Abstract
Fault growth could be achieved by (1) synchronous increases in displacement and length or (2) rapid fault propagation succeeded by displacement-dominated growth. The second of these growth models (here referred to as the constant length model) is rarely applied to small outcrop-scale faults, yet it can account for many of the geometric and kinematic attributes of these faults. The constant length growth model is supported here using displacement profiles, displacement–length relationships and tip geometries for a system of small strike-slip faults (lengths of 1–200 m and maximum displacements of 0.001–3 m) exposed in a coastal platform in New Zealand. Displacement profiles have variable shapes that mainly reflect varying degrees of fault interaction. Increasing average displacement gradients with increasing fault size (maximum displacement and length) may indicate that the degree of interaction increases with fault size. Horsetail and synthetic splays confined to fault-tip regions are compatible with little fault propagation during much of the growth history. Fault displacements and tip geometries are consistent with a two-stage growth process initially dominated by propagation followed by displacement accumulation on faults with near-constant lengths. Retardation of propagation may arise due to fault interactions and associated reduction of tip stresses, with the early transition from propagation- to displacement-dominated growth stages produced by fault-system saturation (i.e. the onset of interactions between all faults). The constant length growth model accounts for different fault types over a range of scales and may have wide application.
Analysis of outcrop-scale faults over the last 30 years has been central to improved understanding of the growth of fault-zone widths, fault dimensions and fault displacements (e.g. Muraoka & Kamata 1983; Walsh & Watterson 1987; Peacock 1991; Peacock & Sanderson 1991; Dawers et al. 1993; Childs et al. 1996, 2009; Vermilye & Scholz 1999; Kim et al. 2000, 2004; Schultz et al. 2008; Nixon et al. 2011, 2012; Rotevatn & Fossen 2012; Nicol et al. 2013; Roche et al. 2016). A growth model has been widely advocated mainly using data for normal faults in which length and displacement accrue synchronously throughout faulting (Watterson 1986; Cowie & Scholz 1992a, b; Gillespie et al. 1992; Cartwright et al. 1995; Peacock & Sanderson 1996) (Fig. 1 left). For such a model, increase in fault length is achieved by propagation of individual faults and/or linkage of initially isolated faults (Cartwright et al. 1995; Cowie et al. 2000; Kim & Sanderson 2005; Bergen & Shaw 2010). Alternatively, fault growth could be achieved by an initial phase of rapid propagation followed by a more prolonged period of displacement accumulation on faults with near-constant lengths (Filbrandt et al. 1994; Morley 1999; Poulimenos 2000; Meyer et al. 2002; Walsh et al. 2002; Nicol et al. 2005, 2010; Manzocchi et al. 2006; Schlagenhauf et al. 2008; Jackson & Rotevatn 2013) (Fig. 1 right). The constant fault length model has been proposed to account for the growth of faults in analogue models and imaged by seismic reflection datasets. It is consistent with fault segmentation in circumstances where segments are kinematically coherent from their initiation and linkage reflects a strain localization process within individual fault zones (Walsh et al. 2003; Childs et al. 2009).
Schematic diagram illustrating two potential fault-growth models. Diagram shows fault length, tip-zone secondary faulting (fault-trace maps) and along-strike displacement profiles at four times (T1–T4) for increasing fault length (left) and constant length (right) growth models. Displacement–length (D–L) ratios are indicated; they are approximately constant for the increasing length model and increase with displacement for the constant length model. Evolution of displacement and length for each model is shown in the lower schematic graphs. The horizontal and vertical scales are dissimilar for both displacement profiles and displacement–length graphs.
The two alternative fault-evolution models can be tested using growth strata (e.g. Meyer et al. 2002; Childs et al. 2003; Jackson & Rotevatn 2013; Tvedt et al. 2013) and analogue or numerical modelling (e.g. Filbrandt et al. 1994; Cowie et al. 2000; Schlagenhauf et al. 2008); however, these types of data rarely furnish information on the development of small-scale faults in outcrop. In the absence of growth strata, analysis of finite fault geometries and displacements provides a basis for discriminating between increasing and constant length growth models illustrated in Figure 1. These fault outcrop data are generally interpreted to support the increasing length fault-growth model (e.g. Peacock & Sanderson 1996); however, it is our contention that they can be equally well explained by the constant fault length model. The present paper focuses on presenting the data and interpretations for an outcrop-scale fault system that support the constant fault length model.
