Seismic variability of subduction thrust faults: Insights from laboratory models

Authors


Abstract

[1] Laboratory models are realized to investigate the role of interface roughness, driving rate, and pressure on friction dynamics. The setup consists of a gelatin block driven at constant velocity over sand paper. The interface roughness is quantified in terms of amplitude and wavelength of protrusions, jointly expressed by a reference roughness parameter obtained by their product. Frictional behavior shows a systematic dependence on system parameters. Both stick slip and stable sliding occur, depending on driving rate and interface roughness. Stress drop and frequency of slip episodes vary directly and inversely, respectively, with the reference roughness parameter, reflecting the fundamental role for the amplitude of protrusions. An increase in pressure tends to favor stick slip. Static friction is a steeply decreasing function of the reference roughness parameter. The velocity strengthening/weakening parameter in the state- and rate-dependent dynamic friction law becomes negative for specific values of the reference roughness parameter which are intermediate with respect to the explored range. Despite the simplifications of the adopted setup, which does not address the problem of off-fault fracturing, a comparison of the experimental results with the depth distribution of seismic energy release along subduction thrust faults leads to the hypothesis that their behavior is primarily controlled by the depth- and time-dependent distribution of protrusions. A rough subduction fault at shallow depths, unable to produce significant seismicity because of low lithostatic pressure, evolves into a moderately rough, velocity-weakening fault at intermediate depths. The magnitude of events in this range is calibrated by the interplay between surface roughness and subduction rate. At larger depths, the roughness further decreases and stable sliding becomes gradually more predominant. Thus, although interplate seismicity is ultimately controlled by tectonic parameters (velocity of the plates/trench and the thermal regime), the direct control is exercised by the resulting frictional properties of the plate interface.

1. Introduction

[2] Subduction thrust faults are the largest natural example of failure surface (Figure 1). Most of the global seismic energy is released by discontinuous slip along the frictional interface between the subducting and the overriding plates [e.g., Scholz, 1990; Pacheco and Sykes, 1992]. The mechanical foundation of frictional behavior is the formula known as the da Vinci-Coulomb-Amontons friction law [Amontons, 1699; Coulomb, 1785], according to which friction is proportional to the applied normal load and independent of the apparent area of contact. Within this simple frictional model, the static friction coefficient (μs) is larger than the dynamic friction coefficient (μd) leading to a possibly unstable slip between the interacting moving surfaces.

Figure 1.

Schematic representation of a subduction fault with (a) histogram showing the seismogenic zone depth limits (worldwide statistics from 46 subduction segments based on thrust event hypocenters distribution) [Heuret et al., 2011]; (b) model for the friction stability parameter, ab, as a function of depth [e.g., Scholz, 1998]; (c) cumulative moment (converted to a magnitude-like value M′ using the Kanamori [1977] moment-magnitude relation) for thrust events with 5.5 ≤ Mw ≤ 7.5 as a function of depth for the 1976–2007 period. Subduction thrust events have been extracted from the CMT Harvard catalog [Dziewonski et al., 1981]. Location of the Harvard events has been improved using the EHB hypocenter catalog [Engdahl et al., 1998]. See auxiliary material for a comprehensive description of sampling criteria and details on data processing.

[3] However, standard frictional models need to be revised to properly describe the behavior characterizing subduction thrust faults. The interplate contact is seismogenic only in a specific depth interval [Scholz, 1998], which globally is comprised between 11 ± 4 km and 51 ± 9 km [Heuret et al., 2011] (Figures 1a and 1b). In several subduction zones, slow slip events are recognized downdip of the limit of the seismogenic zone, even if their physical mechanism still remains elusive [e.g., Schwartz and Rokosky, 2007; Gomberg et al., 2010]. Moreover, cumulative seismic moment (M′) is not homogeneously distributed along the seismogenic zone, but shows an approximately Gaussian distribution with a peak around 20–30 km of depth (Figure 1c). The description of the system requires a rate- and state-dependent frictional model where μd and μs depend upon velocity and aging, respectively [Dieterich, 1979; Ruina, 1983]. Friction as a function of sliding velocity can be described using two parameters a, b, and a state variable θ accounting for memory effects at the contact surface, according to the relation

equation image

where μo is the friction at the reference velocity Vo, V is the imposed velocity and dc the critical slip distance (i.e., the slip distance necessary to change contact junctions [Dieterich, 1981]). When ab > 0, the system is characterized by a velocity strengthening behavior with frictional resistance increasing with any applied velocity increase. Hence, a seismic rupture cannot propagate in this field. Earthquakes, in contrast, can nucleate if ab < 0, which results in velocity weakening behavior [e.g., Scholz, 1998]. In the velocity-weakening field and at constant driving velocity, the stiffness of the system, K, should obey the following relation to ensure stick-slip dynamics

equation image

where W is the normal load exerted on the sample and Kc is a critical stiffness value below which stick-slip oscillations can occur [e.g., Voisin et al., 2007].

[4] While the rate-and-state friction law offers a simple mechanical explanation of interplate earthquake nucleation, the exact physical basis controlling this behavior is still an argument of debate. It is generally accepted that the temperature range at which interplate seismogenic zones develop is from 100–150°C to 350–450°C [i.e., Hyndman and Wang, 1993; Wang, 1995; Hyndman et al., 1997; Currie et al., 2002]. On this basis, the updip limit of seismogenic thrust faulting is alternatively explained by the transition illite-smectite [Pytte and Reynolds, 1988] or by fault gouge lithification processes [Saffer and Marone, 2003; Marone and Saffer, 2007], while the downdip limit is possibly controlled by the brittle–ductile transition of the crustal material [i.e., Brace and Kohlstedt, 1980] or by the intersection of the slab with the forearc mantle wedge [Peacock and Hyndman, 1999].

