Subnetworks of percolation backbones to model karst systems around Tulum, Mexico

Abstract

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Karstic caves, which play a key role in groundwater transport, are often organized as complex connected networks resulting from the dissolution of carbonate rocks. In this work, we propose a new model to describe and study the structures of the two largest submersed karst networks in the world. Both of these networks are located in the area of Tulum (Quintana Roo, Mexico). In a previous work cite{hendrick2016fractal} we showed that these networks behave asself-similar structures exhibiting well-defined scaling behaviours. In this paper, we suggest that these networks can be modeled using substructures of percolation clusters ($theta$-subnetworks) having similar structural behaviour (in terms of fractal dimension and conductivity exponent) to those observed in Tulum's karst networks. We show in addition that these $theta$-subnetworks correspond to structures that minimise a global function, where this global function includes energy dissipation by the viscous forces when water flows through the network, and the cost of network formation itself.

Keywords

• Percolation backbone
• Percolation model
• Optimal network
• Karst network
• Scaling behaviour