Fault geometries and displacements constrain the evolution of an outcrop-scale system of faults with apparent strike-slip displacements from the east coast of New Zealand's North Island (Fig. 2). These faults displace a moderately dipping (c. 50°) sequence of well-bedded turbidites exposed in a near-horizontal shore platform. The outcrop geometry is equivalent to small (lengths of 1–200 m and maximum displacements of 0.001–3 m) normal faults cropping out in cliff sections, but with the dimensions of the platform permitting easy access to a large stratigraphic interval and many faults (compared to typical outcrop cross sections). Local variations in the fault displacement profiles support suggestions that all faults interact to varying degrees, with individual faults being both hard- and soft-linked (cf. Walsh & Watterson 1991). The increase in displacement gradients with increasing fault size also supports the view that fault interactions play a critical role in establishing fault dimensions and displacement distributions. The outcrop data, including the concentration of secondary splays and minor faults at the tips of some faults, are consistent with a model in which faults propagate rapidly until they reach saturation and subsequently grow mainly by displacement accumulation with near-constant lengths.
Study area location map. (a) New Zealand location of the outcrop examined and plate boundary setting. The white open arrow shows the present relative plate motion vector of Beavan et al. (2002). AF, Alpine Fault; HT, Hikurangi Trough (front of the subduction accretionary prism). (b) Map of the shore platform showing faults (thin black lines), bedding (dotted lines) and locations of Figures 3 and 7 (boxes). The shore platform is bounded by the high- and low-tide shorelines. Areas of data collection are shown by the black rectangles; faults outside of these areas are not shown.
Fault system geometry and kinematics
Outcrop-scale strike-slip to oblique-slip faults displace moderately dipping (c. 45–55°) turbidites (Whakataki Formation) in coastal exposures on the east coast of New Zealand's North Island (Figs 2, 3, 4a). The Whakataki Formation is an Early Miocene (c. 20–24 Ma) deep-water turbidite succession (Johnston 1980) that, at low tide, forms a spectacular wave-cut platform up to 120 m wide and several kilometres long (e.g. Figs 2 & 3). This formation comprises interbedded sandstone and siltstone beds (net to gross locally varies from 20 to 80%) ≤40 cm thick that mainly strike NNE approximately parallel to the coast and dip to the west (Johnston 1980; Edbrooke & Browne 1996; Field 2005) (Figs 2 & 4a). Bedding on the wave-cut platform is displaced by hundreds of small post-depositional faults, with apparent strike slip displacement of <3 m. In addition, some early bedding-parallel slip and thrusts are present, which may have partly formed during folding and associated bedding-parallel shortening (see early thrust in Fig. 3). Late-stage strike-slip faults are the focus of this study. These faults formed post-lithification and displace bedding-parallel (and sub-parallel) faults (e.g. Fig. 3), from which we suggest that they mainly post-date folding and bed rotation. The timing of formation of strike-slip faults is poorly constrained; however, given that the Whakataki Formation was probably buried by up to 3 km (Edbrooke & Browne 1996; Field 2005) and then tilted prior to strike-slip faulting, a mid-Miocene or younger age is inferred here.
Interpreted oblique aerial photo of the Whakataki Formation shore platform illustrating the fault system and its relationship to bedding (photograph by Lloyd Homer). White lines indicate faults and coloured lines indicate individual beds mapped across the platform. Arrows indicate the sense of slip on the faults. Location of photo is shown in Figure 2. Location of fault 18 (Fig. 9a) is indicated.
Equal-area stereonets showing bedding, fault and slickenside striation orientations (a & b) together with frequency histogram of slip rake (c) from the areas enclosed by the dataset rectangles in Figure 2. (a) Stereonet of poles to bedding and mean bedding plane orientation. (b) Poles to faults, mean orientations for two main fault sets (c. 135° set 1 and c. 175° set 2) and fault-slip striation orientations. (c) Histogram of rake for measured slip data. Number of observations (N) is indicated for each plot.
The coastal platform trends approximately 030° and provides map data for the apparent strike-slip faults (Fig. 2). The horizontal outcrop, moderate bed dips and well-defined bed boundaries every c. 20–40 cm enable fault lengths, intersection relationships and displacements to be analysed. The fault locations, lengths and apparent strike-slip displacements of bedding have been delineated using high-resolution aerial photographs (both vertical and oblique, c. 1:50 to 1:1000 scales) together with outcrop tape and compass measurements. Detailed data for a total of about 150 faults include: fault surface and slip orientations, fault maximum displacements, fault lengths and along-strike displacement profiles. The fault system comprises two dominant fault sets that strike c. 135° (fault-set 1) and c. 175° (fault-set 2) and cross-cut each other to form conjugates (Figs 3 & 4b). Fault dips are predominantly steep (>60°) and, in many cases, exceed 80°, with fault-set 1 mainly dipping north and fault-set 2 dipping both east and west (Fig. 4b). The faults observed in the platform range in length from c. 0.4 to 200 m and in apparent strike slip from 0.001 to 3 m. Spacings of faults mapped in aerial photos generally range from 1 to 40 m with fault intersections and fault tips being common. Cross-cutting and abutting relationships between individual faults indicate that the two main fault sets formed synchronously on geological timescales.