[5] The dynamical behavior of the seismogenic thrust fault, as of any other seismogenic fault, can also be described by the “asperity model” [Lay and Kanamori, 1981; Lay et al., 1982], according to which asperity size correlates positively with earthquake magnitude. Although the term “asperity” originally denoted a physical entity (a bulge on an otherwise smooth surface), it is often thought as a conceptual entity, i.e., a region of increased strength on the fault plane [Byerlee, 1970; Scholz and Engelder, 1976] dominated by stick-slip behavior, and/or a location of high slip during an earthquake [Lay and Kanamori, 1981; Lay et al., 1982]. What can cause an asperity is even more elusive: upper plate strength, frictional variation within the fault zone, and subducting plate features have all been considered valid ingredients (see Bilek [2007] for a review). While the importance of protrusions in controlling the behavior of the subduction thrust fault is generally recognized, there is still relatively little understanding of the way frictional motion varies with asperity size and distribution.

[6] In this paper, we present a laboratory study of the role played by the distribution of contact roughness in friction dynamics. We show how it is possible to reconcile the physical and the seismological meaning of asperity, combining experimental observations into a simple description of subduction thrust fault behavior. For this purpose, spring-block-like models [e.g., Burridge and Knopoff, 1967; Voisin et al., 2008] have been realized as analogs of the subduction thrust fault. Our models introduce the following new features: (1) using a gelatin slider reproducing the complex visco-elasto-brittle rheology representative of a properly scaled crustal/lithospheric behavior [Di Giuseppe et al., 2009] and, therefore, specifically taking into account the time dependence of the interseismic deformations; (2) testing a wide range of contact materials with roughness profiles characterized by well-sorted protrusions; (3) investigating the effect of lithostatic pressure at seismogenic depths; (4) exploring both frictional static and rate-and-state effects.

[7] After a description of the experimental procedure, we show how the static friction depends on the real contact surface (i.e., the small portions of the area where roughness irregularities are in contact with the gelatin sample) and how the velocity dependence of the steady state friction varies with the spacing and amplitude of the geometric irregularities distributed along the rupture surface. Moreover, we show that the maximum characteristic stick-slip event obtained in each experimental run depends both on the roughness of the contact surface and the mass and velocity of the slider. Our experimental results are used to propose a physical interpretation of the seismic regimes along the subduction thrust plane (as described, e.g., by Scholz [1998]).

2. Experimental Setup

2.1. Apparatus

[8] Spring blocks [e.g., Burridge and Knopoff, 1967; Baumberger et al., 1994; Vargas et al., 2008] are simplified models reproducing the seismic cycle, where the block-basement interface represents a generic fault and the spring stiffness represents the elastic properties of the surrounding medium. In this work, we used a spring-block-like setup where the elastic strain is directly stored in the gelatin block without the necessity to include a real spring. The experimental setup thus consists of an isothermal device in which a gelatin block of mass 182 g is forced to slide over a 30 cm long frictional horizontal surface with protrusions. For clarity, we hereafter use the term “protrusions” to describe the geometrical irregularities on the contact surface (see discussion in Section 2.2) while the term “asperities” is used in the seismological sense (i.e., referring to areas of large slip). A schematic view of the system is shown in Figure 2. After its preparation, the gelatin block is shaped as a parallelepiped (8.5 × 5.3 × 4 cm3) and positioned in a rigid holder. The bottom layer of the gelatin (thickness 0.2 cm) is left free, allowing the localization of the deformation related to sliding. This configuration has been selected as giving the best control of the frictional contact surface, minimizing possible boundary effects and ensuring the most regular and reproducible dynamical behavior of the experimental system. The gelatin holder is coupled by means of a steel cable to a stepping motor moving at a constant velocity. The shear force required to move the gelatin block is measured through a digital force sensor characterized by an accuracy of 0.02 N and a sampling rate of 1 Hz. Since the steel cable can be assumed to be inextensible and the digital force sensor stiffness is much higher with respect to the gelatin sample, the elastic strain is stored in the sand paper–gelatine contact characterizing the bottom layer of the system. There is no displacement control in the adopted setup. For this reason, we were not able to detect preseismic or postseismic creep signal.

Figure 2.

Line drawing of the experimental setup. A gelatin slider of size 8.5 × 5.5 × 4 cm3, in contact with a rough surface with variable spacing and amplitude of irregularities, is driven at constant velocity V. A digital force sensor measures the shear force exerted on the slider.

2.2. Materials

[9] We use gelatin and sand paper as analogs of lithosphere and subduction fault, respectively. The selected gelatin is prepared diluting small percentages (2.5%wt) of pig skin powder, an animal biopolymer, in distilled water which is stirred for 30 min at the preparation temperature of 60°C. The mixture is then poured in the mold and left for 24 h at the temperature of 10°C, resulting in the formation of a gel (i.e., solid) state. This material properly scales for length, density, stress, and viscosity in the natural gravity field (cf. Weijermars and Schmeling [1986] for a discussion of scaling procedure).

[10] In particular, pig skin 2.5%wt gelatin at 10°C satisfies two necessary conditions characterizing a viscoelastic solid: (1) G′ and G″, which are standard rheological quantities defining the stored and dissipated energy respectively [e.g., Nelson and Dealy, 1993], are about the same order of magnitude (i.e., the elastic deformation counterbalances the viscous one); and (2) G′ > G″ (cf. Di Giuseppe et al. [2009] for a detailed discussion).

