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_Journal of Structural Geology 33 (2011) 280-291_ _Contents lists available at ScienceDirect_ _Journal of Structural Geology_ _journal homepage: www.elsevier.com locate jsg_ _Key-ring structure gradients and sheath folds in the Goantagab Domain of NW Namibia_ _Cees Passchier a,*, Rudolph Trouw b, Sara Coelho a, Eric de Kemp c, Renata Schmitt b_ _a Department of Earth Sciences, University of Mainz, Germany_ _b Federal University of Rio de Janeiro, Brazil_ _c Canadian Geological Survey, Ottawa, Canada_ _article info_ _Article history: Received 23 June 2010 Received in revised form 22 November 2010 Accepted 5 December 2010 Available online 24 December 2010_ _Keywords: Deformation phase Sheath fold Namibia Foliation_ _abstract_ _The concept of deformation phases is one of the cornerstones of structural geology but, despite its simplicity, there are situations where the concept breaks down. In the Goantagab Domain of NW Namibia, structures in an area of complex deformation can be subdivided into at least four sets, attributed to four deformation phases on the basis of overprinting relations. Three of these sets of structures, however, formed during the same tectonic event under similar metamorphic circumstances but slightly different flow conditions. These sets of structures show gradational transitions in space that can be understood by a concept of "key-ring structure gradients," where older DA structures are reoriented and overprinted by new structures DA>1 that have similar orientation, and seem to grade into DA structures outside the overprinted area. This kind of behavior may be common in inhomogeneous non-coaxial flow. In the core of the Goantagab Domain, D2 structures are thus reoriented and overprinted by local D2b folds and foliations that have the same orientation and style as D2 structures outside the domain core._ _© 2010 Elsevier Ltd. All rights reserved._ _1. Introduction_ _In structural geology, we traditionally organize deformation structures such as foliations, lineations, and folds into groups that we attribute to deformation phases (e.g., Ramsay, 1967; Hobbs et al., 1976; Ramsay and Huber, 1987; Marshak and Mitra, 1988; Passchier and Trouw, 2005). In all cases, dating of minerals or intrusions can be attempted to obtain absolute ages, but this should only be done after detailed information on structural relations has been obtained by careful analysis of the relative age and style of structures in the field. The relative age of groups of structures is established through overprinting relations. The deformation phases, thus defined, represent deformation over a certain period of time at any location, although they may be diachronous over a larger area._ _Besides overprinting relations, deformation phases are usually characterized by a distinct style of the structures produced, which is an effect of imposed deformation conditions, e.g., metamorphic grade, stress field orientation or flow type: A change in style may mean that imposed deformation conditions locally changed (Hobbs et al., 1976; Ramsay and Huber, 1987; Marshak and Mitra, 1988; Passchier and Trouw, 2005). In some areas, the style of deformation structures may be different enough to be used as a distinguishing_ _† Corresponding author. Fax: +4961313923863. E-mail address: cpasschi@uni-mainz.de (C. Passchier)._ _0191-8141 $ e see front matter © 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.jsg.2010.12.005_ _criterion in the absence of overprinting relations, although this is less reliable. If deformation phases recognized in a volume of rock are separated by long time intervals without deformation, they may represent tectonic events within orogenies, or even distinct orogenic events (Passchier and Trouw, 2005)._ _Despite the simplicity of this concept, there are transitional situations where the method cannot be easily applied. Some deformation structures cannot be easily attributed to chronologically distinct phases. For example, shear band cleavage in mylonites represents a second, overprinting foliation that forms during the same mylonitisation process that produced the main mylonitic foliation in the first place. We do not normally label these foliations as S1 and S2, belonging to separate deformation phases. Normal crenulation cleavage, however, which may form by small shifts in the orientation of the stress field, is labelled as belonging to a separate phase by most geologists; although there are similar overprinting relations in both cases, the difference is that imposed conditions are considered to have remained the same for shear band cleavage, while crenulation cleavage formed because the external stress frame changed orientation with respect to the fabric._ _It is obvious that the distinction structural geologists make between shear band cleavage and crenulation cleavage is rather ambiguous and confusing for students. Where do we start to use different labels, and how can this ambiguity be handled? How can we distinguish structures that form by overprinting of