Articles | Volume 16, issue 11
https://doi.org/10.5194/se-16-1351-2025
© Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/se-16-1351-2025
© Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
12 Nov 2025
Research article |
| 12 Nov 2025
| 12 Nov 2025
An integrated workflow for parametrization of fracture network geometry in digital outcrop models
Stefano Casiraghi
CORRESPONDING AUTHOR
Dipartimento di Scienze dell'Ambiente e della Terra, Università degli Studi di Milano-Bicocca, Milan, 20126, Italy
Gabriele Benedetti
Dipartimento di Scienze dell'Ambiente e della Terra, Università degli Studi di Milano-Bicocca, Milan, 20126, Italy
Daniela Bertacchi
Dipartimento di Matematica e Applicazioni, Università degli Studi di Milano-Bicocca, Milan, 20125, Italy
Silvia Mittempergher
Dipartimento di Scienze dell'Ambiente e della Terra, Università degli Studi di Milano-Bicocca, Milan, 20126, Italy
Federico Agliardi
Dipartimento di Scienze dell'Ambiente e della Terra, Università degli Studi di Milano-Bicocca, Milan, 20126, Italy
Bruno Monopoli
LTS s.r.l., Treviso, 31020, Italy
Fabio La Valle
Eni S.p.A, Global Natural Resources, San Donato Milanese, Italy
Mattia Martinelli
Eni S.p.A, Global Natural Resources, San Donato Milanese, Italy
Francesco Bigoni
Eni S.p.A, Global Natural Resources, San Donato Milanese, Italy
Cristian Albertini
Eni S.p.A, Global Natural Resources, San Donato Milanese, Italy
Andrea Bistacchi
Dipartimento di Scienze dell'Ambiente e della Terra, Università degli Studi di Milano-Bicocca, Milan, 20126, Italy
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Cited articles
Ackermann, R. V. and Schlische, R. W.: Anticlustering of small normal faults around larger faults, Geology, 25, 1127–1130, https://doi.org/10.1130/0091-7613(1997)025<1127:AOSNFA>2.3.CO;2, 1997.
Agliardi, F., Zanchetta, S., and Crosta, G. B.: Fabric controls on the brittle failure of folded gneiss and schist, Tectonophysics, 637, 150–162, https://doi.org/10.1016/j.tecto.2014.10.006, 2014.
Agliardi, F., Dobbs, M. R., Zanchetta, S., and Vinciguerra, S.: Folded fabric tunes rock deformation and failure mode in the upper crust, Sci. Rep., 7, 15290, https://doi.org/10.1038/s41598-017-15523-1, 2017.
Akaike, H.: A new look at the statistical model identification, IEEE Trans. Autom. Control, 19, 716–723, https://doi.org/10.1109/TAC.1974.1100705, 1974.
Andrews, B. J., Roberts, J. J., Shipton, Z. K., Bigi, S., Tartarello, M. C., and Johnson, G.: How do we see fractures? Quantifying subjective bias in fracture data collection, Solid Earth, 10, 487–516, https://doi.org/10.5194/se-10-487-2019, 2019.
Antonellini, M., Cilona, A., Tondi, E., Zambrano, M., and Agosta, F.: Fluid flow numerical experiments of faulted porous carbonates, Northwest Sicily (Italy), Mar. Pet. Geol., 55, 186–201, https://doi.org/10.1016/j.marpetgeo.2013.12.003, 2014.
Baecher, G. B.: Progressively censored sampling of rock joint traces, J. Int. Assoc. Math. Geol., 12, 33–40, https://doi.org/10.1007/BF01039902, 1980.
Baecher, G. B. and Lanney, N. A.: Trace Length Biases in Joint Surveys, 19th US Symposium on Rock Mechanics (USRMS), AMRA-78-0080, 1978.
Barton, C. C., Hsieh, P. A., Angelier, J., Bergerat, F., Bouroz, C., Dettinger, M. D., and Weeks, E. P.: Physical and Hydrologic-Flow Properties of Fractures Las Vegas, Nevada – Zion Canyon, Utah – Grand Canyon, Arizona – Yucca Mountain, Nevada 20–24 July 1989, American Geophysical Union, Washington DC, https://doi.org/10.1029/FT385, 1989.
