5.1. Relations Between Composition, Friction, and Prism Structure
All samples in this study have bulk clay contents of at least ∼45 wt%, with the exception of sample C0007D-11X4, which contains only ∼30 wt% [Shipboard Scientific Party, 2001b; Expedition 316 Scientists, 2009a, 2009b]. Based on available XRD analyses of clay mineral separates from Site 1174, the clay sized fraction of the bulk sediment is composed primarily of smectite and illite, but chlorite + kaolinite comprise as much as 30 wt% [Steurer and Underwood, 2005]. The overall values of friction coefficient we observe for our clay-rich Nankai samples are 0.20 to 0.46, which compare favorably with previous experimental studies of saturated clay-rich gouges [e.g., Morrow et al., 1992; Crawford et al., 2008; Ikari et al., 2009a; Smith and Faulkner, 2010] including studies of samples recovered during ODP Leg 190 [Brown et al., 2003; Kopf and Brown, 2003; Bourlange et al., 2004; McKiernan et al., 2005]. Morrow et al.  sheared layers of powdered gouge in a standard triaxial configuration, and obtained friction coefficients of ∼0.38 to 0.48 for a powdered illite shale and ∼0.18 to 0.29 for pure montmorillonite; for mixtures of kaolinite and quartz, Crawford et al.  reported residual friction values < 0.45 under water saturated conditions (after accounting for strain hardening effects observed in the triaxial testing apparatus). Kopf and Brown  and Brown et al.  sheared remolded natural samples from the incoming sedimentary sections at Nankai and Barbados using a ring (rotary) shear system, and report friction values of μ = 0.10–0.30 and μ = 0.17–0.27, respectively. Friction coefficients of 0.20–0.30 were measured on samples from Site 1174 by McKiernan et al.  in a triaxial configuration, and values of 0.37–0.40, also measured in a triaxial cell, were reported by Bourlange et al.  on mudstone samples from Site 1173, which is a reference site outboard of the trench along the Muroto transect.
We observe significant differences in friction coefficient between specimens from the three sites we studied, although the samples we tested are primarily hemipelagic silty claystones/clayey siltstones and therefore lithologically similar. Clay content is known to exert a control on friction coefficient [e.g., Lupini et al., 1981; Logan and Rauenzahn, 1987; Brown et al., 2003; Ikari et al., 2007], so it is possible that second-order variations in composition drive some of the patterns in friction that we observe. These include (1) the step increase μ from the fault zone to the footwall at Site C0004, which coincides with an increase in quartz + plagioclase content (and decrease in clay content) (Figures 3 and 7), (2) the overall decrease in μ and corresponding increase in clay content with depth at Site C0007 (Figures 4 and 7), and (3) the slight overall decrease in μ and corresponding slight increase in clay content with depth at Site 1174 (Figures 5 and 7).
However, the range in bulk clay content is similar for all three sites, suggesting that other factors may also strongly influence friction coefficient. For example, the gradual decrease in μ with depth observed in intact wafers from Sites 1174 and C0007 (Figure 7) suggests that fabric development associated with consolidation and early diagenesis may affect friction coefficient at burial depths greater than ∼400–500 m. Overall, however, we observe little difference in friction coefficient between samples trimmed as wafers with minimal disturbance to in situ fabric and consolidation state, and those tested either as powders or remolded sediment (Figure 7). This applies to both Site C0007 and 1174, is consistent with previous findings from C0004, and probably indicates that at depths of up to ∼1 km, fabric development and consolidation have not advanced to the point that they exert a significant influence on frictional strength.
In the megasplay fault zone, material from within the fault zone is frictionally weaker than the wall rocks. In contrast, our measurements document little difference between fault rock and wall rock friction coefficient at Sites 1174 or C0007. This is consistent with the observation that the clay contents of the décollement and fault zones within the frontal thrust region are similar to those of the wall rock. However, due to sampling limitations, it is also possible that very thin, localized zones of slip in a material with very low frictional strength could exist at all three sites, but were not sampled [e.g., Collettini et al., 2009].
