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  • Publication
    Accès libre
    Analysis and stochastic simulation of geometrical properties of conduits in karstic networks
    (2020-11)
    Frantz, Yves
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    Collon, Pauline
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    Viseur, Sophie
    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.
  • Publication
    Accès libre
    A model ensemble generator to explore structural uncertainty in karst systems with unmapped conduits
    (2020-10)
    Fandel, Chloé
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    Férré, Ty
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    Chen, Zhao
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    ;
    Goldscheider, Nico
    Karst aquifers are characterized by high-conductivity conduits embedded in a low-conductivity fractured matrix, resulting in extreme heterogeneity and variable groundwater flow behavior. The conduit network controls groundwater flow, but is often unmapped, making it difficult to apply numerical models to predict system behavior. This paper presents a multi-model ensemble method to represent structural and conceptual uncertainty inherent in simulation of systems with limited spatial information, and to guide data collection. The study tests the new method by applying it to a well-mapped, geologically complex long-term study site: the Gottesacker alpine karst system (Austria/Germany). The ensemble generation process, linking existing tools, consists of three steps: creating 3D geologic models using GemPy (a Python package), generating multiple conduit networks constrained by the geology using the Stochastic Karst Simulator (a MATLAB script), and, finally, running multiple flow simulations through each network using the Storm Water Management Model (C-based software) to reject nonbehavioral models based on the fit of the simulated spring discharge to the observed discharge. This approach captures a diversity of plausible system configurations and behaviors using minimal initial data. The ensemble can then be used to explore the importance of hydraulic flow parameters, and to guide additional data collection. For the ensemble generated in this study, the network structure was more determinant of flow behavior than the hydraulic parameters, but multiple different structures yielded similar fits to the observed flow behavior. This suggests that while modeling multiple network structures is important, additional types of data are needed to discriminate between networks.
  • Publication
    Accès libre
    An optical laser device for mapping 3D geometry of underwater karst structures: first tests in the Ox Bel’Ha system, Yucatan, Mexico
    (2016)
    Schiller, A
    ;
    In the course of extended hydrological studies in the coastal Karst plain of Yucatan, near the town of Tulum amongst others, a novel laser scanning device was developed and applied for the acquisition of the 3d-geometry of ground water conduits. The method is derived from similar industrial systems and for the first time adapted to the specific measurement conditions in underwater cave systems. The device projects a laser line over the whole perimeter at a certain position. This line represents the intersection of a plane with the cave walls. The line is imaged with a wide angle camera system. Through proper design and calibration of the device it is possible to derive the true scale geometry of the perimeter via special image processing techniques. By acquiring regularly spaced images it is possible to reconstruct the true scale and 3 d-shape of a tunnel through the incorporation of location and attitude data. In a first test in the Ox Bel Ha under-water cave system, about 800 metres of tunnels have been scanned down to water depths of 20 metres. The raw data is further interpolated using the ODSIM-algorithm in order to delineate the 3D geometry of the cave system. The method provides easy, operable acquisition of the 3-D geometry of caves in clear water with superior resolution and speed and significantly facilitates the measurement in underwater tunnels as well as in dry tunnels. The data gathered represents crucial input to the study of the state, dynamics and genesis of the complex karst water regime., Durante el transcurso de intensivos estudios hidrológicos realizados en la llanura costera kárstica de Yucatán, cerca de la ciudad de Tulum entre otras, se desarrolló un novedoso dispositivo de escaneo láser, que se aplicó a la adquisición de la geometría 3D de conductos de agua subterránea. El método se deriva de sistemas industriales similares y que ha sido adaptado por primera vez a las condiciones de medición específicas de los sistemas de cuevas submarinas. El dispositivo proyecta una línea láser sobre todo el perímetro en una localización dada. Esta línea representa la intersección de un plano con las paredes de las cuevas. La línea es fotografiada con un sistema de cámara de gran angular. A través de un apropiado diseño y calibración del dispositivo es posible obtener la geometría verdadera del perímetro a través de técnicas especiales de procesamiento de imágenes. De este modo, adquiriendo regularmente imágenes a intervalos espaciados es posible reconstruir la escala verdadera y la forma 3D de un túnel con la incorporación de los datos de posición e inclinación. En una primera prueba en el sistema de la cueva submarina Ox Bel Ha, se escanearon alrededor de 800 metros de túneles hasta profundidades, bajo el agua, de 20 metros. Los datos en bruto son interpolados utilizando el algoritmo de ODSIM para delinear la geometría 3D del sistema de cuevas. El método proporciona una adquisición sencilla y operativa de la geometría tridimensional de cuevas submarinas con aguas claras, con muy buenas resolución y velocidad lo que facilita la medición en conductos submarinos así como en túneles subaéreos. Los datos recogidos representan una información fundamental para el estudio del estado, dinámica y génesis del complejo régimen del agua kárstica.
