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Non-uniform B-spline curve analyses of sigmoid brittle shear P- and ductile shear S-planes

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Abstract

Ideal morphologic representation of geologic structures using standard curves/surfaces can have far-reaching implications in estimating resources. From NW Lesser Himalaya (Uttarakhand state, India), field photographs of fully developed sigmoid-shaped brittle shear P- and ductile shear S- planes that crop out on the NW–SE (sub)vertical natural sections of rocks are matched by drawing curves using the B-spline tool in Rhinoceros software 5 SR service in 2D. These curves are advantageous to handle since the user can control their degrees, the control points are not the deciding factors, and that local modifications in shapes are permitted, unlike the Bézier curves. Sigmoid shapes are analyzed in detail using six shape parameters (lengths in between control points: L1, L2 and L3; angles in between control points: α1, α2 and α3). Good correlations between L3 vs. L1, L2 vs. L3 and L1 vs. L2 reveal the relation between wavelength (λ) and amplitude of the sigmoids that are classified into four types. Strong correlation between α2 vs. α3 and (α3−α1) vs. (α1− α2) suggest only the Type I, II and III sigmoids possess 180° rotational symmetry. Regression models (R2 values) demonstrate that the sigmoid geometries are governed by (1) pre-existing or co-evolving regional structures and (2) lithologic composition.

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taken from Bose and Mukherjee (2019a)

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Acknowledgements

Part of the Ph.D. thesis of TB (Biswas, submitted). Research Progress Committee members Profs. G.N. Jadhav and P. Naraga (IIT Bombay) raised many useful comments. Fieldwork was conducted with IIT Bombay’s CPDA grant provided to SM. Narayan Bose (IIT Kharagpur) assisted in fieldwork. Wolf-Christian Dullo (Chief Editor), Associate Editor, and the Managing Editor (Monika Dullo) are thanked. Lucie Novakova (reviewer) and an anonymous reviewer provided detail critical comments in three rounds.

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  1. Department of Earth Sciences, Indian Institute of Technology Bombay, Powai, Mumbai, 400 076, Maharashtra, India

    Tuhin Biswas & Soumyajit Mukherjee

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  1. Tuhin Biswas
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Correspondence to Soumyajit Mukherjee.

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Appendix 1

Appendix 1

Pre-existing regional structures distribute and orient subsequent structures (Misra and Mukherjee 2015; Fossen et al. 2017). For example, taper geometry of the sediment pile, litho-tectonic stratigraphy and overall margin of the shelf influenced the fold-thrust belt in the Cordilleran sedimentary basin (Mitra 1997). Earlier developed compressional structures in the Alpine Corsica affected the geometry of later developed extensional structures (Jolivet et al. 1991).

Balda et al. (1995) argued orogen-parallel deformation (extension) to be a syn-collisional product as documented form the Variscan Belt. In the Western Coast Belt, orogen-perpendicular shortening shares syn-kinematic relationship with orogen-parallel extension recorded from conjugate shear during the mid-Cretaceous (Angen et al. 2014).

These ideas from other orogens lead us to evaluate the possibility of impact of regional structures (e.g., Munsuari Thrust, Berinag Thrust, Singuini Thrust, Dharasu Thrust, Tons Thrust, Basul Thrust, Deosari syncline, Aglar Thrust, Mussoorie syncline, Kathu-ki-chail Thrust, Main Boundary Thrust) over the geometries of the smaller scale P- and S- shear planes.

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Biswas, T., Mukherjee, S. Non-uniform B-spline curve analyses of sigmoid brittle shear P- and ductile shear S-planes. Int J Earth Sci (Geol Rundsch) 111, 929–948 (2022). https://doi.org/10.1007/s00531-022-02159-4

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