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_Journal of Structural Geology 32 (2010) 1629–1642_ Contents lists available at ScienceDirect Journal of Structural Geology journal homepage: www.elsevier.com locate jsg Analysis of the growth of strike-slip faults using effective medium theory Atilla Aydin a,*, James G. Berryman b a Rock Fracture Project, Department of Geological and Environmental Sciences, Stanford University, Stanford, CA, USA b Lawrence Berkeley National Laboratory, Earth Science Division, One Cyclotron Road, MS 90R1116, Berkeley, CA, USA Article info Article history: Received 14 March 2009 Received in revised form 9 November 2009 Accepted 16 November 2009 Available online 27 November 2009 Keywords: Fault growth Fault scaling Fault linkage and coalescence Fault damage zone Cataclastic deformation Effective moduli Effective medium model Abstract Increases in the dimensions of strike-slip faults including fault length, thickness of fault rock and the surrounding damage zone collectively provide quantitative definition of fault growth and are commonly measured in terms of the maximum fault slip. Field observations indicate that a common mechanism for fault growth in the brittle upper crust is fault lengthening by linkage and coalescence of neighboring fault segments or strands, and fault rock-zone widening into highly fractured inner damage zone via cataclastic deformation. The most important underlying mechanical reason in both cases is prior weakening of the rocks surrounding a fault’s core and between neighboring fault segments by faulting-related fractures. In this paper, using field observations together with effective medium models, we analyze the reduction in the effective elastic properties of rock in terms of density of the fault-related brittle fractures and fracture intersection angles controlled primarily by the splay angles. Fracture densities or equivalent fracture spacing values corresponding to the vanishing Young’s, shear, and quasipure shear moduli were obtained by extrapolation from the calculated range of these parameters. The fracture densities or the equivalent spacing values obtained using this method compare well with field data measured along scan lines across the faults in the study area. These findings should be helpful for a better understanding of the fracture density spacing distribution around faults and the transition from discrete fracturing to cataclastic deformation associated with fault growth and the related instabilities. © 2009 Elsevier Ltd. All rights reserved. 1. Introduction Strike-slip faults, similar to other types of faults, typically have complex architectures with numerous segments or strands of various trace lengths separated by steps or relays of various sizes (Fig. 1a). This discontinuous characteristic of strike-slip faults has been reported for simple incipient faults (Segall and Pollard, 1980, 1983; Gamond, 1983; Sibson, 1986; Willemse et al., 1997; Peacock and Sanderson, 1995) as well as for mature crustal-scale faults (Aydin and Nur, 1982; Barka and Kadinsky-Cade, 1988; Wesnousky, 1988; Stirling et al., 1996; Kim et al., 2004) and is thought to be pertinent to a number of properties of strike-slip fault systems including their permeability structure (Sibson, 1985; Martel and Peterson, 1991; Aydin, 2000; Odling et al., 2004), the dynamics and size of earthquake ruptures (Aki, 1989; Harris and Day, 1999; Harris et al., 1999; Wesnousky, 2006; Shaw and Dieterich, 2007), the spatial and temporal evolution of earthquakes (Dewey, 1976). * Corresponding author. E-mail address: aydin@stanford.edu (A. Aydin). 0191-8141 $ – see front matter © 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.jsg.2009.11.007 Toksoz et al., 1979; Stein et al., 1997), and growth and scaling of faults (de Joussineau and Aydin, 2009; Scholz, 2002). One of the fault scaling relationships concerns fault length (L) to maximum fault slip or displacement (D). Various studies of mostly normal faults (Watterson, 1986; Walsh and Watterson, 1987; Cowie and Scholz, 1992; Schlische et al., 1996; Scholz, 2002) concluded that the length–slip relationship has the form, L ? Dn, where n was proposed to be between 1 and 2. Neighboring segments of strike-slip faults are separated by steps (Fig. 1a). These steps have self-similar geometry regardless of the sense of stepping and sense of shearing (Aydin and Schultz, 1990; Aydin and Nur, 1982). However, the failure modes and the distribution of the shearing-related structures may be different from one sense of step to another depending on loading, stress perturbations, rheology, and the geometry of initial pre-faulting discontinuities (Kim et al., 2004; Myers and Aydin, 2004; Peacock and Sanderson, 1991, 1995; Burgmann and Pollard, 1994; Sibson, 1986; Gamond, 1983; Rispoli, 1981). A data set collected by Wesnousky (1988) from crustal-scale strike-slip faults suggests that the number of steps per kilometer along strike-slip faults decreases as fault slip increases. Although it is difficult to define uncertainty regarding the fault dimensions measured from published geologic and seismologic maps, recent experimental (Otsuki and Dilov, 2005) and site-specific field data from the same tectonic region and lithology and similar resolution (de Joussineau and Aydin, 2009) appear to confirm this trend. It is also interesting to note that larger size of steps is associated with faults having larger maximum slip magnitudes (Aydin and Nur, 1982; de Joussineau and Aydin; 2009), possibly related to the ability of fault slip to jump from one fault segment to next over the fault steps between them (Shaw and Dieterich, 2007; Harris and Day, 1999; Harris et al., 1999). The fault length-slip, and step count per kilometer length relationships, regardless of their exact form, imply that faults, like other types of geological structures having different senses of displacement discontinuity, start small in length and grow larger in time and space. As faults grow longer, they are able to interact with the neighboring faults at greater distances. Consequently, faults extend their lengths by linkage and coalescence of smaller