Abstract
Multiple-point statistics are used to model facies heterogeneities in the vadose zone of the Komadugu-Yobe River valley (southeastern Niger) which is presently submitted to an undergoing intensive agricultural development; therefore, increasing quantitative and qualitative pressures are exerted on groundwater resources. The sand–clay heterogeneities are analyzed by means of a Landsat image acquired during a high flow period over a 160 km stretch in the downstream part of the valley and a set of 50 boreholes drilled near the town of Diffa (4 km×4 km area). The horizontal variograms of heterogeneities are characterized by a noticeably constant length scale of 380 m and clayey objects are shown to be randomly distributed in space according to a Poisson process. A set of two-dimensional vertical images is built based on a Boolean procedure and the Snesim algorithm is used to simulate synthetic three-dimensional media. When the vertical correlation length is fitted, the three-dimensional model satisfactorily reproduces the second order statistics of heterogeneities and the specific facies patterns.
This is a preview of subscription content, log in via an institution to check access.
References
Ahmed AA (2009) Using generic and pesticide DRASTIC GIS-based models for vulnerability assessment of the quaternary aquifer at Sohag, Egypt. Hydrogeol J 17(5):1203–1217
Allen JRL (1965) A review of the origin and characteristics of recent alluvial sediments. Sedimentology 5(2):89–191
Beucher H, Garcia-Morales MB, Geoffroy F (2005) Fitting the Boolean parameters in a non-stationary case. In: Leuangthong O, Deutch CV (eds) Geostatistics Banff 2004. Springer, Dordrecht
Caers J (2001) Geostatistical reservoir modelling using statistical pattern recognition. J Pet Sci Eng 29(3–4):177–188
Chilès JP, Delfiner P (1999) Geostatistics: modeling spatial uncertainty. Wiley, New York
Chugunova TL, Hu LY (2008) Mulitple-point simulations constrained by continuous auxiliary data. Math Geosci 40(2):133–146
de Marsily G, Delay F, Goncalves J, Renard P, Teles V, Violette S (2005) Dealing with spatial heterogeneity. Hydrogeol J 13(1):161–183
Deutsch CV, Tran TT (2002) FLUVSIM: a program for object-based stochastic modeling of fluvial depositional systems. Comput Geosci 28(4):525–535
Dimitrakopoulos R, Mustapha H, Gloaguen E (2010) High-order statistics of spatial random fields: exploring spatial cumulants for modeling complex non-Gaussian and non-linear phenomena. Math Geosci 42(1):65–99
Durand A (1995) Quaternary sediments and climatic changes in the central Sahel (Niger and Chad). Afr Geosci Rev 2(3–4):323–614
Feyen L, Caers J (2006) Quantifying geological uncertainty for flow and transport modeling in multi-modal heterogeneous formations. Adv Water Resour 29(6):912–929
Fogg GE, Noyes CD, Carle SF (1998) Geologically based model of heterogeneous hydraulic conductivity in an alluvial setting. Hydrogeol J 6(1):131–143
Frazier PS, Page KJ (2000) Water body detection and delineation with Landsat TM data. Photogramm Eng Remote Sens 66(12):1461–1467
Garrigues S, Allard D, Baret F, Weiss M (2006) Influence of landscape spatial heterogeneity on the non-linear estimation of leaf area index from moderate spatial resolution remote sensing data. Remote Sens Environ 105(4):286–298
Gumnior M, Preusser F (2007) Late quaternary river development in the southwest Chad Basin: OSL dating of sediment from the Komadugu palaeofloodplain (northeast Nigeria). J Quat Sci 22(7):709–719
Haldorsen HH, Damsleth E (1990) Stochastic modeling. J Pet Technol 42(4):404–412
Klise KA, Weissmann GS, McKenna SA, Nichols EM, Frechette JD, Wawrzyniec TF, Tidwell VC (2009) Exploring solute transport and streamline connectivity using Lidar-based outcrop images and geostatistical representations of heterogeneity. Water Resour Res 45:W05413
Koltermann CE, Gorelick SM (1996) Heterogeneity in sedimentary deposits: a review of structure-imitating, process-imitating, and descriptive approaches. Water Resour Res 32(9):2617–2658
Leblanc M (2002) The use of remote sensing and GIS for water resources managements of large semi-arid regions: a case study of the lake Chad basin, Africa. PhD thesis, The University of Glamorgan, UK, The University of Poitiers, France, 218 p
Le Coz M, Delclaux F, Genthon P, Favreau G (2009) Assessment of Digital Elevation Model (DEM) aggregation methods for hydrological modeling: Lake Chad Basin, Africa. Comput Geosci 35(8):1661–1670
Liu YH (2006) Using the Snesim program for multiple-point statistical simulation. Comput Geosci 32(10):1544–1563
Mariethoz G, Renard P, Cornaton F, Jaquet O (2009) Truncated Plurigaussian simulations to characterize aquifer heterogeneity. Ground Water 47(1):13–24
Miall AD (1996) The geology of fluvial deposits: sedimentary facies, Basin analysis and petroleum geology. Springer, Berlin
Mirowski PW, Tetzlaff DM, Davies RC, McCormick DS, Williams N, Signer C (2009) Stationarity scores on training images for multipoint geostatistics. Math Geosci 41(4):447–474
Mustapha H, Dimitrakopoulos R (2010) A new approach for geological pattern recognition using high-order spatial cumulants. Comput Geosci 36(3):313–334
Okabe H, Blunt MJ (2005) Pore space reconstruction using multiple-point statistics. J Pet Sci Eng 46(1–2):121–137
Pyrcz MJ, Boisvert JB, Deutsch CV (2008) A library of training images for fluvial and deepwater reservoirs and associated code. Comput Geosci 34(5):542–560
Ronayne MJ, Gorelick SM, Caers J (2008) Identifying discrete geologic structures that produce anomalous hydraulic response: an inverse modeling approach. Water Resour Res 44:W08426
Sisavath S, Mourzenko V, Genthon P, Thovert JF, Adler PM (2004) Geometry, percolation and transport properties of fracture networks derived from line data. Geophys J Int 157(2):917–934
Strebelle S (2002) Conditional simulation of complex geological structures using multiple-points statistics. Math Geol 34(1):1–21
Vargas-Guzámn JA, Al-Qassab H (2006) Spatial conditional simulation of facies objects for modeling complex clastic reservoirs. J Pet Sci Technol 54(1–2):1–9
Ye M, Khaleel R (2008) A Markov chain model for characterizing medium heterogeneity and sediment layering structure. Water Resour Res 44:W09427
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Le Coz, M., Genthon, P. & Adler, P.M. Multiple-Point Statistics for Modeling Facies Heterogeneities in a Porous Medium: The Komadugu-Yobe Alluvium, Lake Chad Basin. Math Geosci 43, 861–878 (2011). https://doi.org/10.1007/s11004-011-9353-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11004-011-9353-6