Bear, J.: Dynamics of Fluids in Porous Media, Soil Sci., 120, 162, ISBN 0-486-65675-6, 1975.
Bellian, J. A., Kerans, C., and Jennette, D. C.: Digital Outcrop Models: Applications of Terrestrial Scanning Lidar Technology in Stratigraphic Modeling, J. Sediment. Res., 75, 166–176, https://doi.org/10.2110/jsr.2005.013, 2005.
Benedetti, G.: gecos-lab/FracAbility: FracAbility: Python toolbox to analyse fracture networks for digitalized rock outcrops (v1.5.3), Zenodo [code], https://doi.org/10.5281/zenodo.14893964, 2025.
Benedetti, G., Casiraghi, S., Bertacchi, D., and Bistacchi, A.: Unbiased statistical length analysis of linear features: adapting survival analysis to geological applications, Solid Earth, 16, 367–390, https://doi.org/10.5194/se-16-367-2025, 2025.
Bisdom, K., Gauthier, B. D. M., Bertotti, G., and Hardebol, N. J.: Calibrating discrete fracture-network models with a carbonate three-dimensional outcrop fracture network: Implications for naturally fractured reservoir modeling, AAPG Bull., 98, 1351–1376, https://doi.org/10.1306/02031413060, 2014.
Bistacchi, A.: FracAttitude, Zenodo [code], https://doi.org/10.5281/zenodo.17492139, 2025a.
Bistacchi, A.: gecos-lab/DomStudioOrientation: DomStudioOrientation v2.0 (v2.0), Zenodo [code], https://doi.org/10.5281/zenodo.17486587, 2025b.
Bistacchi, A., Griffith, W. A., Smith, S. A. F., Di Toro, G., Jones, R., and Nielsen, S.: Fault Roughness at Seismogenic Depths from LIDAR and Photogrammetric Analysis, Pure Appl. Geophys., 168, 2345–2363, https://doi.org/10.1007/s00024-011-0301-7, 2011.
Bistacchi, A., Balsamo, F., Storti, F., Mozafari, M., Swennen, R., Solum, J., Tueckmantel, C., and Taberner, C.: Photogrammetric digital outcrop reconstruction, visualization with textured surfaces, and three-dimensional structural analysis and modeling: Innovative methodologies applied to fault-related dolomitization (Vajont Limestone, Southern Alps, Italy), Geosphere, 11, 2031–2048, https://doi.org/10.1130/GES01005.1, 2015.
Bistacchi, A., Mittempergher, S., Martinelli, M., and Storti, F.: On a new robust workflow for the statistical and spatial analysis of fracture data collected with scanlines (or the importance of stationarity), Solid Earth, 11, 2535–2547, https://doi.org/10.5194/se-11-2535-2020, 2020.
Bistacchi, A., Massironi, M., and Viseur, S. (Eds.): 3D Digital Geological Models: From Terrestrial Outcrops to Planetary Surfaces, 1st ed., Wiley, https://doi.org/10.1002/9781119313922, 2022a.
Bistacchi, A., Mittempergher, S., and Martinelli, M.: Digital Outcrop Model Reconstruction and Interpretation, in: 3D Digital Geological Models, edited by: Bistacchi, A., Massironi, M., and Viseur, S., Wiley, 11–32, https://doi.org/10.1002/9781119313922.ch2, 2022b.
Bonneau, F., Henrion, V., Caumon, G., Renard, P., and Sausse, J.: A methodology for pseudo-genetic stochastic modeling of discrete fracture networks, Comput. Geosci., 56, 12–22, https://doi.org/10.1016/j.cageo.2013.02.004, 2013.
Bonneau, F., Caumon, G., and Renard, P.: Impact of a stochastic sequential initiation of fractures on the spatial correlations and connectivity of discrete fracture networks, J. Geophys. Res. Solid Earth, 121, 5641–5658, https://doi.org/10.1002/2015JB012451, 2016.
Boro, H., Rosero, E., and Bertotti, G.: Fracture-network analysis of the Latemar Platform (northern Italy): integrating outcrop studies to constrain the hydraulic properties of fractures in reservoir models, Pet. Geosci., 20, 79–92, https://doi.org/10.1144/petgeo2013-007, 2014.
