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A list of MPS related references (updated June 2014)

This list is not exhaustive (last update April 2017). Thanks for letting me know if I forgot to mention a specific reference at

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Reference papers and books

·         Caers, J. (2005), Petroleum Geostatistics, 88 pp., Society of Petroleum Engineers, Richardson.

·         Hu, L., and T. Chugunova (2008), Multiple-Point Geostatistics for Modeling Subsurface Heterogeneity: a Comprehensive Review, Water Resour. Res., 44(W11413), doi:10.1029/2008WR006993.

·         Koltermann, C., and S. Gorelick (1996), Heterogeneity in sedimentary deposits: A review of structure-imitating, process-imitating, and descriptive approaches, Water Resour. Res., 32(9), 2617-2658.

·         Mariethoz, G. and J. Caers (2014). Multiple-point Geostatistics: Stochastic Modeling with Training Images, Wiley-Blackwell.

·         Remy, N., A. Boucher, and J. Wu (2009), Applied Geostatistics with SGeMS: A User's Guide, 284 pp., Cambridge University Press, Cambridge.

MPS simulation algorithms

·         Abdollahifard, M. J., and K. Faez (2013), Stochastic simulation of patterns using Bayesian pattern modeling, Comput. Geosc., 17(1), 99-116.

·         Abdollahifard, M. J. (2016). "Fast multiple-point simulation using a data-driven path and an efficient gradient-based search." Computers and Geosciences 86: 64-74.

·         Allard, D., R. Froidevaux, and P. Biver (2006), Conditional Simulation of Multi-Type Non Stationary Markov Object Models Respecting Specified Proportions Math. Geosci., 38(8), 959-986, 10.1007/s11004-006-9057-5.

·         Arpat, B., and J. Caers (2007), Conditional simulations with patterns, Math. Geol., 39(2), 177-203.

·         Chatterjee, S., R. Dimitrakopoulos, and H. Mustapha (2012), Dimensional Reduction of Pattern-Based Simulation Using Wavelet Analysis, Math. Geosci., 44(3), 343-374.

·         El Ouassini, A., A. Saucier, D. Marcotte, and B. Favis (2008), A patchwork approach to stochastic simulation: A route towards the analysis of morphology in multiphase systems, Chaos Solit. Fract., 36(2008), 418-436.

·         Eskandaridalvand, K., and S. Srinivasan (2010), Reservoir modelling of complex geological systems - A multiple-point perspective, Journal of Canadian Petroleum Technology, 49(8), 59-68.

·         Faucher, C., A. Saucier, and D. Marcotte (2013), A new patchwork simulation method with control of the local-mean histogram, Stochastic Environmental Research and Risk Assessment, 27(1), 253-273.

·         Guardiano, F., and M. Srivastava (1993), Multivariate geostatistics: Beyond bivariate moments, in Geostatistics-Troia, edited by A. Soares, pp. 133-144, Kluwier Academic, Dordrecht.

·         Honarkhah, M., and J. Caers (2010), Stochastic Simulation of Patterns Using Distance-Based Pattern Modeling, Math. Geosci., 42(5), 487-517, 10.1007/s11004-010-9276-7.

·         Kalantari, S. and M. J. Abdollahifard (2016). "Optimization-based multiple-point geostatistics: A sparse way." Computers and Geosciences 95: 85-98.

·         Li, X., et al. (2016). "Patch-based iterative conditional geostatistical simulation using graph cuts." Water Resources Research.

·         Mariethoz, G., P. Renard, and J. Straubhaar (2010), The direct sampling method to perform multiple-point simulations, Water Resour. Res., 46(W11536), 10.1029/2008WR007621.

·         Mahmud, K., G. Mariethoz, J. Caers, P. Tahmasebi, and A. Baker (2014), Simulation of Earth textures by conditional image quilting, Water Resour. Res., 50(4), 3088-3107, 10.1002/2013wr015069.

·         Mustapha, H., S. Chatterjee, and R. Dimitrakopoulos (2014), CDFSIM: Efficient Stochastic Simulation Through Decomposition of Cumulative Distribution Functions of Transformed Spatial Patterns, Math. Geosci., 46(1), 95-123.

·         Mustapha, H., and R. Dimitrakopoulos (2011), HOSIM: A high-order stochastic simulation algorithm for generating three-dimensional complex geological patterns, Computers and Geosciences, 37(9), 1242-1253.

·         Stien, M., and O. Kolbjørnsen (2011), Facies Modeling Using a Markov Mesh Model Specification, Math. Geosci., 43(6), 611-624.

·         Straubhaar, J., P. Renard, G. Mariethoz, R. Froidevaux, and O. Besson (2011), An improved parallel multiple-point algorithm using a list approach, Math. Geosci., 43(3), 305-328, 10.1007/s11004-011-9328-7.

·         Strebelle, S. (2002), Conditional Simulation of Complex Geological Structures Using Multiple-Point Statistics, Math. Geol., 34(1), 1-22.

·         Tahmasebi, P., A. Hezarkhani, and M. Sahimi (2012), Multiple-point geostatistical modeling based on the cross-correlation functions, Comput. Geosc., doi 10.1007/s10596-012-9287-1.

·         Tahmasebi, P. and M. Sahimi (2016). "Enhancing multiple-point geostatistical modeling: 1. Graph theory and pattern adjustment." Water Resources Research 52(3): 2074-2098.

·         Tahmasebi, P. and M. Sahimi (2016). "Enhancing multiple-point geostatistical modeling: 2. Iterative simulation and multiple distance function." Water Resources Research 52(3): 2099-2122.

·         Yang, L., et al. (2016). "GOSIM: A multi-scale iterative multiple-point statistics algorithm with global optimization." Computers and Geosciences 89: 57-70.

·         Zhang, T., P. Switzer, and A. Journel (2006), Filter-based classification of training image patterns for spatial simulation, Math. Geol., 38(1), 63-80.

