Slip rate determined from cosmogenic nuclides on normal-fault facets

Facets are characteristic landforms associated with the activity of normal faults (Wallace, 1978; Armijo et al., 1986). However, their potential as tectonic markers and the possibility of retrieving quantitative information on long-term slip rates from their morphological attributes and rates of evolution have seldom been considered (Petit et al., 2009; Tucker et al., 2011). This potential is an attractive prospect because faceted spur development integrates cumulative displacements over a longer time frame (hundreds of thousands of years) than most other geomorphological markers and are ubiquitous in uplifting landscapes bounded by active normal faults.

Quantifying tectonic deformation over Quaternary time scales usually relies on the analysis of passive morphological markers formed by various types of processes, such as fluvial or marine terraces, moraines, and landslides. In many settings, the temporal record of such markers spans only a few tens of thousands of years, usually leaving the 100 k.y. time scale poorly documented (Ryerson et al., 2006; Gold et al., 2017), which is a major hindrance to our understanding of how deformation is accommodated. Triangular facets, on the other hand, are not passively deformed markers but result from the combination of sustained rock uplift of the normal-fault footwall and its long-term erosion (Burbank and Anderson, 2011).

Here, we provide the first systematic investigation of the use of the ³⁶Cl cosmogenic nuclide to assess the rates of facet evolution. Our goal is to link cosmogenic nuclide buildup on limestone faceted spurs and fault slip rate by investigating four sites in the Central Apennines, Italy, of different shape and height (Fig. 1). Following on Tucker et al. (2011)’s assumptions linking facet slope, denudation rate, and fault slip rate, we compute the theoretical ³⁶Cl concentration buildup of a facet as a function of its evolution with time (Fig. 2). The inversion of data acquired from the four studied sites demonstrates that our approach provides accurate constraints on fault slip rates over time spans ≤200 k.y. (Figs. 3 and 4).

Faceted spurs are near-planar triangular or trapezoidal surfaces produced by the erosion of normal fault scarps that are continuously rejuvenated at their base by sustained slip (Wallace, 1978). Here we focus on normal-fault footwalls formed in resistant bedrock and undergoing a weathering-limited evolution (Tucker et al., 2011). Morphological evolution models (Tucker et al., 2011, 2020; Strak et al., 2011) suggest that facet morphology reflects an equilibrium between rock uplift from fault slip and erosion.

At the base of the facets, well-preserved bedrock fault scarps representing the cumulative displacement on the fault since the Last Glacial Maximum can be observed (Wallace, 1978; Armijo et al., 1992). This has been confirmed in the Mediterranean by exposure-age dating in Greece, Italy, Israel, and Turkey (e.g., Benedetti et al., 2013; Cowie et al., 2017). Post-glacial changes in climatic conditions result in a decrease in hillslope erosion rates and preservation of those bedrock fault scarps (Armijo et al., 1992; Allen et al., 1999). The timing of this shift is not accurately dated and may spatially vary. In the Apennines, it is estimated to have occurred at 12–21 ka (Giraudi and Giaccio, 2017).

Based on these previous observations, we use a two-stage kinematic model to predict ³⁶Cl buildup in material currently exposed along the facet surface. First, we assume topographic steady state under glacial conditions, such that rock uplift of the footwall is equal to the denudation rate of the facet surface. Rock samples are progressively exhumed parallel to the slip vector at a rate set by the fault slip rate (Fig. 2). Second, we assume denudation of the facet to be negligible in postglacial conditions, such that rock samples are continuously exposed at the surface, with no significant regolith cover (Tucker et al., 2011).

Our approach relies on the interpretation of measured ³⁶Cl concentration at the surface in terms of this exhumation and exposure history of the facet. Based on the conceptual evolution described above, we parametrize this evolution using the time at which the sample starts moving toward the surface (T_exhum), the rate at which the sample moves parallel to fault motion prior to postglacial conditions (slip rate; SR), and the duration of postglacial exposure assumed without erosion (T_pg). We combine this simple model with equations describing cosmogenic nuclide buildup to predict ³⁶Cl concentrations at the surface of the facet for any combination of the three parameters (T_exhum, T_pg, SR) defining the prescribed history (see the Supplemental Material¹).

We focus on four facets formed in limestones located along three active faults in the central Apennines (Italy). Since the late Pliocene-early Pleistocene, active normal faults accommodate the southwest-northeast extension in the area (Roberts and Michetti 2004). The Velino-Magnola fault is a major structure of the Apennines (∼30 km long; Fig. 1) with facets up to 300–800 m high, where we sampled two sites (MA1 and MA3) along the northern and central part of the fault, respectively. The Roccapreturo fault is shorter (10 km), with lower facets (100–150 m), and was sampled at site AR in the center of the fault. The Bazzano fault is a small (3-km-long) antithetic fault, with several facets reaching 100–150 m high, sampled in its southern section at site BAZ (see the Supplemental Material). The surfaces of the four sampled facets display regular slope, 30–35° (Fig 3). The surfaces of the facets are characterized by an alternation of bedrock outcrop, small bedrock protrusions (<1 m high), and patches of soil and screes less than a few centimeteres thick. The facets are generally bounded by entrenched non-perennial streams that flow perpendicular to the fault’s strike, which suggests recent incision that is contemporaneous with fault development. The slopes of the colluvial wedge surface (α ∼25–30) and of the facets (γ ∼30–35) are similar across sites; the fault dips (β) from 40° at site MA1, to 65° at BAZ (see the Supplemental Material).

