this work, we propose a generalization of directional variograms to general partitions of spatial data, and introduce a parallel estimation algorithm that can efficiently handle large data sets with more than 105 points. This partition variogram generalization is motivated by a five-spot point pattern in the petroleum industry, which we named more generally as the isolated-lines arrangement. In such an arrangement, traditional estimators of directional variograms such as r-tube estimators very often fail to incorporate measurements from adjacent lines (e.g. vertical wells) without also incorporating measurements from other planes (e.g. horizontal layers). We provide illustrations of this new concept, and assess the approximation error of the proposed estimators with bootstrap methods and synthetic Gaussian process data.}
}

@article{Wickham2011,
  title={The Split-Apply-Combine Strategy for Data Analysis},
  volume={40},
  url={https://www.jstatsoft.org/index.php/jss/article/view/v040i01},
  doi={10.18637/jss.v040.i01},
  abstract={Many data analysis problems involve the application of a split-apply-combine strategy, where you break up a big problem into manageable pieces, operate on each piece independently and then put all the pieces back together. This insight gives rise to a new R package that allows you to smoothly apply this strategy, without having to worry about the type of structure in which your data is stored. The paper includes two case studies showing how these insights make it easier to work with batting records for veteran baseball players and a large 3d array of spatio-temporal ozone measurements.},
  number={1},
  journal={Journal of Statistical Software},
  author={Wickham, Hadley},
  year={2011},
  pages={1–29}
}

@book{Chiles2012,
  doi = {10.1002/9781118136188},
  url = {https://doi.org/10.1002/9781118136188},
  year = {2012},
  month = {feb},
  publisher = {Wiley},
  author = {Jean-Paul Chil{\`{e}}s and Pierre Delfiner},
  title = {Geostatistics}
}

@book{Webster2007,
	doi = {10.1002/9780470517277},
	url = {https://doi.org/10.1002%2F9780470517277},
	year = {2007},
	month = {jan},
	publisher = {Wiley},
	author = {Richard Webster and Margaret A. Oliver},
	title = {Geostatistics for Environmental Scientists}
}

@article{Cressie1980,
	doi = {10.1007/bf01035243},
	url = {https://doi.org/10.1007%2Fbf01035243},
	year = {1980},
	month = {apr},
	publisher = {Springer Science and Business Media {LLC}},
	volume = {12},
	number = {2},
	pages = {115--125},
	author = {Noel Cressie and Douglas M. Hawkins},
	title = {Robust estimation of the variogram: I},
	journal = {Journal of the International Association for Mathematical Geology}
}

@article{Myers1992,
  title = {Kriging, cokriging, radial basis functions and the role of positive definiteness},
  journal = {Computers & Mathematics with Applications},
  volume = {24},
  number = {12},
  pages = {139-148},
  year = {1992},
  issn = {0898-1221},
  doi = {https://doi.org/10.1016/0898-1221(92)90176-I},
  url = {https://www.sciencedirect.com/science/article/pii/089812219290176I},
  author = {Donald E. Myers},
  abstract = {There are at least three developments for interpolators that lead to the same functional form for the interpolator; the thin plate spline, radial basis functions and the regression method known as kriging. The key to the interrelationship lies in the positive definiteness of the kernel function. Micchelli has known that a weak form of positive definiteness is sufficient to ensure a unique solution to the system of equations determining the coefficients in the interpolator. Both the positive definiteness and the interpolator can be extended to vector valued functions via the kriging approach which is also independent of the dimension of the underlying space. The kriging approach leads naturally to various methods for simulation as well.}
}

@article{Shepard1968,
  title={A two-dimensional interpolation function for irregularly-spaced data},
  author={Donald S. Shepard},
  journal={Proceedings of the 1968 23rd ACM national conference},
  year={1968},
  url={https://api.semanticscholar.org/CorpusID:42723195}
}

@book{Matheron1971,
  title={The Theory of Regionalized Variables and Its Applications},
  author={Georges Fran\c cois Paul Marie Matheron},
  year={1971}
}

@book{Olea1999,
	doi = {10.1007/978-1-4615-5001-3},
	url = {https://doi.org/10.1007%2F978-1-4615-5001-3},
	year = {1999},
	publisher = {Springer {US}},
	author = {Ricardo A. Olea},
	title = {Geostatistics for Engineers and Earth Scientists}
}

