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_Journal of Structural Geology 32 (2010) 1466-1475_ Contents lists available at ScienceDirect Journal of Structural Geology journal homepage: www.elsevier.com/locate/jsg Insights into fold growth using fold-related joint patterns and mechanical stratigraphy Heather M. Savage a,*, J. Ryan Shackleton b, Michele L. Cooke b, Jeffrey J. Riedel c Lamont-Doherty Earth Observatory, Columbia University, Palisades, NY 10964, USA b University of Massachusetts, Amherst, 611 North Pleasant St., Amherst, MA 01003-9297, USA c 2907 Secor Avenue, Bozeman, MT 59715, USA Article info Article history: Received 5 April 2010 Received in revised form 30 August 2010 Accepted 10 September 2010 Available online 17 September 2010 Keywords: Sheep Mountain Anticline Joint pattern Mechanical stratigraphy Plate bending Abstract Despite how common folds are as structural features, along-strike fold propagation has proven elusive to document. However, if a fold grows laterally along its axis, early-formed fold-related joints may differ significantly in orientation from joints that form later. In this paper, we integrate mechanical stratigraphy with joint pattern analysis to determine relative timing of jointing. Additionally, we demonstrate that joint patterns can be related to stresses on both the top and bottom of the bed during flexure. We present joint data from eight sedimentary beds on the fold terminus at Sheep Mountain Anticline, Wyoming, USA. The joint patterns around the terminus show two distinct patterns: joints in six of the beds show a radial pattern around the terminus whereas joint patterns in the two remaining beds differ from proximal units, despite being in the same structural position. Fracture resistance calculations confirm that the beds with mis-oriented fractures are less resistant to fracturing than other units in the study, and therefore would have fractured earlier in fold growth history. We present a plate bending model that illustrates potential joint patterns around a plunging fold nose from stresses along both the top and bottom of the bed. The joint strike predictions for the area in front of the inflection line on the fold nose match the orientations in our less resistant beds, which are now positioned behind the inflection line, suggesting that the fold grew laterally. The combined analysis of fracture pattern and mechanical stratigraphy provides a new way to investigate fold evolution. © 2010 Elsevier Ltd. All rights reserved. 1. Introduction Folds are ubiquitous deformational structures, found in every tectonic setting, with economic impacts in both oil exploration and mining. Understanding the formation and growth of these structures will illuminate how progressive deformation is achieved; however, direct observations of active folding are elusive. Active folding is assumed to be largely aseismic (Scholz, 2002), with some notable exceptions like the 1983 Coalinga earthquake (Stein and King, 1984), and GPS velocities attribute 100% of the observed deformation to fault slip. Nevertheless, the omnipresence of folding within all deformational settings speaks to the role that this inelastic process must play in accommodating deformation during or between earthquakes. Past growth of folds along their strike has been observed in the field through quartz deformation lamellae (e.g., Pavlis and Bruhn, 1988) as well as through geomorphic indicators (e.g., Jackson et al., 1996; Keller et al., 1999). Fischer and Wilkerson (2000) used kinematic models to demonstrate how fold-related jointing may record fold growth. The key region for unraveling the evolution of folding is at fold terminations where material is incorporated into the fold structure. These inherently three-dimensional regions must be carefully investigated with attention to temporal and spatial variations in fold shape as well as variations in stratigraphy. Here we further explore the relationship between fold growth and joint orientation, by considering the mechanical properties of different layers to provide a relative timescale of fracturing at Sheep Mountain Anticline, WY, USA. Furthermore, we consider stresses on the bottom as well as the top of a folded layer and compare these patterns to observed joint patterns. Natural fractures are extremely common in folded sedimentary strata (e.g., Nelson, 1985). When bending stresses dominate, fold-related joints initiate along the outer arc of the fold where tangential longitudinal stresses are effectively tensile (e.g., Price and Cosgrove, 1990; Fig. 1A). These joints develop perpendicular to the direction of maximum curvature, which produces fractures that form a radial fanning pattern in map view around fold terminations. H.M. Savage et al. Journal of Structural Geology 32 (2010) 1466-1475 Fig. 1. A) Cross-section of a convex upwards fold. Tangential longitudinal stresses are greater for