Precise factors controlling the coevolution of deformation and topography in tectonically active landscapes remain poorly understood due to complex feedbacks between numerous possible variables. Here we examine the links between fault kinematics, emergent topography, and environmental factors on a global data set of active fault-driven mountain ranges (n = 41). Using simple regressions between tectonic, climatic, and topographic variables, we explore the controls on fault-driven landscape development at the range scale. For each fault in our Google Earth accessible database, we compiled (1) topographic metrics from a 30-m digital elevation model including along-strike changes in elevation and relief, fault length, and tip zone length (the along-strike distance from fault tip to where the associated relief stops increasing) and gradient; (2) long-term (104–6 yr) tectonic variables including fault slip rate, displacement rate, displacement, and age; (3) climatic variables including annual precipitation; and (4) rock type from geologic maps. Our results show that all mountain ranges reach a uniform value of relief within some distance from their tips and the length scale of this relief growth correlates with long-term vertical displacement rate (R = 0.55) and slip rate (R = 0.51). We apply a well-established framework for fault growth as the tectonic boundary condition to estimate the time required to achieve this uniform relief (∼104–6 yr) and suggest that this threshold time indicates regional tectonomorphic equilibrium. Strong correlations between annual precipitation and deformation rates (R > 0.60), and between lithologic strength and mountain relief (R > 0.70), allude to other principal forces affecting emergent landscape form that are often ignored. Our findings demonstrate that fault-driven topography always saturates in relief, suggest there are quantifiable fault-kinematic controls on landscape form, and hint that landscape relief patterns may, in turn, be used to estimate rates of faulting.
Mountain belts possess diverse topographies that hold important clues about the tectonic and climate-driven erosion processes that shape them. Many studies of these landscapes have focused on the relative effects of relief or climate on erosion without explicitly considering tectonics (Ahnert, 1970; Pinet and Souriau, 1988; Montgomery and Brandon, 2002; Willenbring and von Blanckenburg, 2010). Other attempts have been made to relate worldwide mountain belt topography (orogen scale, thousands of km) to quantitative measures of both tectonics and climate (Champagnac et al., 2012). At the orogen scale, climatic and tectonic variables (mean annual precipitation, latitude, and shortening rates) can explain only limited variance (<50%), presumably because substantial complexities exist at this large scale (e.g., Champagnac et al., 2012). Perhaps as a result, most research addressing the relative roles of tectonics and climate in shaping landscapes has maintained a more regional focus, considering single mountain belts and often neglecting lithologic variations (Dahlen and Suppe, 1988; Montgomery et al., 2001; Stolar et al., 2006; Carretier et al., 2013). However, even a single region often encompasses multiple structures that overprint each other in space and time (Mouslopoulou et al., 2009; Pavlis et al., 2014). An alternative, more tractable approach to explore how topography and tectonics are linked is to focus on individual structures and their smaller (10–100 km fault trace length), emergent landforms associated with the earliest phases of fault growth (e.g., Barnes et al., 2011).
Across the globe, individual mountain ranges within a given tectonic setting tend to display similar morphologies to neighboring ranges, with equivalent widths, lengths, and relief (e.g., the U.S. Basin and Range Province; Ellis et al., 1999). These landscapes reflect feedbacks between tectonic processes that raise Earth’s surface and erosive processes that lower it (Schmidt and Montgomery, 1995; Montgomery and Brandon, 2002). For example, the tectonically driven uplift of mountain ranges increases relief, leading to enhanced erosion by concentration of erosional mechanisms such as river incision and landsliding (Ahnert, 1970; Willett and Brandon, 2002). Within a tectonic province, environmental factors controlling these feedbacks (e.g., isostasy, climate, lithology, tectonic topography, and crustal properties) tend to be the same; so it is not surprising that the ensuing morphologies are also similar. However, similarities that span across tectonic settings are more intriguing. For example, research continues to address the fact that topographic relief eventually reaches a limit within small, simple ranges as well as orogenic belts, regardless of the tectonic setting (Densmore et al., 2004; Densmore et al., 2007b; Stolar et al., 2007; Burbank and Anderson, 2012; Champagnac et al., 2012). This global-scale observation indicates that there may be more universal controls determining how deformation and topography are linked.