Borradaile, G.: Statistics of Earth Science Data, Springer Berlin Heidelberg, Berlin, Heidelberg, https://doi.org/10.1007/978-3-662-05223-5, 2003.
Burnham, K. P. and Anderson, D. R.: Multimodel Inference: Understanding AIC and BIC in Model Selection, Sociol. Methods Res., 33, 261–304, https://doi.org/10.1177/0049124104268644, 2004.
Candela, T., Renard, F., Klinger, Y., Mair, K., Schmittbuhl, J., and Brodsky, E. E.: Roughness of fault surfaces over nine decades of length scales, J. Geophys. Res. Solid Earth, 117, 2011JB009041, https://doi.org/10.1029/2011JB009041, 2012.
Casiraghi, S.: Pontrelli quarry dataset, Zenodo [data set], https://doi.org/10.5281/zenodo.17483588, 2025a.
Casiraghi, S.: FracAspect, Zenodo [code], https://doi.org/10.5281/zenodo.17492257, 2025b.
Casiraghi, S.: FracElementary, Zenodo [code], https://doi.org/10.5281/zenodo.17492055, 2025c.
Cherubini, C.: A Modeling Approach for the Study of Contamination in a Fractured Aquifer, Geotech. Geol. Eng., 26, 519–533, https://doi.org/10.1007/s10706-008-9186-3, 2008.
Davy, P., Le Goc, R., and Darcel, C.: A model of fracture nucleation, growth and arrest, and consequences for fracture density and scaling, J. Geophys. Res. Solid Earth, 118, 1393–1407, https://doi.org/10.1002/jgrb.50120, 2013.
Dershowitz, W. S. and Einstein, H. H.: Characterizing rock joint geometry with joint system models, Rock Mech. Rock Eng., 21, 21–51, https://doi.org/10.1007/BF01019674, 1988.
Dershowitz, W. S. and Herda, H. H.: Interpretation of fracture spacing and intensity, 33rd US Symposium on Rock Mechanics (USRMS), ARMA-92-0757, 1992.
Dewez, T. J. B., Girardeau-Montaut, D., Allanic, C., and Rohmer, J.: Facets: A cloudcompare plugin to extract geological planes from unstructured 3D point clouds, Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci., XLI-B5, 799–804, https://doi.org/10.5194/isprs-archives-XLI-B5-799-2016, 2016.
Eberhardt, E., Stead, D., and Coggan, J. S.: Numerical analysis of initiation and progressive failure in natural rock slopes – The 1991 Randa rockslide, Int. J. Rock Mech. Min. Sci., 41, 69–87, https://doi.org/10.1016/S1365-1609(03)00076-5, 2004.
Eppes, M. C., Rinehart, A., Aldred, J., Berberich, S., Dahlquist, M. P., Evans, S. G., Keanini, R., Laubach, S. E., Moser, F., Morovati, M., Porson, S., Rasmussen, M., and Shaanan, U.: Introducing standardized field methods for fracture-focused surface process research, Earth Surf. Dynam., 12, 35–66, https://doi.org/10.5194/esurf-12-35-2024, 2024.
Fisher, R.: Dispersion on a sphere, Proc. R. Soc. Lond., 217, 295–305, 1953.
Fisher, R. A.: Statistical Methods, Experimental Design, and Scientific Inference, edited by: Bennett, J. H., Oxford University Press, https://doi.org/10.1093/oso/9780198522294.001.0001, 1990.
Fisher, R. A.: Statistical Methods for Research Workers, in: Breakthroughs in Statistics: Methodology and Distribution, edited by: Kotz, S. and Johnson, N. L., Springer, New York, NY, 66–70, https://doi.org/10.1007/978-1-4612-4380-9_6, 1992.
Fisher, N. I. and Best, D. J.: Goodness-of-Fit Tests For Fisher's Distribution On The Sphere, Aust. J. Stat., 26, 142–150, https://doi.org/10.1111/j.1467-842X.1984.tb01228.x, 1984.