  • Publication
    Accès libre
    A pseudo-genetic stochastic model to generate karstic networks
    (2012) ; ;
    Jenni, Sandra
    In this paper, we present a methodology for the stochastic simulation of 3D karstic conduits accounting for conceptual knowledge about the speleogenesis processes and accounting for a wide variety of field measurements.
    The methodology consists of four main steps. First, a 3D geological model of the region is built. The second step consists in the stochastic modeling of the internal heterogeneity of the karst formations (e.g. initial fracturation, bedding planes, inception horizons, etc.). Then a study of the regional hydrology/hydrogeology is conducted to identify the potential inlets and outlets of the system, the base levels and the possibility of having different phases of karstification. The last step consists in generating the conduits in an iterative manner using a fast marching algorithm. In most of these steps, a probabilistic model can be used to represent the degree of knowledge available and the remaining uncertainty depending on the data at hand.
    The conduits are assumed to follow minimum effort paths in a heterogeneous medium from sinkholes or dolines toward springs. The search of the shortest path is performed using a fast marching algorithm. This process can be iterative, allowing to account for the presence of already simulated conduits and to produce a hierarchical network.
    The final result is a stochastic ensemble of 3D karst reservoir models that are all constrained by the regional geology, the local heterogeneities and the regional flow conditions. These networks can then be used to simulate flow and transport. Several levels of uncertainty can be considered (large scale geological structures, local heterogeneity, position of possible inlets and outlets, phases of karstification).
    Compared to other techniques, this method is fast, to account for the main factors controlling the 3D geometry of the network, and to allow conditioning from available field observations.
  • Publication
    Accès libre
    A method for the stochastic modeling of karstic systems accounting for geophysical data:: an example of application in the region of Tulum, Yucatan Peninsula (Mexico)
    Vuilleumier, Cécile
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    ; ;
    Ottowitz, David
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    Schiller, A.
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    Supper, Robert
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    The eastern coast of the Yucatan Peninsula, Mexico, contains one of the most developed karst systems in the world. This natural wonder is undergoing increasing pollution threat due to rapid economic development in the region of Tulum, together with a lack of wastewater treatment facilities. A preliminary numerical model has been developed to assess the vulnerability of the resource. Maps of explored caves have been completed using data from two airborne geophysical campaigns. These electromagnetic measurements allow for the mapping of unexplored karstic conduits. The completion of the network map is achieved through a stochastic pseudo-genetic karst simulator, previously developed but adapted as part of this study to account for the geophysical data. Together with the cave mapping by speleologists, the simulated networks are integrated into the finite-element flow-model mesh as pipe networks where turbulent flow is modeled. The calibration of the karstic network parameters (density, radius of the conduits) is conducted through a comparison with measured piezometric levels. Although the proposed model shows great uncertainty, it reproduces realistically the heterogeneous flow of the aquifer. Simulated velocities in conduits are greater than 1 cm s−1, suggesting that the reinjection of Tulum wastewater constitutes a pollution risk for the nearby ecosystems.