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Fractal Geometry-Based Quantification of Shock-Induced Rock Fragmentation in and around an Impact Crater

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Abstract

Shock-induced fragmentation structures of basement rocks and their limestone cover in and around the Ries impact crater (Germany) were recorded on outcrop, hand sample, and thin-section scale, and quantified mainly by fractal geometry methods. Quantification was performed by automated procedures and in areas of square-centimetres to square-decametres with a maximum resolution of micrometre scale. In 2D and on all scales, the fragmentation structures form complex, statistically self-similar patterns (fractals) with specific characteristics: (i) The pattern fractality is scale-dependent. (ii) Three different power-law relationships exist, which reflect the effect of three fragmentation processes. (iii) The fracture patterns are anisotropic and inhomogeneous over larger areas. (iv) Complexity and anisotropy of the fracture patterns vary systematically. Such systematic variation appears typical for impact-related fragmentation.

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Acknowledgments

We are grateful to the colleagues from the Centre for Ries Crater Impact Research (ZERIN) in Nördlingen for providing core samples, to Mark Peternell for giving access to the map-counting and MORFA program system, and to Christian Stäb, Tim Yilmaz, Thomas Kenkmann, Alison Ord, and Tom Blenkinsop for helpful discussions. Reviews by Mark Peternell and an anonymous reviewer greatly improved the manuscript. We also express our gratitude to Namvar Jahanmehr and Klaus Mayer for sample and thin-section preparation. MD.S.H. gratefully acknowledges financial support by the German Academic Exchange Service DAAD (Grant A/11/75209).

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Authors and Affiliations

  1. Tectonics and Material Fabrics Section, Faculty of Civil, Geo and Environmental Engineering, Technical University Munich, 80333, Munich, Germany

    MD. Sakawat Hossain & Jörn H. Kruhl

  2. Department of Geological Sciences, Jahangirnagar University, 1342, Dhaka, Bangladesh

    MD. Sakawat Hossain

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  1. MD. Sakawat Hossain
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Correspondence to MD. Sakawat Hossain.

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24_2014_922_MOESM1_ESM.jpg

Supplementary material 1: Fig. 1 Illustrates the work steps undertaken from image acquisition to final processing by using different methods (JPEG 3598 kb)

24_2014_922_MOESM2_ESM.jpg

Supplementary material 2: Fig. 2 Variation of fractal box-counting dimension D 1 for 27 sub-sections along the section-1 (JPEG 1493 kb)

24_2014_922_MOESM3_ESM.jpg

Supplementary material 3: Fig. 3 Contour diagram of the 2D box-counting dimension using map-counting method applied to the fracture pattern of section-1. See text for description of the map-counting method. The contour color spectrum represents the intensity of inhomogeneity of the fracture pattern’s complexity in term of 2D box-counting dimension, with 1.1 = low complexity (light yellow) and 1.87 = high complexity (blue). Black lines are the original fractures superimposed on top of the contour diagram. Note: Very low D-value contour at the margin is the artifacts due to partial data fillings of the sub-image window (JPEG 7540 kb)

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Hossain, M.S., Kruhl, J.H. Fractal Geometry-Based Quantification of Shock-Induced Rock Fragmentation in and around an Impact Crater. Pure Appl. Geophys. 172, 2009–2023 (2015). https://doi.org/10.1007/s00024-014-0922-8

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  • DOI: https://doi.org/10.1007/s00024-014-0922-8

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