Follin, S., Hartley, L., Rhén, I., Jackson, P., Joyce, S., Roberts, D., and Swift, B.: A methodology to constrain the parameters of a hydrogeological discrete fracture network model for sparsely fractured crystalline rock, exemplified by data from the proposed high-level nuclear waste repository site at Forsmark, Sweden, Hydrogeol. J., 22, 313–331, https://doi.org/10.1007/s10040-013-1080-2, 2014.
Forstner, S. R. and Laubach, S. E.: Scale-dependent fracture networks, J. Struct. Geol., 165, 104748, https://doi.org/10.1016/j.jsg.2022.104748, 2022.
Forstner, S. R., Corrêa, R., Wang, Q., and Laubach, S. E.: Fracture length data for geothermal applications, Energy Geosci. Conf. Ser., 1, egc1-2024-17, https://doi.org/10.1144/egc1-2024-17, 2025.
Franzosi, F., Casiraghi, S., Colombo, R., Crippa, C., and Agliardi, F.: Quantitative Evaluation of the Fracturing State of Crystalline Rocks Using Infrared Thermography, Rock Mech. Rock Eng., 56, 6337–6355, https://doi.org/10.1007/s00603-023-03389-x, 2023a.
Franzosi, F., Crippa, C., Derron, M.-H., Jaboyedoff, M., and Agliardi, F.: Slope-Scale Remote Mapping of Rock Mass Fracturing by Modeling Cooling Trends Derived from Infrared Thermography, Remote Sens., 15, 4525, https://doi.org/10.3390/rs15184525, 2023b.
Gigli, G. and Casagli, N.: Semi-automatic extraction of rock mass structural data from high resolution LIDAR point clouds, Int. J. Rock Mech. Min. Sci., 48, 187–198, https://doi.org/10.1016/j.ijrmms.2010.11.009, 2011.
Gilitschenski, I., Kurz, G., Julier, S. J., and Hanebeck, U. D.: Unscented Orientation Estimation Based on the Bingham Distribution, IEEE Trans. Autom. Control, 61, 172–177, https://doi.org/10.1109/TAC.2015.2423831, 2016.
Giuffrida, A., Agosta, F., Rustichelli, A., Panza, E., La Bruna, V., Eriksson, M., Torrieri, S., and Giorgioni, M.: Fracture stratigraphy and DFN modelling of tight carbonates, the case study of the Lower Cretaceous carbonates exposed at the Monte Alpi (Basilicata, Italy), Mar. Pet. Geol., 112, 104045, https://doi.org/10.1016/j.marpetgeo.2019.104045, 2020.
Hadgu, T., Karra, S., Kalinina, E., Makedonska, N., Hyman, J. D., Klise, K., Viswanathan, H. S., and Wang, Y.: A comparative study of discrete fracture network and equivalent continuum models for simulating flow and transport in the far field of a hypothetical nuclear waste repository in crystalline host rock, J. Hydrol., 553, 59–70, https://doi.org/10.1016/j.jhydrol.2017.07.046, 2017.
Hancock, P. L.: Brittle microtectonics: principles and practice, J. Struct. Geol., 7, 437–457, https://doi.org/10.1016/0191-8141(85)90048-3, 1985.
Haridy, M. G., Sedighi, F., Ghahri, P., Ussenova, K., and Zhiyenkulov, M.: Comprehensive Study of the Oda Corrected Permeability Upscaling Method, in: Day 2 Wed, 30 October 2019, SPE/IATMI Asia Pacific Oil and Gas Conference and Exhibition, Bali, Indonesia, D022S006R006, https://doi.org/10.2118/196399-MS, 2020.
Healy, D., Rizzo, R. E., Cornwell, D. G., Farrell, N. J. C., Watkins, H., Timms, N. E., Gomez-Rivas, E., and Smith, M.: FracPaQ: A MATLAB™ toolbox for the quantification of fracture patterns, J. Struct. Geol., 95, 1–16, https://doi.org/10.1016/j.jsg.2016.12.003, 2017.
Hooker, J. N., Laubach, S. E., and Marrett, R.: Fracture-aperture size—frequency, spatial distribution, and growth processes in strata-bounded and non-strata-bounded fractures, Cambrian Mesón Group, NW Argentina, J. Struct. Geol., 54, 54–71, https://doi.org/10.1016/j.jsg.2013.06.011, 2013.