[11] The spring-block model is designed using a nature/model length scale, L*, of 6.4 × 105 (i.e., 1 cm in the model corresponds to 6.4 km in nature). This scaling factor is derived by assuming that viscous stress in the analog material scales with lithostatic pressure [see Di Giuseppe et al., 2009, equation 7]. For models performed in natural gravity field, the stress scaling factor, σ*, can be obtained from the relation

equation image

where ρ* is the nature/model density scale factor. Since pig skin 2.5%wt gelatin density is about 1000 kg m−3 and the average upper crustal density is 2700 kg m−3, we have σ* = 1.7 × 106 (1 Pa in the model corresponds to 1.7 MPa in nature).

[12] For the above stress scaling factor the experimental shear modulus, ranging between 103–104 Pa depending on material aging, is properly scaled with the natural prototype (∼1010 Pa). The experiments are therefore appropriate to model the elastic component of the lithosphere.

[13] The timescale, t*, is set using the relation

equation image

where t is time, σ is stress, μ is viscosity and g is the gravitational acceleration; subscripts n and m marks the natural and model values respectively. The previous relation gives t* = 1.2*1011 assuming a lower bound lithospheric viscosity of 1019 Pa s and considering the model complex viscosity of 50 Pa s [Di Giuseppe et al., 2009]. Hence, the experimental time of few seconds corresponds to thousands of years in nature. The resulting velocity scaling factor, V* (derived as the length scaling factor L* divided by the time scaling factor t*), is 5.5*10−6 so that the experimental loading rate (0.2–2 cm/min) scale to approximately 0.6–6 cm/yr in nature. This timescale confirms that the model material is correctly scaled for the relatively long sticking/interseismic period, while a secondary scaling should be adopted to properly define the coseismic time [Rosenau et al., 2009]. The gelatin is characterized by a Maxwell time of ∼45 s. The material thus responds as a viscoelastic solid during the interseimic phase, and it is mainly elastic during the few seconds characterizing the slip phase. The rheological properties of gelatin are a fundamental factor to obtain a comprehensive model throughout the entire earthquake cycle including the interseismic viscoelastic deformation [e.g., Rice, 1993; Lapusta et al., 2000]. Tuning the lithospheric viscosity to higher values would increase the timescale without changing the essence of the physical process.

[14] The fixed basal plate, analog of the subduction fault, is covered by various types of sand paper. Sand paper has been selected from a variety of contact materials for the regularity and reproducibility of its frictional properties. This choice allows the study of frictional behavior as a function of the size and distribution of contact protrusions. For this purpose, we prepared a wide range of sand papers using classed abrasive material (silicon carbide) glued to impermeable paper. The roughness of the contact material is quantified as a deviation from straightness consisting of amplitude (i.e., topographical variations of peaks and valleys) and wavelength (i.e., distance between peaks). Both parameters are crucial to a quantitative description of surface roughness when studying frictional constitutive parameters [Marone and Cox, 1994]. To account for topographical variations, we adopt the peak-to-valley mean height roughness Rmh, defined as [Choi et al., 2007]

equation image

where Mp and Mv are the total number of peaks and valleys respectively, and Z is the corresponding height. The wavelength λ has been characterized measuring the average distance between peaks. Data are collected along 5 cm long linear profiles parallel to the direction of sliding using microscopic analysis (resolution 2.6 μm) and postprocessed with an ad hoc commercial software (Optimas 6.5). Rmh in the selected sand papers ranges between 0.100 ± 0.011 and 0.013 ± 0.001 mm, while λ is comprised between 0.714 ± 0.068 and 0.029 ± 0.002 mm (Table 1). In sand papers, the size and wavelength of protrusions are usually positively correlated (Table 1). However, deviation from this trend are available (samples #3 and 6), providing important additional constraints. To describe univocally both the amplitude and the wavelength of the protrusions with a single parameter, we define the reference roughness parameter, Rmh* λ. Adopted Rmh* λ values range between 0.0714 and 0.0004 (Table 1). For crustal faults, field studies suggest that geometrical irregularities are characterized by a wavelength which relates to amplitude with a ratio of 100–1000 [e.g., Power et al., 1988; Renard et al., 2006; Sagy et al., 2007]; however, no strict geometrical relationship can be assumed between the experimental roughness and the weakly constrained natural prototype. The experimental subduction fault simulates a natural prototype characterized by protrusions of vertical height varying from a few to about one hundred meters, representing a pervasive small-scale roughness. Our choice is supported by the recognized role of small-scale features in tuning the overall bathymetry [Jordan et al., 1983; Abers et al., 1988; Smith and Jordan, 1988] and, in turn, the “characteristic” seafloor roughness, which is estimated to be in the 100–300 m range [Hayes and Kane, 1991]. As a counterpart, we are forced to consider only moderately sized earthquakes since greater events are supposed to require either the rupture of larger asperities [e.g., Cloos, 1992; Seno, 2003] and/or along-strike rupture propagation [e.g., Ruff, 1989; McCaffrey, 2007, 2008].

Table 1. Parameters Characterizing the Experimental Materialsa
 Sample NumberRmh (mm)λ (mm)Rmh * λ (mm2)
  • a

    Sand paper asperity distribution (means ± standard errors) and gelatin physical/rheological properties.

