R. V. Bibliographie, R. W. Ackermann, and . Schlische, Anticlustering of small normal faults around larger faults, Geology, vol.25, issue.12, pp.1127-1130, 1997.

G. Barrenblatt, I. Zheltov, and I. Kochina, Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks [strata], Journal of Applied Mathematics and Mechanics, vol.24, issue.5, pp.852-864, 1960.
DOI : 10.1016/0021-8928(60)90107-6

J. Barthélémy, Effective Permeability of Media with a Dense Network of Long and Micro Fractures, Transport in Porous Media, vol.452, issue.1950, 2009.
DOI : 10.1007/s11242-008-9241-9

C. Barton, Fractal Scaling of Fracture Networks, chapter Fractal Scaling of Fracture Networks, pp.141-178, 1995.

W. Belfield, Simulation of Subseismic Faults Using Fractal and Multifractal Geometry, SPE Annual Technical Conference and Exhibition, p.24751, 1992.
DOI : 10.2118/24751-MS

W. C. Belfield, Incorporating spatial distribution into stochastic modelling of fractures: multifractals and Levy-stable statistics, Journal of Structural Geology, vol.20, issue.4, pp.473-486, 1998.
DOI : 10.1016/S0191-8141(97)00118-1

B. Berkowitz and A. Hadad, Fractal and multifractal measures of natural and synthetic fracture networks, Journal of Geophysical Research: Solid Earth, vol.15, issue.12, 1997.
DOI : 10.1029/97JB00304

J. Bì-es and B. Feuga, La fracturation des roches. Manuels et méthodes ? 1, 1981.

J. Bonnans, J. Gilbert, C. Lemaréchal, and C. Sagastizába, Numerical optimization : theoretical and practical aspects, 2006.
DOI : 10.1007/978-3-662-05078-1

E. Bonnet, O. Bour, N. E. Odling, P. Davy, I. Main et al., Scaling of fracture systems in geological media, Reviews of Geophysics, vol.91, issue.11, pp.347-383, 2001.
DOI : 10.1029/1999RG000074

O. Bour and P. Davy, Connectivity of random fault networks following a power law fault length distribution, Water Resources Research, vol.17, issue.1, pp.1567-1583, 1997.
DOI : 10.1029/96WR00433

O. Bour and P. Davy, Clustering and size distributions of fault patterns: Theory and measurements, Geophysical Research Letters, vol.1515, issue.2, pp.2001-2004, 1999.
DOI : 10.1029/1999GL900419

B. Bourbiaux, M. C. Cacas, S. Sarda, and J. C. Sabathier, A Fast and Efficient Methodology to Convert Fractured Reservoir Images Into a Dual-Porosity Model, SPE Annual Technical Conference and Exhibition, 1997.
DOI : 10.2118/38907-MS

B. Bourbiaux, M. Cacas, S. Sarda, and J. Sabathier, A Rapid and Efficient Methodology to Convert Fractured Reservoir Images Into a Dual-Porosity Model, Revue de l'Institut Fran??ais du P??trole, vol.53, issue.6, pp.785-799, 1998.
DOI : 10.2516/ogst:1998069
URL : http://doi.org/10.2516/ogst:1998069

B. Bourbiaux, S. Granet, P. Landereau, B. Noetinger, S. Sarda et al., Scaling Up Matrix-Fracture Transfers in Dual-Porosity Models: Theory and Application, SPE Annual Technical Conference and Exhibition, pp.3-6, 1999.
DOI : 10.2118/56557-MS

B. Bourbiaux, R. Basquet, M. Cacas, J. Daniel, and S. Sarda, An Integrated Workflow to Account for Multi-Scale Fractures in Reservoir Simulation Models: Implementation and Benefits, Abu Dhabi International Petroleum Exhibition and Conference, 2002.
DOI : 10.2118/78489-MS

G. Bourdarot, Essais de puits : Méthodes d'interprétation, 1996.

D. Bruel, M. Cacas, and E. Ledoux, Exploitation de la chaleur des roches chaudes et s` eches : présentation d'un modèle couplé hydro-mécanique, 1990.