The facets were sampled following an updip fault transect (see the Supplemental Material). We focused sampling on the lower part of the facet, where the surface appears less rugged, and near the facet center to avoid increased erosion by bounding gullies. Samples are 5–10-cm-thick pieces of bedrock, taken on the top of protruding (>0.5 m) bedrock surfaces, avoiding places that could have been covered by regolith. Each sample was chemically prepared for ³⁶Cl measurements (see the Supplemental Material). At sites MA3 and ARC (Fig. 1), the ³⁶Cl concentrations are roughly constant all along the facet (Fig. 3), except at the base where they increase by ∼30%. At sites MA1 and BAZ, facets are shorter and there are fewer points of measurement, but at MA1 we observe a pattern similar to that at sites MA3 and ARC, with constant values at the top, a slight decrease, and an abrupt increase at the base of the facet. There are only three data points at site BAZ, with decreasing concentrations toward the base. The ³⁶Cl concentrations along all studied facets are thus roughly constant, suggesting that the denudation rate on those features is approximately constant. This observation is consistent with a facet-development model that assumes a constant denudation rate. Moreover, while it has been usually assumed that erosion would vary with facet height (Tucker et al., 2020, and references therein), our results suggest that on the facets we studied, this is not the case.

To constrain the fault slip rate, we carried out a Bayesian inversion of the observed ³⁶Cl concentrations, where the model parameters are the individual slip rates of the faults (SR_MA3, SR_MA1, SR_ARC, SR_BAZ) and the postglacial period duration (T_pg), assumed to be the same for the four sites (T_exhum is fixed a priori; see the Supplemental Material). A complete description of the inversion procedure using the GW-MCMC algorithm (Goodman and Weare, 2010), the corresponding parameters, and the numerical code are provided in the Supplemental Material. The inversion yielded mean slip rates of 3.0 ± 1.2 mm/yr for site MA3, 0.2 ± 0.02 mm/yr for site MA1, 0.4 ± 0.3 mm/yr for site ARC, and 0.06 ± 0.02 mm/yr for site BAZ (Figs. 3 and 4). The mean postglacial duration, common to all sites, is 18.7 ± 2 k.y.

The modeled ³⁶Cl concentrations recover the average observed values at the scale of the facet, but do not account for the variability in ³⁶Cl concentrations observed in the lower part of the transects (Fig. 3).

In most cases, for the upper part of the facet, the inversion reproduces the mean ³⁶Cl concentration. Overall, the discrepancy between observed and modeled concentrations is at most 0.5 × 10⁵ at ³⁶Cl/g rock, except for the points at the base of each site where observed concentrations are systematically higher by as much as 20% (except at site BAZ). The discrepancy for the upper part of the profile could be attributed to the stochastic dynamics of local processes such as temporary cover by a few centimeters of scree or abrupt removal of bedrock fragments that would lower the observed amount of ³⁶Cl with respect to the predictions of our model. A scree cover of 10 cm would yield a 10% decrease in ³⁶Cl concentration and could account for a large fraction of the observed intrasite variability (see the Supplemental Material). On the contrary, simulations for site MA3 show that a scree cover of less than 5–10 cm yields an increase in ³⁶Cl concentration. This is due to a relatively large slip rate (3 mm/yr) and high natural chlorine content of some samples (>50 ppm) that maximize ³⁶Cl production at depth 0–100 cm (Schimmelpfennig et al., 2009). Another possibility that explains such a discrepancy could be that the facet slope might be locally steeper than the mean value used in the model. A difference of 10° could increase ³⁶Cl concentration by ∼7% (see the Supplemental Material). At the base of the profile, where observed concentrations are systematically higher by as much as 20% (except site BAZ), the observed systematic increase in ³⁶Cl concentration cannot be attributed to such short-wavelength random variability in surface processes. This portion is at the intersection between the bedrock scarp and the facet slope, which is defined in the model by the altitude of the bedrock scarp top. There is a high uncertainty in the altitude of this point, usually affected by sliding scree that could explain the discrepancy. The shielding calculation might also underestimate the effect of secondary neutrons produced through colluvial material or bedrock (Masarik and Wieler, 2003; Balco, 2014). The colluvial density and the dip of the colluvial slope also affect the ³⁶Cl content at the base of the profile and could additionally account for this discrepancy (Supplemental Material).