segments through fault steps in order to accommodate larger amount of slip (Segall and Pollard, 1983; Martel et al., 1988; Martel, 1990; Peacock and Sanderson, 1995; Cartwright et al., 1995; Dawers and Anders, 1995; Pachell and Evans, 2002; Scholz, 2002; Myers and Aydin, 2004; de Joussineau and Aydin, 2009). It follows that the fault length-maximum fault slip plots for faults which grew by linkage and coalescence for any single fault zone is not actually continuous but rather have sharp ‘‘jumps’’ coinciding with large increases in lengths at the merger of neighboring segments and ‘‘flats’’, corresponding to the time span between the consecutive merger instances, in which fault lengths stay nearly constant while fault slips increase to the limiting length slip ratio (Cartwright et al., 1995). Another type of fault scaling relationship illuminates how fault zones become wider as they grow (Fig. 1b). Field data (Hull, 1988; Robertson, 1983; Knott et al., 1996) and theoretical considerations (Scholz, 2002) suggest that the width or thickness of faults increases linearly with fault slip. Agosta and Aydin (2006) and de Joussineau and Aydin (2007) proposed that fault rock zones grow or widen perpendicular to their trend at the expense of highly fractured inner damage zone via cataclastic deformation. This widening is also influenced by the width of the steps along faults (Kim et al., 2004; Childs et al., 2009), which are precursors of fault cores. An important consequence of lengthening of faults by linkage and coalescence is that larger magnitude of slip takes place in merged or composite segments which tend to straighten the overall through-going fault trace with respect to the earlier segmented or discontinuous trace. This process, which appears to be a second order shear localization phenomenon immediately after the fault zone attains the next composite configuration, is referred to as through-going faulting, fault straightening, and fault zone simplification (Cox and Scholz, 1988; Reches and Lockner, 1994; Le Pichon et al., 2001; Scholz, 2002; Ben-Zion and Sammis, 2003). As this short introductory account indicates, the discontinuous geometry of strike-slip faults, their segmentation, the geometry and scaling of the segments and steps, and their impact on earthquake rupture, fluid flow and mineralization have attracted considerable interest in the literature. However, aside from a number of papers addressing the stress state between neighboring faults and the type and orientation of the linkage structure (Segall and Pollard, 1980; Pollard and Segall, 1987; Du and Aydin, 1993; Crider and Pollard, 1998; De Bremaecker and Ferris, 2004), very little attention has been paid to quantification of the elastic parameters leading to the growth of the fault dimensions. To this end, only a handful of studies address these criteria. The first group of these papers includes those dealing with calculation of the critical damage parameters at fault steps in terms of strain invariants (Lyakhovsky and Ben-Zion, in review; Lyakhovsky et al., 1997). The second category is rather empirical and is based on field survey of normal faults and subsequent analysis of displacement-segment separation ratio to define those fields with unlinked and linked configurations (Soliva and Benedicto, 2004). A large number of publications deal with calculating effective moduli of fractured materials (Lockner, ...)_ Ключевые слова: critical density, echelon, fragmentation process, pollard, property, compliance matrix, journal structural, strike slip fault, earthquake rupture, youngs modulus, spacing, geology, doi, uniaxial strength, earlier, strike-slip fault, fault step, watterson, fault-related fracture, triangular pocket, linkage criterion, harris, physical, matrix, fracture set, structural, transversely isotropic, stress, length, valley, aydin, pure shear, fractured, eld observation, study, growth, de?ned, upper bound, elastic matrix, tectonics, geophysical, structure, left-lateral fault, slip fault, fault zone, eigenvalue, mechanical property, segall, damage zone, data, overlapping set, slip surface, brittle, geological, petroleum, nature, strike slip, through-going, international, displacement, failure mode, detailed map, critical, elastic, intersection, neighboring fault, peacock, average, aydin berryman, map, barka, intersection angle, cataclastic deformation, fault slip, set, structural geology, parallel fracture, average spacing, bed thickness, aydin crider, fault core, sandstone journal, sheared, model, distribution, isolated fault, multiple set, mode, left hand, slip, sibson, quasi-shear modulus, minimum spacing, zone, normal, splay, deformation, large number, shearing, linkage, cm, rupture initiation, splay angle, aydin flodin, scholz, damage, pattern, park nevada, work, martel, journal structural geology, letters, journal geophysical, berryman journal, joussineau, increase, joussineau aydin, earthquake, modulus, slip vector, relay ramp, journal, ?eld, cataclastic failure, spacing distribution, sheared joint, occur earlier, thickness, northern, number, fractured medium, fault, maximum, splay fracture, strike-slip, eld data, effective, shear modulus, effective property, press, faulting, conceptual model, relationship, myers, neighboring segment, identied dotted, ha, fracture congurations, elastic modulus, lockner, science, segment, mechanics, joint, engineering, fault rock, mechanical, shear, applied, result, con?gurations, fracture, elastic parameter, elsevier, averaging, angle, fracture spacing, neighboring, geophysical letters, earlier fracture, tectonophysics, area, aggregate slip, density, geophysics, faultingrelated fracture, failure, component, step, kachanov, well-exposed fault, cataclastic, study area, density range, splay joint, left-lateral slip, equivalent spacing, echelon joint, medium, core, shear strain, linear trend, joint zone, axis, fault segment, self-similar geometry, rock mass, rock, fracture density, initial stage, review lyakhovsky, physical property, young, highly fractured, berryman, pure, range, strike, layer, fault linkage, fracture formed, day harris, surface, fault growth, wesnousky