J. Bruyelle and A. Lange, Automated characterization of fracture conductivities from well tests inversion, EUROPEC/EAGE Conference and Exhibition, pp.8-11, 2009.
DOI : 10.2118/121172-MS

M. Cacas, J. Daniel, and J. Letouzey, Nested geological modelling of naturally fractured reservoirs, Petroleum Geoscience, vol.7, issue.S, pp.43-52, 2001.
DOI : 10.1144/petgeo.7.S.S43

J. Caers, Geostatistical History Matching Under Training-Image Based Geological Model Constraints, SPE Annual Technical Conference and Exhibition, pp.218-226, 2003.
DOI : 10.2118/77429-MS

P. Chainais, Infinitely Divisible Cascades to Model the Statistics of Natural Images, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.29, issue.12, 2007.
DOI : 10.1109/TPAMI.2007.1113

J. Chiì-es, Fractal and geostatistical methods for modeling of a fracture network, Mathematical Geology, vol.20, issue.6, pp.631-654, 1988.

J. Chiì-es, B. Bourgine, C. Castaing, and A. Genter, Stochastic modeling and simulation of fracture networks in petroleum and geothermal reservoirs, Cape Town, vol.1, pp.413-423, 2000.

T. T. Cladouhos and R. Marrett, Are fault growth and linkage models consistent with power-law distributions of fault lengths?, Journal of Structural Geology, vol.18, issue.2-3, pp.281-293, 1996.
DOI : 10.1016/S0191-8141(96)80050-2

C. Darcel, Correlations dans les réseaux de fractures : caractérisation et conséquences sur les propriétés hydrauliques, Géosciences Rennes, 2002.

C. Darcel, O. Bour, P. Davy, and J. R. De-dreuzy, Connectivity properties of twodimensional fracture networks with stochastic fractal correlation, Water Resour. Res, vol.39, 2003.

P. Davy, A. Hansen, E. Bonnet, and S. Zhang, Localization and fault growth in layered brittle-ductile systems: Implications for deformations of the continental lithosphere, Journal of Geophysical Research: Solid Earth, vol.337, issue.B4, pp.6281-6294, 1995.
DOI : 10.1029/94JB02983

D. Arcangelis and H. Herrmann, Scaling and multiscaling laws in random fuse networks, Physical Review B, vol.39, issue.4, pp.2678-2684, 1983.
DOI : 10.1103/PhysRevB.39.2678

G. De-marsilly, De l'identification des systèmes hydrologiques, 1978.

F. Delbos, D. Sinoquet, and T. Feng, Adapted nonlinear optimization method for production data and 4d seismic inversion, ECMOR European Conference on the Mathematics of Oil Recovery, pp.8-11, 2008.

M. Delorme, Calculs analytiques de paramètresparamètreséquivalents en milieux fracturés, 2005.

W. Dershowitz, A. Winberg, J. Hermansson, J. Byegård, E. Tullborg et al., Task 6c, : a semi-synthetic model of block scale conductive structures at thëthë Aspö hard rock laboratory. international progress report ipr-03-13, swedish nuclear fuel and waste management co., stockholm, Aspö Task Force on modelling of groundwater flow and transport of solutes, 2003.

C. Deutsch and A. , GSLIB : Geostatistical Software Library and User's Guide, 1997.

L. J. Durlofsky, Upscaling of geocellular models for reservoir flow simulation : A review of recent progres, 7th International Forum on Reservoir Simulation Buhl, 2003.

R. Fisher, Dispersion on a Sphere, Proc. Royal Society, pp.295-305, 1953.
DOI : 10.1098/rspa.1953.0064

A. Fourno and B. Bourbiaux, Cas synthétique vercors, 2007.

B. Gauthier, A. Zellou, A. Toublanc, M. Garcia, and J. Daniel, Integrated fractured reservoir characterization : A case study in north africa, SPE European Petroleum Conference, pp.24-25, 2000.