The value of 18.7 ± 2 k.y. obtained for the postglacial duration is consistent with the timing of the most important glacial retreat in the Apennines estimated at ca. 21 ka from lake deposit records and morainic deposits (Giraudi and Giaccio, 2017). It also corroborates the exposure ages from the top of the bedrock scarp at 11–15 ka at similar sites around the Apennines (Benedetti et al., 2013; Cowie et al., 2017). The amount of ³⁶Cl accumulated during the exhumation phase under glacial conditions is controlled primarily by fault slip rates and accounts for 9% of the total ³⁶Cl budget for site MA3, 58% for site MA1, 24% for site ARC, and 66% for site BAZ. It means that at site MA3, 95% of the measured ³⁶Cl has been accumulated over the past 20 k.y., at the other sites, this integration time is much longer, with durations of 185 k.y., 47 k.y., and 210 k.y. at sites MA1, ARC, and BAZ, respectively. Our approach thus allows determining slip rates averaged over time scales that range from 20 to 210 k.y. It is noteworthy that slower slip rates are more tightly constrained because the ³⁶Cl buildup at depth outweighs the postglacial ³⁶Cl production.

Slip rates derived from inversion for the four studied sites are between 3 and 0.06 mm/yr, which is within the range of observations over the Holocene for similar faults in the Apennines (Benedetti et al., 2013; Cowie et al., 2017). Sites MA3 and MA1 are <5 km apart and located on two segments of the Magnola fault (Supplemental Material). ³⁶Cl exposure dating of the bedrock scarp at each site yields Holocene-averaged slip rates of 1–1.5 mm/yr at sites MA3 and MA1 (Schlagenhauf et al., 2011), which is comparable with our result obtained at site MA3 (3 ± 1.2 mm/yr over 20 k.y.). On the other hand, the slip rate at site MA1 (0.2 ± 0.02 mm/yr over 185 k.y.) is much lower than the one determined over the past ≈15 k.y. by Schlagenhauf et al. (2011). This discrepancy may be related to the difference in time scale, suggesting that the slip on the fault has considerably accelerated over the past ≈15 k.y. Slip-rate variability through time has already been reported for the few faults worldwide where multiple-time-scale records are available (Pérouse and Wernicke, 2017; Friedrich et al., 2003). Studies on normal-fault growth have shown that slip rate can be highly variable over the fault length and over time (Manighetti et al., 2005). Our results confirm those observations and provide data to link incremental earthquake slip events and fault growth. The Bazzano fault (site BAZ) is an antithetic fault of the Paganica fault that ruptured during the 2009 L’Aquila earthquake. Several studies have allowed determining the Paganica slip rate over a few thousand years to the Middle Pleistocene (Pucci et al., 2019); all converge toward a slip rate of <0.4 mm/yr. The rate obtained for the antithetic Bazzano fault of 0.06 ± 0.02 mm/yr over the past 210 k.y. would thus account for ∼15% of the Paganica synthetic fault slip, which appears to be realistic (Boncio et al., 2010). The slip rate at site ARC of 0.4 ± 0.3 mm/yr over the past 47 k.y. is similar to the rate previously estimated by Falcucci et al. (2015) of 0.2–0.3 mm/yr over the last 1 ± 0.2 m.y.

The slip rates obtained for the four sites vary with facet height, with the highest rate at site MA3 where the facet is 800 m high (Schlagenhauf et al., 2011). This is in agreement with DePolo and Anderson (2000), who carried out a statistical analysis on normal faults located in the Basin and Range (western United States) and observed a logarithmic relationship between the height of the facet and the vertical slip rate of the fault (ranging from 0.001 to 2 mm/yr). Based on numerical modeling experiments, Petit et al. (2009) and Strak et al. (2011) also derived a linear relationship between facet height and throw rate, in agreement with our results.

Our study presents the first systematic cosmogenic nuclide measurements across facets developed above normal faults. We observe strikingly consistent signals with near-constant ³⁶Cl concentrations over the height of the studied facets, which suggests the facets are close to a morphological steady state with a constant denudation rate during their development. Accordingly, we performed inverse modeling of the concentration profiles and inferred slip rates over the past 20–200 k.y., the results of which are in agreement with long-term rates independently determined on some of those faults over the past 1 m.y. The integration time span for ³⁶Cl accumulation over the facets is longer than the postglacial history of these landscapes, suggesting that such measurements could provide slip-rate estimates over a time window that is usually undersampled in most tectonic geomorphology studies.

This work has been partly funded by the Laboratory of Excellence (LABEX) 211 Objectif Terre–Méditerranée (OT MED) (Aix-en-Provence, France) by the Centre National D’Etudes Spatiales (CNES) project TEMIS 2019 and by the Agence Nationale de la Recherche project EQTIME ANR-19-CE31-0031-01. M. Rizza and B. Ourion are greatly acknowledged for their help and support in the field. Constructive reviews by G. Hilley, E. Cowgill, L. Gregory, G. Roberts, and one anonymous reviewer helped improve the original manuscript.