@book{Mariethoz2014,
  title={Multiple-point Geostatistics: Stochastic Modeling with Training Images},
  author={Gregoire Mariethoz and Jef Caers},
  year={2014},
  month={dec},
  isbn={978-1-118-66275-5},
  url={https://www.wiley.com/en-gb/Multiple+point+Geostatistics%3A+Stochastic+Modeling+with+Training+Images-p-9781118662755}
}

@dataset{Hoffimann2022_1,
  author       = {Hoffimann, Júlio and
                  Augusto, José and
                  Resende, Lucas and
                  Mathias, Marlon and
                  Mazzinghy, Douglas and
                  Bianchetti, Matheus and
                  Mendes, Mônica and
                  Souza, Thiago and
                  Andrade, Vitor and
                  Domingues, Tarcísio and
                  Silva, Wesley and
                  Silva, Ruberlan and
                  Couto, Danielly and
                  Fonseca, Elisabeth and
                  Gonçalves, Keila},
  title        = {GeoMet dataset},
  month        = {mar},
  year         = {2022},
  publisher    = {Zenodo},
  doi          = {10.5281/zenodo.7051975},
  url          = {https://doi.org/10.5281/zenodo.7051975}
}

@article{Hoffimann2022_2,
  doi = {10.1007/s11004-022-10013-1},
  url = {https://doi.org/10.1007/s11004-022-10013-1},
  year = {2022},
  month = aug,
  publisher = {Springer Science and Business Media {LLC}},
  volume = {54},
  number = {7},
  pages = {1227--1253},
  author = {J{\'{u}}lio Hoffimann and Jos{\'{e}} Augusto and Lucas Resende and Marlon Mathias and Douglas Mazzinghy and Matheus Bianchetti and M{\^{o}}nica Mendes and Thiago Souza and Vitor Andrade and Tarc{\'{\i}}sio Domingues and Wesley Silva and Ruberlan Silva and Danielly Couto and Elisabeth Fonseca and Keila Gon{\c{c}}alves},
  title = {Modeling Geospatial Uncertainty of Geometallurgical Variables with Bayesian Models and Hilbert{\textendash}Kriging},
  journal = {Mathematical Geosciences}
}

@article{Aitchison1982,
 ISSN = {00359246},
 URL = {http://www.jstor.org/stable/2345821},
 abstract = {The simplex plays an important role as sample space in many practical situations where compositional data, in the form of proportions of some whole, require interpretation. It is argued that the statistical analysis of such data has proved difficult because of a lack both of concepts of independence and of rich enough parametric classes of distributions in the simplex. A variety of independence hypotheses are introduced and interrelated, and new classes of transformed-normal distributions in the simplex are provided as models within which the independence hypotheses can be tested through standard theory of parametric hypothesis testing. The new concepts and statistical methodology are illustrated by a number of applications.},
 author = {J. Aitchison},
 journal = {Journal of the Royal Statistical Society. Series B (Methodological)},
 number = {2},
 pages = {139--177},
 publisher = {[Royal Statistical Society, Wiley]},
 title = {The Statistical Analysis of Compositional Data},
 urldate = {2023-09-28},
 volume = {44},
 year = {1982}
}