S. Guillon and N. Keskes, Sismage and the 3d visualization at total, AAPG International Conference, 2004.

N. Hansen, S. Müller, and P. Koumoutsakos, Reducing the Time Complexity of the Derandomized Evolution Strategy with Covariance Matrix Adaptation (CMA-ES), Evolutionary Computation, vol.11, issue.1, pp.1-18, 2003.
DOI : 10.1162/106365601750190398

N. Henn, M. Quintard, B. Bourbiaux, and S. Sakthikumar, Modelling of Conductive Faults with a Multiscale Approach, Oil & Gas Science and Technology, vol.59, issue.2, pp.197-214, 2004.
DOI : 10.2516/ogst:2004015

H. G. Hentschel and I. Procaccia, The infinite number of generalized dimensions of fractals and strange attractors, Physica D: Nonlinear Phenomena, vol.8, issue.3, pp.435-444, 1983.
DOI : 10.1016/0167-2789(83)90235-X

L. Holden, P. Mostad, B. F. Nielsen, J. Gjerde, C. Townsend et al., Stochastic Structural Modeling, Mathematical Geology, vol.35, issue.8, pp.899-914, 2003.
DOI : 10.1023/B:MATG.0000011584.51162.69

K. Hollund, P. Mostad, B. F. Nielsen, L. Holden, J. Gjerde et al., Havana ??? a fault modeling tool, Hydrocarbon Seal Quantification, pp.157-171, 2002.
DOI : 10.1016/S0928-8937(02)80013-3

L. Hu, Gradual deformation and iterative calibration of gaussian-related stochastic models, Mathematical Geology, pp.32-33, 2000.

L. Y. Hu and S. Jenni, History Matching of Object-Based Stochastic Reservoir Models, SPE Journal, vol.10, issue.03, pp.312-323, 2005.
DOI : 10.2118/81503-PA

M. Jern, Determination of the In situ Block Size Distribution in Fractured Rock, an Approach for Comparing In-situ Rock with Rock Sieve Analysis, Rock Mechanics and Rock Engineering, vol.37, issue.5, pp.391-401, 2004.
DOI : 10.1007/s00603-004-0029-0

A. G. Journel, C. Deutsch, and A. Desbarats, Power averaging for block effective permeability , spe paper 15128-ms, SPE California Regional Meeting, pp.2-4, 1986.
DOI : 10.2118/15128-ms

H. Kazemi, L. M. Jr, K. Porterfield, and P. Zeman, Numerical Simulation of Water-Oil Flow in Naturally Fractured Reservoirs, Society of Petroleum Engineers Journal, vol.16, issue.06, pp.317-326, 1976.
DOI : 10.2118/5719-PA

E. Koenig and P. Chainais, Virtual resolution enhancement of scale invariant textured images using stochastic processes, 2009 16th IEEE International Conference on Image Processing (ICIP), 2009.
DOI : 10.1109/ICIP.2009.5414442
URL : https://hal.archives-ouvertes.fr/hal-00707597

A. Lange, R. Basquet, and B. Bourbiaux, Hydraulic Characterization of Faults and Fractures Using a Dual Medium Discrete Fracture Network Simulator, Abu Dhabi International Conference and Exhibition, pp.10-13, 2004.
DOI : 10.2118/88675-MS

. Lariani, Perception et interprétation de sections et blocs sismiques : oculometrie et analyse d'Images, 2000.

M. and L. Ravalec-dupin, Inverse Stochastic Modeling of Flow in Porous Media, 2005.

M. and L. Ravalec-dupin, Pilot Block Method Methodology to Calibrate Stochastic Permeability Fields to Dynamic Data, Mathematical Geosciences, vol.34, issue.6, pp.165-185, 2010.
DOI : 10.1007/s11004-009-9249-x

M. , L. Ravalec-dupin, and B. Noetinger, Optimization with the gradual deformation method, Math. Geol, vol.34, issue.2, pp.125-142, 2002.

S. H. Lee, C. L. Jensen, and M. F. Lough, Efficient finite-difference model for flow in a reservoir with multiple length-scale fractures, SPE Journal, vol.5, issue.3, pp.65095-268, 2000.

P. Lemonnier, Les modèles de simulation numérique des réservoirs, 2010.

P. Lemonnier and B. Bourbiaux, Simulation of naturaly fractured reservoirs. state of the art : Part 2 -matrix-fracture transfers and typical features of numerical studies, OGST -Rev. IFP, vol.65, issue.2, pp.263-286, 2010.