Variations in friction coefficient between the three sampling locations are also broadly consistent with observed large-scale along-strike differences in the accretionary complex structure. Samples obtained from the megasplay are consistently stronger than those from both the frontal thrust zone and the décollement zone, and the samples from Site 1174 are the weakest in this study. The lower friction of the samples from Site 1174 compared to that of the frontal thrust samples from Site C0007 is consistent with the higher taper angle of the outermost accretionary wedge along the Kumano transect (∼8–10°) than along the Muroto transect (∼4°) [e.g., Davis et al., 1983; Davis and von Huene, 1987; Dahlen, 1990; Kimura et al., 2007], assuming that the frontal thrust is similar in strength and composition to the décollement along the Kumano transect (which was not sampled). However, the differences in taper angle could also be explained by lower basal shear strength along the Muroto transect due to higher pore fluid pressures there, as suggested by several previous studies [Kopf and Brown, 2003; Moore et al., 2005; Screaton et al., 2009; Skarbek and Saffer, 2009; Tobin and Saffer, 2009; Saffer, 2010], or by the influence of seamounts on the subducting plate that perturb the overriding accretionary wedge [Park et al., 1999; Bangs et al., 2006]. Taken together, our data and the results of previous analyses suggest that differences in friction coefficient play a role in driving along-strike differences in taper angle, although they are probably not the only factor.
5.2. Rate- and State-Dependent Friction and Fault Slip Behavior
In order to better quantify frictional rate dependence, we expand on previous studies [e.g., Saffer and Marone, 2003; Ikari et al., 2009a] by allowing use of a two state variable constitutive law. In contrast to friction coefficient, the velocity dependence of friction shows little dependence on mineralogic variation or position across the fault zones (Figure 8). This is consistent with previous work showing that a-b is less sensitive to changes in clay mineral content than is friction coefficient [Ikari et al., 2007]. We do, however, observe that at Site 1174, values of a-b are generally higher for samples that were tested as powdered or remolded specimens than for those tested as intact wafers. This is not observed in the samples from Sites C0004 and C0007, where burial depths are significantly shallower and the in situ temperature is lower. This may indicate that the lower values of a-b are linked to more advanced consolidation and lithification at the higher in situ pressures and temperatures at Site 1174. If true, this would support the hypothesis that lithification is one key factor in promoting slip instability [Moore and Saffer, 2001; Saffer and Marone, 2003; J. C. Moore et al., 2007].
Our observation of mostly velocity-strengthening behavior is in agreement with several previous experimental studies on clay-rich gouges [e.g., Logan and Rauenzahn, 1987; Morrow et al., 1992; Saffer and Marone, 2003; Ikari et al., 2009a; Tembe et al., 2010], and with analyses suggesting that seismic slip is not expected to occur at shallow depths [Marone and Scholz, 1988; Hyndman, 2007]. We observe a few occurrences of velocity weakening, although the magnitude is small (a-b ≥ −0.0005). Fitting velocity steps that yield the lowest values of a-b (including all instances of velocity weakening we observe) generally requires a two state variable constitutive law. This may indicate a change in underlying frictional mechanisms at the grain scale, but verification of this will require further research because the physical processes represented by the two state variable friction law remain speculative [Marone and Cox, 1994; Blanpied et al., 1998].
Analysis of the rate-dependent friction parameters obtained from constitutive modeling show that trends in the parameter b as a function of slip velocity are inversely correlated with a-b; values of a-b are lowest for sliding velocities in the range 1–3 μm/s, and values of b are highest in this range. This is consistent with previous observations suggesting that the parameter b is the primary control on the evolution of friction and its velocity dependence [e.g., Saffer and Marone, 2003; Ikari et al., 2009a]. The parameter b is interpreted to be a measure of the change in friction resulting from a change in the real area of contact at the grain scale during grain boundary sliding [e.g., Dieterich and Kilgore, 1994]. Low values of b imply that contact area is already maximized, perhaps due to the presence of soft and/or platy clay grains. In this case, and because the parameter a is always positive, a-b is more likely to be positive, leading to velocity-strengthening behavior. This process may provide an explanation for the common observations of a-b > 0 in clay-rich gouges [e.g., Morrow et al., 1992; Saffer and Marone, 2003; Ikari et al., 2009a] and low values of b that can be negative in some cases [Ikari et al., 2009a; Smith and Faulkner, 2010]. In contrast, large rates of contact area growth may lead to high values of b, and thus to reduced values of a-b. It is unclear why a minimum would occur within a specific velocity range, however this could be related to the average grain size in the gouge, which would modulate the lifetime of grain-scale contacts (i.e., Θ).