separate_ _C. Passchier et al. Journal of Structural Geology 33 (2011) 280-291_ _281_ _deformation events separated in time from those that form in the course of one tectonic event? These are the questions that we address in this paper based on a complex structural domain in NW Namibia._ _2. The concept of expression_ _In biology, the shape of an organism is defined by its genes and their "expression," i.e., the extent to which they produce biological structures; different expression levels mean different final shapes. By analogy, in structural geology we could use the term "expression of a deformation phase" to mean the final geometry of structures locally produced by that phase due to the combination of (1) lithology; (2) previous structure; (3) imposed conditions such as stress orientation and geometry, metamorphic conditions and flow type and (4) accumulation state of the deformation, i.e., local finite strain. The "expression" of a deformation phase for identical imposed conditions and finite strain can be a continuous schistosity in schist, an open fold and spaced cleavage in sandstone, a crenulation cleavage in previously foliated schist; and no visible structure in a marble. Deformation phase expression can therefore vary strongly over an area even though finite strain, bulk stress orientation and other external deformation conditions were similar. In structural geology, it is tradition to concentrate on a comparison of deformation structures, focussing on the exact nature and geometry of structural expression in each deformation phase. However, this hampers interpretation if no attention is paid to the cause of the differences. Levels of expression are only of significance to understand the tectonic history of an area if they are due to different imposed conditions, not if they are due to differences in lithology or finite strain. In this paper we stress the importance of separating expression gradients that are due to changes in imposed conditions from those due to these other factors._ _3. Handling deformation phases_ _One of the difficulties in structural geology is to recognize structures of different shape and orientation as being of the same age, i.e., to determine whether different structures are just different expressions of one deformation phase or of different phases. In our dealing with deformation structures on a regional scale, we have to deal not only with variable expression in any one place but also with complex spatial gradients and changes in expression with time. The nature of such gradients is best illustrated by an example from biology where similar gradients are common._ _Organisms that have evolved in isolation for a long time are clearly distinguishable as different species, while those more closely related are regarded as subspecies. The subdivision of animal groups into species may seem more robust than the geological concept of deformation phases, but it can also break down if considered in adjacent regions. As an example, the European herring gull Larus Argentatus is separated in Europe from the Lesser Black-Backed Gull Larus Graelsii as separate species since they do not interbreed in the wild. The former, however, does interbreed with a north American subspecies, which interbreeds with an east Siberian subspecies and so forth, until the last subspecies is interbreeding with Larus Graelsii, creating a ring-shaped distribution around the northern hemisphere. Differences between individuals gradually change from east to west until in Europe both gradients produce a full separation of species that do not interbreed (Irwin et al., 2001a). Because of the similarity with a key-ring, species with this characteristic are known in biology as ring species (Irwin et al., 2001a,b; Alström, 2006)._ _In structural geology we are occasionally dealing with similar situations. Within one highly deformed zone, shear sense can grade from well defined and sinistral through a less defined zone into a dextral sense; domains with two overprinting foliations grade into areas with one or three foliations. At present, we know that these gradients may exist but we lack the proper tools to deal with them in an efficient way. In some cases, gradients in structure may even turn back on themselves in a similar way as that of "ring species" in biology. This paper describes such features which we name "key-ring structure gradients" in a complex area in NW Namibia where they can be reconstructed because of the generally excellent outcrop. Such gradients may also exist in other areas, hidden by poor outcrop._ _4. Regional geology_ _The Lower Ugab Domain in Namibia (Hoffman et al., 1994) is the center of a Neoproterozoic to Cambrian triple junction between the Kaoko, Gariep and Damara Belts, separating the Congo, Kalahari and Rio de la Plata Cratons (Miller, 1983; Goscombe et al., 2003a,b; 2004, 2005; Passchier et al., 2007; Gray et al., 2006, 2008). We concentrate on a dome'_ _† Corresponding author. Fax: +4961313923863. E-mail address: cpasschi@uni-mainz.de (C. Passchier)._ Ключевые слова: e, r, o