Intersecting kink bands quantified by laser scanning and differential geometry

Microtopography derived from laser scanning is expressed by DEMs that can be analyzed using differential geometry. We apply this technique to rock hand samples containing intersecting kink bands in order to quantitatively describe the shape of a folded surface and understand the localization of strain in deformed rocks. This study is the first to apply laser scanning and geometric curvature analysis to intersecting kink bands in order to better describe the variation of kink band geometries and intersections in plan view and to evaluate relationships between different kink band parameters. A complex set of monoclinal contractional kink bands is well exposed in outcrops of the Darrington Phyllite on Samish Island, northwestern Washington, which provide a three-dimensional view of kink band geometries. Kink bands in cross section have straight, parallel boundaries that deform a well-defined foliation; in plan view, however, kink band hinges curve and anastomose across the foliation surface, and adjacent bands commonly intersect. Three types of intersections are common: crossing (X), bifurcating (Y), and obliquely truncating (λ); many kink bands also taper out along strike. Geometric curvature analyses were performed on millimeter-resolution DEMs of hand samples containing intersecting kink bands. Maps of different curvature parameters (e.g. mean curvature, geologic curvature) clearly outline kink bands in the samples and illuminate the behavior of kink band hinges in each type of intersection. In X-type intersections, curvature increases where two hinges of similar kink sense cross (i.e. anticlinal/anticlinal hinges), increasing strain; where two hinges of opposing sense cross (anticlinal/synclinal), curvature decreases and the surface is effectively unfolded. In Y-type intersections, a single parent band widens and splits into two equally narrow daughter bands, and new inner hinges are nucleated below the bifurcation point. The two daughter bands accommodate similar shortening as the single parent band. In λ-type intersections, one hinge of a parent band sprouts a thin offshoot band that veers off at an oblique angle, while the parent band continues unchanged; this behavior is difficult to observe in the field and has not been previously described. Curvature data extracted from transects across samples show positive correlations among hinge curvature, band gradient, and rotation angle, suggesting that kink band hinges tighten as rotation progresses; however, despite qualitative interactions between closely spaced kink bands, there are no statistical correlations between kink band spacing and any other measured parameters. The curvature analysis presented here indicates that even small topographic features can be successfully characterized by differential geometry, and features such as kink bands and small folds can be distinguished from faults and fractures of the same scale. The observations presented here can be used to develop a model that explains the variation of kink bands on the foliation surface. These techniques also can be applied to broader scans of outcrops containing kink bands or other deformation features in order to more accurately map these structures.