Reference works in texture synthesis that are related to MPS

·         Efros, A., and T. Leung (1999), Texture synthesis by non-parametric sampling, paper presented at The Proceedings of the Seventh IEEE International Conference on Computer Vision, 1999, Kerkyra , Greece

·         Mariethoz, G., and S. Lefebvre (2014), Bridges between multiple-point geostatistics and texture synthesis: Review and guidelines for future research, Comp. & Geosci., 66(0), 66-80, http://dx.doi.org/10.1016/j.cageo.2014.01.001.

·         Wei, L., and M. Levoy (2000), Fast Texture Synthesis using Tree-structured Vector Quantization, paper presented at SIGGRAPH '00: 27th annual conference on Computer graphics and interactive techniques, ACM Press/Addison-Wesley, New Orleans.

Improvement of the methods and theoretical contributions

·         Abdollahifard, M. J., and K. Faez (2013), Fast direct sampling for multiple-point stochastic simulation, Arabian Journal of Geosciences, 1-13.

·         Bai, H., et al. (2016). "Utilizing spatial association analysis to determine the number of multiple grids for multiple-point statistics." Spatial Statistics 17: 83-104.

·         Boucher, A. (2009), Considering complex training images with search tree partitioning, Comp. & Geosci., 35(6), 1151-1158.

·         Calderón, H., et al. (2015). "Reconstruction of channelized geological facies based on RIPless compressed sensing." Computers & Geosciences 77: 54-65.

·         Chatterjee, S., and R. Dimitrakopoulos (2012), Multi-scale stochastic simulation with a wavelet-based approach, Computers & Geosciences, 45, 177-189.

·         Chatterjee, S. and M. M. Mohanty (2015). "Automatic cluster selection using gap statistics for pattern-based multi-point geostatistical simulation." Arabian Journal of Geosciences 8(9): 7691-7704.

·         Chugunova, T., and L. Hu (2008), Multiple-Point Simulations Constrained by Continuous Auxiliary Data, Math. Geosci., 40(2), 133-146.

·         Comunian, A., P. Renard, and J. Straubhaar (2012), 3D multiple-point statistics simulation using 2D training images, Computers and Geosciences, 40, 49-65.

·         Cordua, K., T. Hansen, and K. Mosegaard (2014), Improving the Pattern Reproducibility of Multiple-Point-Based Prior Models Using Frequency Matching, Math. Geosci., 1-27.

·         Cordua, K. S., et al. (2016). "Mixed-point geostatistical simulation: A combination of two- and multiple-point geostatistics." Geophysical Research Letters 43(17): 9030-9037.

·         de Vries, L., J. Carrera, O. Falivene, O. Gratacos, and L. Slooten (2009), Application of Multiple Point Geostatistics to Non-Stationary Images, Math. Geosci., 41(1), 29-42.

·         Faucher, C., A. Saucier, and D. Marcotte (2014), Corrective pattern-matching simulation with controlled local-mean histogram, Stochastic Environmental Research and Risk Assessment, 1-24, 10.1007/s00477-014-0864-9.

·         Gardet, C., et al. (2016). "Pattern-based conditional simulation with a raster path: a few techniques to make it more efficient." Stochastic Environmental Research and Risk Assessment 30(2): 429-446.

·         Hajizadeh, A., and Z. Farhadpour (2012), An Algorithm for 3D Pore Space Reconstruction from a 2D Image Using Sequential Simulation and Gradual Deformation with the Probability Perturbation Sampler, Transport in Porous Media, 94(3), 859-881.

·         Hu, L. Y., Y. Liu, C. Scheepens, A. W. Shultz, and R. D. Thompson (2014), Multiple-Point Simulation with an Existing Reservoir Model as Training Image, Math. Geosci., 46(2), 227-240, 10.1007/s11004-013-9488-8.

·         Huang, T., D. T. Lu, X. Li, and L. Wang (2013), GPU-based SNESIM implementation for multiple-point statistical simulation, Computers and Geosciences, 54, 75-87.

·         Huang, T. S., X. Li, T. Zhang, and D. Lu (2013), GPU-accelerated Direct Sampling method for multiple-point statistics simulation, Comp. & Geosci., 57, 13-23.

·         Huysmans, M., and A. Dassargues (2011), Direct Multiple-Point Geostatistical Simulation of Edge Properties for Modeling Thin Irregularly Shaped Surfaces, Math. Geosci., 43(5), 521-536, 10.1007/s11004-011-9336-7.

·         Kolbjørnsen, O., M. Stien, H. Kjønsberg, B. Fjellvoll, and P. Abrahamsen (2014), Using Multiple Grids in Markov Mesh Facies Modeling, Math. Geosci., 46(2), 205-225, 10.1007/s11004-013-9499-5.

·         Li, L., A. Boucher, and J. Caers (2014), SGEMS-UQ: An uncertainty quantification toolkit for SGEMS, Comp. & Geosci., 62(0), 12-24, http://dx.doi.org/10.1016/j.cageo.2013.09.009.

·         Li, L., et al. (2015). "Universal kriging with training images." Spatial Statistics 14: 240-268.

·         Li, X., T. Huang, D.-T. Lu, and C. Niu Accelerating experimental High-order spatial statistics Calculations using GPUs, Comp. & Geosci.(0), http://dx.doi.org/10.1016/j.cageo.2014.05.012.

·         Liu, Y. (2006), Using the Snesim program for multiple-point statistical simulation, Comp. & Geosci., 23(2006), 1544-1563.

·         Maharaja, A. (2008), TiGenerator : Object-based training image generator, Comp. & Geosci., 34(12).

·         Mariethoz, G. (2010), A general parallelization strategy for random path based geostatistical simulation methods, Comp. & Geosci., 37(7), 953-958, doi: 10.1016/j.cageo.2009.11.001.

·         Mariethoz, G., and B. F. J. Kelly (2011), Modeling complex geological structures with elementary training images and transform-invariant distances, Water Resour. Res., 47(W07527), doi:10.1029/2011WR010412.

