Segment linkage process at the origin of slip surface roughness: Evidence from the Dixie Valley fault
Highlights
► The morphology of the Dixie Valley fault has been measured in 3D. ► The fault slip surface is characterized by a fractal geometry. ► This geometry is explained by the formation of lenses of damaged material. ► A geometrical correlation exists between the slip surface and the damaged zone. ► This correlation is explained through a mechanical model.
Introduction
The geometry of active faults evolves as a result of a series of physico–chemical processes that occur over time scales ranging from 1 s during an earthquake to millions of years following loading and cumulative slip due to plate tectonics, and on spatial scales of the order of one micron to several tens of kilometers. These processes include friction-induced wear associated with rock fragmentation (Power et al., 1988), the formation of a damaged area and of secondary fractures (Shipton and Cowie, 2001), the linkage of fault segments (Walsh et al., 2003), and various mineralogical phase transformations that occur during either an earthquake or the interseismic period. The presence of these various time and space scales may suggest that fault morphology is dominated by stochastic processes and that no specific organization could emerge.
However, pioneering measurements of the topography of exhumed fault planes (Brown and Scholz, 1985; Power et al., 1987; Power and Tullis, 1991; Lee and Bruhn, 1996) indicated that fault roughness can be described by various scaling regimes over a limited range of wavelengths, bounded by characteristic length scales. This phenomenon has been attributed to different processes acting at various length scales. For example, Lee and Bruhn (1996) observed several characteristic length scales between 1 mm and several meters and attributed them to a combination of frictional ploughing, secondary fracturing and intersections between anastomosing fractures along sliding surfaces. Sagy and Brodsky (2009) proposed that roughness of large slip fault surfaces is dominated by elongated bumps and depressions with characteristic length scales of up to several meters, reflecting flow instabilities within fault zones.
The common factor of all these previous works is that they use statistical physics approaches to describe rough profiles extracted from the fault surface. Some definitions related to the scaling properties of a rough profile are given hereafter. A self-affine profile remains unchanged under the scaling transformation , where is the coordinate along the profile, is the roughness amplitude, and is the Hurst exponent or roughness exponent. In the particular case where , the profile is called self-similar. Therefore, if a profile is compliant with a self-similar description, a small portion of the profile, when magnified isotropically, has a statistically identical appearance to a larger part of the profile. In contrast to a self-similar profile, a self-affine profile with is flatter at large scales but still includes a wide variety of amplitudes of small-scale asperities. Therefore, if a profile has a best fit with a self-affine model, different magnification factors will be needed for the directions parallel and perpendicular to the profile in order for a small portion of the profile to appear statistically similar to the entire profile.
Several recent studies on fault surface scaling analysis claim that fault morphology is described by a simple self-affine regime over a broad range of scales (Schmittbuhl et al., 1993; Renard et al., 2006, 2010; Candela et al., 2009; Angheluta et al., 2011; Candela et al., 2011a,b), and because it is difficult to estimate the scaling parameters, most data reported to date lie within the confidence limits of a single self-affine regime. This self-affine geometrical description indicates that the ratio between roughness amplitude and spatial scale decreases when the spatial scale increases. More precisely, these studies show that the roughness morphology of fault surfaces is described by two power laws, one parallel and one perpendicular to the slip direction. Such a self-affine morphology implies that fault roughness is preserved at all scales and that physical processes, that both generate and destroy roughness at all scales, control the scaling regime of this roughness.
In the present study, by combining quantitative structural analysis of the damaged structure of the fault zone with measurements of fault surface roughness, the mechanisms leading to the self-affine geometrical properties of the fault surfaces are addressed. It is suggested that one of these mechanisms is the multi-scale coalescence/linkage of fault segments that creates elongated lenses of deformed rocks that build a self-affine slip surface.
This analysis focuses on the Dixie Valley normal fault (Candela et al., 2011b) because it presents both: (i) particularly well-preserved slip surfaces, and (ii) many field-exposed cross-sections oriented perpendicular to the fault zone. Consequently, this fault offers an excellent opportunity to investigate the relationship between fault surface geometry and fault zone internal architecture. It is worth pointing out that even if the analysis is primarily based on the Dixie Valley fault, the geometrical characteristics of the slip surface and its internal structure are similar to other faults, such as the Vuache-Sillingy fault (Renard et al., 2006; Candela et al., 2009; Angheluta et al., 2011), Magnola fault (Candela et al., 2009), Corona Heights fault (Candela et al., 2011a), and Bolu fault (Renard et al., 2010). In particular, even if this set of faults samples a wide range of different control parameters (cumulative displacement, lithology, tectonic regime, Table 1) which may have controlled fault surface roughness, these fault zones show both: (i) a similar damaged structure characterized by a network of anastomosing sliding surfaces that individualize lenses of damaged material, and (ii) identical self-affine properties of their slip surfaces.