Apparent strike-slip displacements were measured on bedding boundaries (Fig. 3). Slip indicators (slickenside striations) mainly plunge at shallow to moderate angles (mostly ≤50°), at a high angle to bedding (mainly ≥60°) (Fig. 4b, c). Slickenside striations indicate a significant component of strike-slip displacement with the c. 135° fault set (1) being right-lateral and the c. 175° fault set (2) being left-lateral (the faults are hereafter referred to as strike slip). These faults formed in association with principal horizontal shortening oriented approximately SSE–NNW sub-parallel to the regional direction of shortening along the east coast of the North Island, which is associated with subduction of the Pacific Plate during the late Cenozoic (e.g. Nicol et al. 2007) (Fig. 2a).
Fault displacement profiles
Displacement profiles and fault-trace maps have been widely employed in the literature to constrain the mechanics, kinematics and growth of faults over a range of scales (e.g. Muraoka & Kamata 1983; Barnett et al. 1987; Walsh & Watterson 1987, 1988; Ellis & Dunlap 1988; Peacock 1991, 2002; Peacock & Sanderson 1991, 1992, 1996; Cowie & Scholz 1992a, b; Dawers et al. 1993; Dawers & Anders 1995; Nicol et al. 1996, 2005, 2010; Cowie & Shipton 1998; Manighetti et al. 2001, 2004; Wilkins & Gross 2002; Manzocchi et al. 2006; Schlagenhauf et al. 2008; Bergen & Shaw 2010; Rotevatn & Fossen 2012; Jackson & Rotevatn 2013; Tvedt et al. 2013; Roche et al. 2016). In this study strike-parallel displacement profiles display variations in strike slip along the length of fault traces confined to the shore platform (Figs 5 & 6). The maximum displacements for the faults profiled range from 7 mm to 37 cm (Fig. 5) with uncertainties on displacement measurements typically in the range of 2–10 mm. The profiles presented in Figure 5 have a number of characteristics that are consistent with the results of many previous studies (see papers referred to previously in this section). These are: (i) the displacement profiles show a range of geometries including near-triangular with a centrally located maximum (Fig. 5; faults 10, 11 and 13), asymmetrical with relatively steep gradients towards one tip (Fig. 5; fault 8 and faults 2, 6 and 7) and flat-topped profiles with high gradients at both tips (e.g. Fig. 5; faults 3 and 5). (ii) Approximately bell-shaped profiles were rarely sampled in the Whakataki Formation outcrop and many of the faults do not display a decrease in displacement gradient approaching fault tips (Fig. 5). (iii) Intersecting or closely spaced faults (e.g. <10 m spacing) often display complementary displacement profiles, with equal and opposite displacement gradients (Fig. 7). (iv) Average displacement gradients from the point of maximum displacement to the fault tip typically increase with fault size (Fig. 8).
Along-strike displacement profiles for strike-slip faults entirely contained within the platform. Note that horizontal and vertical scales change between graphs with displacements and lengths varying from 0.007 to 0.37 m and 8 to 90 m, respectively. Locations of faults 8–15 are shown in Figure 7.
Normalized displacement profiles (n=31) from maximum displacement to tip for 16 faults (black lines). The plot primarily uses data from Figure 5. The thick line is the mean curve for the entire dataset (n=435 displacement measurements) constructed using a running average with a ten-observation bin size and bin centres at 0.01 increments of normalized length. The near-linear general slope of the mean curve is comparable to many of the underpinning profiles and was not significantly modified using a range of bin sizes (5–50 observations) and bin location increments (0.005–0.1). Profiles above the mean curve are considered to be more influenced by interactions than profiles below the mean.
Fault map and strike-slip displacement profiles projected onto planes normal to bedding. Fault numbers indicated on the map apply to the profiles in this figure and those presented in Figure 5. The displacement scale is the same for all profiles. Beds A, C, E, F and H are shown on both map and profiles.