Observations of both fault growth and topographic growth are beginning to reveal how they are linked. Step one is the recognition that faults grow in systematic ways. Faults tend to exhibit predictable relationships between their spatiotemporal variations in length, offset, and slip rate. For example, fault displacement scales linearly with length regardless of fault type (Cowie and Scholz, 1992a, 1992b; Dawers et al., 1993; Schlische et al., 1996; Gupta and Scholz, 2000). At the earliest stages of growth, faults grow laterally by tip propagation; when fault segments begin to interact with neighboring segments, the stress field is altered, and those in favorable spatial arrangements will experience an increase in displacement rates. The result is an integrated displacement gradient that increases from zero at the fault tips to central maxima (Fig. 1A; Dawers and Anders, 1995; Cowie, 1998; McLeod et al., 2000; Cowie and Roberts, 2001; Roberts et al., 2004). Due to mechanical breakdown and decreased friction along a fault plane, slip rate follows a similar pattern with highest slip rates in the fault center and tapering to zero at the tips (Cowie, 1998; Cowie and Shipton, 1998). A few studies have exploited this simple fault-growth framework as a tectonic boundary condition to examine the topography of isolated, emergent mountain ranges associated with active fault systems (e.g., Densmore et al., 2004; Densmore et al., 2007a; Barnes et al., 2011). They observed that (1) faulting and relief remain correlated within some distance from the tips (called the “tip zone”) but become disconnected toward the along-strike center (Fig. 1B), and (2) the temporal scale over which faulting and topography remain connected within the tip zone, and by proxy the timescale to reach topographic steady state, can be estimated by substituting space for time (Harbor, 1997; Densmore et al., 2004, 2007b; Barnes et al., 2011).
In this paper we use a worldwide data set of fault-driven mountain ranges to better quantify the relative contribution of tectonics, climate, and lithology in shaping the topography of mountain ranges. Consideration of our results within the established conceptual framework for fault growth leads to new ideas on the temporal scales of mountain relief growth. We note this contribution is the first comprehensive, global analysis of patterns of along-strike relief development for active dip-slip faults. In order to best exploit the existing conceptual models for fault growth as a boundary condition (Fig. 1A), we focus on active, isolated faults or fault systems (after Barnes et al., 2011) and use long-term (104–6 yr) tectonic rates to understand the landforms they produce rather than less representative short-term geodetic rates (Friedrich et al., 2003). We find significant correlations between topographic metrics and independent variables (i.e., tectonic rate, climate, and lithology), which lead to new insights about the relative importance of each in shaping fault-driven landscapes.
DATA AND METHODS
We examined 41 mountain ranges evolving in response to active dip-slip faults from diverse tectonic and climatic settings across the globe (Fig. 2). We attempted to choose a representative population of mountain ranges from regions with different tectonic settings and rates, but our strict criteria made it impossible to include every tectonic region and limit the size of our data set to n = 41. We built this database using the following range selection criteria: (1) long-term (geologic, >104 yr) fault slip rate estimates exist; (2) the mountain range has at least one unimpeded fault tip zone; and (3) the topography is not obviously inherited, thus it can be assumed to result from the observed active faulting alone (e.g., Densmore et al., 2004). The analyzed mountains have average fault trace lengths of 81 km (16–350 km) and are on average ∼5× the length of the measured tip zone. We divided the chosen ranges into two tiers based on the quality of the available fault kinematic data. Tier 1 ranges (n = 22) have reliable long-term slip rate data (i.e., thermochronology with structural mapping and reconstructions), whereas Tier 2 (n = 19) consists of ranges for which ideal long-term fault slip data are unavailable (i.e., geomorphic analysis or less than ideal geochronologic sampling locations), the kinematics are more complex (i.e., oblique slip), or the morphology could be partially inherited. For each range, we compiled data including fault geometry and kinematics, topographic variables, climatic data, and lithology (Tables 1 and 2). We also include all data and imagery in the Supplemental File1.