@article{Friedman1987,
  ISSN = {01621459},
  URL = {http://www.jstor.org/stable/2289161},
  abstract = {A new projection pursuit algorithm for exploring multivariate data is presented that has both statistical and computational advantages over previous methods. A number of practical issues concerning its application are addressed. A connection to multivariate density estimation is established, and its properties are investigated through simulation studies and application to real data. The goal of exploratory projection pursuit is to use the data to find low- (one-, two-, or three-) dimensional projections that provide the most revealing views of the full-dimensional data. With these views the human gift for pattern recognition can be applied to help discover effects that may not have been anticipated in advance. Since linear effects are directly captured by the covariance structure of the variable pairs (which are straightforward to estimate) the emphasis here is on the discovery of nonlinear effects such as clustering or other general nonlinear associations among the variables. Although arbitrary nonlinear effects are impossible to parameterize in full generality, they are easily recognized when presented in a low-dimensional visual representation of the data density. Projection pursuit assigns a numerical index to every projection that is a functional of the projected data density. The intent of this index is to capture the degree of nonlinear structuring present in the projected distribution. The pursuit consists of maximizing this index with respect to the parameters defining the projection. Since it is unlikely that there is only one interesting view of a multivariate data set, this procedure is iterated to find further revealing projections. After each maximizing projection has been found, a transformation is applied to the data that removes the structure present in the solution projection while preserving the multivariate structure that is not captured by it. The projection pursuit algorithm is then applied to these transformed data to find additional views that may yield further insight. This projection pursuit algorithm has potential advantages over other dimensionality reduction methods that are commonly used for data exploration. It focuses directly on the "interestingness" of a projection rather than indirectly through the interpoint distances. This allows it to be unaffected by the scale and (linear) correlational structure of the data, helping it to overcome the "curse of dimensionality" that tends to plague methods based on multidimensional scaling, parametric mapping, cluster analysis, and principal components.},
  author = {Jerome H. Friedman},
  journal = {Journal of the American Statistical Association},
  number = {397},
  pages = {249--266},
  publisher = {[American Statistical Association, Taylor & Francis, Ltd.]},
  title = {Exploratory Projection Pursuit},
  urldate = {2023-09-28},
  volume = {82},
  year = {1987}
}

@book{Devadoss2011,
  title     = "Discrete and computational geometry",
  author    = "Devadoss, Satyan L and O'Rourke, Joseph",
  publisher = "Princeton University Press",
  month     =  {may},
  year      =  {2011},
  address   = "Princeton, NJ",
  language  = "en"
}

@article{Held2001,
  doi = {10.1007/s00453-001-0028-4},
  url = {https://doi.org/10.1007/s00453-001-0028-4},
  year = {2001},
  month = {oct},
  publisher = {Springer Science and Business Media {LLC}},
  volume = {30},
  number = {4},
  pages = {563--596},
  author = {M. Held},
  title = {{FIST}: Fast Industrial-Strength Triangulation of Polygons},
  journal = {Algorithmica}
}

@book{Cheng2012,
  title = {Delaunay Mesh Generation},
  author = {Siu-Wing Cheng and Tamal K. Dey and Jonathan Shewchuk},
  publisher = {Chapman and Hall/CRC},
  isbn = {978-1584887300},
  url = {https://people.eecs.berkeley.edu/~jrs/meshbook.html},
  year = {2012},
  month = {dec},
}

@article{Moyner2024,
   author = "M{\o}yner, O.",
   title = "JutulDarcy.jl - a Fully Differentiable High-Performance Reservoir Simulator Based on Automatic Differentiation", 
   year = "2024",
   volume = "2024",
   number = "1",
   pages = "1-9",
   doi = "https://doi.org/10.3997/2214-4609.202437111",
   publisher = "European Association of Geoscientists \& Engineers",
   issn = "2214-4609",
}

@article{Fouedjio2016,
  title = {A hierarchical clustering method for multivariate geostatistical data},
  journal = {Spatial Statistics},
  volume = {18},
  pages = {333-351},
  year = {2016},
  issn = {2211-6753},
  doi = {https://doi.org/10.1016/j.spasta.2016.07.003},
  url = {https://www.sciencedirect.com/science/article/pii/S2211675316300367},
  author = {Francky Fouedjio},
  keywords = {Clustering, Geostatistics, Non-parametric, Multivariate data, Spatial correlation, Spatial contiguity},
  abstract = {Multivariate geostatistical data have become omnipresent in the geosciences and pose substantial analysis challenges. One of them is the grouping of data locations into spatially contiguous clusters so that data locations within the same cluster are more similar while clusters are different from each other. Spatially contiguous clusters can significantly improve the interpretation that turns the resulting clusters into meaningful geographical subregions. In this paper, we develop an agglomerative hierarchical clustering approach that takes into account the spatial dependency between observations. It relies on a dissimilarity matrix built from a non-parametric kernel estimator of the multivariate spatial dependence structure of data. It integrates existing methods to find the optimal number of clusters and to evaluate the contribution of variables to the clustering. The capability of the proposed approach to provide spatially compact, connected and meaningful clusters is assessed using multivariate synthetic and real datasets. The proposed clustering method gives satisfactory results compared to other similar geostatistical clustering methods.}
}