The present article is organized as follows. After introducing the geological setting of the Dixie Valley fault in Section 2, Section 3 presents field observations and fault rock microstructural analyses to identify the deformation mechanisms involved, as discussed in Section 4. An attempt is then made to connect the segment-linkage mechanism at the origin of the multi-scale lenses, with the roughness properties of the fault surface. In this way, the geometrical properties of the lenses constituting the Dixie fault zone are presented in Section 5, and roughness measurements of the slip surfaces are described in Sections 6 Roughness measurements on the Dixie Valley slip surfaces, 7 Results of roughness analysis. Based on experimental studies on fault growth (Otsuki and Dilov, 2005), Section 8 proposes a link between the process of multi-scale aggregation of lenses and the generation of fault roughness. Finally, a fault growth model by segment linkage is proposed that is controlled by the mechanical interactions between fault segments before coalescence.
Section snippets
Geological setting
The Dixie Valley fault (Basin and Range province in Nevada) cuts through rhyolite rocks at the location of the outcrop studied. It was exhumed by normal faulting activity (Fig. 1). Based on gravity studies, combined with reflection seismology studies (Okaya and Thompson, 1985), Power and Tullis (1989) estimated that the total normal cumulated slip is probably between 3 and 6 km. Geological and mineralogical constraints indicate that the slickenside surface formed at depths of less than 2 km and
An array of anastomosed slip surfaces
An important aspect of the architecture of the Dixie Valley fault is that it is composed of a network of anastomosed slip surfaces (Fig. 2). It should be noted that our analysis focused on the structure of the fault core, whilst the damaged zone surrounding it has not been described. A similar structural arrangement in the form of multi-scale anastomosed slip surfaces characterizes fault zones studied in several previous works (Fig. 2 and Table 1). This fault data set covers a wide range of
Deformation mechanisms
As pointed out by Power and Tullis (1989), observations of the textures and microstructures of the Dixie Valley fault highlight cycles of alternating cataclasis and continuous/ductile deformation controlled by fluid influx. Indeed, high strain rates related to the formation of the cataclasites were probably initiated by high pore-fluid pressure due to the trapping of fluid in the fault zone. The CPO in the principal slip zone was then probably formed by an anisotropic dissolution-growth
Geometrical properties of the lenses
The geometrical properties of the lenses were measured on the Dixie Valley fault outcrop. This was possible because many natural transverse topographical depressions cut the damaged area, offering the opportunity to measure the 3-D geometry of multi-scale lenses bounded by sliding surfaces. The length of the axis of symmetry of the lens (Table 2 and Fig. 4) was measured in the same manner as in Lindanger et al. (2007). This approach has methodological limitations because the lenses are rarely
Roughness measurements on the Dixie Valley slip surfaces
The 3-D out-of-plane fault roughness was measured in the field with a LiDAR apparatus (HDS3000; Leica, www.leica-geosystems.com/hds) with a centimeter spatial length scale resolution. Four sub-surfaces of the Dixie Valley fault were selected for analysis because they were particularly well preserved, with few pits or weathering patterns. Note that measurements are limited here to the footwall roughness and the maximum dimension analyzed is 6 m parallel and 10 m perpendicular to the slip
Results of roughness analysis
The two spectral methods are very consistent and show that the roughness of the Dixie Valley fault can be described by two scaling roughness exponents in both structural directions over two orders of length scales, between 5 cm and 10 m. These are and for the Fourier method, and and for the wavelet method (see Fig. 6 and Table 3).
The compiled results of this analysis and previous works (Schmittbuhl et al., 1993; Renard et al., 2006, 2010;
Comparison of natural lenses with experimental fault zones
The observations of elongated lenses described here are complementary to the experimental work of Otsuki and Dilov (2005) who visualized the development of fault zones in a limestone rock deformed experimentally. They observed the progressive development of fault surfaces with cumulated slip, and demonstrated that the faults were formed by coalescence of individual cracks of gradually increasing length and nesting of the resulting multi-scale lenses.
Otsuki and Dilov (2005) have shown that the
Conclusion
The Dixie Valley fault outcrop is characterized by both very fresh slip surfaces free of erosion and many exposed cross-sections perpendicular to the fault. As a result, it is possible to compare the damaged structure of the fault zone with its surface topography. It seems likely that, during fault growth, the mechanism that builds the self-affine fault surface could be the multi-scale coalescence of fault segments that creates elongated lenses of deformed rock with progressive nesting of these
Acknowledgments
This study was supported by the Agence Nationale pour la Recherche grant ANR-JCJC-0011-01 and a Fullbright grant awarded to Thibault Candela. The authors are grateful to Jonathan Imber and Steven A.F. Smith for their constructive comments that helped to improve the manuscript. We acknowledge Emily E. Brodsky and Karen Mair for fruitful discussions.
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