We compiled fault type, slip rate, vertical displacement rate, vertical displacement magnitude, and fault age for each mountain range with several considerations in mind to ensure database integrity. The first consideration is that published tectonic slip rates are difficult to compile and compare due to inconsistent nomenclature (e.g., slip, throw, uplift, etc.) and differing methods by which they were estimated (e.g., thermochronology, seismic reflection data, geologic mapping, etc.). We strived to compile tectonic rate data in a way to ensure that the type of rate reported for each structure is comparable. We carefully distinguished between slip rate (fault-parallel motion) and vertical displacement rate (vertical component of slip). For brevity, we use the term “displacement” for the remainder of this paper to refer to the vertical component of slip. Our compiled values for displacement reflect maximum displacement on the structure and were either (1) reported explicitly in the original data source, (2) inferred from geologic cross sections and maps, or (3) calculated from reported deformation rate and age. Slip and deformation rate reflect the long-term average and were either (1) reported explicitly in the original data source or (2) calculated using slip or displacement and age determinations reported in the original data source. We acknowledge that using a long-term average for tectonic rate can introduce uncertainty, particularly for older faults that have long recurrence intervals, but a long-term average rate is most appropriate for comparison to range-scale topographies spread across the globe. If the original data source only reported slip rate or displacement rate, we calculated the other value using either the reported fault angle or estimated it using Anderson’s theory of faulting for approximating fault angle (Anderson, 1905). Similarly, if fault displacement was not reported, we estimated it using a linear scaling relationship between fault displacement (D) and length (L) for dip-slip faults >1 km long (D = L*0.03; Schlische et al., 1996; Densmore et al., 2004). Specifics of each location are collated in the Supplemental File (see footnote 1). Although using these models to relate fault-plane parallel slip and the vertical component of slip introduces uncertainty, they are useful estimates from a brittle deformation mechanics perspective (Scholz, 2002).
The second consideration is that the underlying control on topographic growth driven by faulting is the relative vertical displacement rate in the footwall compared to the hanging wall (for a normal fault, opposite for a reverse fault) because that is what sets local base level and hence affects the landscapes erosional response to slip (e.g., Barnes et al., 2011). We acknowledge that fault geometry can significantly affect the corresponding topography. The topography we observe may not be entirely attributable to slip on the underlying fault, particularly for thrust faults where fault-bend folding may result in cessation of topographic growth (i.e., surface uplift) once slip exceeds the vertical dimension of the ramp. Unfortunately, we cannot rule out that fault-bend folding is not a factor in some of the mountain ranges we analyzed (e.g., Coalinga fold, California; see the Supplemental File [see footnote 1] for details). However, by reporting the vertical displacement on a fault (as opposed to total slip) we attempt to focus on the dimension of fault growth that primarily contributes to topographic development. We include the fault geometry of every analyzed structure in the Supplemental File (see footnote 1) for reference. We also assume that our compiled tectonic rates are the best estimates of relative displacement rate because (1) studies rarely measure tectonic rates explicitly in both the hanging walls and footwalls as well as footwall sedimentation rates; (2) it is beyond the scope of this paper to independently measure such rates; and (3) our principal intent is to explore the links between tectonic and topographic metrics that are the most commonly available.
We used the advanced spaceborne thermal emission and reflection radiometer (ASTER) 30-m global digital elevation model (DEM) (METI and NASA, 2012) to conduct the topographic analysis. Variables we measured include tip zone length and gradient, maximum and uniform relief, fault trace length, and along-strike changes in elevation and relief (Fig. 3; Supplemental File [see footnote 1]). We manually clipped the DEM based on the topographic extent of each mountain range (Fig. 3A) and then collected one-pixel (∼30-m)–wide swaths perpendicular to the strike of the fault. We extracted along-strike minimum, mean, and maximum elevation and relief (defined as max–min elevation) profiles (Figs. 3B and 3C; see the Supplemental File [see footnote 1] for all profiles) and finally measured remaining parameters from these profiles (tip zone length and gradient). For example, tip zone length is the along-strike distance from the fault tip to the point where the relief stops increasing (Fig. 3C); this key metric is the scale over which topography reaches a steady form (Densmore et al., 2004; Densmore et al., 2007b). We developed a quantitative method for selecting the along-strike location where relief transitions from increasing in value to becoming uniform in order to measure and compare tip zone lengths. After smoothing the relief profile with a spline function (red line, Fig. 3C), we define the tip zone length as the first zero crossing of the first derivative. Tip zone gradient is the rate of surface elevation change within this zone (green dashed line, Fig. 3C; after Densmore et al., 2004). Uniform relief (RU) is the mean local relief value within the fault interior (purple region in Fig. 3C) that excludes the tip zones. Fault trace length is defined as the farthest along-strike extent of range topography. Subsurface fault length may be longer than the surface fault trace particularly in thrust systems (e.g., Wells and Coppersmith, 1994; Davis et al., 2005); thus we consider fault trace length to be a topographic rather than a tectonic variable.