Sand paper10.100 ± 0.0110.714 ± 0.0680.0714
20.093 ± 0.0090.373 ± 0.0230.0347
30.068 ± 0.0060.202 ± 0.0160.0137
40.038 ± 0.0040.143 ± 0.0090.0054
50.029 ± 0.0030.087 ± 0.0070.0025
60.018 ± 0.0020.103 ± 0.0060.0019
70.021 ± 0.0020.040 ± 0.0030.0008
80.016 ± 0.0010.035 ± 0.0020.0006
90.013 ± 0.0010.029 ± 0.0020.0004
 Sample NumberDensity (kg/m3)Shear Modulus (Pa)Temperature (°C)
Pig skin 2.5%wt gelatin1∼1000∼100010

2.3. Experimental Procedure

[15] Models are run in a thermally insulated room maintaining constant working temperature (10°C) and humidity, necessary conditions for the rheological control of gelatins. Since the models are designed to study the dependence of friction on the contact surface roughness, we systematically vary the fixed basal plate using nine different sand papers (Table 1). A new gelatin sample is used for each run in order to minimize possible aging and wear effects (a specific experimental study on these effects has been presented by Voisin et al. [2007]).

[16] The experimental procedure consists of pulling the slider at a constant velocity, increasing the shear force until the gelatin block begins to slide. As a characterization of the tribological properties of the system, we measure the static and dynamic coefficients of friction (μs and μd, respectively) and ab (see equation (1)). The reading on the force gauge when the block begins to slide is a measure of μs, while the reading while the block is sliding is a measure of μd. Moreover, in order to correlate experimental observations with seismological quantities, we determine stress drop Δσ and number of stick-slip phases (i.e., earthquakes) occurring within a fixed sliding distance once the steady state regime is reached. The stress drop is obtained by dividing the experimental force drop by the gelatin trailing edge area.

[17] A first set of models is used to measure μs on the contact surface between the gelatin and the different sand papers. Each model consists of a set of three runs performed with different masses of the sliding block (Table 2). The fixed mass of the gelatin is increased by adding calibrated masses atop the slider. We choose additional masses to scale the pressure acting at the interface with the lithostatic pressures operating at shallow, intermediate and deep depths along the subduction thrust fault (24 km, 43 km, and 64 km, respectively; Table 2), neglecting the contribution of the pore fluids pressure. We verified that under these conditions, the plastic yield stress of the gelatin is never exceeded. The static friction coefficient μs is determined for each sand paper, by measuring the force required for moving the sample under the applied normal pressure (i.e., from the slope of the regression line between shear stress and normal stress, normalized by the sample's areas on which these forces act).

Table 2. Experimental Conditions: Velocity and Normal Pressure Ranges
ConditionRange
Velocity (cm/min)
   V 10.2
   V 20.6
   V 31.2
   V 42.0
Normal pressure (Pa)
   NP 1381
   NP 2675
   NP 3991

[18] In a second set of models, the influence of the contact roughness profile on ab was investigated by performing dynamic friction (i.e., velocity stepping) tests at variable normal loads (381 Pa, 675 Pa, 991 Pa; Table 2) and variable driving rates (four velocities tested: 0.2 cm/min, 0.6 cm/min, 1.2 cm/min, and 2 cm/min, corresponding to 0.6 cm/yr, 1.8 cm/yr, 3.6 cm/yr and 6 cm/yr in nature; Table 2). The ab value is derived from the log linear correlation between dynamic friction coefficient (estimated on the basis of the residual stress) and velocity [Scholz, 1998; Rosenau et al., 2009].

[19] At the end of each run, the morphological evolution of the gelatin contact surface is examined using a 3D laser scan, to verify that wear did not affect the sample.

3. Experimental Results

[20] The common behavior of each model shows an initial linear increase of the shear force while the slider is at rest (“initial stick phase”; Figure 3). This phase corresponds to the elastic response of the gelatin. When the critical value is reached, the shear force suddenly drops while the block starts to move. Once the sliding is initiated, the system can exhibit two dynamical regimes:

Figure 3.

Typical time series of shear force values recorded by the digital force sensor for a gelatin–sand paper system characterized by Rmh*λ = 0.0714 mm2, a normal load of 381 Pa, and variable driving velocities indicated by different markers. The dynamical behavior of the system shows a bifurcation as a function of driving rate: stick slip at low driving velocity (V = 0.2–0.6 cm/min); stable sliding at high velocity (V = 1.2–2.0 cm/min). The stable sliding regime occurs when the recorded force readings do not change within a range of ±0.02 N in the sampling window (1 s).

[21] 1. Stick-slip behavior, where the shear force shows a see-saw profile characterized by increases occurring when the gelatin block “sticks” on the contact sand paper, and abrupt decreases when the block slides (Figure 3). Slip phases are associated with the propagation of self-healing pulses originated at the trailing edge of the gelatin slider and emerging at the leading edge [cf. e.g., Rubio and Galeano, 1994; Baumberger et al., 2003].

[22] 2. Stable sliding, characterized by a continuous sliding of the gelatin sample over the sand paper (Figure 3).

[23] The controlled protrusion distribution of each sand paper and the lack of wear on the gelatin contact surface result in reproducible behavior over the imposed deformation cycle. For stick-slip behavior, the initial shear force peak is consistently higher than the following ones (Figure 3). Spring-block models focused on friction at gel-glass interface show that there exists a logarithmic dependence of the yield strength on the sticking time (i.e., interfacial aging) [Baumberger et al., 2002]. During the sticking phase, polymer chains get pinned to the track through adhesive bonds resulting in a strength increase. Upon sliding, bonds have only a finite lifetime and their number decreases resulting in a weakening. A similar behavior has been observed in granular media/natural rocks where strain hardening occurs prior to failure and is followed by strain softening as result of compaction–decompaction cycles [Lohrmann et al., 2003].