Kaplan, E. L. and Meier, P.: Nonparametric Estimation from Incomplete Observations, J. Am. Stat. Assoc., 53, 457–481, https://doi.org/10.1080/01621459.1958.10501452, 1958.
Kaufman, L. and Rousseeuw, P. J.: Finding groups in data: an introduction to cluster analysis, Wiley, Hoboken, NJ, 342 pp., ISBN 0-471-73578-7, 2005.
Kent, J. T.: The Fisher-Bingham Distribution on the Sphere, J. R. Stat. Soc. Ser. B Methodol., 44, 71–80, https://doi.org/10.1111/j.2517-6161.1982.tb01189.x, 1982.
Kulatilake, P. H. S. W. and Wu, T. H.: Estimation of mean trace length of discontinuities, Rock Mech. Rock Eng., 17, 215–232, https://doi.org/10.1007/BF01032335, 1984.
Kurz, G., Gilitschenski, I., Julier, S., and Hanebeck, U. D.: Recursive Bingham Filter for Directional Estimation Involving 180 Degree Symmetry, J. Adv. Inf. Fusion, 9, 2014.
Laubach, S. E., Lander, R. H., Criscenti, L. J., Anovitz, L. M., Urai, J. L., Pollyea, R. M., Hooker, J. N., Narr, W., Evans, M. A., Kerisit, S. N., Olson, J. E., Dewers, T., Fisher, D., Bodnar, R., Evans, B., Dove, P., Bonnell, L. M., Marder, M. P., and Pyrak-Nolte, L.: The Role of Chemistry in Fracture Pattern Development and Opportunities to Advance Interpretations of Geological Materials, Rev. Geophys., 57, 1065–1111, https://doi.org/10.1029/2019RG000671, 2019.
Lawless, J. F.: Statistical Models and Methods for Lifetime Data, John Wiley & Sons, 662 pp., ISBN 0.471-37215-3, 2011.
Leung, K.-M., Elashoff, R. M., and Afifi, A. A.: Censoring Issues in Survival Analysis, Annu. Rev. Public Health, 18, 83–104, https://doi.org/10.1146/annurev.publhealth.18.1.83, 1997.
Lewis, T. and Fisher, N. I.: Graphical methods for investigating the fit of a Fisher distribution to spherical data, Geophys. J. Int., 69, 1–13, https://doi.org/10.1111/j.1365-246X.1982.tb04931.x, 1982.
Mandl, G.: Rock Joints, Springer-Verlag, Berlin/Heidelberg, https://doi.org/10.1007/b137623, 2005.
Manzocchi, T.: The connectivity of two-dimensional networks of spatially correlated fractures, Water Resour. Res., 38, 1-1–1-20, https://doi.org/10.1029/2000WR000180, 2002.
March, R., Elder, H., Doster, F., and Geiger, S.: Accurate Dual-Porosity Modeling of CO2 Storage in Fractured Reservoirs, in: Day 3 Wed, 22 February 2017, SPE Reservoir Simulation Conference, Montgomery, Texas, USA, D031S012R004, https://doi.org/10.2118/182646-MS, 2017.
Mardia, K. V. and Jupp, P. E.: Directional statistics, J. Wiley, Chichester, New York, 429 pp., https://doi.org/10.1002/9780470316979, 2000.
Martinelli, M., Bistacchi, A., Mittempergher, S., Bonneau, F., Balsamo, F., Caumon, G., and Meda, M.: Damage zone characterization combining scan-line and scan-area analysis on a km-scale Digital Outcrop Model: The Qala Fault (Gozo), J. Struct. Geol., 140, 104144, https://doi.org/10.1016/j.jsg.2020.104144, 2020.
Mauldon, M.: Estimating Mean Fracture Trace Length and Density from Observations in Convex Windows, Rock Mech. Rock Eng., 31, 201–216, https://doi.org/10.1007/s006030050021, 1998.
Mauldon, M., Dunne, W. M., and Rohrbaugh, M. B.: Circular scanlines and circular windows: new tools for characterizing the geometry of fracture traces, J. Struct. Geol., 23, 247–258, https://doi.org/10.1016/S0191-8141(00)00094-8, 2001.
