Discrete-element modelling of detachment folding Stuart Hardy n and Emma Finchw n ICREA (Institucio¤ Catalana de Recerca i Estudis Avanc° ats) and GGAC, Facultat de Geologia, Universitat de Barcelona, Barcelona, Spain wBasin and Stratigraphic Studies Group, Department of Earth Sciences,The University of Manchester, Manchester, UK ABSTRACT A two-dimensional, discrete-element modelling technique is used to investigate the initiation and growth of detachment folds in sedimentary rocks above a weak de¤ collement level.The model depicts the sedimentary rocks as an assemblage of spheres that obey Newton’s equations of motion and that interact with elastic forces under the in£uence of gravity. Faulting or fracturing between neighbouring elements is represented by a transition from repulsive^attractive forces to solely repulsive forces.The sedimentary sequence is mechanically heterogeneous, consisting of intercalated layers of markedly di¡erent strengths and thicknesses.The interlayering of weak and strong layers within the sedimentary rocks promotes the localization of £exural £ow deformation within the weak layers. Even with simple displacement boundary conditions, and straightforward interlayering of weak and strong layers, the structural geometries that develop are complex, with a combination of box, lift-o¡ and disharmonic detachment fold styles forming above the de¤ collement. In detail, it is found that the modelled folds grow by both limb rotation and limb lengthening.The combination of these two mechanisms results in uplift patterns above the folds that are di⁄cult, or misleading, to interpret in terms of simple kinematic models. Comparison of modelling results with natural examples and with kinematic models highlights the complexities of structural interpretation in such settings. INTRODUCTION Detachment folding (or de¤ collement folding) is distinct from fault-bend or fault-propagation folding in that it is not necessarily associated with a ramp or a propagating fault tip (Jamison, 1987). Detachment folds are most com- monly found in mechanically layered stratigraphic se- quences, particularly where thick, competent units overlie an incompetent unit or de¤ collement (e.g. Poblet & Hardy, 1995; Anastasio et al., 1997; Homza & Wallace, 1997; Grando & McClay, 2004; Fig.1). Natural detachment folds are often classi¢ed into two geometric end members: dis- harmonic detachment folds and lift-o¡ folds. Disharmo- nic detachment folds exhibit parallel geometries in outer layers and disharmonic geometries in lower layers, whereas lift-o¡ folds exhibit tight isoclinal geometries of all layers and a weak lower unit in the core of the anticline (for a review, see Mitra, 2003). In recent years, there has been a plethora of publications on the subject of detach- ment folding (e.g. Hardy & Poblet, 1994; Epard & Groshong, 1995; Atkinson & Wallace, 2003; Mitra, 2003; Scharer et al., 2004; Wallace & Homza, 2004), and interest in such folds continues unabated. It is clear that under- standing the nature and development of such structures has important implications for hydrocarbon location (e.g. Poblet & McClay, 1996), evaluation of stratigraphic archi- tectures associated with fault-related folds (e.g. Poblet & Hardy, 1995; Castelltort et al., 2004) and for the estimation of shortening rates in sedimentary basins (e.g. Scharer et al., 2004). To better understand the development of detachment folds, numerical modelling of detachment fold kinematics has proven useful (e.g. Poblet & McClay, 1996; Mitra, 2003; Wallace & Homza, 2004). Many geometric models for de- tachment folds have been proposed, o¡ering a variety of explanations as to how the observed geometry (and uplift patterns) developed, based on kinematic constraints such as conservation of line length, bed thickness and cross- sectional area (e.g. Hardy & Poblet,1994; Homza & Wallace, 1995,1997; Mitra, 2003). Broadly, these models fall into two categories (and hybrids combining the two end members): their kinematics are either based on limb lengthening (through kink-band migration) or on limb rotation (Fig. 2). These geometric models have been applied to natural ex- amples to explain observed relationships between slip, up- lift, de¤ collement depth, pregrowth and growth stratal geometries (e.g. Rockwell et al., 1988; Hardy & Poblet, 1994; Poblet & McClay, 1996; Atkinson & Wallace, 2003; Grando & McClay, 2004; Scharer et al., 2004). Despite these studies, the evolution of these structures remains controversial, and in particular, the relative im- portance of limb rotation vs. limb lengthening during the development of the folds remains unanswered. In some Correspondence: Stuart Hardy, ICREA (Institucio¤ Catalana de Recerca i Estudis Avanc°ats) and GGAC, Facultat de Geologia, Universitat deBarcelona,c/Mart|¤ i Franque' s s/n,08028 Barcelona, Spain. E-mail: stuart.hardy@icrea.es Basin Research (2005) 17, 507–520, doi: 10.1111/j.1365-2117.2005.00280.x r 2005 The Authors. Journal compilation r 2005 Blackwell Publishing Ltd 507