[24] For any given gelatin–sand paper system, the driving rate is an important controlling factor (Figure 3). Increasing driving rate increases the frequency of slip episodes, tending to stable sliding after a single shear force drop. For a given block mass and driving rate, the magnitude of characteristic events and their recurrence time scale directly and inversely, respectively, with the reference roughness parameter, Rmh*λ, with a major control exerted by the size of protrusions (Figures 4a4d). In particular, the amplitude and frequency of stick-slip episodes change by ∼−60% and +50%, respectively, for a Rmh*λ decreasing from 0.0714 to 0.00056 mm2 (Figures 4e4f). The inverse correlations between the magnitude of characteristic events and their frequency (Figures 4a4d) highlights the invariance of the seismic coupling during the evolution of the model.

Figure 4.

(a–d) Typical time series of shear force values for a gelatin–sand paper system characterized by a normal load of 381 Pa, driving rate of 0.6 cm/min, and variable Rmh* λ (arranged in the order of decreasing Rmh* λ). (e–f) Variations of stick-slip amplitude (i.e., force drop) and frequency with Rmh* λ under the same experimental conditions.

[25] The overall behavior, however, is more complex when all the system variables are taken into account. Figure 5 shows the dependence of stress drop, Δσ, and dynamical regime on the mass of the sliding block and its velocity for six reference sand papers. While Δσ is usually largest for sand papers characterized by the highest Rmh, it is clear that Rmh is not the exclusive controlling factor. The largest Δσ (278 Pa) is observed for Rmh = 0.068 mm and λ = 0.202 mm, highlighting the importance of the interplay between amplitude and wavelength of asperity distribution along the contact surface in tuning stick-slip behavior. This observation is supported by the fact that a contact surface characterized by a comparable Rmh but sparser asperites results in lower Δσ (see Table 1).

Figure 5.

Phase maps of frictional dynamics in the driving rate-normal load space for gelatin–sand paper systems characterized by different roughness profiles. Panels are arranged in the order of decreasing Rmh* λ. Small black dots indicate measurement steps. Stress drop scale at the bottom.

[26] An increasing stress drop with increasing normal load is commonly observed, and follows from the stability criterion (equation (2)), In particular, experimental results confirm that Δσ increases with increasing normal load and decreasing driving rate for 0.0019 mm2 < Rmh*λ < 0.0714 mm2. In the same roughness range, increasing the driving rate and/or decreasing the normal load cause the sliding dynamics of the system to shift from the stick slip to the stable sliding regime. For Rmh*λ < 0.0019 mm2, the behavior of the system becomes independent of both the mass and velocity of the gelatin block and shows stable sliding (within instrumental resolution) at all experimental conditions.

[27] From the typical time series recorded in the experiments, we quantify the frictional process by measuring μs, μd and ab (Figure 6). We find that μs is strongly dependent on the roughness parameter, rapidly decreasing from ∼1 to 0.24 with Rmh*λ decreasing from 0.0008 mm2 to 0.0004 mm2 and μs < 0.22 for Rmh*λ > 0.0019 mm2 (Figure 6a).

Figure 6.

Diagrams showing the relations between (a) static friction μS and Rmh* λ; (b) friction velocity dependence parameter ab and Rmh* λ; (c) μS and Rmh (black dots) and μS and λ (gray dots plotted on the supplementary horizontal axis on the top); (d) ab versus Rmh (black dots) and λ (gray dots plotted on the supplementary horizontal axis on the top). Figures 6c and 6d show the individual role of Rmh and λ in tuning the frictional parameters. The error bars are constrained by the minimum and maximum values obtained from different (at least four) runs. The parameter ab is measured in the 1.78–4.63 N normal load range (i.e., 381–991 Pa).

[28] In the same range, the frictional parameter ab in the rate and state friction law varies from 0.099 to −0.08, showing a nonlinear dependence on the contact surface roughness profile (Figures 6b and 6d). The value of ab is negative (i.e., unstable velocity weakening regime) for Rmh*λ ≥ 0.0054 mm2, and becomes positive (stable velocity strengthening regime) for Rmh*λ ≤ 0.0054 mm2 (Figure 6b).

4. Discussion: Relevance to Seismic Behavior

4.1. Control of Experimental Parameters on Slip Regime

[29] We have tested how interface roughness (i.e., size and wavelength of protrusions), mass (i.e., pressure) and velocity of a sliding block of gelatin over sand paper affect frictional behavior. The analysis gives some general insights into salient features of low-velocity frictional dynamics. The magnitude of the static friction, the character of the frictional motion, and the magnitude of the stress drop are sensitive to the system parameters.

[30] Static friction is inversely related to Rmh*λ (Figure 6a and Table 1). The smoothest interfaces show the highest static friction [e.g., Marone and Cox, 1994]. This confirms the adhesion friction model (also called plastic junction model) [Bowden and Tabor, 1950] which assumes that static friction is related to the real contact area (i.e., asperity contact characterizing irregular surfaces). A similar behavior, occurring when several frictional resistances (i.e., shear friction, indentation and plounghing force to groove the contact surface, e.g., Byerlee [1967] and Scholz and Engelder [1976] for description of mechanisms related to rock friction) are active, reduces to the classic da Vinci-Coulomb-Amontons friction law for undeformable surfaces. In this apparently counterintuitive view, a perfectly flat and undeformable contact surface (i.e., glass) would produce the highest static friction [Baumberger et al., 2002]. However, the frictional strength in our experiments is also inversely related to the driving rate (Figure 4) [Heslot et al., 1994; Baumberger et al., 2003]. Following Baumberger et al. [2003], we speculate that the static friction of our gelatin-on-sand paper system is tuned by the intrinsical nature of the physical contact and, in particular, by the capability of the gelatin polymeric chains to establish and maintain adhesive bonds with the underlying material. For comparable sample aging, the density/unit area of the polymeric chains forming bonds with the sand paper increases with the number of contact points. This process is controlled by the roughness contact profile, but is also favored by slow driving rate applied to the system [e.g., Engelder and Scholz, 1976; Charitat and Joanny, 2000]. The increase of the threshold stress with time necessary to overcome the static frictional resistance (Figure 3) is the clearest manifestation of this aging effect and can be speculatively compared to natural faults aging/healing [e.g., Marone et al., 1995].