Climate and Lithology
To account for variations in climate, we used mean annual and monthly precipitation. Precipitation values were compiled from the Global Precipitation Climatology Centre worldwide database (GPCC Normals Version 2010; http://gpcc.dwd.de) with a 0.25° grid size (Becker et al., 2013; Schneider et al., 2014). We avoided heavily glaciated ranges. We also used a semiquantitative scale for lithologic variations across each range (1–5, weak to strong) based on the dominant exposed lithology. The ranking is based on physical and mechanical properties (uniaxial compressive/tensile strength, elastic modulus, point load index, and Schmidt hammer rebound values) generalized for rock type (Obert and Duvall, 1967; Zhang, 2005).
We performed two bivariate statistical analyses on our database. First, we performed a test of linear dependence, or Pearson correlation, between all noncategorical variables (Tables 3 and 4; Davis, 2002). Second, because the lithologic strength variable is categorical, we conducted a test of monotonic dependence, or Spearman correlation, between lithologic strength and all other variables (last column, Tables 3 and 4). A Spearman correlation is a nonparametric measure of dependence and is well suited for ranked data (Spearman, 1904). For both tests, we report R and p-values. The closer the correlation coefficient, R, is to 1, the better the correlation. P-values are the probability that the results could be obtained by random chance such that lower p-values indicate a more robust correlation (Davis, 2002). We performed these analyses on Tier 1 (Table 3) and on all data (Table 4) to explore relationships between the various tectonic and topographic variables. In the discussion below, we focus on (1) the best correlations (R > 0.5; p-values < 0.01) and (2) the surprising noncorrelations, both of which lead to new insights into the links between faulting and the resultant landscape form.
To understand the controls of fault-driven landscapes, we investigate the statistical relationships between topographic metrics (listed above) and tectonic, climatic, and lithologic parameters using correlation statistics. Because our primary interest is to understand the controlling variables in shaping the landscape, we only elaborate on strong relationships that relate to the landscape. For brevity, we only show plots for statistically significant regressions or for those that seem to have the most meaningful insights. Below we report the R and p-values for Tier 1 data (Table 3), with the corresponding R and p-values for all data (Tier 1 + Tier 2; Table 4) in brackets immediately following.
Tip Zone Length and Faulting Rate
There is a significant (p-value < 0.01) negative correlation between tip zone length and faulting rate (Fig. 4; Tables 3 and 4). Our database includes fault slip rates from 0.15 to 13.8 km/m.y., displacement rates from 0.075 to 8.3 km/m.y., and tip zones from 3.2 to 44 km (3.2–22 km for Tier 1) long (Tables 1 and 2). In the range interiors, relief reaches mean values (RU; e.g., Fig. 3) of ∼150–2650 m. Regression between tip zone length and displacement rate shows that faster rock uplift results in shorter tip zone length (R = –0.55 [–0.36], p-value 0.008 [0.019]; Fig. 4A; Tables 3 and 4). This correlation is lower for slip rates (R = –0.51 [–0.31], p-value 0.015 [0.043]; Fig. 4B; Tables 3 and 4), presumably because it is the vertical component of rock motion that affects relief growth the most. However, no topographic metric shows any significant trend related to fault type. At low faulting rates (<∼1 km/m.y.), the increased scatter in tip zone length may be related to regional-to-local factors such as lithology and climate. For example, the White Mountains, California, have one of the largest tip zones (20 km) and are (1) classified as arid, cold desert (Kottek et al., 2006) and (2) made up of hard granitic and metamorphic rock (Tables 1 and 2) (Stockli et al., 2003). Overall, the main results are that the faster the fault slips, the shorter the distance over which relief saturates (tip zone distance) and that regional-scale factors such as climate and lithology may impart influence on some of the more extreme outlier tip zones in a predictable way.
Precipitation and Deformation Rate
Two of the strongest correlations in our database are between precipitation and slip rate and precipitation and displacement rate (R = 0.64 [0.62] and 0.67 [0.64]; p-value = 0.001 [0.000] for both; Fig. 4C; Tables 3 and 4). Documented mean monthly precipitation ranges from 2 ± 2 mm/month (21 mm/yr mean annual; S. Aksai Range, China) to 180 ± 150 mm/month (2103 mm/yr mean annual; Pakuashan anticline, Taiwan). Here we define the uncertainty as one standard deviation, which reflects the seasonal variability in rainfall. For example, the S. Aksai Range, China, receives <1 mm/month of precipitation for ∼8 months out of the year. The positive correlation indicates that mountain ranges with faster faulting rates tend to also have higher rates of precipitation. Precipitation also has a moderately significant negative correlation with age of faulting (R = –0.51 [–0.47], p-value = 0.016 [0.002]), with younger locations tending toward higher amounts of precipitation (Table 2). Collectively, these results statistically link rainfall, tectonic rates, and age of faulting.