Displacement–length plot for Whakataki faults sampled from the shore platform (open circles) and a global compilation of faults (grey symbols). The global compilation is primarily from Bailey et al. (2005) with additional data from subsequent publications (Lamarche et al. 2005; Fossen et al. 2007; Bergen & Shaw 2010; Nicol et al. 2010; Reilly et al. 2016) and unpublished measurements. Uncertainties on the fault length and displacement measured at Whakataki are typically small (<1 m and <1 cm, respectively), and do not impact on the general distribution of the data points on the log–log graph or the first-order conclusions. The line of best fit (D=0.0007L1.52) is a least-squares regression on the y-axis variable. Contours labelled 0.00001 to 0.1 are D–L ratios (i.e. 0.5 of displacement gradients). The average line for earthquake data (i.e. D=0.00005L) is dashed and from Wells & Coppersmith (1994). Vertical arrows show growth trends for the constant length model (Walsh et al. 2002).
Variations in the shapes of displacement profiles and associated displacement gradients can be influenced by a number of factors, including fault and host rock mechanical properties, the magnitudes and orientations of stresses imposed on the fault, the displacement history of the fault and its individual slip increments, and interactions with other faults in the array (e.g. Walsh & Watterson 1987; Peacock & Sanderson 1996; Schultz 1999; Peacock 2002; Manzocchi et al. 2006). In multilayer sequences comprising beds with variable rheologies the geometry of the fault surface (strike or dip), the displacement on the primary slip surface and the location of fault tips may be strongly influenced by changes in rock properties (e.g. Muraoka & Kamata 1983; Peacock & Sanderson 1992; Nicol et al. 1996; Manighetti et al. 2001; Wilkins & Gross 2002; Schöpfer et al. 2006; Roche et al. 2016). In particular, it is common for displacements to decrease across, and fault tips to be located within, mechanically weak beds dominated by mudstone (e.g. Nicol et al. 1996; Wilkins & Gross 2002). In the Whakataki Formation fault tips are largely confined to mudstone beds or to the boundaries of mudstone beds. In addition, some mudstone beds appear to contain a greater number of fault tips than would be predicted if the tips were randomly distributed in the sequence. Inspection of the faults in Figure 3, for example, confirms that a similar geometry and density of faults occurs on either side of a mudstone-rich zone that contains bed z; however, in detail 30–40% of individual faults or fault segments terminate in this zone, suggesting that its mechanical properties may have impacted on the continuity (and propagation) of some faults. These observations support the view that bed rheology and architecture can influence fault growth (Peacock & Sanderson 1992; Peacock 2002; Schultz & Fossen 2002; Wilkins & Gross 2002).
The ideal isolated fault is a valuable concept for generating initial models that contribute to improved understanding of faulting processes and evolution (Barnett et al. 1987; Walsh & Watterson 1987); however, it is widely recognized that few faults are likely to form in complete kinematic or dynamic isolation from other structures. On both geological (millions of years) and earthquake (<1000 years) timescales faults generally represent interacting elements within kinematically coherent systems (e.g. Peacock 1991, 2002; Walsh & Watterson 1991; Bürgmann et al. 1994; Nicol et al. 1996, 2010; Stein 1999; Cowie et al. 2000; Nixon et al. 2014). Fault interactions provide an important (in many cases the primary) control on the shapes of displacement profiles with the degree of interaction and the magnitude of displacement gradients inferred to be positively related (e.g. Muraoka & Kamata 1983; Peacock 1991, 2002; Nicol et al. 1996, 2010; Manighetti et al. 2001). This relationship may arise because fault interaction retards fault propagation without significantly impacting the rate of increase in maximum displacement (Peacock & Sanderson 1996). The role of fault interactions in determining the shape of displacement profiles is supported by this study. Here, as is common in other fault systems, flat-topped or highly asymmetrical profiles with high tip displacement gradients are associated with those faults that intersect, or relay displacement to, nearby faults (e.g. faults 2, 3, 5, 6, 7, 12, 14 and 15, Fig. 5). By contrast, the faults with symmetrical profiles that generally have the lowest displacement gradients tend to be those that are farthest from other faults in the system of similar size. These conclusions are supported by the fault map and displacement profiles in Figure 7. Faults 13–15 and 16–17 intersect and produce complementary displacement profiles; displacement is transferred southwards from fault 17 to 16, while the displacements on faults 13 and 15 largely fill the displacement low down on fault 14. Faults 9 and 10 do not intersect in the plane of the platform and appear to be separated by a zone across which displacement is transferred between faults. Such fault interactions are difficult to unequivocally demonstrate on the shore platform for faults with spacings of tens of metres or greater, in part because the faults are small, with changes in displacement and displacement gradients typically being low (typically <1 cm per metre for faults that are not hard-linked). However, fault interactions over length scales of kilometres have been inferred for normal faults with maximum displacements of tens of metres to kilometres and lengths of kilometres or more (e.g. Walsh & Watterson 1991; Nicol et al. 1996, 2010). These observations are consistent with the notion that all faults interact and the degree of interaction is positively related to the lateral displacement gradients (i.e. low displacement gradient faults are inferred to indicate less interaction and displacement transfer with nearby faults than high-gradient faults).