[31] The models exhibit two different dynamical regimes, stick slip and stable sliding, once the static frictional resistance is overcome (Figures 4 and 5). Stick slip is enhanced by rougher contact surfaces (i.e., higher Rmh*λ), lower sliding velocities and higher pressures (Figure 5). In particular, we verified that the stiffness of the system, K, is lower than the critical value Kc (see equation (2)) only for a specific interval of Rmh*λ. In the same interval, ab is negative.

[32] The transition from stick slip to stable sliding appears to be primarily controlled by Rmh, which tunes the maximum stress drop possible in the system. Regular stick-slip instabilities occur only for contact surfaces with Rmh > 0.018 mm.

[33] Within the Rmh range 0.03–0.100 mm considered in our experiments, slip can nucleate and easily propagate (i.e., ab < 0) otherwise the propagation is rapidly inhibited (i.e., ab > 0; Figure 6d). The dynamic regime switches to stable sliding and velocity strengthening behavior for Rmh < 0.03 mm.

[34] The role played by pressure and driving rate seems to be secondary, although not negligible. Independently from the roughness of the contact surface, stable sliding is always achieved for the lowest normal loads and the highest sliding velocities. This behavior can be interpreted by assuming that Rmh and the vertical pressure are factors controlling the magnitude of adhesive bonds of the gelatin polymeric chains. The influence of the normal stress in tuning the stress drop changing from stable sliding to stick-slip behavior is similar to what is observed for rock-rock friction [e.g., Byerlee, 1970; Scholz et al., 1972; Engelder, 1978].

[35] The effect of the driving rate is probably linked to the finite lifetime of the adhesive bonds and their potential to restick after the occurrence of self-healing slip pulses [Baumberger et al., 2002]. At large velocities adhesive bonding becomes negligible and the dynamics of the system is determined by the viscous drag of the gelatin [Bird et al., 1987].

[36] Another important observation is the complexity of ab as a function of Rmh*λ (Figure 6b). Similar complexity was recognized in rock friction [e.g., Dieterich, 1981; Biegel et al., 1989; Marone and Kilgore, 1993]. We interpret the nonlinearity of ab as depending on the relative weight of two competing factors, amplitude and spacing of protrusions, which in nature can be viewed as two aspects of the time dependence of rock strength. The former tunes the magnitude of the slip event [e.g., Ruff and Kanamori, 1983], the latter controls the capability to transmit the triggered deformation along the rupture plane and is linearly related with the critical slip distance [Ohnaka, 2003]. In this view, we speculate that just after the initiation of the slip phase, the geometry of the contact surface determines whether protrusions behave as “asperity-like” or “barrier-like” structures [Aki, 1984], promoting or inhibiting slip propagation, respectively. In the upper limit, a large amplitude and long wavelength roughness profile generates an initial large slip which propagates for a relatively long distance before reaching the neighboring protrusion. The initial signal is unable to overcome the resistance offered by this protrusion, which behaves as a barrier. In the lower limit, a low amplitude and short wavelength roughness profile tends to a flat surface, having a number of contact points above a critical frictional threshold and, consequently, favoring stable sliding. Hence, only surfaces having intermediate amplitude and wavelength roughness profiles can properly simulate a self-sustaining stick-slip process. In particular, we find experimentally that the protrusions amplitude and spacing for stick slip ranges between 0.10 and 0.038 mm (which is equal to 65–25 m in nature) and 0.714–0.143 mm (which is equal to 450–90 m in nature), respectively.

4.2. Implications for Subduction Zone Seismogenesis

[37] Although our simplified models are not intended to reproduce the detailed seismic record of any particular fault and do not address the significant effects of off-fault fracturing on the seismic processes [Wang et al., 2010a], the experimental observations are qualitatively applicable at all scales, highlighting some key features of the seismogenic process. We concentrate our attention on the depth-dependent behavior of the subduction fault, for which the models have been specifically designed and scaled.

[38] Figure 7 shows the cumulative magnitude of moderately sized earthquakes (Mw 5.5–7.5) occurring along worldwide subduction interplate faults in the 1976–2007 period, as a function of depth and subduction velocity [Heuret et al., 2011] (see Text S1 of the auxiliary material for a comprehensive description of sampling criteria and details on data processing). Despite the short length of the time record [McCaffrey, 2008] (see auxiliary material), this information catches the essence of subduction fault behavior. Seismic energy release is maximum in the 20–35 km depth interval. Moreover, seismic energy release is systematically lower for slower subduction velocities.

Figure 7.