Tip Zone Gradient
Tip zone gradient (relief increase per unit tip zone length, Fig. 3C) has no correlation with any other non-landscape variable in our database (Tables 3 and 4). The strongest correlation is between tip zone gradient and lithology, but it is a poor correlation at best (R = 0.29 [0.24], p-value = 0.210 [0.122], Tables 3 and 4). Tip zone gradient has a mean value of 0.076 and a standard deviation of 0.033 (Table 2; Fig. 5A). The maximum value is 0.15, and the minimum is 0.026. There is little variation in tip zone gradient—the majority (80%) of values fall between 0.05 and 0.15—suggesting that this parameter converges around a common value.
Relief and Tectonic Variables
There are moderate-to-strong correlations (R = ∼0.5–0.6) between measures of relief (RU and RMAX) and tectonic variables (slip and displacement rate, total displacement) (Tables 3 and 4). Both RU and RMAX have negative correlations with slip rate (R = –0.53 [–0.21], R = –0.48 [–0.23], respectively) and displacement rate (R = –0.56 [–0.24], R = –0.49 [–0.26], respectively). Relief metrics have slightly stronger correlations with magnitude of displacement (R = 0.52 [0.56] for RMAX; R = 0.64 [0.52] for RU; Tables 3 and 4). Magnitudes of uniform relief are between 130 m (Balachaur fold, Siwalik Hills) and 2645 m (Kyrgyz Range, Kyrgyzstan) with most (91%) relief measurements at <1500 m (Fig. 5B). Maximum relief magnitudes are between 172 m (Balachaur fold, Siwalik Hills) and 3567 m (Kyrgyz Range, Kyrgyzstan) with most (84%) values at <2000 m. The general trend is that slower slip and displacement rates and higher magnitudes of displacement correlate with higher relief.
Our classification of lithologic strength has strong correlations with tectonic and topographic variables (R = 0.60–0.76) (Tables 3 and 4). We reiterate here that this variable is based on assumptions about rock strength and is spatially averaged over the entire analyzed mountain range. Due to the semiquantitative nature of the lithology variable, we calculated a Spearman correlation coefficient rather than a Pearson correlation coefficient, which is intended to evaluate monotonic relationships. Our analysis provides a correlation coefficient of R = 0.66 (0.60) and 0.73 (0.64) (p-value = ≤0.001 for all, Tables 3 and 4) between lithologic strength and uniform and maximum relief, respectively. Mountains with higher relief tend to be composed of stronger (less erodible) rock. The correlation coefficient between lithologic strength and displacement is R = 0.64 (0.46), and with slip and displacement rate, it is R = –0.76 (–0.59) and R = –0.64 (–0.52) (p-value = ≤0.001 for all, Tables 3 and 4). These results suggest that substrate strength is a central control on mountain tectonomorphic systems.
What controls fault-driven topography? Landscapes are a reflection of the dynamic feedbacks between tectonics, climate, and erosion. As expected, our results do not support a single driver for landscape development, as is evident by the large scatter in our data set. That said, we do observe two constants in our data set. First, all ranges cease increasing in relief at some distance from their tips, reaching a saturation in relief within their interiors. Second, the distance over which that relief saturation is achieved is measurable as some distance from the tip (“tip zone”). Collectively, our results show significant correlations between definable topographic metrics and variables that shape the landscapes (i.e., tectonic rate, climate, and lithology). In the next section, we discuss the results of our data analysis that shed light onto dominant drivers of fault-driven landscapes, and we focus primarily on the strong, negative correlation between tip zone length and tectonic rate and the implications of that relationship for estimating the timescales of relief generation.
Climate and Tectonics
The strong positive correlation between modern precipitation and tectonic rate alludes to a feedback between tectonics and climate, but whether this is a causal relationship or coincidence remains an open question. In recent decades, the role climate plays in tectonic evolution has become increasingly appreciated (e.g., Whipple, 2009) with several studies documenting the coupled increase in denudation and deformation (e.g., Willett et al., 1993; Beaumont et al., 2001; Zeitler et al., 2001; Berger et al., 2008). One way to interpret our results is as further evidence for such coupling, which suggests a universal link between rapid deformation and rainfall. A second interpretation is that the most rapidly slipping faults are at the fronts of active orogenic belts (e.g., Himalayas and Taiwan), which tend to possess high orographic precipitation. In this case, our results are simple coincidence. Regardless of the interpretation, there is an observed correlation between rapidly moving faults and the amount of regional precipitation; whether the relationship is causal, coincidence, or both remains a path for continued investigation.