Medici, G., Munn, J. D., and Parker, B. L.: Delineating aquitard characteristics within a Silurian dolostone aquifer using high-density hydraulic head and fracture datasets, Hydrogeol. J., 32, 1663–1691, https://doi.org/10.1007/s10040-024-02824-9, 2024.
Menegoni, N., Giordan, D., Perotti, C., and Tannant, D. D.: Detection and geometric characterization of rock mass discontinuities using a 3D high-resolution digital outcrop model generated from RPAS imagery – Ormea rock slope, Italy, Eng. Geol., 252, 145–163, https://doi.org/10.1016/j.enggeo.2019.02.028, 2019.
Moder, K.: Alternatives to F-Test in One Way ANOVA in case of heterogeneity of variances (a simulation study), Psychological Test and Assessment Modeling, 52, 343–353, 2010.
Nicosia, U., Marino, M., Mariotti, N., Muraro, C., Panigutti, S., Petti, F. M., and Sacchi, E.: The Late Cretaceus dinosaur tracksite near Altamura (Bari, Southern Italy), Geol. Romana, 35, 237–247, 1999.
Nyberg, B., Nixon, C. W., and Sanderson, D. J.: NetworkGT: A GIS tool for geometric and topological analysis of two-dimensional fracture networks, Geosphere, 14, 1618–1634, https://doi.org/10.1130/GES01595.1, 2018.
Odling, N. E.: Scaling and connectivity of joint systems in sandstones from western Norway, J. Struct. Geol., 19, 1257–1271, https://doi.org/10.1016/S0191-8141(97)00041-2, 1997.
Odling, N. E., Gillespie, P., Bourgine, B., Castaing, C., Chiles, J.-P., Christensen, N. P., Fillion, E., Genter, A., Olsen, C., Thrane, L., Trice, R., Aarseth, E., Walsh, J. J., and Watterson, J.: Variations in fracture system geometry and their implications for fluid flow in fractured hydrocarbon reservoirs, Pet. Geosci., 5, 373–384, https://doi.org/10.1144/petgeo.5.4.373, 1999.
Ortega, O. and Marrett, R.: Prediction of macrofracture properties using microfracture information, Mesaverde Group sandstones, San Juan basin, New Mexico, J. Struct. Geol., 22, 571–588, https://doi.org/10.1016/S0191-8141(99)00186-8, 2000.
Ortega, O. J., Marrett, R. A., and Laubach, S. E.: A scale-independent approach to fracture intensity and average spacing measurement, AAPG Bull., 90, 193–208, https://doi.org/10.1306/08250505059, 2006.
Pahl, P. J.: Estimating the Mean Length of Discontinuity Traces, Int. J. Rock Mech. Min. Sci. Geomech., 18, 221–228, 1981.
Panara, Y., Menegoni, N., Finkbeiner, T., Zühlke, R., and Vahrenkamp, V.: High-resolution analysis of 3D fracture networks from Digital Outcrop Models, correlation to plate-tectonic events and calibration of subsurface models (Jurassic, Arabian Plate), Mar. Pet. Geol., 167, 106998, https://doi.org/10.1016/j.marpetgeo.2024.106998, 2024.
Panza, E., Berto, C., Luzi, E., Agosta, F., Zambrano, M., Tondi, E., Prosser, G., Giorgioni, M., and Janiseck, J. M.: Structural architecture and Discrete Fracture Network modelling of layered fractured carbonates (Altamura Fm., Italy), Ital. J. Geosci., 134, 409–422, https://doi.org/10.3301/IJG.2014.28, 2015.
Panza, E., Agosta, F., Rustichelli, A., Zambrano, M., Tondi, E., Prosser, G., Giorgioni, M., and Janiseck, J. M.: Fracture stratigraphy and fluid flow properties of shallow-water, tight carbonates: The case study of the Murge Plateau (southern Italy), Mar. Pet. Geol., 73, 350–370, https://doi.org/10.1016/j.marpetgeo.2016.03.022, 2016.
Panza, E., Agosta, F., Rustichelli, A., Vinciguerra, S. C., Ougier-Simonin, A., Dobbs, M., and Prosser, G.: Meso-to-microscale fracture porosity in tight limestones, results of an integrated field and laboratory study, Mar. Pet. Geol., 103, 581–595, https://doi.org/10.1016/j.marpetgeo.2019.01.043, 2019.