In addition to reflecting fault interactions, the shapes of displacement profiles have the potential to provide information about fault propagation (Peacock & Sanderson 1996; Manighetti et al. 2001; Childs et al. 2003; Manzocchi et al. 2006). Finite displacement profiles are often approximately triangular with varying degrees of asymmetry and near-linear displacement gradients from maximum displacement to fault tip (e.g. Walsh & Watterson 1987; Nicol et al. 1996; Cowie & Shipton 1998; Manighetti et al. 2001, 2004; Manzocchi et al. 2006). The triangular-shaped profiles observed for different fault types (mainly strike slip and normal) in many fault systems are consistent with the observations of this study, where many of the faults and the average profile (see thick red line on Fig. 6) have approximately linear gradients. Near-triangular displacement profiles do not display the low displacement tails predicted for faults by post-yield fracture mechanics (Cowie & Scholz 1992b) or for rapidly propagating faults (Peacock & Sanderson 1996). Low displacement concave-upwards tails are observed for up to c. 27% of the faults in Figure 5 (i.e. 8 of 30 tips in Fig. 5; fault 1 right tip, fault 7 left and right tip, fault 9 right tip, fault 10 right tip, fault 11 left tip, fault 13 right tip and fault 15 right tip). In such cases the displacement profiles can be interpreted to reflect fault propagation; however, it is also possible that incremental and finite displacement profiles had comparable shapes (when normalized to their respective maximum displacements), with little propagation during the majority of displacement accumulation. Similarly, the fact that the remaining c. 75% of faults have approximately uniform displacement gradients approaching their tips and these fault displacement profiles provide no basis for favouring a fault propagation model over one in which little or no propagation occurs for much of the duration of faulting (Fig. 5).
Mutually cross-cutting relationships at the intersections of the two main fault sets indicate that the faults in this study accrued displacement synchronously (on geological timescales) during multiple slip events. Therefore, the history of fault growth and the shape of incremental displacement profiles is not uniquely constrained by the finite displacement profiles in the shore platform. The semi-elliptical incremental profiles modelled for linear elastic materials (e.g. Pollard & Segall 1987) are rarely replicated in the finite profiles of the Whakataki Formation (e.g. Fig. 5). Field mapping provides little evidence to support the model that departure of finite displacement profiles from semi-elliptical arises due to off-fault deformation (see Manighetti et al. 2004); however, we cannot discount the possibility that slip during these discrete events was semi-elliptical. In circumstances where the shape of incremental slip profiles is not known, stochastic earthquake modelling shows that for a range of incremental slip profile shapes (including elliptical), triangular finite profiles and a propagating fault are not compatible with the displacement gradients typically observed for outcrop-scale faults (Manzocchi et al. 2006; see next section for further discussion). Stochastic modelling of Manzocchi et al. (2006) indicates that the near-triangular profiles widely observed (including in this study; Figs 5 & 6) are consistent with a fault-growth model in which fault lengths are established rapidly and subsequent faulting is dominated by the accumulation of displacement and tip restriction, resulting in little or no propagation.
Displacement–length relationship
The ratio of displacement–length and how it varies with fault size constrains fault-growth models (Walsh & Watterson 1988; Cowie & Scholz 1992c; Gillespie et al. 1992; Dawers & Anders 1995; Schultz & Fossen 2002; Walsh et al. 2002; Wilkins & Gross 2002; Bailey et al. 2005; Kim & Sanderson 2005; Manzocchi et al. 2006; Schultz et al. 2008; Nicol et al. 2010; Rotevatn & Fossen 2012). Displacement–length relations are described by the expression D=cLn, where D is displacement, L is fault length, c is a constant defined by the y-intercept and n is a constant defined by the slope of the distribution (e.g. Fig. 8). The most widely accepted value of n is 1; however, displacement–length (D–L) plots for individual fault systems typically reveal slopes (n) of 0.5–1.5 over 2–3 orders of magnitude of displacement and length (e.g. Walsh & Watterson 1988; Schlische et al. 1996; Fossen & Hesthammer 1997; Bailey et al. 2005; Kim & Sanderson 2005). Debate remains about the value of the D–L slope of the power-law distribution and whether or not the positive slope of the data cloud represents a growth trend, consistent with the increasing fault length growth model (e.g. Walsh & Watterson 1988; Cowie & Scholz 1992c; Walsh et al. 2002) (Fig. 1 left). Resolving each of these questions has significant implications for the evolution of faults.
