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. 2019 Jun 13;9:8603. doi: 10.1038/s41598-019-45057-7

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© The Author(s) 2019

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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The size range of potentially interconnected fractures are represented by the plateau stage of the curve, where present, for all the identified clusters of LEHAF (a). Where the slope breaks after the plateau the LEHAF distribution ceases to be fractal. The corresponding log(l) value represents the maximum thickness of the fractured medium that connects the surface to the subsurface (Uco). (b) The distribution of LEHAF compared to a Power Law (solid line) for values between Lco and Uco. The goodness of the Uco value picked in the previous graph is tested. A fractal distribution should follow a Power Law. Where data matches the solid line the distribution of LEHAF/fractures is fractal. l: fracture length [m]; C(l): correlation integral defines the correlation between point at a distance lower than l; Local Slope: represents the ΔLog (C(l))/ΔLog(l) ratio].