Lithology and Mountain Relief
What controls the limit to mountain relief? The morphology of all the investigated mountain ranges is characterized by increasing relief from the tip to a maximum threshold value, which we call uniform relief (RU). The strongest correlation (with a non-topographic metric) for uniform relief of Tier 1 ranges is with displacement (R = 0.64, p-value = 0.001) and lithologic strength (R = 0.66, p-value = 0.001; Tables 3 and 4). Lithology, which we use as a proxy for substrate erodibility, has a significant influence on fault-driven landscapes. In addition to a correlation with uniform relief, lithologic strength has strong, positive monotonic relationships with maximum relief, age of onset, and displacement (Tables 3 and 4). Erosion rates are dependent on rock type, with weaker rocks displaying higher erosion rates and more mass wasting events than stronger lithologies (Schmidt and Montgomery, 1995; Molnar et al., 2007; Chen et al., 2011; Burbank and Anderson, 2012). Lithologic strength is intuitively linked with age and displacement: as uplift progresses over time, erosion removes younger, softer rocks and exposes harder, underlying rocks (Burbank et al., 1999). Thus, large-magnitude displacement tends to expose deeper, stronger rocks that decrease the erodibility of the system, which in turn results in a higher magnitude of relief. Exceptions to this generalization include crystalline intrusive bodies and thrust fault settings where older, more robust rock can be superimposed above younger, softer rock. In the absence of quantitative data on the mechanical properties of each location, this observation is somewhat speculative and presents an interesting avenue for future research. To what degree does lithology control mountain topography? Substrate properties are often impossible to compile across large areas and as a result are often overlooked in favor of tectonics or climate as dominant drivers of mountain-scale landscapes (e.g., Densmore et al., 2007b; Champagnac et al., 2012). Our results, although qualitative, suggest a significant influence of substrate strength on mountain relief.
Tip Zone Gradient and Fault Tip Taper
Our geomorphic measurements of tip zone gradient may be a reflection of underlying fault geometry, providing support for mechanical models of rock deformation. The convergence of tip zone gradient values around a mean of 0.08 (Table 2) coupled with the lack of significant trends between tip zone gradient and any other variable (Tables 3 and 4) may be indicative of critical fault tip taper (e.g., Scholz, 2002). Displacement profiles of faults show a maximum near the center of the fault and displacement tapering to zero at the tips (e.g., Fig. 1A). Fault mechanics require that displacement taper off in such a way that stresses remain finite at the tips; as slip accumulates in the fault interior, stress builds up at the fault tips until it reaches the yield strength of the rock, at which point the fault grows laterally (Cowie and Scholz, 1992c; Scholz, 2002). The angle the displacement profile forms as it tapers is called fault tip taper (FTT; Fig. 1A) and is proportional to the strength of the material (Cowie and Scholz, 1992c; Scholz et al., 1993; Scholz, 2002). Thus, based on fracture mechanics models, we would expect the tip zone slope to correlate with rock strength. The lack of correlation observed here could be because our lithology database is not very robust and/or because isolated faults grow with a constant FTT (Kanninen and Popelar, 1985; Dawers et al., 1993). If the latter, our observation that tip zone gradient values cluster between 0.07 and 0.1 may be indicative of a threshold gradient due to FTT. This speculation is further supported by the strong link between relief and tip zone length in all studied mountain ranges (R = 0.74 [0.72] for maximum relief; R = 0.70 [0.73] for uniform relief). Implicit in this observation is that if tip zone gradient converges to a threshold value, then the tip zone length and relief would have a coupled increase or decrease.
Tip Zone Length and Tectonic Rate
We find the strong correlation between deformation rates and tip zone length to be particularly interesting due to the implications for relief saturation and the temporal scales of relief growth. Why do faster deformation rates result in shorter tip zones? Assuming that the range-forming faults adhere to the well-established relationship between distance along strike and slip rate/displacement (Fig. 1), the highest slip rates will be in the along-strike center. High tectonic rates are correlated with frequent mass wasting events (Binnie et al., 2007) that contribute to rapid denudation and lower relief of mountains (Champel et al., 2002; Korup et al., 2007). If the transition from increasing to uniform relief is coincident with higher deformation rates, as predicted by conceptual models of fault growth (Fig. 1), then those higher deformation rates could in turn be coincident with more efficient erosive processes (Densmore et al., 2007b). Thus the transition to uniform relief is the landscape reflection of an erosional and tectonic balance. We can in turn speculate that temporally, ranges with faster deformation rates will experience a more rapid shift to uniform relief (i.e., shorter tip zones), especially if they consist of weak rocks in humid climates. Unfortunately, our data set for slip rates includes far more slowly moving faults (<2 km/m.y.; n = 28) than rapidly moving ones (>2 km/m.y.; n = 13; Fig. 4B and Table 1). This bias is a natural consequence of examining global fault populations; due to the processes involved in the evolution of fault populations, less active faults far outnumber highly active faults in nature (Cowie, 1998). Although the relationship between tip zone and deformation rate is strongly affected by a small number of ranges with fast deformation rates, it is the best global-scale estimate that exists.