To examine our understanding of the growth of faults we have plotted displacement and length for faults contained within the platform (open circles) along with a compilation of global fault data (grey symbols; see figure caption for data sources, Fig. 8). Faults from the Whakataki Formation are located towards the centre of the global compilation, suggesting that their D–L relations are broadly comparable to faults of similar size in other fault systems. While we have a small number of data (n=67), cover a limited size range (<3 orders of magnitude in length and displacement) and display a significant spread of both displacement and length (as is common on these types of plots), it is clear that in this case n is significantly greater than 1 (Fig. 8). A value of n>1 requires that average displacement gradients increase with fault size. Lines labelled 0.00001–0.1 on Figure 8 are contours of D–L and highlight the rise in average displacement gradients from c. 0.0006 to 0.06 with increasing fault displacement and length. In this fault system retardation of fault-tip propagation by thick weak mudstone beds or by fault interaction provide possible explanations for the relatively high n. In circumstances where retardation is complete (i.e. faults do not propagate) fault growth is associated with an increase in displacement without a change in fault length, resulting in vertical growth trends on D–L plots (Walsh et al. 2002) (Fig. 8).
In recent years it has been proposed that faults mainly grow vertically into the D–L distribution rather than evolving along it (Walsh et al. 2002; Nicol et al. 2010). Such vertical growth trends require that after initial rapid propagation, which typically occurs on timescales shorter than the resolution of the data, faults do not grow significantly in length (Filbrandt et al. 1994; Morley 1999; Meyer et al. 2002; Walsh et al. 2002; Schlagenhauf et al. 2008; Jackson & Rotevatn 2013). The constant length growth model of Walsh et al. (2002) (Fig. 1 right) has the advantage that it provides a rationale for the evolution of faults from individual slip increments (e.g. earthquakes), for which n may be 0.5–1 (e.g. Cowie & Scholz 1992a; Wells & Coppersmith 1994; Fossen & Hesthammer 1997; Schultz et al. 2008; Nicol et al. 2010; Rotevatn & Fossen 2012), to their finite displacement–length population (Fig. 8). In circumstances where individual faults grow along trends steeper than the D–L distribution, their average displacement gradients increase as strain accrues in an array (Schultz 1999; Poulimenos 2000; Walsh et al. 2002; Schlagenhauf et al. 2008). Proportional increases in average displacement gradients for all faults in a system will produce upward migration of the D–L distribution as strain accrues without a change in n. Recent work suggests, however, that n may increase with fault-system maturity and strain accumulation (Nicol et al. 2010; Rotevatn & Fossen 2012; Nicol 2014) (Fig. 8). Preferential death of smaller faults in a system, coupled with continued displacement on larger faults of near-constant length, represents one set of conditions that could produce an increase in n (Meyer et al. 2002; Walsh et al. 2002; Nicol et al. 2010). Increasing n with fault-system maturity would require that fault-growth processes are scale dependent (i.e. there are differences in the growth of small and large faults); however, further data analysis is required to test the hypothesis that n could change with fault-system evolution.
Fault-tip splays and propagation
Small-scale faulting and fracturing around fault tips is widely observed and can provide information about their propagation (e.g. King 1986; Cowie & Scholz 1992b; McGrath & Davison 1995; Vermilye & Scholz 1999; Kim et al. 2000, 2004; d'Alessio & Martel 2004; Nixon et al. 2011; Perrin et al. 2016). For strike-slip faults in map view, the strike of secondary faults can vary dramatically from moderate to high angles (e.g. >30°) to the main fault (e.g. horsetails, wing cracks or tail cracks) to being sub-parallel to the primary fault (e.g. synthetic splays, see Kim et al. 2004). Numerous models have been proposed to account for the formation of these fault-tip structures (e.g. Chinnery 1966; Cowie & Scholz 1992b; Kim et al. 2000, 2004; d'Alessio & Martel 2004). Common to most of these models is the notion that slip on the primary fault surface locally produces stress concentrations at the fault tip that are relieved by distributed strains in the rock volume enclosing the tip.
Fault-tip splays and associated decreases in displacement along the primary fault can be interpreted to provide evidence of fault propagation towards the finite fault tip (e.g. Kim et al. 2004; Perrin et al. 2016). In circumstances where fault splays form due to tip processes, the distribution of secondary faults along a primary fault has the potential to provide information about whether increasing (i.e. gradually propagating) or constant length fault-growth models best explain the observed fault outcrop patterns (see Fig. 1). For a propagating primary fault, secondary faults formed along the tip line will be abandoned as the tip propagates and remain preserved along the length of a fault as part of the finite strain field (Fig. 1 left). Alternatively, if a fault tip remains stationary for much of the duration of faulting, then secondary faults formed in association with termination processes will be localized near to the present tip (Fig. 1 right).