·         Mariethoz, G., and P. Renard (2010), Reconstruction of incomplete data sets or images using Direct Sampling, Math. Geosci., 42(3), 245-268, doi: 10.1007/s11004-010-9270-0.

·         Mariethoz, G., et al. (2015). "Feature-preserving interpolation and filtering of environmental time series." Environmental Modelling and Software 72: 71-76.

·         Mariethoz, G., et al. (2015). "Constraining distance-based multipoint simulations to proportions and trends." Environmental Modelling and Software 72: 184-197.

·         Meerschman, E., G. Pirot, G. Mariethoz, J. Straubhaar, M. Van Meirvenne, and P. Renard (2013), A practical guide to performing multiple-point statistical simulations with the Direct Sampling algorithm, Computers and Geosciences, 52, 307-324.

·         P. Mohammadmoradi, "Facies and Fracture Network Modeling by a Novel Image Processing Based Method," Geomaterials, Vol. 3 No. 4, 2013, pp. 156-164. doi: 10.4236/gm.2013.34020.

·         Ortiz, J. M., and C. V. Deutsch (2004), Indicator Simulation Accounting for Multiple-Point Statistics, Math. Geol., 36(5), 545-565.

·         Peredo, O., and J. M. Ortiz (2011), Parallel implementation of simulated annealing to reproduce multiple-point statistics, Computers and Geosciences, 37(8), 1110-1121.

·         Peredo, O., J. M. Ortiz, J. R. Herrero, and C. Samaniego (2014), Tuning and hybrid parallelization of a genetic-based multi-point statistics simulation code, Parallel Computing, 40(5–6), 144-158.

·         Parra, A., and J. M. Ortiz (2011), Adapting a texture synthesis algorithm for conditional multiple point geostatistical simulation, Stochastic Environmental Research and Risk Assessment, 25(8), 1101-1111.

·         Pourfard, M., et al. (2017). "PCTO-SIM: Multiple-point geostatistical modeling using parallel conditional texture optimization." Computers and Geosciences 102: 116-138.

·         Renard, P., et al. (2011). "Conditioning Facies Simulations with Connectivity Data." Mathematical Geosciences 43(8): 879-903.

·         Rezaee, H., G. Mariethoz, M. Koneshloo, and O. Asghari (2013), Multiple-point geostatistical simulation using the bunch-pasting direct sampling method, Computers and Geosciences, 54, 293-308.

·         Stien, M., P. Abrahmsen, R. Hauge, and O. Kolbjørnsen (2007), Modification of the Snesim Algorithm, paper presented at Petroleum Geostatistics 2007, 10-14 September 2007, EAGE, Cascais, Portugal.

·         Strebelle, S., and C. Cavelius (2014), Solving Speed and Memory Issues in Multiple-Point Statistics Simulation Program SNESIM, Math. Geosci., 46(2), 171-186, 10.1007/s11004-013-9489-7.

·         Straubhaar, J., A. Walgenwitz, and P. Renard (2013), Parallel Multiple-Point Statistics Algorithm Based on List and Tree Structures, Math. Geosci., 45(2), 131-147.

·         Straubhaar, J., and D. Malinverni (2014), Addressing Conditioning Data in Multiple-Point Statistics Simulation Algorithms Based on a Multiple Grid Approach, Math. Geosci., 46(2), 187-204, 10.1007/s11004-013-9479-9.

·         Straubhaar, J., et al. (2016). "Conditioning multiple-point statistics simulations to block data." Spatial Statistics 16: 53-71.

·         Tahmasebi, P., M. Sahimi, G. Mariethoz, and A. Hezarkhani (2012), Accelerating geostatistical simulations using graphics processing units (GPU), Computers and Geosciences, 46, 51-59.

·         Tahmasebi, P., M. Sahimi, and J. Caers (2014), MS-CCSIM: Accelerating pattern-based geostatistical simulation of categorical variables using a multi-scale search in Fourier space, Comp. & Geosci., 67(0), 75-88.

·         Tahmasebi, P. and M. Sahimi (2015). "Geostatistical Simulation and Reconstruction of Porous Media by a Cross-Correlation Function and Integration of Hard and Soft Data." Transport in Porous Media 107(3): 871-905.

·         Toftaker, H., and H. Tjelmeland (2013), Construction of Binary Multi-grid Markov Random Field Prior Models from Training Images, Math. Geosci., 45(4), 383-409.

·         Wu, J., T. Zhang, et al. (2008). Fast FILTERSIM simulation with score-based distance. Mathematical Geosciences 40(7): 773-788.

·         Zhang, T., S. I. Pedersen, C. Knudby, and D. McCormick (2012), Memory-Efficient Categorical Multi-point Statistics Algorithms Based on Compact Search Trees, Math. Geosci., 44(7), 863-879.

·         Zhang, T., et al. (2015). "Reconstruction of spatial data using isometric mapping and multiple-point statistics." Computational Geosciences 19(5): 1047-1062.

·         Zhang, T., et al. (2015). "Stochastic simulation of patterns using ISOMAP for dimensionality reduction of training images." Computers and Geosciences 79: 82-93.

·         Zhang, T., et al. (2016). "Reconstruction of porous media using ISOMAP-based MPS." Stochastic Environmental Research and Risk Assessment 30(1): 395-412.

·         Zhang, T., et al. (2016). "Stochastic simulation of geological data using isometric mapping and multiple-point geostatistics with data incorporation." Journal of Applied Geophysics 125: 14-25.

·         Zhang, T., et al. (2017). "Stochastic reconstruction of spatial data using LLE and MPS." Stochastic Environmental Research and Risk Assessment 31(1): 243-256.

Applications

·         Abdollahifard, M. J., et al. (2016). "Improving in situ data acquisition using training images and a Bayesian mixture model." Computers and Geosciences 91: 49-63.

·         Ahmadi, R., and E. Khamehchi (2013), Reservoir Modeling by Data Integration via Intermediate Spaces and Artificial Intelligence Tools in MPS Simulation Frameworks, Natural Resources Research, 22(4), 321-336.

