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_Journal of Structural Geology 32 (2010) 1137-1146_ Contents lists available at ScienceDirect Journal of Structural Geology journal homepage: www.elsevier.com/locate/jsg Stochastic modeling for the stress inversion of vein orientations: Paleostress analysis of Pliocene epithermal veins in southwestern Kyushu, Japan Atsushi Yamaji*, Katsushi Sato, Satoshi Tonai1 Division of Earth and Planetary Sciences, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan Article info Article history: Received 27 December 2009 Received in revised form 25 June 2010 Accepted 2 July 2010 Available online 15 July 2010 Keywords: Geothermal fluid Tectonic stress Bingham distribution Vein-type ore Abstract Plio-Pleistocene epithermal quartz veins in southern Kyushu, Japan, include gold deposits. The coherent trend of the ore veins suggests tectonic control for their formation. However, the stress regime during the formation has been controversial. To solve this problem, we improved existing methods for inferring paleostresses from vein orientations. It was assumed that veins making a cluster were formed intermittently from thermal fluids with various pressures. The present method determines stress ratio and stress axes with 95% confidence regions. The method was applied to mid Pliocene quartz veins cropping out at Hashima, southwestern Kyushu. We obtained a normal-faulting regime of stress with the trend of σ3 at 167 ± 14 × 10^4 and the stress ratio at 0.20 ± 0.13 ± 0.09. The low stress ratio and the lack of slickenlines and slickenfibers on vein walls suggest that the host rock was subject to a small differential stress, i.e., a weak tectonic stress, when the veins were formed. © 2010 Elsevier Ltd. All rights reserved. 1. Introduction Mineral veins are fossils of episodic venting of fluids from deep earth. Understanding their formation is important not only to mining but also to hydrocarbon exploration (Hood et al., 2003; Sorkhabi, 2005; Tamagawa and Pollard, 2008), geological disposal or storage (Shipton et al., 2004) and earthquake disaster prevention (Sibson, 1987, 2000; Beeler et al., 2000; Miller et al., 2004). There are Plio-Pleistocene epithermal gold veins in the southern part of Kyushu Island, northern Ryukyu arc, Japan (e.g., Izawa and Urashima, 2001; Izawa and Watanabe, 2001), where most ore veins have coherent trends (Fig. 1). Therefore, following Newhouse (1942) and McKinstry (1948), regional tectonics has been regarded as an important factor for the vein formation (e.g., Shiobara and Yoshikawa, 1958; Ikeda, 1962; Matsutoya, 1967; Sanematsu et al., 2006). However, it has been unclear which stress regime, normal or strike-slip faulting, prevailed in the metallogenic province (Ikeda, 1962; Matsutoya, 1967; Uto et al., 2001; Sillitoe and Hedenquist, 2003; Yamaji, 2003; Yamaji et al., 2003; Hikichi and Yamaji, 2008). To solve this problem, we observed quartz veins at the Hashima site, southwest Kyushu (Fig. 1), where gold-silver deposits were mined until the early 20th Century. * Corresponding author. Tel.: +81 75 753 4189. E-mail address: yamaji@kueps.kyoto-u.ac.jp (A. Yamaji). 1 Present address: National Institute of Advanced Industrial Science and Technology (AIST), Geological Survey of Japan, Tsukuba, Ibaraki 305-8567, Japan. 0191-8141 © 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.jsg.2010.07.001 At the beginning of this project, we planned to employ the method of Jolly and Sanderson (1997), which has been applied to veins and dikes in several areas (e.g., Andre et al., 2001; McKeagney et al., 2004; Mazzarini and Isola, 2007; Mazzarini and Musumeci, 2008). The method makes use of vein orientations to infer the paleostress during vein formation. For this purpose, it is expected that poles to veins are oriented in an elliptical cone or along a girdle, and that domains with and without data points are clearly separated on a stereogram (Fig. 2a). The s3 orientation is then determined as the axis of the cone or the densest point on the girdle; and the s2-s3 principal stress plane coincides with the major axis orientation of the ellipse or with the girdle. This method is based on the principle