The densities of small-scale faults adjacent to larger structures are dependent on many factors, including pressure and temperature conditions during faulting (including fluid and confining pressures), size of the primary fault, orientation of the maximum compressive stress, mechanical properties of the rock at the time of faulting, geometry of the primary fault (e.g. degree of segmentation) and its linkage or intersection with other similar-sized faults in the system (see Kim et al. 2004 and references therein). Despite the wide range of factors that could control the formation of small-scale faults and their often complex geometries (e.g. variable orientations and intersection relationships), field studies suggest that elevated numbers of small-scale faults are most often observed at fault segment boundaries (e.g. relay zones or fault steps), fault intersections, fault tips and stratigraphic mechanical boundaries (e.g. McGrath & Davison 1995; Childs et al. 1996, 2009; Kim et al. 2000, 2004; Nicol et al. 2013; Roche et al. 2016). As a result of these different geometrical associations, the densities of secondary faults can vary along the length of the primary fault. Along-strike variation in the densities of secondary faults in the immediate wall rock of larger structures occurs in the Whakataki Formation, with high densities being particularly common at the intersections of the two main fault sets. In addition, some of the primary faults in the shore platform are associated with secondary faults localized at the free tips of the main fault (Fig. 9). The resulting splays can accommodate a significant component of the apparent strike-slip displacement approaching the fault tip and combine to produce near-triangular cumulative displacement profiles (e.g. Fig. 10). These splays are inferred to form during the interaction phase of faulting and to facilitate a rise in displacement gradients without significant propagation. On fault 19 (Fig. 10), for example, the average displacement gradient of c. 0.01 is towards the upper limit of data in Figure 8 for faults with maximum displacements of 0.04 m. The examples presented show horsetail and synthetic branching geometries with, in two cases, the main fault being a member of fault-set 2 and the tip splays parallel to fault-set 1 (Fig. 9a, c; faults 18 and 20). Despite the occurrence of both fault orientations at tip locations, none of the examples presented in Figure 9 appears to have formed due to hard-linkage of these sets or due to segmentation of a single fault set. Instead, the occurrence of secondary faults in tip zones parallel to each fault orientation may reflect the far-field stresses producing the conjugate fault system.
Maps of tip splays at the terminations of four faults. Arrows indicate slip sense and open circles indicate tip locations. See Figure 3 for the location of fault 18.
Fault-trace map and displacement profiles for the main slip surface, fault splays and total displacement along fault 19. Horizontal scales in both diagrams are equal, enabling displacements and fault geometries to be correlated.
Fault-tip splays are consistent with the constant fault length model (Fig. 1 right). They do not occur on all faults in the Whakataki platform; however, where secondary fault splays do occur, they are mainly restricted to the area around the present fault tip. In Figure 9a (fault 18), for example, the fault extends for a further c. 30 m on the platform north of the tip splays and is associated with no additional splays of comparable length and displacement to those at the tip (Fig. 3). Fault-tip geometries in Figure 9 are comparable to those reported in the literature, where secondary faulting is mainly restricted to the region surrounding the present fault tip (e.g. King 1986; McGrath & Davison 1995; Kim et al. 2000, 2004; Perrin et al. 2016). Secondary faults that are similar in geometry and size to tip splays are not routinely observed distal to fault tips on the Whakataki shore platform, from which we infer that the gradually propagating fault model is unlikely to be correct for the tips in Figure 9. Instead, the observed fault-tip geometries can be explained if faults initially propagate rapidly, due to the presence of a pre-existing plane of weakness and/or low fracture toughness of the faulted materials, with near-constant fault lengths and stationary fault-tip locations subsequently maintained for much of the duration of faulting (Fig. 1 right). For the constant length model the initial stage of propagation is sufficiently rapid that few fault-tip structures form prior to the fault reaching its final length. When the fault tips become stationary new secondary faults may form in the fault zone around the tip as displacement accrues on the principal slip surface (Fig. 1 right). Secondary faulting restricted to the area around the fault tip has been replicated by numerical models in which tip stresses and strains are localized by a pre-existing plane of weakness that does not propagate (e.g. Pollard & Segall 1987; Bürgmann et al. 1994). Therefore, both outcrop and modelling could be consistent with the constant fault length model, although in the absence of growth strata, neither the constant length nor propagating faults can be unequivocally demonstrated at Whakataki.
