Numerical simulation of ®bre growth in antitaxial strain fringes p Daniel Koehn a, *, Chris Hilgers b , Paul D. Bons a , Cees W. Passchier a a Institut fuÈr Geowissenschaften, Tectonophysics, Johannes Gutenberg UniversitaÈt, Becherweg 21, 55099 Mainz, Germany b Geologie-Endogene Dynamik, RWTH Aachen, Lochnerstrasse 4-20, 52056 Aachen, Germany Received 28 June 1999; accepted 8 March 2000 Abstract A two-dimensional computer model (`Fringe Growth') is used to simulate the incremental growth of crystal ®bres in undeformed antitaxial strain fringes. The user can de®ne the shape of a core-object (e.g. a pyrite crystal), the growth velocity and anisotropy of growing crystals, the rotation of fringes and core-object with respect to a horizontal datum and with respect to each other, and the opening velocity of fringes. Growth is simulated by movement of nodes connecting line segments that de®ne the grain boundaries. Modelling results predict that face-controlled strain fringes will grow around smooth core-objects and strain fringes with displacement-controlled and face-controlled ®bres around core-objects with rough surfaces. The surface roughness of the core- object determines if ®bres in the fringes track the opening trajectory, since ®bres follow asperities on the surface of the core- object. Rotation of the core-object and the fringes with respect to an external reference frame and with respect to each other in¯uences the geometry of the ®bres. Our modelling results indicate that ®bre growth direction is not directly dependent on the orientation of the extensional instantaneous stretching axes or the ®nite maximum strain axes. 7 2000 Elsevier Science Ltd. All rights reserved. 1. Introduction Rigid objects in a matrix deformed by non-coaxial or coaxial progressive deformation cause perturbations of the stress ®eld and ¯ow pattern. Increased pressure solution may occur adjacent to the rigid object on the side of the shortening instantaneous stretching axes (ISA), while new crystals may grow on the side of the extensional ISA and form strain fringes (MuÈgge, 1928; Pabst, 1931). For over 70 years, geologists have attempted to use crystal ®bres in strain fringes that lie on both sides of a rigid core-object such as a pyrite crystal to evaluate the deformation history in the host- rock (MuÈgge, 1928; Pabst, 1931; Durney and Ramsay, 1973; Cox and Etheridge, 1983; Beutner and Diegel, 1985; Ellis, 1986; Etchecopar and Malavielle, 1987; Aerden, 1996; Kanagawa, 1996). Despite much pro- gress in this ®eld, the methods used are still based on assumptions which have not been tested experimen- tally. We developed a method to test assumptions of fringe growth in numerical experiments in order to improve the reliability of these structures as providers of kinematic data. The basic assumptions and pro- blems of existing models are outlined below. Fibre growth in fringes takes place either syntaxially at the matrix±fringe interface or antitaxially at the interface of the core-object and the fringe, and ®bres may or may not deform during ongoing deformation (reviews in Ramsay and Huber, 1983; Passchier and Trouw, 1996). This study deals with undeformed anti- taxial strain fringes that are most common in nature. Fig. 1 shows examples of such antitaxial non-deform- ing strain fringes. The core-object can be a spherical framboidal pyrite (Fig. 1a) or an angular iron-oxide object (Fig. 1b). Both examples are inferred to have developed during progressive non-coaxial deformation with a dextral shear sense (Passchier and Trouw, Journal of Structural Geology 22 (2000) 1311±1324 0191-8141/00/$ - see front matter 7 2000 Elsevier Science Ltd. All rights reserved. PII: S0191-8141(00)00039-0 www.elsevier.nl/locate/jstrugeo p Figs. 6±8 visible as Quick Time movies on http://veo.elsevier.nl/ sg/Publish/925. * Corresponding author. E-mail address: koehn@mail.uni-mainz.de (D. Koehn).