__A list of MPS related references (updated June 2017)__

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

__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. More here.
- 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,
*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,
*Geosci.*,*43*(3), 305-328, 10.1007/s11004-011-9328-7. - Strebelle, S. (2002), Conditional Simulation of Complex Geological Structures Using Multiple-Point Statistics,
*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., doi1007/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,
*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,
*& 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,
*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,
*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,
*& Geosci.*,*23*(2006), 1544-1563. - Maharaja, A. (2008), TiGenerator : Object-based training image generator,
*& Geosci.*,*34*(12). - Mariethoz, G. (2010), A general parallelization strategy for random path based geostatistical simulation methods,
*& 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,
*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.
- 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,
*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,
*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,
*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. AlborConsuegra, 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,
*& 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,
*& 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,
*Geol.*,*39*(1), 27-52. - Caers, J., and T. Hoffman (2006), The probability perturbation method: A new look at Bayesian inverse modeling,
*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,
*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,
*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,
*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?, 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,
*Water Resour.*,*21*(1), 47-61. - Journel, A., and T. Zhang (2006), The Necessity of a Multiple-Point Prior Model,
*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.