Another possible explanation of the tip zone observations is that range relief saturation is related to seismogenic zone thickness or décollement depth. Brittle failure is limited to the uppermost portion of the crust, and the thickness varies depending on several factors including geothermal gradient, rheology, composition, and overall crustal thickness (Watts and Burov, 2003). Faults reaching the brittle-ductile transition have been evoked to explain observed maximum displacements and fault segment lengths (Scholz and Contreras, 1998); thus it may follow that tip zone length also follows a similar scaling. Shallower brittle-ductile transitions reduce the fault length, displacement, and down-dip extent of faulting (Watts and Burov, 2003); thus we would predict shallow décollements to be associated with shorter tip zones. The décollement beneath the Siwalik Hills at the Himalayan front is ∼5–7 km (Powers et al., 1998), where short (5–6 km) measured tip zones are located (Barnes et al., 2011). In the U.S. Basin and Range, in comparison, the seismogenic zone is 15–20 km thick (Anderson et al., 1983; Stein et al., 1988), and tip zones are ∼14 km long on average (9.5–20 km, Table 1). Although precise estimates for depths to décollements do not exist for many faults in our database, this example hints at a link between tip zone length and décollement depth.
It is worth mentioning that fault geometry, particularly fault-plane angle and its variation with depth, can influence the magnitude and rate of uplift and hence the resulting topography of fault-driven mountain ranges (Wickham, 1995; Hubert-Ferrari et al., 2007; Burbank and Anderson, 2012). In exerting control on rock uplift and advection, fault geometry has the potential to significantly influence mountain relief, range width, and tip zone length and gradient (Miller and Slingerland, 2006; Barnes et al., 2011; Burbank and Anderson, 2012; Styron et al., 2013). For example, in a compressional setting with ramp-flat geometry, if fault slip has overcome the vertical dimension of the ramp, then surface uplift may cease (Burbank and Anderson, 2012). The size, angle, and continuity of the ramp relative to the total slip are factors in the ratio of shortening to uplift (Suppe and Medwedeff, 1990; Hubert-Ferrari et al., 2007). It is possible that some observed tip zones are actually fault-propagation folds in transition to fault-bend folds, in which case the observed tip zone slope and length may be a combined reflection of rock properties, fault geometry, rheology, and décollement kinetics (e.g., Suppe and Medwedeff, 1990; Champel et al., 2002).
Time for Relief Generation
Our observations have implications for estimating the timescale for relief generation—in other words, the time it takes to reach a steady form, within the established fault growth framework (e.g., Fig. 1A). One idea is that the length over which uniform relief is achieved, the tip zone length, can be converted to a timescale using the fault tip propagation rate (henceforth referred to as the tip zone method), which assumes the latter is a gradual and steady process (Fig. 6A; after Densmore et al., 2004). Unfortunately, (1) few data exist on fault tip propagation rate; so it often must be estimated (here and elsewhere assumed to be ∼10× the fault slip rate; e.g., Densmore et al., 2004; Barnes et al., 2011); and (2) the assumption that faults grow by systematic and simultaneous increases in both displacement and length may be inaccurate (e.g., Cowie and Scholz, 1992c; Walsh et al., 2002; Amos et al., 2010; Mouslopoulou et al., 2012). Instead, scaling properties of both earthquakes and faults support the idea that fault length may become established early on and that further growth is achieved by increases in displacement without tip propagation (Walsh et al., 2002). Due to these caveats associated with fault tip propagation, we propose another method for estimating the timescale for relief generation where the uniform relief (RU) is divided by the long-term displacement rate (henceforth referred to as the uniform relief [RU] method; Fig. 6B). RU represents the mean relief accumulated in response to active faulting combined with the evolving erosional processes that shape the uplifting landscape. Thus, dividing RU by the long-term displacement rate provides an estimate for the minimum amount of time required to accumulate the relief because presumably the range crest itself has lowered some due to erosion. Both methods discussed here produce similar estimates for the timescale to reach steady relief (Fig. 6C). That said, we favor the uniform relief method because estimating fault tip propagation rate using a 10:1 ratio to fault slip rate is based on theory with limited supporting data (Morewood and Roberts, 1999), whereas displacement rate is more likely to be independently constrained.
