Analysis and stochastic simulation of geometrical properties of conduits in karstic networks

Yves Frantz and Pauline Collon and Philippe Renard and Sophie Viseur. ( 2021 )
in: Geomorphology, 377 (107480)

Abstract

Despite intensive explorations by speleologists, karstic systems remain only partially described as many conduits are not accessible to humans. The classical exploration techniques produce sparse data, leading to various uncertainties about the conduit dimensions, essential parameters for flow simulations. Stochastic simulations offer a possibility to better assess these uncertainties. In this paper, we propose different methods to stochastically simulate the properties (size and shape anisotropy) of karstic conduits on already existing skeletons. These approaches, based on Sequential Gaussian Simulations (SGS), allow taking different conditioning data into account, while respecting the intricacy of the networks. To infer the input parameters, we perform a statistical study of the conduit dimensions of 49 explored karstic networks, focusing on their equivalent radius and width-height ratio. Thanks to the definition of 1D-curvilinear variograms, we demonstrate the existence of a spatial correlation along the networks, which is even higher when considering independently each conduit. Finally, using ad hoc algorithms implemented for computing both a conduit hierarchy inside karstic networks and a relative position regarding outputs, we find no evidence of an obvious link between these two entities and the studied metrics. The simulation methods are then demonstrated on the karstic network of Arrestelia (Pyrénées-Atlantiques, France), and show the consistency of the proposed approach with the observations made on the explored natural systems.

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BibTeX Reference

@ARTICLE{,
    author = { Frantz, Yves and Collon, Pauline and Renard, Philippe and Viseur, Sophie },
     title = { Analysis and stochastic simulation of geometrical properties of conduits in karstic networks },
   journal = { Geomorphology },
    volume = { 377 },
      year = { 2021 },
     pages = { 107480 },
       url = { https://hal.univ-lorraine.fr/hal-03117327 },
       doi = { 10.1016/j.geomorph.2020.107480 },
  abstract = { Despite intensive explorations by speleologists, karstic systems remain only partially described as many conduits are not accessible to humans. The classical exploration techniques produce sparse data, leading to various uncertainties about the conduit dimensions, essential parameters for flow simulations. Stochastic simulations offer a possibility to better assess these uncertainties. In this paper, we propose different methods to stochastically simulate the properties (size and shape anisotropy) of karstic conduits on already existing skeletons. These approaches, based on Sequential Gaussian Simulations (SGS), allow taking different conditioning data into account, while respecting the intricacy of the networks. To infer the input parameters, we perform a statistical study of the conduit dimensions of 49 explored karstic networks, focusing on their equivalent radius and width-height ratio. Thanks to the definition of 1D-curvilinear variograms, we demonstrate the existence of a spatial correlation along the networks, which is even higher when considering independently each conduit. Finally, using ad hoc algorithms implemented for computing both a conduit hierarchy inside karstic networks and a relative position regarding outputs, we find no evidence of an obvious link between these two entities and the studied metrics. The simulation methods are then demonstrated on the karstic network of Arrestelia (Pyrénées-Atlantiques, France), and show the consistency of the proposed approach with the observations made on the explored natural systems. }
}