·         Ahmadi, R., M. Masihi, M. Rasaei, K. Eskandaridalvand, and R. Shahalipour (2014), A sensitivity study of FILTERSIM algorithm when applied to DFN modeling, J Petrol Explor Prod Technol, 4(2), 153-174, 10.1007/s13202-014-0107-0.

·         Bastante, F., C. Ordóñez, J. Taboada, and J. Matías (2008), Comparison of indicator kriging, conditional indicator simulation and multiple-point statistics used to model slate deposits, Engineering Geology, 98(1-2), 50-59, 10.1016/j.enggeo.2008.01.006.

·         Blouin, M., R. Martel, and E. Gloaguen (2013), Accounting for Aquifer Heterogeneity from Geological Data to Management Tools, Ground Water, 51(3), 421-431.

·         Boucher, A., C. Kyriakidis, and C. Cronkite-Ratcliff (2008), Geostatistical Solutions for Super-Resolution Land Cover Mapping, IEEE Trans. Geosc. Rem. Sen., 46(1), 272-283.

·         Boucher, A., and R. Dimitrakopoulos (2012), Multivariate Block-Support Simulation of the Yandi Iron Ore Deposit, Western Australia, Math. Geosci., 44(4), 449-468.

·         Boucher, A., J. Costa, L. Rasera, and E. Motta (2014), Simulation of Geological Contacts from Interpreted Geological Model Using Multiple-Point Statistics, Math. Geosci., 1-12.

·         Caers, J., S. Strebelle, and K. Payrazyan (2003), Stochastic integration of seismic data and geologic scenarios: a West Africa submarine channel saga, The Leading Edge, 22(3), 192-196.

·         Caers, J., and T. Zhang (2004), Multiple-point geostatistics: a quantitative vehicle for integrating geologic analogs into multiple reservoir models, in Integration of outcrop and modern analog data in reservoir models, AAPG memoir 80, edited by G. M. Grammer, Harris, P. M., and Eberli, G. P., pp. 383-394, American Association of Petroleum Geologists, Tulsa.

·         de Carvalho, P. R. M., et al. (2016). "Geostatistical facies simulation with geometric patterns of a petroleum reservoir." Stochastic Environmental Research and Risk Assessment: 1-18.

·         Comunian, A., P. Renard, J. Straubhaar, and P. Bayer (2011), Three-dimensional high resolution fluvio-glacial aquifer analog: Part 2: geostatistical modeling, J. Hydrol., 405(1-2), 10-23.

·         Comunian, A., S. Jha, B. S. Giambastiani, G. Mariethoz, and B. J. Kelly (2014), Training Images from Process-Imitating Methods, Math. Geosci., 46(2), 241-260, 10.1007/s11004-013-9505-y.

·         Dickson, N. E. M., et al. (2015). "Integrating aerial geophysical data in multiple-point statistics simulations to assist groundwater flow models." Hydrogeology Journal 23(5): 883-900.

·         Falivene, O., P. Arbués, A. Gardiner, G. Pickup, J. A. Munõz, and L. Cabrera (2006), Best practice stochastic facies modeling from a channel-fill turbidite sandstone analog (the Quarry outcrop, Eocene Ainsa basin, northeast Spain), AAPG Bulletin, 90(7), 1003-1029.

·         Feng, W. and S. Wu (2016). "A multiple-point geostatistical method based on geological vector information." Arabian Journal of Geosciences 9(10).

·         Feyen, L., and J. Caers (2006), Quantifying geological uncertainty for flow and transport modelling in multi-modal heterogeneous formations, Adv. Water Resour., 29(6), 912-929.

·         Ge, Y. and H. Bai (2010). "MPS-based information extraction method for remotely sensed imagery: A comparison of fusion methods." Canadian Journal of Remote Sensing 36(6): 763-779.

·         Ge, Y., and H. Bai (2011), Multiple-point simulation-based method for extraction of objects with spatial structure from remotely sensed imagery, International Journal of Remote Sensing, 32(8), 2311-2335, 10.1080/01431161003698278.

·         Ge, Y. (2013). "Sub-pixel land-cover mapping with improved fraction images upon multiple-point simulation." International Journal of Applied Earth Observation and Geoinformation 22(1): 115-126.

·         Gonzales, E., T. Mukerji, and G. Mavko (2008), Seismic inversion combining rock physics and multiple-point geostatistics, Geophysics, 73(1), R11-R21, 10.1190/1.2803748.

·         Goodfellow, R., F. Albor Consuegra, R. Dimitrakopoulos, and T. Lloyd (2012), Quantifying multi-element and volumetric uncertainty, Coleman McCreedy deposit, Ontario, Canada, Computers & Geosciences, 42(0), 71-78, 10.1016/j.cageo.2012.02.018.

·         Hashemi, S., et al. (2014). "Channel characterization using multiple-point geostatistics, neural network, and modern analogy: A case study from a carbonate reservoir, southwest Iran." Journal of Applied Geophysics 111: 47-58.

·         He, X., T. O. Sonnenborg, F. Jørgensen, and K. H. Jensen (2013), The effect of training image and secondary data integration with multiple-point geostatistics in groundwater modeling, Hydrol. Earth Syst. Sci. Discuss., 10(9), 11829-11860, 10.5194/hessd-10-11829-2013.

·         Hoffman, B. T., and J. Caers (2007), History matching by jointly perturbing local facies proportions and their spatial distribution: Application to a North Sea reservoir, Journal of Petroleum Science and Engineering, 57(3-4), 257-272.

·         Huysmans, M., and A. Dassargues (2009), Application of multiple-point geostatistics on modelling groundwater flow and transport in a cross-bedded aquifer (Belgium), Hydrogeol. J., 17, 1901-1911.

·         Huysmans, M., and A. Dassargues (2012), Modeling the effect of clay drapes on pumping test response in a cross-bedded aquifer using multiple-point geostatistics, J. Hydrol., 450-451, 159-167.