Magnitude M′ is obtained from the cumulative moment, MRR, released by N events of the segment during a century and along 1000 km of the trench [Peterson and Seno, 1984]. MMR is then converted into an equivalent representative magnitude M′ using the moment-magnitude relation by Kanamori [1977] (see Heuret et al. [2011] for details). Worldwide subduction zones are divided into 61 segments and Mw 5.5–7.5 events are extracted from CMT [Dziewonski et al., 1981] and EHB [Engdahl et al., 1998] global seismicity catalogs (1976–2007 time period; see Heuret et al. [2011] and auxiliary material). Mw > 7.5 events are not sampled so that we explore a typical background seismicity of the subduction fault, characterized by trench-normal rupture propagations and relatively limited along-strike propagations. Seismic moments are grouped into 10 mm/yr subduction velocities vs 5 km depth cells. Isomagnitudes (grouped into 20 mm/yr subduction velocities vs 10 km depth cells) are shown by white lines. White cells denote lack of data. Subduction zones: Cal, Calabria; Yap, Yap; Pal, Palau; Pat, Patagonia; And, Andaman; Ven, Venezuela; Mak, Makran; H, Halmahera; Ant, Antilles; Pan, Panama; E-Aeg, Eastern Aegean; Tim, Timor; We, Wetar; C, Cotobato; W-Aeg, Western Aegean; Casc, Cascadia; Puy, Puysegur; Col, Colombia; F, Flores; Nank, Nankai; Phil, Philippines; Hik, Hikurangi; Mex, Mexico; E-Ala, Eastern Alaska; Mar, Marianas; Izu, Izu-Bonin; Sand, Sandwich; S-Ker, Southern Kermadec; Su, Sulu; Sum, Sumatra; E-Ale, Eastern Aleutians; N-Pe, Northern Peru; Java, Java; N-Ker, Northern Kermadec; W-Ala, Western Alaska; S-Chi, Southern Chile; Se, Seram; Kam, Kamchatka; N-Chi, Northern Chile; S-Pe, Southern Peru; W-Ale, Western Aleutians; S, Sangihe; Cost, Costa-Rica; C-Ale, Central Aleutians; D'Ent, D'Entrcasteaux; N-Ryu, Northern Ryukyu; Sula, Sulawesi; N-Kur, Northern Kuriles; S-Kur, Southern Kuriles; Coc, Cocos; Man, Manila; Sal, Salomon; Jap, Japan; S-Ton, Southern Tonga; S-Ryu, Southern Ryukyu; Boug, Bougainville; Nbrit, New Britain; S-Heb, Southern New Hebrides; N-Heb, Northern New Hebrides; N-Ton, Northern Tonga.

[39] A qualitative comparison between experimental and natural data (Figures 5 and 7) shows interesting similarities. Low energy release correlates with low normal load. This suggests that low overburden pressure can be a factor controlling the updip limit of significant subduction seismicity. Moreover, the experimental negative relation between energy release (i.e., stress drop) and driving rate (Figure 3) for intermediate-to-high values of the latter parameter is consistent with the nonlinear relation between seismicity in subduction zones and relative plate velocity. This observation highlights the complex role played by subduction velocity in tuning seismic interplate behavior, explaining why faster subduction zones (i.e., Tonga, New Hebrides) are not associated with powerful activity [Pacheco and Sykes, 1992; Pacheco et al., 1993; Gutscher and Westbrook, 2009; Heuret et al., 2011].

[40] The lack of correspondence between natural and experimental frictional behavior for low sliding/subduction velocities is probably related to the impossibility for the real case to sample a complete seismic cycle (>100 Myr long [Gutscher and Westbrook, 2009]) (see auxiliary material). Additional problems are represented by our experimental limitations which neglect the role of temperature, and by the impossibility for our gelatin-sand paper system to reproduce the depth variations of seismogenic behavior by varying only normal load and driving rate for a single roughness profile. If the roughness profile of the subduction fault is an ingredient for interplate seismic activity, its properties must change with depth (and possibly with time and plate subduction; i.e., with total accommodated displacement) to justify the observations. A qualitative account of subduction thrust seismicity would consist of the following elements:

[41] 1. A rough fault at shallow depths, unable to produce significant seismicity because of low lithospheric pressure (see Figure 5) [Das and Scholz, 1983], with a seismologically conditionally stable roughness profile (Figure 6b);

[42] 2. A moderately rough, velocity-weakening fault at intermediate depths, able to produce seismic events whose magnitude is calibrated by the interplay between Rmh, λ, normal load, and subduction velocity;

[43] 3. A smooth, velocity-strengthening fault at larger depth, showing transitional behavior from shallower stick slip to deeper stable sliding.

[44] We thus suggest that the change from stable sliding to stick slip and, again, to stable sliding observed in natural subduction zones (Figures 1 and 7) can be a consequence of simple frictional processes driven by the characteristics of depth- and time-dependent subduction fault protrusions. The proposed interpretation seems feasible since the frictional contact properties between the subducting and the overriding plates depend on deformation, temperature and pressure, which lead to downdip changes in porosity, permeability, pore fluid pressure and comminution. These factors result in changes in the roughness profile of the subduction fault.

[45] A similar model has been proposed by Voisin et al. [2007], who using frictional salt-on-glass models found a progressive change from stick slip to stable sliding occurring over several deformation cycles, concomitant with the morphological evolution of the contact surface produced by physicochemical aging. In nature, progressive rock comminution during the evolution of active faults has been observed and constrained at smaller scales [Storti et al., 2007; Sagy et al., 2007; Balsamo and Storti, 2010; Brodsky et al., 2010]. Its relation with stress drop has been experimentally simulated with granular flow models [e.g., Higashi and Sumita, 2009]. Similar factors can play a role in subduction thrusts, favored by dehydration reactions in the subducting lithosphere [e.g., Pytte and Reynolds, 1988], changes in lithification state [Marone and Scholz, 1988; Marone and Saffer, 2007] and diagenetic processes [Moore and Saffer, 2001]. Thus, the initially rough profile of the lithosphere at the trench will be gradually smoothed as subduction evolves, minimizing roughness fluctuations with depth [Wang, 2010a]. However, this process is controlled not only by the inherited seafloor topography of the slab's surface and trench fills (see Bilek [2007] for a review) but also by the geometry and kinematics of the subducting system. The dip of the slab and the velocity of subduction regulate the state of stress on the interplate thrust fault. This interpretation is confirmed by an analysis of 100 years of global seismicity, showing that velocity of subduction and seismogenic zone geometry and energy release are correlated [Heuret et al., 2011].

