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

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: L 1 , L 2 and L 3 ; angles in between control points: α 1 , α 2 and α 3 ). Good correlations between L 3 vs. L 1 , L 2 vs. L 3 and L 1 vs. L 2 reveal the relation between wavelength ( λ ) and amplitude of the sigmoids that are classified into four types . Strong correlation between α 2 vs. α 3 and ( α 3 −α 1 ) vs. ( α 1 − α 2 ) suggest only the Type I, II and III sigmoids possess 180° rotational symmetry. Regression models ( R 2 values) demonstrate that the sigmoid geometries are governed by (1) pre-existing or co-evolving regional structures and (2) lithologic composition.