Applying the uniform relief method provides timescales to reach steady relief varying from ∼30 k.y. to 4 m.y. for the Tier 1 ranges (Fig. 6B). What does it mean when range topography reaches a steady form? We suggest that beyond time periods greater than those required to achieve uniform relief, the range begins acting as a tectonically and geomorphically coherent system. Upon reaching this evolved phase of development, fault-driven ranges are in equilibrium with their regional tectonomorphic setting. For example, ranges within the same tectonic province, with similar size, slip rate, and climate, require similar timescales to reach a steady form. The nine (Tier 1) faults in our database from the U.S. Basin and Range are estimated to take between 1 and 5 m.y. to saturate in relief (green circle, Fig. 6); the two (Tier 1) faults from the Siwalik Hills take between 30 and 70 k.y. (purple oval, Fig. 6). Our results are consistent with landscape evolution models that predict steady-state topography in the Basin and Range takes ∼1–4 m.y. to develop (Ellis et al., 1999). Basin and Range faults have longer tip zones, greater relief, slower slip rates, and lower rates of precipitation than Siwalik Hills faults (Fig. 6; Tables 1 and 2), resulting in overall lower erosivity in the Basin and Range. Our findings suggest that emergent ranges uplifting due to active faults display regionally consistent self-similar forms that reflect their particular environmental balance between tectonic input and erosional output similar to what other studies have shown at orogenic-belt scales (e.g., Willett and Brandon, 2002; Champagnac et al., 2012). The implication is that distinctive, identifiable equilibrium landscape forms may be used to estimate the timescale for their development.
Predicting Faulting Rate from Topography?
Our data analysis also suggests we can predict first-order fault kinematics from emergent topography in places where faulting rate estimates do not exist. Learning how to exploit landscape form to unravel tectonics remains an overarching goal of tectonic geomorphologic research (e.g., Kirby et al., 2003; Wobus et al., 2006; Boulton and Whittaker, 2009). For example, little is known about displacement or slip rates in the seismically active region of Iran’s border with Afghanistan and Pakistan (Walker and Jackson, 2004). One thrust fault tip zone in the Makran Region measured 7.7 ± 0.8 km long (blue diamond, Fig. 2). Using the relationship between displacement rate and tip zone length from our analysis, this tip zone implies a displacement rate of 4.6 ± 0.7 km/m.y. and a slip rate of 8.1 ± 1.4 km/m.y. (yellow diamond, Figs. 4A and 4B). This estimate is consistent with sparse geomorphic and global positioning system (GPS) evidence that estimates regional slip rates are between 2.5 and 6 mm/yr (Walker and Jackson, 2004). For mountain ranges with long tip zones (>15 km), the potential to predict the deformation rate with precision is somewhat limited based on the scatter in our data set. While caution should be noted, the data and relationships presented here have the power to provide (1) a starting point for more thorough study or (2) an estimate for a remote location where thorough investigation is difficult.
Our global analysis of tectonomorphic variables from active fault-driven ranges shows that emergent ranges always achieve uniform relief, and the spatiotemporal scales over which this steady form is achieved correlate with the long-term (104–6 yr) fault slip and displacement rate. In short, rapidly slipping faults produce mountain ranges that saturate in relief over shorter distances and in less time than slowly slipping faults. Furthermore, maximum mountain relief has stronger correlations with lithology and total fault displacement than displacement rate. Our results (1) imply that there are broad tectonic controls on the early phases of topographic growth that can be modulated by regional variations in lithology and climate; (2) warn that the impacts of climate and lithology on mountain relief should not be ignored; and (3) suggest that relief patterns in uplifting landscapes may be used as a first-order predictor of faulting rate. Our results may provide further insights into basic links between tectonics, topography, and climate when compared with data from other scales.
M. Ellis thanks the University of North Carolina Department of Geological Sciences Martin Fund, Geological Society of America, and Sigma Xi for financial support. James Spotila, Dylan Ward, Patience Cowie, Nancye Dawers, Mike Taylor, Associate Editor Colin Amos, and an anonymous reviewer provided many helpful comments that helped improve this paper.