[46] The interpretation proposed here qualitatively accounts also for the capability of the subduction fault to reproduce the Gutenberg-Richter magnitude-frequency law [Gutenberg and Richter, 1954]. Events of different size are characterized by different temporal cycles (Figures 3 and 4). This results confirm a common feature of frictional dynamics observed in laboratory models [e.g., Baumberger et al., 1994; Vargas et al., 2008] and theoretical calculations of fault slip rates [Molnar, 1979; McCaffrey, 1997]. Moreover, this observation is consistent with the nonlinear relation found by Bird et al. [2009] between earthquake production and relative plate velocity in subduction zones (slower subduction zones with subduction velocity ≤ 66 mm yr−1 are found to represent only 20% of earthquake productivity and 35% of the cumulative tectonic moment rate). Obviously, the experimental b exponent is not related to the b exponent of real seismicity because of the simplified (quasi two-dimensional) experimental setting which considers only a discrete variability of roughness heterogeneities (see Vargas et al. [2008] for quantitative details). However, this additional observation strengthens the hypothesis that a common frictional root controls the physics of stable/unstable sliding.

[47] Finally, the experimental results emphasize the nonlinearity of ab (Figures 6b and 6d), which we ascribe to the competing role played by amplitude and spacing of protrusions, calibrating the magnitude of the slip event and the ease to transmit the triggered deformation, respectively. This behavior may be applicable to other scales and tectonic settings, even if the physical environment of the subduction thrust fault is different from those of normal and transform faults [see Scholz, 1998 for a comprehensive review]. In particular, a similar mechanism may also be behind the occurrence of subduction megaearthquakes. It is commonly accepted that megaevents cannot be produced by the rupture of an isolated asperity, as seismic moment is a function of the event rupture area [cf., e.g., Hanks and Kanamori, 1979]. Hence, the potential earthquake magnitude is a function of the maximum possible width and the maximum along-trench length of the rupture zone [Ruff, 1989; McCaffrey, 2007, 2008; Hayes and Conrad, 2007]. An analysis of the behavior of subduction interface seismogenic zones has recently recognized that the tectonic regime of the overriding plate (determined from the focal mechanisms of shallow earthquakes occurring at depths less than 40 km from the surface of the upper plate, far from the subduction interface) is likely to play a fundamental role in triggering megaearthquakes [Heuret et al., 2011]. The statistical results presented by Heuret et al. [2011] show that 85% of the recorded M ≥ 8.5 events occurred in areas that are characterized by a neutral back-arc regime (i.e., no significant deformation or strike slip in the upper plate [Lallemand et al., 2008; Wang, 2010b], challenging the common idea that megaearthquakes are generally associated with compressive back-arc deformations [e.g., Uyeda and Kanamori, 1979]. It has been thus proposed that the statistical association of megaearthquakes with neutral subduction zones can be explained as being related to the most favorable interplay between a significantly large initial released seismic moment and a low critical stress for lateral rupture propagation [Hayes and Conrad, 2007; Rosenau and Oncken, 2010; Heuret et al., 2011].

[48] In view of our experiments, we can suggest that a neutral tectonic regime in the overriding plate favors the accumulation of sediments along the subducting fault, which helps reducing the seafloor roughness, creating a smooth coupling capable of localizing deformation and rupturing a large area [Wang, 2010a, 2010b].

5. Conclusions

[49] We have used spring-block-like gelatin-sand paper models as analogs of the subduction thrust fault, and have analyzed the role played by sliding velocity (i.e., subduction rate), normal stress on the sliding surface (i.e., lithospheric pressure), and roughness of the interplate contact (i.e., “interplate protrusions”) speculating about the slip behavior characterizing convergent margins. Our experimental results illustrate the usefulness of the conceptual seismological asperity model, and highlight the competing role played by size and distribution of protrusions in determining frictional contact properties.

[50] Two important conclusions that can be drawn from our experiments are:

[51] 1. If surface roughness is taken as the fixed variable of the system, changes from stick slip to continuous sliding can be tuned by variations in the driving velocity and in the normal load;

[52] 2. Interface geometrical irregularities control both the static friction and the rate friction parameter ab, the latter showing negative values (i.e., seismic) only for a specific roughness amplitude and spacing values. This observation, in combination with an analysis of global seismicity, can be speculatively used to support a wear-controlled hypothesis for the downdip limit of the seismogenic zone.

Acknowledgments

[53] Fabrizio Balsamo and Fabrizio Storti are thanked for useful discussions and practical suggestions which helped us to quantify the concept of interface roughness. Erika Di Giuseppe is acknowledged for her assistance with gelatin rheology and helpful suggestions. We thank also S. Pizzichetti for his help in preparing sand papers and part of the EURYI crew (Claudia Piromallo, Ylona van Dinther, Debora Presti, and Giorgio Mojoli) for their suggestions and continuous support. We also thank the reviewers Matthias Rosenau, André Niemeijer, and Kelin Wang for constructive comments. This research was supported by the European Young Investigators (EURYI) Awards Scheme (Eurohorcs/ESF including funds the National Research Council of Italy) to F.F. G.R.'s participation has been supported by a grant from Natural Sciences and Engineering Research Council of Canada (NSERC). Experiments have been performed in the “Laboratory of Experimental Tectonics” Dipartimento Scienze Geologiche Universita' Roma TRE, Rome, Italy.