·         Huysmans, M., P. Orban, E. Cochet, M. Possemiers, B. Ronchi, K. Lauriks, O. Batelaan, and A. Dassargues (2013), Using Multiple-Point Geostatistics for Tracer Test Modeling in a Clay-Drape Environment with Spatially Variable Conductivity and Sorption Coefficient, Math. Geosci., 1-19, 10.1007/s11004-013-9502-1.

·         Janson, X., and D. D. Madriz (2012), Geomodelling of carbonate mounds using two-point and multipoint statistics, edited, pp. 229-246.

·         Jeong, H., S. Srinivasan, and S. Bryant (2013), Uncertainty Quantification of CO2 Plume Migration Using Static Connectivity of Geologic Features, Energy Procedia, 37(0), 3771-3779.

·         Jha, S. K., G. Mariethoz, J. P. Evans, and M. F. McCabe (2013), Demonstration of a geostatistical approach to physically consistent downscaling of climate modeling simulations, Water Resour. Res., 49(1), 245-259.

·         Jha, S. K., G. Mariethoz, and B. F. J. Kelly (2013), Bathymetry fusion using multiple-point geostatistics: Novelty and challenges in representing non-stationary bedforms, Environmental Modelling and Software, 50, 66-76.

·         Jha, S. K., et al. (2014). "Parameterization of training images for aquifer 3-D facies modeling integrating geological interpretations and statistical inference." Water Resources Research 50(10): 7731-7749.

·         Jha, S. K., et al. (2015). "A space and time scale-dependent nonlinear geostatistical approach for downscaling daily precipitation and temperature." Water Resources Research 51(8): 6244-6261.

·         Jones, P., I. Douglas, and A. Jewbali (2013), Modeling Combined Geological and Grade Uncertainty: Application of Multiple-Point Simulation at the Apensu Gold Deposit, Ghana, Math. Geosci., 45(8), 949-965, 10.1007/s11004-013-9500-3.

·         Jørgensen, F., et al. (2015). "Combining 3D geological modelling techniques to address variations in geology, data type and density - An example from Southern Denmark." Computers and Geosciences 81: 53-63.

·         Jung, A., D. H. Fenwick, and J. Caers (2013), Training image-based scenario modeling of fractured reservoirs for flow uncertainty quantification, Comput. Geosc., 17(6), 1015-1031.

·         Kessler, T. C., A. Comunian, F. Oriani, P. Renard, B. Nilsson, K. E. Klint, and P. L. Bjerg (2013), Modeling fine-scale geological heterogeneity-examples of sand lenses in tills, Groundwater, 51(5), 692-705.

·         Lallier, F., S. Vignau, and H. Kombrink The use of Geophysical Data in MPS Facies Simulation in a Seismically Tuned Reservoir - a new Approach Based on the Direct Sampling Algorithm, edited, Society of Petroleum Engineers.

·         Le Coz, M., P. Genthon, and P. M. Adler (2011), Multiple-Point Statistics for Modeling Facies Heterogeneities in a Porous Medium: The Komadugu-Yobe Alluvium, Lake Chad Basin, Math. Geosci., 43(7), 861-878.

·         Le Coz, M., et al. (2017). "On the use of multiple-point statistics to improve groundwater flow modeling in karst aquifers: A case study from the Hydrogeological Experimental Site of Poitiers, France." Journal of hydrology 545: 109-119.

·         Li, L. and G. Huang (2016). "Groundwater level mapping using multiple-point geostatistics." Water (Switzerland) 8(9).

·         Linde, N., et al. (2015). "Tomogram-based comparison of geostatistical models: Application to the Macrodispersion Experiment (MADE) site." Journal of hydrology 531: 543-556.

·         Liu, Y., A. Harding, W. Abriel, and S. Strebelle (2004), Multiple-point simulation integrating wells, three-dimensional seismic data, and geology, AAPG Bulletin, 88(7), 905-921.

·         Lochbühler, T., G. Pirot, J. Straubhaar, and N. Linde (2013), Conditioning of Multiple-Point Statistics Facies Simulations to Tomographic Images, Math. Geosci., 1-21, 10.1007/s11004-013-9484-z.

·         Mahmud, K., et al. (2015). "Integrating multiple scales of hydraulic conductivity measurements in training image-based stochastic models." Water Resources Research 51(1): 465-480.

·         Malone, B. P., et al. (2016). "Comparing regression-based digital soil mapping and multiple-point geostatistics for the spatial extrapolation of soil data." Geoderma 262: 243-253.

·         Mariethoz, G., A. Comunian, I. Irarrazaval, and P. Renard (2014), Analog-based meandering river simulation Water Resour. Res., 50(2), 836-854, 10.1002/2013WR013730.

·         McCallum, J., D. Herckenrath, and C. Simmons (2014), Impact of Data Density and Geostatistical Simulation Technique on the Estimation of Residence Times in a Synthetic Two-dimensional Aquifer, Math. Geosci., 1-22, 10.1007/s11004-013-9518-6.

·         McCallum, J. L., et al. (2014). "Bias of Apparent Tracer Ages in Heterogeneous Environments." Groundwater 52(2): 239-250.

·         Meerschman, E., M. Van Meirvenne, E. Van De Vijver, P. De Smedt, M. M. Islam, and T. Saey (2013), Mapping complex soil patterns with multiple-point geostatistics, European Journal of Soil Science, 64(2), 183-191.

·         Meerschman, E., M. Van Meirvenne, G. Mariethoz, M. M. Islam, P. De Smedt, E. Van De Vijver, and T. Saey (2013), Using bivariate multiple-point statistics and proximal soil sensor data to map fossil ice-wedge polygons, Geoderma.

·         Michael, H., A. Boucher, T. Sun, J. Caers, and S. Gorelick (2010), Combining geologic-process models and geostatistics for conditional simulation of 3-D subsurface heterogeneity, Water Resour. Res., 46(W05527), doi:10.1029/2009WR008414.

