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_Journal of Structural Geology 32 (2010) 1519-1551_ Contents lists available at ScienceDirect Journal of Structural Geology journal homepage: www.elsevier.com/locate/jsg Review Article Structural geology, petrofabrics and magnetic fabrics (AMS, AARM, AIRM) Graham J. Borradaile a,*, Mike Jackson b a Faculty of Science, Lakehead University, Thunder Bay P7B 5E4, Canada b Institute of Rock Magnetism, University of Minnesota, MN 55455, USA Article history: Received 14 April 2009; Received in revised form 19 August 2009; Accepted 13 September 2009; Available online 2 December 2009 Keywords: Magnetic fabrics Petrofabric Anisotropy of magnetic susceptibility AMS Abstract Anisotropy of magnetic susceptibility (AMS) was recognized as a feature of minerals in 1899, and petrofabric-compatible AMS fabrics were reported from 1942-1958. Shortly thereafter, cleavage and mineral lineation were associated with the principal axes of the AMS ellipsoid. AMS is describable by a magnitude ellipsoid, somewhat similar in concept to the finite strain ellipsoid, with principal susceptibilities (kMAX, kINT, kMIN) as its axes and their average value being the mean susceptibility (k). Orientations of the AMS axes usually have a reasonably straightforward structural significance but their magnitudes are more difficult to interpret, being the result of mineral abundances and different mineral-AMS. The strain ellipsoid is dimensionless (i.e., of unit-volume) and readily compared from one outcrop to another but the AMS ellipsoid represents the anisotropy of a physical property. Thus, (k) determines the relative importance of AMS for different specimens or compared outcrops or component AMS subfabrics. AMS provides a petrofabric tool, unlike any other, averaging and sampling the orientation-distribution of all minerals and all subfabrics in a specimen. Sophisticated laboratory techniques may isolate the AMS contributions of certain minerals from one another, and of certain subfabrics (e.g., depositional from tectonic). However, suitable data processing of the basic AMS measurements (kMAX, kINT, kMIN magnitudes and orientations, and the mean susceptibility, k) may provide the same information. Thus, AMS provides the structural geologist with a unique tool that may isolate the orientations of subfabrics of different origins (sedimentary, tectonic, tectonic overprints etc.). © 2010 Published by Elsevier Ltd. 1. Purpose and background Structural geology infers the axes of finite strain or solid-state flow from the orientations of crystals or the orientation of grain shapes. Preferred crystallographic orientation (PCO) is less easily measured and interpreted than preferred dimensional orientation (PDO) but received attention earlier mainly due to brilliant insights based on field studies, Universal stage and early X-ray methods (March, 1932; also by Schmidt, 1917-1929 and Sander, 1909-1948, summarized in Sander, 1970). They associated girdle-cluster orientation distributions (ODs) of crystals (and in some cases grain shapes) on the stereogram (Fig. 1) with macroscopic structures (folds, cleavage and mineral lineation). Now we accept that a homogeneous single fabric (e.g., “D1”) comprises a composite lineation-schistosity fabric of minerals described in the L-S continuous spectrum (Flinn, 1962, 1965) (Fig. 1a-ee). We may * Corresponding author at: Department of Geology & Physics, Lakehead University, 955 Oliver Road, Thunder Bay, Ontario P7B 5E4, Canada. Tel.: +1 807 683 0680. E-mail addresses: borradaile@lakeheadu.ca (G.J. Borradaile), irm@tc.umn.edu (M. Jackson). 0191-8141 $ e see front matter © 2010 Published by Elsevier Ltd. doi:10.1016/j.jsg.2009.09.006 readily identify orientation-distributions (ODs) of aligned elements or the shapes of strained objects and perhaps quantify these in terms of a strain or fabric ellipsoid (Flinn, 1965; Ramsay, 1967). PCOs are quantifiable by the Eigenvectors method (Scheidegger, 1965; Woodcock, 1977) but usually they do not directly relate to strain. The finite strain ellipsoid, and by analogy the fabric ellipsoid, range over a smooth continuum of shapes ranging from oblate (X ? Y > Z), through neutral (X = Y ? Y = Z) to prolate (X > Y ? Z). Thus, no homogeneous single-event fabric may possess any symmetry lower than orthorhombic and only the extreme end-cases are tetragonal. Flinn’s fabric scheme (L, L > S, L ? S, L < S, S) is universally accepted in structure (Fig. 1a) but the Cartesian graph of (a - max int, b - int min) has an awkward asymmetric radial shape parameter _?