Renshaw, C. E.: Influence of subcritical fracture growth on the connectivity of fracture networks, Water Resour. Res., 32, 1519–1530, https://doi.org/10.1029/96WR00711, 1996.
Riquelme, A. J., Abellán, A., Tomás, R., and Jaboyedoff, M.: A new approach for semi-automatic rock mass joints recognition from 3D point clouds, Comput. Geosci., 68, 38–52, https://doi.org/10.1016/j.cageo.2014.03.014, 2014.
Riquelme, A. J., Abellán, A., and Tomás, R.: Discontinuity spacing analysis in rock masses using 3D point clouds, Eng. Geol., 195, 185–195, https://doi.org/10.1016/j.enggeo.2015.06.009, 2015.
Rohrbaugh Jr., M. B., Dunne, W. M., and Mauldon, M.: Estimating fracture trace intensity, density, and mean length using circular scan lines and windows, AAPG Bull., 86, https://doi.org/10.1306/61EEDE0E-173E-11D7-8645000102C1865D, 2002.
Sanderson, D. J. and Nixon, C. W.: The use of topology in fracture network characterization, J. Struct. Geol., 72, 55–66, https://doi.org/10.1016/j.jsg.2015.01.005, 2015.
Sanderson, D. J., Peacock, D. C. P., Nixon, C. W., and Rotevatn, A.: Graph theory and the analysis of fracture networks, J. Struct. Geol., 125, https://doi.org/10.1016/j.jsg.2018.04.011, 2019.
Schultz, R. A.: Geologic Fracture Mechanics, https://doi.org/10.1017/9781316996737, 2019.
Schultz, R. A. and Fossen, H.: Displacement–length scaling in three dimensions: the importance of aspect ratio and application to deformation bands, J. Struct. Geol., 24, 1389–1411, https://doi.org/10.1016/S0191-8141(01)00146-8, 2002.
Sethian, J. A.: Fast Marching Methods, SIAM Rev., 41, 199–235, https://doi.org/10.1137/S0036144598347059, 1999.
Shakiba, M., Lake, L. W., Gale, J. F. W., Laubach, S. E., and Pyrcz, M. J.: Stochastic reconstruction of fracture network pattern using spatial point processes, Geoenergy Sci. Eng., 236, 212741, https://doi.org/10.1016/j.geoen.2024.212741, 2024.
Smeraglia, L., Mercuri, M., Tavani, S., Pignalosa, A., Kettermann, M., Billi, A., and Carminati, E.: 3D Discrete Fracture Network (DFN) models of damage zone fluid corridors within a reservoir-scale normal fault in carbonates: Multiscale approach using field data and UAV imagery, Mar. Pet. Geol., 126, 104902, https://doi.org/10.1016/j.marpetgeo.2021.104902, 2021.
Smith, S. A. F., Bistacchi, A., Mitchell, T. M., Mittempergher, S., and Di Toro, G.: The structure of an exhumed intraplate seismogenic fault in crystalline basement, Tectonophysics, 599, 29–44, https://doi.org/10.1016/j.tecto.2013.03.031, 2013.
Stahle, L. and Wold, S.: Analysis of variance (ANOVA), Chemom. Intell. Lab. Syst., 6, 259–272, https://doi.org/10.1016/0169-7439(89)80095-4, 1989.
Stephens, M. A.: EDF Statistics for Goodness of Fit and Some Comparisons, J. Am. Stat. Assoc., 69, 730–737, https://doi.org/10.1080/01621459.1974.10480196, 1974.
Storti, F., Bistacchi, A., Borsani, A., Balsamo, F., Fetter, M., and Ogata, K.: Spatial and spacing distribution of joints at (over-) saturation in the turbidite sandstones of the Marnoso-Arenacea Fm. (Northern Apennines, Italy), J. Struct. Geol., 156, 104551, https://doi.org/10.1016/j.jsg.2022.104551, 2022.
Sturzenegger, M. and Stead, D.: Close-range terrestrial digital photogrammetry and terrestrial laser scanning for discontinuity characterization on rock cuts, Eng. Geol., 106, 163–182, https://doi.org/10.1016/j.enggeo.2009.03.004, 2009.