·         Mustapha, H., S. Chatterjee, R. Dimitrakopoulos, and T. Graf (2013), Geologic heterogeneity recognition using discrete wavelet transformation for subsurface flow solute transport simulations, Adv. Water Resour., 54, 22-37.

·         Okabe, H., and M. Blunt (2004), Multiple-point Statistics to Generate Pore Space Images in Geostatistics Banff 2004, edited by O. L. a. C. V. Deutsch, pp. 763-768, Springer Netherlands.

·         Okabe, H., and M. Blunt (2007), Pore space reconstruction of vuggy carbonates using microtomography and multiple-point statistics, Water Resour. Res., 43(W12S02), 10.1029/2006WR005680.

·         Oriani, F., et al. (2014). "Simulation of rainfall time series from different climatic regions using the direct sampling technique." Hydrology and Earth System Sciences 18(8): 3015-3031.

·         Oriani, F., et al. (2016). "Missing data simulation inside flow rate time-series using multiple-point statistics." Environmental Modelling and Software 86: 264-276.

·         Pham, T. D. (2012), Supervised restoration of degraded medical images using multiple-point geostatistics, Computer Methods and Programs in Biomedicine, 106(3), 201-209.

·         Pirot, G., J. Straubhaar, and P. Renard (2014), Simulation of braided river elevation model time series with multiple-point statistics, Geomorphology, 214(0), 148-156.

·         Possemiers, M., et al. (2015). "Application of multiple-point geostatistics to simulate the effect of small-scale aquifer heterogeneity on the efficiency of aquifer thermal energy storage." Hydrogeology Journal 23(5): 971-981.

·         Pyrcz, M., J. Boisvert, and C. V. Deutsch (2008), A library of training images for fluvial and deepwater reservoirs and associated code, Comp. & Geosci.(34), 542-560.

·         Rezaee, H., O. Asghari, M. Koneshloo, and J. Ortiz (2014), Multiple-point geostatistical simulation of dykes: application at Sungun porphyry copper system, Iran, Stochastic Environmental Research and Risk Assessment, 1-15.

·         Ronayne, M., S. Gorelick, and J. Caers (2008), Identifying discrete geologic structures that produce anomalous hydraulic response: An inverse modeling approach, Water Resour. Res., 44(W08426).

·         Sacchi, Q., et al. (2016). "Increasing the predictive power of geostatistical reservoir models by integration of geological constraints from stratigraphic forward modeling." Marine and Petroleum Geology 69: 112-126.

·         Scheidt, C., and J. Caers (2009), Uncertainty Quantification in Reservoir Performance Using Distances and Kernel Methods—Application to a West Africa Deepwater Turbidite Reservoir, SPE Journal, 14(4), 680-692.

·         Strebelle, S. (2007), Simulation of Petrophysical Property Trends within Facies Geobodies, in Petroleum Geostatistics, edited, EAGE, Cascais, Portugal.

·         Strebelle, S., K. Payrazyan, and J. Caers (2003), Modeling of a deepwater turbidite reservoir conditional to seismic data using principal component analysis and multiple-point geostatistics, SPE Journal, 8(3), 227-235.

·         Tahmasebi, P., and M. Sahimi (2012), Reconstruction of three-dimensional porous media using a single thin section, Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 85(6).

·         Tamayo-Mas, E., et al. (2016). "Testing geological heterogeneity representations for enhanced oil recovery techniques." Journal of Petroleum Science and Engineering 146: 222-240.

·         Tang, Y., P. Atkinson, A. Wardrop, and J. Zhang (2013), Multiple-point geostatistical simulation for post-processing a remotely sensed land cover classification, Spatial Statistics.

·         Tang, Y., et al. (2015). "Downscaling remotely sensed imagery using area-to-point cokriging and multiple-point geostatistical simulation." ISPRS Journal of Photogrammetry and Remote Sensing 101: 174-185.

·         Tang, Y., et al. (2015). "Digital Elevation Data Fusion Using Multiple-Point Geostatistical Simulation." IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing 8(10): 4922-4933.

·         Tsunoyama, T., T. D. Pham, T. Fujita, and T. Sakamoto (2014) Identification of intestinal wall abnormalities and ischemia by modeling spatial uncertainty in computed tomography imaging findings, Computer Methods and Programs in Biomedicine, 10.1016/j.cmpb.2014.05.003.

·         Van Der Grijp, Y. and R. C. A. Minnitt (2015). "Application of direct sampling multi-point statistic and sequential gaussian simulation algorithms for modelling uncertainty in gold deposits." Journal of the Southern African Institute of Mining and Metallurgy 115(1): 73-85.

·         Vannametee, E., L. V. Babel, M. R. Hendriks, J. Schuur, S. M. de Jong, M. F. P. Bierkens, and D. Karssenberg (2014), Semi-automated mapping of landforms using multiple point geostatistics, Geomorphology, http://dx.doi.org/10.1016/j.geomorph.2014.05.032.

·         Xu, Z., Q. Teng, X. He, and Z. Li (2013), A reconstruction method for three-dimensional pore space using multiple-point geology statistic based on statistical pattern recognition and microstructure characterization, International Journal for Numerical and Analytical Methods in Geomechanics, 37(1), 97-110.

·         Xu, Z., Q. Teng, X. He, X. Yang, and Z. Li (2012), Multiple-point statistics method based on array structure for 3D reconstruction of Fontainebleau sandstone, Journal of Petroleum Science and Engineering, 100, 71-80.

·         Xu, T., J. Gómez Hernández, H. Zhou, and L. Li (2013), The Power of Transient Piezometric Head Data in Inverse Modeling: An Application of the Localized Normal-score EnKF with Covariance Inflation in a Heterogenous Bimodal Hydraulic Conductivity Field, Advances in Water Resources, http://dx.doi.org/http://dx.doi.org/10.1016/j.advwatres.2013.01.006.