(a - 1)(b - 1)_. For applications in magnetic fabrics, in which anisotropy is usually rather low, Jelinek (1981) introduced improved parameters; Pj for the eccentricity of the ellipsoid (“anisotropy degree”) and Tj for its shape. These are equally valid for strain, fabric ellipsoids and ODs. TJ ln?F? ? ln?L? ln?F? ? ln?L? where L ? x18kMAX x19 kINT F ? x18 kINT x19 kMIN (1) 1520 G.J. Borradaile, M. Jackson Journal of Structural Geology 32 (2010) 1519-1551 Fig. 1. Structural geologists define homogeneous, anisotropic preferred crystallographic orientations (PCO) and preferred dimensional orientations (PDO) in terms of fabric ellipsoids (Flinn, 1962, 1965; Scheidegger, 1965; Woodcock, 1977) that relate to the finite strain ellipsoid (Ramsay, 1967). (a) In structural geology, the ellipsoid is plotted on Cartesian axes. (b) However, for magnetic fabric ellipsoids which usually have very low anisotropy degree, Jelinek’s (1981) more symmetric parameters (Pj for anisotropy degree (eccentricity) and Tj for shape) are greatly preferred. These plot more faithfully on a polar plot. (c, d) Samples for AMS ellipsoids on a Cartesian and on a polar plot compared. The isotropic case occurs at a unique location in (d). (e) AMS ellipsoids compared for some well-known metamorphic rocks and a non-deformed sandstone. Tj ranges symmetrically over the spectrum of ellipsoid shapes: Tj ? -1 for oblate, Tj ? 1 for prolate, Tj ? 0 for neutral and -1 > Tj > 1 for the general ellipsoid. Jelinek’s parameter for the degree of anisotropy is ?? ln PJ ? p?2?? x18 x16ln x16kMkAX x17 x172 ? x16ln x16kIkNT x17 x172 ? x16ln x16kMkIN x17 x172 x19 1 2 (2) It includes a reference to shape and is therefore preferable to an older but still commonly used simple ratio (P ? kMAX kMIN) of Nagata (1961). It is derived from older Nagata’s P-values with ?? ln PJ ? ln?P?v u u t????1??????????T?3?J?2??!???. (3) A polar plot of (Pj, Tj) (Fig. 1b) gives an unbiased distribution of ellipsoid shapes (Fig. 1c-e), especially for those with low Pj, (Borradaile and Jackson, 2004). Importantly, the isotropic case plots uniquely whereas Cartesian plots of (Pj, Tj) are ambiguous. 1.1. Why magnetic fabrics? The OD of a certain mineral is remarkably difficult to measure and is restricted to oriented thin-sections or slabs cut for X-ray work. Before many such ODs were available from Universal-stage microscopy, a remarkably early study recognized that the LeS scheme of crystal ODs would arise if crystals were to spin passively without -impingement (March, 1932). Subsequently, field or laboratory tests verified that March’s hypothesis was an acceptable qualitative approximation, albeit with many caveats (Frost and Siddans, 1979; Oertel, 1983; Tullis, 1976; Hobbs et al., 1976). More recently, neutron texture goniometry has overcome some of the difficulties of PCO quantification - the large penetration depth allows analysis of volumes of material comparable to AMS specimens without any special surface preparation and complete pole figures can be measured with only one specimen (Brokmeier, 1994; Ullemeyer et al., 2000). However, neutron diffraction instrumentation is not readily accessible to most researchers. The impetus to develop or apply magnetic techniques to determine ODs stalled until the early 1980s until continuum mechanics (Ramsay, 1967; Ramsay and Huber, 1983) and material science concepts verified that PCOs were a readily interpretable consequence of tectonic strain. Concepts concerning crystal plasticity, dynamic recrystallization, diffusive mechanisms, pressure solution and particulate flow were not absorbed into structural analysis until relatively recently (e.g., Boland and Fitzgerald, 1993; Blenkinsop, 2000; Knipe and Rutter, 1994; Nicolas and Poirier, 1976; Nicolas, 1987; Poirier, 1985; Paaschier and Trouw, 2005). Armed with means to interpret ODs, it became reasonable to apply magnetic methods to measure PCOs. Magnetic properties, especially low-field susceptibility (k) have large ranges and are readily measured by mostly non-destructive methods. The development of the “personal” computer in 1980 expanded the routine measurement of anisotropy of low-field susceptibility (AMS) for suitably prepared standard-size specimens. Finite strain, ODs and AMS all share the underlying convenience that as homogeneous fabrics, they may be visualized as a magnitude ellipsoid with orthogonal principal axes. Their relative magnitudes will determine whether a point-cluster, a partial girdle or a full-girdle exist for the crystal OD. For AMS, as long as all principal susceptibilities have the same sign, a homogeneous sub-fabric or a single crystal, will have a magnitude ellipsoid, or AMS ellipsoid with orthogonal axes (kMAX, kINT and kMIN). The magnitude ellipsoids in these cases are properties of a state of matter, the permanent features of a material tensor (Nye, 1957) like finite strain (X ! Y ! Z). In contrast to the dismay of structural geology, stress is an ephemeral field tensor (Nye, 1957) that rarely correlates directly with any specific finite strain, orientation-distribution or instant in time. There is a major difference between the strain ellipsoid concept in structural geology and the AMS ellipsoid. Strain ellipsoids are dimensionless, with axes normalized so that the ellipsoid has the same volume as the initial sphere. 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