K. Lim and K. Aziz, Matrix-fracture transfer shape factors for dual-porosity simulators, Journal of Petroleum Science and Engineering, vol.13, issue.3-4, pp.169-178, 1995.
DOI : 10.1016/0920-4105(95)00010-F

X. Liu and S. Srinivasan, Combining pattern statistics with geomechanical criteria for fracture growth, pp.75-84, 2004.

L. Lonergan, R. Jolly, K. Rawnsley, and D. Sanderson, Fractured Reservoirs, 2007.

L. Maerten, P. Gillespie, and J. Daniel, Three-dimensional geomechanical modeling for constraint of subseismic fault simulation, AAPG Bulletin, vol.90, issue.9, pp.1337-1358, 2006.
DOI : 10.1306/03130605148

S. Mallick, K. Craft, L. Meister, and R. Chambers, Determination of the principal directions of azimuthal anisotropy from p-wave seismic data, Geophysics, 1998.

B. Mandelbrot, Intermittent turbulence in self-similar cascades: divergence of high moments and dimension of the carrier, Journal of Fluid Mechanics, vol.15, issue.02, pp.331-358, 1974.
DOI : 10.1063/1.1693226

V. J. Martinez, B. J. Jones, R. Dominguez-tenreiro, and R. V. De-weygaert, Clustering paradigms and multifractal measures, The Astrophysical Journal, vol.357, pp.50-61, 1990.
DOI : 10.1086/168890

P. Mostad and J. Gjerde, Multifractal fault simulation Cape Town, South Africa, 6th International Geostatistical Congress 10, 2000.

J. Nelder and R. Mead, A Simplex Method for Function Minimization, The Computer Journal, vol.7, issue.4, pp.308-313, 1965.
DOI : 10.1093/comjnl/7.4.308

M. Oda, Permeability tensor for discontinuous rock masses, G??otechnique, vol.35, issue.4, 1985.
DOI : 10.1680/geot.1985.35.4.483

N. Odling, Network properties of a two-dimensional natural fracture pattern, Pure and Applied Geophysics PAGEOPH, vol.32, issue.B1, pp.90-90, 1993.
DOI : 10.1007/BF00876716

N. E. Odling, P. Gillespie, B. Bourgine, C. Castaing, J. P. Chiles et al., Variations in fracture system geometry and their implications for fluid flow in fractures hydrocarbon reservoirs, Petroleum Geoscience, vol.5, issue.4, pp.373-384, 1999.
DOI : 10.1144/petgeo.5.4.373

G. Ouillon, D. Sornette, and C. Castaing, Organisation of joints and faults from 1-cm to 100-km scales revealed by optimized anisotropic wavelet coefficient method and multifractal analysis, Nonlinear Processes in Geophysics, vol.2, issue.3/4, pp.158-177, 1995.
DOI : 10.5194/npg-2-158-1995
URL : https://hal.archives-ouvertes.fr/hal-00331034

S. Ozkaya and L. Bolle, Modeling and Upscaling Fracture Corridors ??? Uncertainties, SPE Technical Symposium of Saudi Arabia Section, 2006.
DOI : 10.2118/106337-MS

D. Peaceman, Fundamentals of Numerical Reservoir Simulation, 1977.

B. S. Ramarao, A. M. Lavenue, G. De-marsily, and M. G. Marietta, Pilot Point Methodology for Automated Calibration of an Ensemble of conditionally Simulated Transmissivity Fields: 1. Theory and Computational Experiments, Water Resources Research, vol.22, issue.2, pp.31475-493, 1995.
DOI : 10.1029/94WR02258

J. Sabathier, B. Bourbiaux, M. Cacas, and S. Sarda, A New Approach of Fractured Reservoirs, International Petroleum Conference and Exhibition of Mexico, pp.3-5, 1998.
DOI : 10.2118/39825-MS

S. Sarda, Full field export module, equivalent fracture parameters computation, vertical block height computation, sub-seismic faults horizontal block size

B. Singhal and R. Gupta, Applied Hydrogeology of Fractured Rocks, 1999.

A. Sornette, P. Davy, and D. Sornette, Fault growth in brittle-ductile experiments and the mechanics of continental collisions, Journal of Geophysical Research: Solid Earth, vol.123, issue.B7, pp.12111-12139, 1993.
DOI : 10.1029/92JB01740

J. Theiler, Estimating fractal dimension, Journal of the Optical Society of America A, vol.7, issue.6, pp.1055-1073, 1990.
DOI : 10.1364/JOSAA.7.001055

X. Tunc, I. Faille, T. Gallouët, M. Cacas, and P. Havé, A Model for Conductive Faults in Heterogeneous Media for Non-matching Grids, 12th European Conference on the Mathematics of Oil Recovery, 2010.
DOI : 10.3997/2214-4609.20144948

C. Vanneste and D. Sornette, The dynamical thermal fuse model, Journal de Physique I, vol.2, issue.8, pp.1621-1644, 1992.
DOI : 10.1051/jp1:1992231
URL : https://hal.archives-ouvertes.fr/jpa-00246644

M. Verscheure, Inversion conjointe des propriétés géométriques et hydrodynamiques d'un réservoir fracturé : Rapport de mi-thèse, 2009.