Discussion and conclusions
Displacement profiles, D–L relationships and tip geometries for a fault system exposed in a large (up to 120 m by 1.2 km) coastal platform constrain fault-growth models. Displacement profiles have variable shapes that mainly reflect fault interactions, with individual faults being both hard- and soft-linked. Many of the displacement profiles and the average profile for all faults are near-triangular, with displacement gradients (and displacement–length ratios) increasing by two orders of magnitude from smallest to largest faults. Within fault zones these gradients are accompanied by secondary faults, which are typically of greatest density close to fault intersections, in relay zones and at fault tips. Where present, horsetail and synthetic splays are mainly confined to the regions around the tips of faults, and are incompatible with gradual fault propagation for the duration of growth. Instead, fault displacements and tip geometries are consistent with growth initially dominated by fault propagation followed by displacement accumulation and approximately stationary tips (Figs 1 & 11). The change from propagation- to displacement-dominated growth stages is inferred to be produced by fault-system saturation (i.e. the onset of the state where all faults are interacting). In this two-phase model fault interactions between neighbouring faults, and associated soft- or hard-linkage, retard propagation by reducing tip stresses and fracture energy (d'Alessio & Martel 2004) (Fig. 11). The relative duration of each stage of faulting is generally not known precisely; however, the available evidence suggests that the initial propagation stage is significantly shorter than the displacement stage (e.g. Walsh et al. 2002). The relative durations of each stage of faulting may vary depending on the properties of the faulted rock volume, the presence of pre-existing faults or joints, and/or the rates and magnitudes of strains and stresses. For example, where faulting utilizes pre-existing heterogeneities or zones of weakness and these structures are optimally oriented in the new stress regime, fault lengths may be established instantaneously on geological timescales (e.g. ≤10 slip increments). Even in circumstances where new faults are formed, their lengths can be established within 20% of the duration of faulting with the remainder of the faulting history dominated by displacement accumulation (e.g. Filbrandt et al. 1994; Schlagenhauf et al. 2008).
Schematic block diagrams showing the evolution of the Whakataki fault system with initial rapid propagation (phase 1) and subsequent growth via increasing displacements and near-constant faults (phase 2) (i.e. constant length model in Fig. 1 right). Orientations of fault sets and bedding approximately match those observed in Figure 2.
Initial rapid fault propagation succeeded by displacement-dominated growth could account for different modes of faults over a range of scales (including outcrop). Fault interactions are a key element of the model and, although variable in degree, occur throughout fault systems over geological and earthquake timescales (e.g. Walsh & Watterson 1991; Stein 1999). Given the important role of fault interactions in the constant length model, it may be equally appropriate to refer to this as the fault interaction or coherent fault growth model (Walsh & Watterson 1991; Walsh et al. 2003; Nicol et al. 2010; Jackson & Rotevatn 2013). Similarly, the increasing length model may apply where fault interactions do not impede propagation, and this could be referred to as the isolated fault-growth model. Although models of isolated faults are of value (Barnett et al. 1987; Walsh & Watterson 1987; Cowie & Shipton 1998; Vermilye & Scholz 1999), they appear to be rare (e.g. Nicol et al. 1996), and future studies would be well served to focus on kinematic and dynamic interactions between faults and their influence on growth. If the two-stage growth model favoured here is correct, analysis of low-strain systems will be required to understand better the early stages of fault evolution and the transition from propagation- to displacement-dominated growth. A two-stage model (Fig. 1b) for fault growth was initially proposed for regional-scale normal faults imaged in seismic reflection lines (Morley 1999; Meyer et al. 2002; Walsh et al. 2002) and also applies to normal faults in analogue models (Filbrandt et al. 1994; Schlagenhauf et al. 2008). If our interpretations are correct, the growth model in Figure 1b applies over at least five orders of magnitude from regional- (e.g. lengths of 1–50 km and displacements of 0.1–3 km: Walsh et al. 2002) to outcrop-scale (e.g. lengths of 0.4–200 m and displacements of 0.002–3 m: this study) faults with significant components of strike slip and dip slip, and for fault dimensions measured parallel and perpendicular to the slip vector. Therefore, we contend that the constant length fault-growth model has wide applications.
Acknowledgments
We are indebted to Juan Watterson who, in addition to proving to be an exceptional mentor, was instrumental in establishing the principles on which this paper is founded: the quantitative analysis and modelling of faults using high-quality datasets. This research was financially supported by GNS Science Core Funding. Adrian Harvison, Cathal Reilly, Hannu Seebeck and Rob Worthington assisted with the collection of field data. Many thanks to Casey Nixon and Chris Jackson who provided journal reviews that helped to improve the paper.
- © 2017 The Author(s). Published by The Geological Society of London. All rights reserved
