The hinge lines of non-cylindrical folds R.J. Lisle a, * , N. Toimil b , J. Aller b , N. Bobillo-Ares c , F. Bastida b a School of Earth and Ocean Sciences, Cardiff University, Cardiff CF10 3YE, UK b Departamento de Geologı ´a, Universidad de Oviedo, Spain c Departamento de Matema ´ticas, Universidad de Oviedo, Spain article info Article history: Received 4 February 2009 Received in revised form 6 October 2009 Accepted 31 October 2009 Available online 6 November 2009 Keywords: Fold analysis Differential geometry Hinge lines Ridge lines Deformation Curvature abstract Hinge lines are loci of high curvature points on folded surfaces. They are significant geometrical features of geological folds, and the arrangement of hinge lines constructed for the surface serves to characterize important aspects of the fold pattern. Since the current definition of hinge line is only appropriate for cylindrical folds, we propose a new definition for use with folds of general shape. Like the concept of ridge lines used in differential geometry, the new definition uses the lines of curvature (principal curvature trajectories) as a reference frame for comparing curvatures across the surface. A hinge line passes through points of extreme principal curvature magnitude observed along the corresponding principal curvature trajectory. Two types of hinge lines are defined and methods for constructing hinge lines are suggested. Ó 2009 Elsevier Ltd. All rights reserved. 1. Introduction Recently developed surveying methods allow the mapping of folded geological surfaces in three dimensions. 3D seismic reflection methods are employed to map subsurface structures, whereas GPS and laser scanning methods are being increasingly used to survey well-exposed structural surfaces (Bergbauer and Pollard, 2004; Pearce et al., 2006). Whilst these data provide the potential for gaining new insights concerning the process of folding (Pollard and Fletcher, 2005), they also highlight the inadequacy of a number of existing methods of geometrical analysis. The latter were mainly devised to cater for folds outcropping at the surface where information on the folded surface is little more than two-dimensional. New 3D methods for describing and analysing folded surfaces, founded on the concepts of differential geometry, are being devised to address the above problems (Pollard and Fletcher, 2005; Lisle and Toimil, 2007; Mynatt et al., 2007). For example, approaches have been proposed for dissecting a general folded surface into individual folds, and for distinguishing antiformal and synformal folds (Lisle and Toimil, 2007). Hinge lines, the subject of this paper, are key geometrical features of folds. The patterns of hinge lines are important in relation to the structural location of hydrocarbon fields (e.g. Al-Mahmoud et al., 2009), fracture prediction in hydrocarbon reservoirs (e.g. Stephenson et al., 2007), prediction of the direction of subsurface elongation of ore-bodies (e.g. Duuring et al., 2007), the analysis of structures produced by multiple folding events (Ramsay, 1967), and to folding processes in shear zones (Ghosh et al., 1999; Alsop and Carreras, 2007) or around diapirs (Jackson et al., 1990). In the present paper, we examine the existing definition of the hinge line. The term, hinge line, refers to the locus of points of maximum curvature on the folded surface (Fig. 1). Sets of hinge lines drawn on a folded surface serve to illustrate the folding pattern, refolded geometries, and relationships between different fold sets. However, we discover that the existing definition of hinge line is inadequate for general use, and therefore a new definition based on the concepts of differential geometry is proposed. In devising the new definition, our aim is to provide a conceptual framework for the practical construction of hinge lines on folded surfaces whilst honouring the essential meaning of the existing term. Fortunately, we have been assisted in our aims by current research in non-geological fields where it is found useful to draw feature lines along the main creases of a curved surface, and to use the pattern of such lines as ‘‘shape fingerprints’’ of the surface. For * Corresponding author. Fax: þ44 29 2087 4326. E-mail address: lisle@cardiff.ac.uk (R.J. Lisle). Contents lists available at ScienceDirect Journal of Structural Geology journal homepage: www.elsevier.com/locate/jsg 0191-8141/$ – see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.jsg.2009.10.011 Journal of Structural Geology 32 (2010) 166–171