Due to the overall velocity-strengthening behavior of the shallow fault zone material, seismic slip is not expected to nucleate at the depths of the fault zones examined in this study. At slip velocities of 1–100 μm/s, we observe that all samples become increasingly velocity strengthening (Figure 9). This suggests that propagation of coseismic slip initiated deeper on the subduction megathrust will likely be decelerated by shallow clay-rich sediments as slip reaches this velocity range, making it difficult for seismic slip to reach the seafloor [Rubin, 2008]. However, recent vitrinite reflectance and geochemical studies have documented significant frictional heating within fault rocks of the shallow megasplay and frontal thrust, suggesting that coseismic (rapid) slip may in fact propagate to within a few hundred meters of the seafloor [Sakaguchi et al., 2011]. High-velocity friction experiments, including recent work on samples from the megasplay fault [Ujiie and Tsutsumi, 2010] have also demonstrated that considerable weakening occurs at slip rates in the m/s range, driven by a number of processes including frictional melting and thermal pressurization of pore fluid [Di Toro et al., 2004; Hirose and Bystricky, 2007; Brantut et al., 2008; Ujiie et al., 2009; Ferri et al., 2010].
Velocity-strengthening behavior would be enhanced in low-permeability sediments and gouge, due to undrained conditions during dilation that accompanies increasing slip rate (dilatancy hardening) [Segall and Rice, 1995; Samuelson et al., 2009]. However, thermal pressurization is also important and can dominate the transient pore pressure signal during slip once sliding velocities reach ∼1 mm/s [Segall and Rice, 2006]. Previous studies have reported low-permeability values (<1 × 10−18 m2) for clay-rich Nankai sediments from Sites C0004 and 1174, including both unsheared and sheared material [Bourlange et al., 2004; Gamage and Screaton, 2006; Ikari et al., 2009b]. This is likely to result in competition between thermal depressurization and dilatancy hardening; detailed modeling of these processes informed by laboratory measurements like those reported here will help to resolve their relative importance and their ultimate effects on fault slip and rupture propagation [Segall and Rice, 2006; Segall et al., 2010].
The velocity range over which we observe minimum values of a-b in all three fault zone settings (1–3 μm/s, or 0.1–0.3 m/d) corresponds to estimated slip rates for slow slip events in both the Nankai area and on the San Andreas fault in California [Linde et al., 1996; Ide et al., 2007]. In a general sense, we expect that of all types of slip events will propagate further in a material characterized by lower values of a-b. Within this particular velocity range, a-b reaches negative values at Site C0004 and C0007 and is near velocity neutral at Site 1174 (Figure 9). Several numerical modeling studies have shown that transitional frictional behavior (near velocity neutral) is necessary for slow slip events to arise [Shibazaki and Iio, 2003; Liu and Rice, 2005; Lowry, 2006; Shibazaki and Shimamoto, 2007]. The models used by Shibazaki and Iio  and Shibazaki and Shimamoto  are based on friction experiments in halite, which exhibits velocity-weakening behavior and a minimum in friction coefficient for slip velocities in the range of ∼0.1–3 μm/s [Shimamoto, 1986]. This coincides with the velocity range over which we observe a minimum in a-b for natural clay-rich fault zone materials. Other numerical modeling studies have shown that slow slip events or earthquake afterslip can occur on faults with near velocity-neutral [Rubin, 2008] or velocity-strengthening [Perfettini and Avouac, 2007; Perfettini and Ampuero, 2008] frictional behavior. The occurrence of slow slip is not considered to be solely driven by rate-dependent frictional behavior, but also may depend on high overall pore pressures [Kodaira et al., 2004; Shelly et al., 2006; Liu and Rice, 2007], pore pressure transients due to dilatancy [Rubin, 2008; Segall et al., 2010], or specific elastic stiffness conditions [Perfettini et al., 2001; Lowry, 2006]. Additionally, the majority of studies investigating slow slip focus on events that occur at the downdip (deeper) limit of the seismogenic zone rather than shallow portions.
Nevertheless, velocity-dependent friction likely plays a role in controlling slow slip occurrence, and in particular a transition from velocity-strengthening to velocity-weakening or near velocity-neutral behavior may be required. Our data show that such behavior occurs at sliding velocities similar to those for some slow slip events (∼1–3 μm/s) in materials from all of the fault zones in our study. This indicates that that slow slip events such as low frequency earthquakes [Ito and Obara, 2006] and earthquake afterslip [Thatcher, 1984; Marone et al., 1991; Perfettini and Ampuero, 2008] may be likely to occur in all shallow fault zone settings within the accretionary prism, including the décollement [e.g., Davis et al., 2006] and the frontal thrust zone.