·         Wu, J., A. Boucher, and T. Zhang (2008), A SGeMS code for pattern simulation of continuous and categorical variables: FILTERSIM, Comp. & Geosci., 34(12), 1863-1876.

·         Yin, Y. (2013). "A New Stochastic Modeling of 3-D Mud Drapes Inside Point Bar Sands in Meandering River Deposits." Natural Resources Research 22(4): 311-320.

·         Yin, G., et al. (2017). "Gap-filling of landsat 7 imagery using the direct sampling method." Remote Sensing 9(1).

·         Zhang, T., S. Bombarde, S. Strebelle, and E. Oatney (2006), 3D porosity modeling of a carbonate reservoir using continuous multiple-point statistics simulation, SPE Journal, 11(3), 375-379.

·         Zhang, T., et al. (2014). "Reconstruction of porous media using multiple-point statistics with data conditioning." Stochastic Environmental Research and Risk Assessment 29(3): 727-738.

·         Zhang, T., et al. (2015). "GPU-accelerated 3D reconstruction of porous media using multiple-point statistics." Computational Geosciences 19(1): 79-98.

Inverse modeling (or history matching)

·         Alcolea, A., and P. Renard (2010), The Blocking Moving Window sampler. Conditioning Multiple-Point Simulations to Hydrogeological data, Water Resour. Res., 46(W08511), 10.1029/2009WR007943.

·         Aydin, O., and J. Caers (2013), Image transforms for determining fit-for-purpose complexity of geostatistical models in flow modeling, Comput. Geosc., 17(2), 417-429.

·         Caers, J. (2003), History matching under a training image-based geological model constraint, SPE Journal, 8(3), 218-226, SPE # 74716.

·         Caers, J. (2007), Comparing the Gradual Deformation with the Probability Perturbation Method for Solving Inverse Problems, Math. Geol., 39(1), 27-52.

·         Caers, J., and T. Hoffman (2006), The probability perturbation method: A new look at Bayesian inverse modeling, Math. Geol., 38(1), 81-100.

·         Ginsbourger, D., B. Rosspopoff, G. Pirot, N. Durrande, and P. Renard (2013), Distance-based kriging relying on proxy simulations for inverse conditioning, Adv. Water Resour., 52, 275-291.

·         Hansen, T. M., K. S. Cordua, and K. Mosegaard (2012), Inverse problems with non-trivial priors: Efficient solution through sequential Gibbs sampling, Comput. Geosc., 16(3), 593-611.

·         Hansen, T., K. Skou Cordua, M. Caroline Looms, and K. Mosegaard (2013), SIPPI: A Matlab toolbox for sampling the solution to inverse problems with complex prior information: Part 1-Methodology, Computers and Geosciences, 52, 470-480.

·         Hansen, T. M., K. S. Cordua, M. C. Looms, and K. Mosegaard (2013), SIPPI: A Matlab toolbox for sampling the solution to inverse problems with complex prior information: Part 2-Application to crosshole GPR tomography, Computers and Geosciences, 52, 481-492.

·         Hu, L., G. Blanc, and B. Noetinger (2001), Gradual Deformation and Iterative Calibration of Sequential Stochastic Simulations, Math. Geol., 33(4), 475-489.

·         Hu, L. Y., Y. Zhao, Y. Liu, C. Scheepens, and A. Bouchard (2013), Updating multipoint simulations using the ensemble Kalman filter, Computers and Geosciences, 51, 7-15.

·         Jafarpour, B., and M. Khodabakhshi (2011), A Probability Conditioning Method (PCM) for Nonlinear Flow Data Integration into Multipoint Statistical Facies Simulation, Math. Geosci., 43(2), 133-164.

·         Josset, L., and I. Lunati (2013), Local and Global Error Models to Improve Uncertainty Quantification, Math. Geosci., 45(5), 601-620.

·         Khaninezhad, M. M., B. Jafarpour, and L. Li (2012), Sparse geologic dictionaries for subsurface flow model calibration: Part I. Inversion formulation, Adv. Water Resour.

·         Khaninezhad, M. M., B. Jafarpour, and L. Li (2012), Sparse geologic dictionaries for subsurface flow model calibration: Part II. Robustness to uncertainty, Adv. Water Resour.

·         Khaninezhad, M. R. M., B. Jafarpour, and L. Lianlin (2011), History matching with learned sparse dictionaries, JPT, Journal of Petroleum Technology, 63(4), 102-104.

·         Khaninezhad, M., and B. Jafarpour (2014), Prior model identification during subsurface flow data integration with adaptive sparse representation techniques, Comput. Geosc., 18(1), 3-16, 10.1007/s10596-013-9378-7.

·         Khaninezhad, M. M., and B. Jafarpour (2014), Sparse Randomized Maximum Likelihood (SpRML) for subsurface flow model calibration and uncertainty quantification, Adv. Water Resour., 69(0), 23-37.

·         Khodabakhshi, M., and B. Jafarpour (2013), A Bayesian mixture-modeling approach for flow-conditioned multiple-point statistical facies simulation from uncertain training images, Water Resour. Res., 49(1), 328-342.

·         Khodabakhshi, M., and B. Jafarpour (2014), Adaptive Conditioning of Multiple-Point Statistical Facies Simulation to Flow Data with Probability Maps, Math. Geosci., 1-23.

·         Laloy, E., et al. (2016). "Merging parallel tempering with sequential geostatistical resampling for improved posterior exploration of high-dimensional subsurface categorical fields." Advances in Water Resources 90: 57-69.

·         Li, L., S. Srinivasan, H. Zhou, and J. J. Gómez-Hernández (2013), A pilot point guided pattern matching approach to integrate dynamic data into geological modeling, Advances in  Water Resources, 62, Part A(0), 125-138.

·         Li, L., S. Srinivasan, H. Zhou, and J. J. Gómez-Hernández (2013), Simultaneous Estimation of Geologic and Reservoir State Variables Within an Ensemble-Based Multiple-Point Statistic Framework, Math. Geosci., 1-27, 10.1007/s11004-013-9504-z.

