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_Journal of Structural Geology 32 (2010) 321–329_ _Contents lists available at ScienceDirect_ _Journal of Structural Geology_ _journal homepage: www.elsevier.com/locate/jsg_ _Strain analysis of heterogeneous ductile shear zones based on the attitudes of planar markers_ _Stefano Vitale*, Stefano Mazzoli_ _Dipartimento di Scienze della Terra, Università degli studi di Napoli ‘Federico II’, Largo San Marcellino 10, 80138 Napoli, Italy_ _article info_ _Article history: Received 28 September 2009; Received in revised form 11 December 2009; Accepted 2 January 2010; Available online 14 January 2010_ _Keywords: Shear strain Strain softening Strain matrix Wrench zones Deformed granitoid plutons_ _abstract_ _Using the simple measurement of the attitude of planar features such as foliation, shear planes and displaced tabular markers (such as veins or dykes), fundamental information is obtained on deformation types and rheology in heterogeneous ductile shear zones. The method outlined in this study is based on the subdivision of the shear zone into n deformed layers, each characterized by approximately homogeneous deformation. For each layer, paired measurements of q0 and G are made, where q0 is the angle that the foliation forms with the shear plane and G is the effective shear strain. By means of suitable q0-G grids, constructed according to strain boundary conditions, values of stretch (k), shear strain (g), strain ratio (R) and kinematic vorticity number (Wk) are calculated. The method has been tested on three ductile wrench zones exposed in a deformed granitoid pluton in the Eastern Alps (Italy). The q0-G data indicate that the shear zones are of dominantly transtensional or transpressional type. Furthermore, finite shear strain and strain ratio peaked profiles suggest that in all instances shear zone evolution was characterized by strain softening. Analysis of the kinematic vorticity indicates that strain softening essentially affected the simple shear component of the deformation._ _© 2010 Elsevier Ltd. All rights reserved._ _1. Introduction_ _Shear zones are very common structures in the lithosphere and their study is fundamental for investigating heterogeneous rock deformation and strain localization processes (e.g., Ramsay and Graham, 1970; Ramsay, 1980; Ramsay and Huber, 1983, 1987). They are the result of complex interactions between controlling factors such as P-T conditions and fluid behavior, and a series of parameters including: (i) partitioning of different deformation types (simple shear, pure shear, volume change), (ii) deformation distribution (i.e., degree of strain localization), and (iii) rheology (involving strain softening or strain hardening). The heterogeneous nature of the deformation in most natural shear zones is evident from the variability of finite strain parameters such as strain ratio or shear strain. The origin of strain heterogeneity depends on the evolution of the active shear zone as a function of time (e.g., Means, 1995; Vitale and Mazzoli, 2008)._ _Most of the strain analysis methods applied to the study of shear zones involve the determination of finite strain ratios, together with the measurement of foliation and shear plane attitudes (q0-R plot; Fossen and Tikoff, 1993; Vitale and Mazzoli, 2008, 2009)._ _* Corresponding author. Tel.: +39 (0) 812538124; fax: +39 (0) 812538338. E-mail address: stefano.vitale@unina.it (S. Vitale)._ _0191-8141 $ – see front matter © 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.jsg.2010.01.002_ _However, the results provided by these techniques often bear large uncertainties because of the difficulties in estimating precisely the finite strain by means of suitable strain markers (such as spherical or ellipsoidal deformed objects). The largest uncertainties are due to the variability of parameters such as object concentration (i.e., the concentration of more competent strain markers embedded in a less competent matrix), viscosity contrast, and object shape (e.g., Treagus and Treagus, 2001; Vitale and Mazzoli, 2005). Furthermore, the most popular methods of finite strain analysis (Fry and Rf4 techniques; Ramsay, 1967; Fry, 1979; Lisle, 1985) require the fulfillment of a number of assumptions, not always satisfied by rocks. The aim of this paper is to provide an alternative and more precise method for the quantitative analysis of natural shear zones. The proposed method is based on the use of the effective shear strain – rather than finite strain ratio – to characterize heterogeneous deformation in shear zones._ _2. q0-G method_ _The method is based on the analysis of the attitudes of foliation, shear plane and displaced planar markers (e.g., vein, dyke) across the shear zone. Therefore, this technique requires the presence of a well-developed foliation and of a planar marker being intersected by the shear zone (Fig. 1)._ _322_ _S. Vitale, S. Mazzoli Journal of Structural Geology 32 (2010) 321–329_ _Fig. 1. (a) 3D shear zone model showing