Sturzenegger, M., Stead, D., and Elmo, D.: Terrestrial remote sensing-based estimation of mean trace length, trace intensity and block size/shape, Eng. Geol., 119, 96–111, https://doi.org/10.1016/j.enggeo.2011.02.005, 2011.
Tavani, S., Granado, P., Corradetti, A., Girundo, M., Iannace, A., Arbués, P., Muñoz, J. A., and Mazzoli, S.: Building a virtual outcrop, extracting geological information from it, and sharing the results in Google Earth via OpenPlot and Photoscan: An example from the Khaviz Anticline (Iran), Comput. Geosci., 63, 44–53, https://doi.org/10.1016/j.cageo.2013.10.013, 2014.
Terzaghi, R. D.: Sources of Error in Joint Surveys, Géotechnique, 15, 287–304, https://doi.org/10.1680/geot.1965.15.3.287, 1965.
Thiele, S. T., Grose, L., Samsu, A., Micklethwaite, S., Vollgger, S. A., and Cruden, A. R.: Rapid, semi-automatic fracture and contact mapping for point clouds, images and geophysical data, Solid Earth, 8, 1241–1253, https://doi.org/10.5194/se-8-1241-2017, 2017
Tukey, J. W.: Exploratory Data Analysis, Addison-Wesley Publ. Co. Read., https://doi.org/10.1002/bimj.4710230408, 1977.
Wallace, R. L., Cai, Z., Zhang, H., Zhang, K., and Guo, C.: Utility-scale subsurface hydrogen storage: UK perspectives and technology, Int. J. Hydrog. Energy, 46, 25137–25159, https://doi.org/10.1016/j.ijhydene.2021.05.034, 2021.
Wang, Y., Vuik, C., and Hajibeygi, H.: CO2 Storage in deep saline aquifers: impacts of fractures on hydrodynamic trapping, Int. J. Greenh. Gas Control, 113, 103552, https://doi.org/10.1016/j.ijggc.2021.103552, 2022.
Warburton, P. M.: A stereological interpretation of joint trace data, Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 17, 181–190, https://doi.org/10.1016/0148-9062(80)91084-0, 1980.
Warren, J. E. and Root, P. J.: The Behavior of Naturally Fractured Reservoirs, Soc. Pet. Eng. J., 3, 245–255, https://doi.org/10.2118/426-PA, 1963.
Yamaji, A.: Genetic algorithm for fitting a mixed Bingham distribution to 3D orientations: a tool for the statistical and paleostress analyses of fracture orientations, Isl. Arc, 25, 72–83, https://doi.org/10.1111/iar.12135, 2016.
Zambrano, M., Tondi, E., Korneva, I., Panza, E., Agosta, F., Janiseck, J. M., and Giorgioni, M.: Fracture properties analysis and discrete fracture network modelling of faulted tight limestones, Murge Plateau, Italy, Ital. J. Geosci., 135, 55–67, https://doi.org/10.3301/IJG.2014.42, 2016.
Zeeb, C., Gomez-Rivas, E., Bons, P. D., and Blum, P.: Evaluation of sampling methods for fracture network characterization using outcrops, AAPG Bull., 97, 1545–1566, https://doi.org/10.1306/02131312042, 2013.
Zhang, L. and Einstein, H. H.: Estimating the Mean Trace Length of Rock Discontinuities, Rock Mech. Rock Eng., 31, 217–235, https://doi.org/10.1007/s006030050022, 1998.
Zhang, L., Einstein, H. H., and Dershowitz, W. S.: Stereological relationship between trace length and size distribution of elliptical discontinuities, Géotechnique, 52, 419–433, https://doi.org/10.1680/geot.2002.52.6.419, 2002.
Short summary
Traditional methods for investigating the subsurface cannot properly investigate fractures between 1m and 100–200m. Digital outcrop models (DOMs) provide a framework for the collection of extensive datasets in outcrop analogues. Here we present a workflow, with a solid statistical foundation, to collect a suite of statistical parameters to be used as input in current stochastic 3D Discrete Fracture Network models, including best practices for an optimal outcrop selection and data acquisition.
Traditional methods for investigating the subsurface cannot properly investigate fractures...