M. Verscheure, Méthode de calage d'historique d'un modèle géologique comportant un réseau de failles sub-sismiques, 2010.

M. Verscheure, A. Fourno, and J. Chiì-es, History Matching of a Realistic Stochastic Fault Model Using Fractal Geometry and the Gradual Deformation Method, SPE 129759, SPE/EAGE -Annual Conference and Exhibition, pp.14-17, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00556997

M. Verscheure, A. Fourno, and J. Chiì-es, History Matching of a Stochastic Multifractal Subesismic Fault Model, 12th European Conference on the Mathematics of Oil Recovery, 2010.
DOI : 10.3997/2214-4609.20144967

J. Walsh, Fractal analysis of fracture patterns using the standard box-counting technique: valid and invalid methodologies, Journal of Structural Geology, vol.15, issue.12, pp.1509-1512, 1993.
DOI : 10.1016/0191-8141(93)90010-8

J. Warren and P. Root, The Behavior of Naturally Fractured Reservoirs, Society of Petroleum Engineers Journal, vol.3, issue.03, pp.245-255, 1963.
DOI : 10.2118/426-PA

K. Weiler and P. Atherton, Hidden surface removal using polygon area sorting, Proceedings of the 4th annual conference on Computer graphics and interactive techniques, pp.214-222, 1977.
DOI : 10.1145/563858.563896
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.137.7161

A. Winberg, P. Andersson, J. Byegård, A. Poteri, V. Cvetkovic et al., Final report of the true block scale project, report 4, synthesis of flow, transport and retention in the block scale. skb technical report tr-02-16, On tire les coordonnées x i = U() × l et y i = U() × L avec U(, 2003.

. Avec-x-la-distance and . La-dimension-fractale, La direction prisè a chaque pas est arbitraire. La figure A.1 en donne une illustration

]. E. Bonnet, O. Bour, N. E. Odling, P. Davy, I. Main et al., Puis onenì eve la partie centrale, et on répète l'opération sur ces deux segments, et on réitère ce procédé indéfiniment (ou après un nombre d'itérations fixées pour une application pratique, voir figure A.2) Le sommet References Scaling of fracture systems in geological media Nested geological modelling of naturally fractured reservoirs Fractal and geostatistical methods for modeling of a fracture network Connectivity properties of two-dimensional fracture networks with stochastic fractal correlation Havana -a fault modeling tool, A.4Poussì ere de Cantor L'ensemble de Cantor est un processus ponctuel autosimilaire. On l'obtient en divisant un segment Hydrocarbon Seal Quantification, pp.347-383, 1988.

Y. Lin, S. Hu, and . Jenni, History matching of object-based stochastic reservoir models

L. Hu, Gradual deformation and iterative calibration of gaussian-related stochastic models, SPE Journal Mathematical Geology, vol.108, issue.3, pp.312-323, 2000.

S. Jenni, N. Metla, F. Delbos, S. D. Veiga, and D. Sinoquet, Calage de la géométrie des réseaux de fractures aux données hydrodynamiques de production d'un champ pétrolier Constrained nonlinear optimization for extreme scenarii evaluation in reservoir characterization, ECMOR European Conference on the Mathematics of Oil Recovery, pp.6-9, 1985.

D. Sinoquet and F. Delbos, Adapted nonlinear optimization method for production data and 4d seismic inversion [12] Marius Verscheure, André Fourno, and Jean-Paul Chilès. History matching of a realistic stochastic fault model using fractal geometry and the gradual deformation method, ECMOR European Conference on the Mathematics of Oil Recovery SPE EUROPEC/EAGE Annual Conference and Exhibition, pp.8-11, 2008.