·         Liu, E., and B. Jafarpour (2013), Learning sparse geologic dictionaries from low-rank representations of facies connectivity for flow model calibration, Water Resour. Res., 49(10).

·         Lange, K., J. Frydendall, K. S. Cordua, T. M. Hansen, Y. Melnikova, and K. Mosegaard (2012), A Frequency Matching Method: Solving Inverse Problems by Use of Geologically Realistic Prior Information, Math. Geosci., 44(7), 783-803.

·         Mariethoz, G., P. Renard, and J. Caers (2010), Bayesian inverse problem and optimization with Iterative Spatial Resampling, Water Resour. Res., 46(W11530), 10.1029/2010WR009274.

·         Park, H., C. Scheidt, D. Fenwick, A. Boucher, and J. Caers (2013), History matching and uncertainty quantification of facies models with multiple geological interpretations, Comput. Geosc., 17(4), 609-621.

·         Pirot, G., et al. (2017). "Probabilistic inversion with graph cuts: Application to the Boise Hydrogeophysical Research Site." Water Resources Research 53(2): 1231-1250.

·         Scheidt, C., and J. Caers (2009), Representing Spatial Uncertainty Using Distances and Kernels, Math. Geosci., 41(4), 397-419.

·         Scheidt, C., and J. Caers (2010), Bootstrap confidence intervals for reservoir model selection techniques, Comput. Geosc., 14, 369-382.

·         Scheidt, C., P. Renard, and J. Caers (2014), Prediction-Focused Subsurface Modeling: Investigating the Need for Accuracy in Flow-Based Inverse Modeling, Math. Geosci., 1-19, 10.1007/s11004-014-9521-6.

·         Suzuki, S., and J. Caers (2008), A Distance-based Prior Model Parameterization for Constraining Solutions of Spatial Inverse Problems, Math. Geosci., 40(4), 445-469.

·         Tavakoli, R., S. Srinivasan, and M. F. Wheeler (2013), Rapid updating of stochastic models using an ensemble filter approach, 1342-1353.

·         Zahner, T., et al. (2016). "Image Synthesis with Graph Cuts: A Fast Model Proposal Mechanism in Probabilistic Inversion." Geophysical Journal International 204: 1179-1190.

·         Zhou, H., J. Gomez-Hernandez, and L. Li (2012), A Pattern Search Based Inverse Method, Water Resour. Res., 48(2), W03505.

·         Zhou, H., J. J. Gómez-Hernández, H. J. Hendricks Franssen, and L. Li (2011), An approach to handling non-Gaussianity of parameters and state variables in ensemble Kalman filtering, Adv. Water Resour., 34(7), 844-864.

Validation and training image inference methods

·         Aydin, O., and J. Caers (2013), Image transforms for determining fit-for-purpose complexity of geostatistical models in flow modeling, Comput. Geosc., 17(2), 417-429.

·         Bayer, P., et al. (2015). "High resolution multi-facies realizations of sedimentary reservoir and aquifer analogs." Scientific Data 2: 150033.

·         Boisvert, J. B., M. J. Pyrcz, and C. V. Deutsch (2010), Multiple point metrics to assess categorical variable models, Natural Resources Research, 19(3), 165-175.

·         Colombera, L., F. Felletti, N. P. Mountney, and W. D. McCaffrey (2012), A database approach for constraining stochastic simulations of the sedimentary heterogeneity of fluvial reservoirs, AAPG Bulletin, 96(11), 2143-2166.

·         de Iaco, S., and S. Maggio (2011), Validation techniques for geological patterns simulations based on variogram and multiple-point statistics, Math. Geosci., 43(4), 483-500.

·         de Iaco, S. (2013), On the use of different metrics for assessing complex pattern reproductions, Journal of Applied Statistics, 40(4), 808-822.

·         Jung, A., and T. Aigner (2012), Carbonate geobodies: Hierarchical classification and database - a new workflow for 3D reservoir modelling, Journal of Petroleum Geology, 35(1), 49-65.

·         Jung, A., T. Aigner, D. Palermo, S. Nardon, and M. Pontiggia (2012), A new workflow for carbonate reservoir modelling based on MPS: Shoal bodies in outcrop analogues (Triassic, SW Germany), edited, pp. 277-293.

·         Pérez, C., et al. (2014). "Verifying the high-order consistency of training images with data for multiple-point geostatistics." Computers and Geosciences 70: 190-205.

·         Pickel, A., et al. (2015). "Building a training image with Digital Outcrop Models." Journal of hydrology 531, Part 1: 53-61.

·         Renard, P. and D. Allard (2011). "Connectivity metrics for subsurface flow and transport." Advances in Water Resources.

·         Tan, X., P. Tahmasebi, and J. Caers (2014), Comparing Training-Image Based Algorithms Using an Analysis of Distance, Math. Geosci., 46(2), 149-169, 10.1007/s11004-013-9482-1.

Issue papers

·         Emery, X., and C. Lantuéjoul (2014), Can a Training Image Be a Substitute for a Random Field Model?, Math. Geosci., 46(2), 133-147, 10.1007/s11004-013-9492-z.

·         Gómez-Hernández, J. J., and X.-H. Wen (1998), To be or not to be multi-gaussian? A reflection on stochastic hydrogeology, Adv. Water Resour., 21(1), 47-61.

·         Journel, A., and T. Zhang (2006), The Necessity of a Multiple-Point Prior Model, Math. Geol., 38(5), 591-610.

·         Zinn, B., and C. Harvey (2003), When good statistical models of aquifer heterogeneity go bad: A comparison of flow, dispersion, and mass transfer in connected and multivariate Gaussian hydraulic conductivity fields, Water Resour. Res., 39(3), WR001146.

Software

·         Hansen, T. M., et al. (2016). "MPSLIB: A C++ class for sequential simulation of multiple-point statistical models." SoftwareX 5: 127-133.