the geometric relationship between a deformed planar marker and oblique foliation. The reference frame (x, y, z) used in this study and a schematic orientation of the finite strain ellipsoid (with principal axes: X, Y, Z) are also shown. (b) Shear zone section parallel to the slip vector (xy plane) showing the subdivision into approximately (at the scale of observation) homogeneously deformed layers and the three angles described in the text._ _In this study, the shear zone reference frame (Fig. 1a) is indicated by means of lowercase letters (x, y, z, where the x axis is parallel to the shear direction and the xz plane is parallel to the shear plane, this being vertical for the analyzed wrench-type shear zones), whereas capital letters (X, Y, Z) are used for the orientation of the principal axes of the finite strain ellipsoid (with the X axis parallel to the maximum extension direction and the Z axis parallel to the minimum one; e.g., Ramsay and Huber, 1983). The analyzed foliation is assumed to be parallel to the XY plane of the finite strain ellipsoid._ _In order to evaluate the effective shear strain G (sensu Fossen and Tikoff, 1993), the cotangent rule is applied to the displaced planar marker (Eq. 2.3, pg. 24 of Ramsay and Huber, 1983):_ _G ≈ cotθa0 – cotθa_ _(1)_ _where a and a0 are the angles between the planar marker and the shear plane in the undeformed host rock and inside the shear zone, respectively (Fig. 1b). In order to collect q0-G data, where q0 is the angle that the foliation forms with the shear plane (Fig. 1b), the heterogeneous ductile shear zone (in this study being of wrench type) is divided into sectors characterized by monotonously increasing or decreasing strain. Each sector, in turn, is divided into n suitable layers parallel to the shear plane and characterized by an approximately homogeneous deformation (in others words the finite strain, resulting from a combination of simple shear, pure shear and volume change, is considered as being homogeneous within each layer volume; however, all together the layers define a heterogeneous deformation in which finite strain parameters such as shear strain and stretch values are spatially variable across the shear zone). The thickness of each layer (i.e., the sampling size) notably influences the accuracy of the measurements. Although closer sampling obviously furnishes more precise estimates (the strain within each layer being closer to homogeneous), also choosing layers of constant or variable thickness influences measurement uncertainty. Taking into account that finite strain generally increases in a non-linear fashion from the margins to the centre of a heterogeneous ductile shear zone, logarithmically-spaced sampling is adopted in this study in order to obtain a more homogenous distribution of measurement precision across the shear zone._ _Let us assume, for each layer, a deformation characterized by simultaneous simple shear, pure shear and volume change. For the i-th layer, the finite strain matrix is in the form (Tikoff and Fossen, 1993):_ _2 3_ _k1(i) G(i) 0_ _A(i) = 4 0 k2(i) 0 5_ _(2)_ _0 0 k3(i)_ _where G(i) = g(i)(k1(i) – k2(i))ln(k1(i)_k2(i)) is the i-th finite effective shear strain (i.e., the off-diagonal term of the strain matrix), k1(i) = (1 + e1(i)), k2(i) = (1 + e2(i)) and k3(i) = (1 + e3(i)) are the i-th finite stretches, and e1(i), e2(i) and e3(i) are the i-th finite extensions._ _Strike-slip deformations may deviate from simple shear because of a component of shortening or extension orthogonal to the deformation zone, determining conditions of transpression or transtension, respectively (sensu Dewey et al., 1998). Two cases of transpressional and transtensional wrench zones have been considered in this study:_ _(a) simple shear in the xy plane and synchronous pure shear in the yz plane (i.e., k1 = 1 and k3 = k2 – 1), represented by the strain matrix (Fossen and Tikoff, 1993):_ _2 3_ _A1 = 64 1 0_ _g(1 – k2) ln(1 – k2) + k2_ _0 0_ _75_ _(3)_ _0 0 1 – k2_ _(b) simple shear and synchronous pure shear, both in the xy plane (i.e., k3 = 1 and k1 = k2 – 1), represented by the strain matrix:_ _2 3_ _A2 = 64 1 – k2 0_ _g(1 – k2 – k2) ln(1 – k22) + k2_ _3 0 0 75_ _(4)_ _S. Vitale, S. Mazzoli Journal of Structural Geology 32 (2010) 321–329_ _323_ _In cases where pure shear is localized within the shear zone only (i.e., it does not involve the host rock), vertical or horizontal stretching occurs for cases (a) and (b) above, respectively (Sanderson and Marchini, 1984; Jones et al., 1997; Dewey et al., 1998)._ _Grids for plotting the q0-G data (Fig. 2) may be constructed by allowing the values of k2 and g to vary in the following equations (Fossen and Tikoff, 1993; Tikoff and Fossen, 1993):_ _G = g(k1 – x11k2)_ _(5)_ _ ln(kk12 q0 = x12 arctan G2 – k2 + k2G lmax x13_ _(6)_ _where lmax is the maximum one among the three eigenvalues of the matrix A1A1T (i.e., the lengths of the finite strain ellipsoid axes):_ _l1;2;3 = 8 >>>>>>< >>>>>>: x12 1 2 G2 + 1 + k22 + rπ_ Ключевые слова: e, r, o