that thermal fluid opens fractures by its pressure, pf, only if the pressure exceeds the normal stresses on the fractures (Delaney et al., 1986). The Mohr diagram in Fig. 2a illustrates this situation. The domains with and without data points correspond to the orientations whether this condition was satisfied or not. The shape and position of the boundary line between the domains indicate the stress in question. Accordingly, the number density of poles should have an abrupt change across this line to estimate the state of stress. However, it was difficult to apply the method to our data. Poles to the Hashima veins showed a nebulous pattern on a stereogram (Fig. 2b). Consequently, we improved the methods of Baer et al. (1994) and Jolly and Sanderson (1997) to cope with vein orientations with such a gradation. 1138 A. Yamaji et al. Journal of Structural Geology 32 (2010) 1137-1146 Fig. 1. Trends of ore veins in southern Kyushu, Japan, after Izawa (2004). Geological map of southern Kyushu simplified from Geological Survey of Japan (1992). H, Hishikari; K, Kushikino; M, Miyazaki; O, Okuchi; QVF, Quaternary volcanic front; Y, Yamagano. 2. Stochastic model 2.1. Normalization The present method aims at determining the state of stress during the formation of veins from their orientations. In general, orientations are dimensionless quantities, whereas stress components have a physical unit, e.g., pascals. Therefore, the absolute stress values cannot be determined only from orientations. Instead, the principal stress axes and stress ratio are inferred. The ratio is defined as F ? (s2 - s3) / (s1 - s3) (Bishop, 1966), where s1, s2 and s3 are the principal stresses (s1 ! s2 ! s3), and compression is positive in sign. Pressure of the fluid, from which veins were formed, is normalized through the equation, p ? (pf - s3) / (s1 - s3). This is identical with the “normalized driving pressure” of Baer et al. (1994). In this article, we use the term “a state of stress” to refer to the stresses collectively that have the principal orientations and stress ratios in common. As the absolute values are not evaluated in this work, we identify the principal stresses as s3 ? 0, s2 ? F and s1 ? 1. Accordingly, stress tensor has the form, s ? Eus0E, where 0 1 1 0 0 s0 = @ 0 F 0 A (1) 0 0 0 is the simplest 3 × 3 matrix to have the information of F, and E is the orthogonal matrix representing the principal orientations. A fracture surface with the unit normal, v, is subject to the traction, t ? sv, which has the normal and shear components, sn = v · ut + vu · Es0Ev (2) ss = |t - sn|; (3) in the ranges 0 ≤ sn ≤ 1 and 0 ≤ ss ≤ 1/2 (Table 1). Equal-area projections in Fig. 3 show the correspondence between sn and v for three F values. a 2.2. Basic assumptions To determine the state of stress from a nebulous pattern of poles to veins, some rule relating vein orientations to stress is necessary. We have four assumptions for the formation of a cluster of veins: b Fig. 2. Schematic illustrations showing the model of Baer et al. (1994) and Jolly and Sanderson (1997) (a), and our model (b) for the formation of epithermal veins. Equal-area projections show the poles to veins; closed circle, cross and solid circle indicate s1, s2 and s3 orientations, respectively. The former model assumes that vein minerals were deposited from thermal fluid with a distinctive pressure, pf. Veins are thought to be formed in fractures with its normal stress, sn, being smaller than pf, when pf is greater than s3. As a result, the poles to veins are confined in an elliptical cone or along a girdle in the deterministic model. In contrast, we assume fluctuating fluid pressure. The poles are thought to show a nebulous pattern on the stereogram in our model due to fluctuating pf: gradation in the stereogram and the Mohr diagram depict the number density of data points. 1. The state of far-field stress did not change during the formation of the cluster. 2. The country rock was effectively isotropic for the vein orientations to inherit orthorhombic symmetry from the stress (Baer et al., 1994) (Fig. 3). 3. Veins were formed on fracture surfaces only if the 4. 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