thicker beds and are maximum at the upper bed surface. B) Map view of plunging fold termination (gray structure contours) with joint strike orientation (black dashes) as predicted by numerical plate bending models from the maximum curvature directions on the top of the bed. C) Cross-section along the fold axis showing the inflection point in the profile where the curvature is zero. D) Cross-section of a convex downward fold. Tangential longitudinal stresses are maximum on the lower surface of the folded bed. E) Map view of plunging fold termination (gray structure contours) with joint strike orientation (black dashes) as predicted by numerical plate bending models from maximum curvature directions on the base of the bed. F) Cross-section along the fold axis showing early and later fold profiles. The gray dashed arrows show potential displacement paths of the bed during lateral fold propagation. Units that are in front of the inflection point early in folding may reside behind the inflection point later in folding. Consequently, joints that develop in front of the inflection point may reflect the former concave upward shape of this portion of the early fold. of doubly-plunging anticlines (e.g., Fischer and Wilkerson, 2000; Fig. 1B). However, many studies document fold-related joint orientations that are uncorrelated with the direction of maximum curvature (e.g., Cruikshank et al., 1991; Engelder et al., 1997; Hennings et al., 2000). Explanations for these uncorrelated cases range from joints forming at some time other than folding, or by some mechanism other than outer arc stretching. Another possible explanation for anomalous joint patterns in folds is the complexity in stress fields at fold terminations, due to the change in concavity at the inflection line across the fold nose (Fig. 1C). Beds on the anticline behind the inflection line, where the fold is convex up, will have a fracture pattern related to the stresses on the top of the layer. However, beds in front of the inflection line, where the fold is concave up, will have joint patterns related to the stresses on the bottom of the layer (Fig. 1D and E). Although tangential longitudinal normal stresses, or fiber stresses, exist on both the top and bottom surfaces of the bed, joints will initiate at the surface with greater effective tensile stress and propagate through the thickness of the bed. Consequently, the joint pattern recorded reflects whether stresses were more effectively tensile on the top or bottom surface of the folded bed. Unlike most studies that only consider the stresses at the top surface during folding, we present a more comprehensive perspective that sheds light on apparently chaotic joint patterns by considering stresses on both the top and bottom of a folded layer that is jointing in response to tangential longitudinal stresses. A second complexity to consider is lateral fault propagation, which changes the shape of associated folds, as well as maximum curvature directions, stresses, and joint orientations (Fischer and Wilkerson, 2000; Fig. 1F). For instance, the fractures that form in the concave up part of the fold could later be translated to a structural position where the fold is concave down and thus the earliest formed fractures will not reflect observed fold curvature. Distinguishing fractures associated with multiple episodes of folding is complicated because joint terminations only record fracture timing with respect to other fractures and not specific folding episodes. However, the mechanical stratigraphy of the fractured units can provide additional information on fracture timing because beds with differing mechanical properties and thickness may fracture at different stages of fold evolution. Within a thin flexed layer, the tangential longitudinal stresses (sTL or fiber stresses) responsible for jointing are related to the layer curvature, k, (Turcotte and Schubert, 2002) as sTL = E/1 - v^2k where E and n are the elastic stiffness and Poisson’s ratio of the material respectively and w is position relative to the neutral surface (Fig. 1A). In this formulation, positive curvature is convex upwards. For convex upwards folds tensile stresses arise for w > 0 and for convex downwards folds, tensile stresses arise for w < 0. Joints are expected to initiate where the sTL is most tensile; the maximum tangential longitudinal stress, ssTuLrf, occurs at the top and bottom surfaces of the layer of thickness, H, where |w| ≤ H/2. ssTuLrf = E/H^2 (1 - v^2k) for k ≥ 0 Thicker and stiffer layers have greater tensile stress on the bed surfaces than thinner and softer layers within the same structural position. Joints will develop when ssTuLrf meets the tensile strength, T, of the bed. For a given structural position the curvature will be equal for all beds but the thickness, elastic properties and tensile strength will differ. 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