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Determination of fault friction from reactivation of abyssal-hill faults in subduction zones M. Billen E. Cowgill E. Buer* Department of Geology, University of California–Davis, Davis, California 95616, USA ABSTRACT Abyssal-hill faults are reactivated on the outer slope of trenches when they strike within 25° from trench parallel; otherwise, new faults form parallel to the trench. We use the observed transition angle (25°) and a three-dimensional failure analysis to determine the coefficient of friction on reactivated abyssal-hill faults. The stress state in the outer slope is modeled as the superposition of the overburden stress and bending-induced plane strain deformation. If new trench-parallel faults fail according to a linear failure relationship with no cohesion, then determination of the coefficient of sliding friction (μ s) on reactivated faults is independent of the absolute value of the principal stresses and depends only on the Poisson ratio of the crust and the slope of the failure law for new faults (μ f). We find that reactivated faults, dipping at 45°, are ~30% weaker than surrounding crust (e.g., μ s = 0.6 for μ f = 0.85). These results suggest that the variation in the strength of oceanic crust due to the seafloor spreading fabric is small, and that the coefficient of sliding friction on oceanic faults is consistent with that observed in the laboratory. Keywords: friction, faulting, Mohr circle, outer slope, oceanic crust. INTRODUCTION Laboratory experiments provide direct quantitative measurements of the strength and frictional properties of rocks, and have shown that with few exceptions the coefficient of sliding friction has a limited range of values (0.5–1.0; Byerlee, 1978). However, application of laboratory-derived friction laws to crustal-scale faults and attempts to estimate fault friction from observations have met with varying success. In continental regions, these studies have largely focused on whether observations support a weak or strong San Andreas fault (e.g., Zoback et al., 1987; Hardebeck and Hauksson, 1999; Scholz, 2000), or whether normal faults can become weak enough to slip at low (<30°) dip angles (e.g., Sibson, 1985; Wernicke, 1995; Collettini and Sibson, 2001). Disagreement on the value of fault friction at the tectonic scale continues due to difficulties in directly estimating fault strength, such as undefined deformation history, weakly defined tectonic stress orientations, interplay of adjacent faults, and the effects of pore fluids on normal stress and heat flow. While most studies of weak faults have focused on the continents, faults formed at oceanic ridges may be inherently weak. In regions of extension, such as mid-ocean ridges or the outer slopes of trenches, fault dip provides a first-order constraint on crustal strength. For *Current affiliation: University of Washington, Seattle, Washington 98195, USA. a typical coefficient of friction (e.g., μ = 0.85), steeply dipping (θ > 65°) normal faults should form in regions of extension. However, the range in observed fault dip from scarps at ridges is 30°–70° (Karson, 1998). Fault dips determined from earthquake moment tensor solutions peak at 45°, with no indication of significant rotation, indicating that either the state of stress in the crust deviates from simple extension, or the faults are weak (Thatcher and Hill, 1995). Active low-angle normal faults have also been imaged at slow spreading ridges (Escartin et al., 1997; Floyd et al., 2001), and are attributed to the exhumation of highly serpentinized mantle peridotites, which are known to have a low coefficient of friction (μ = 0.10–0.55, Moore et al., 2004). At intermediate- and fast-spreading ridges, where abyssal-hill faults may only reach depths of 3–5 km, serpentinites do not form, but hydrothermal activity leads to the formation of clays, which can also have a low coefficient of friction (μ = 0.2–0.4, Morrow et al., 1992). Outer-slope faults are ubiquitous features of subducting oceanic plates, where bendinginduced extension is partially accommodated by normal faulting in the brittle crust (Jones et al., 1978). In most regions, outer-slope faults form parallel to the bending axis (i.e., the trench axis) of the subducting plate (Fig. 1A). However, in regions where abyssal-hill faults strike at a low angle to the trench, the abyssal-hill faults are reactivated instead of forming new faults (Masson, 1991; Fig. 1B). This preferential reacti- vation of abyssal-hill faults suggests that although these faults may heal and strengthen as they cross the ocean basin, they remain weak relative to the surrounding crust. Whereas fault dip is the only geometric constraint on fault strength at ridges, the observation of a consistent transition angle provides an additional constraint on the strength of reactivated Figure 1. Geometry and principal stress axis for outer-slope faulting (see text). A: New faults form parallel to trench (outer-slope fault strike, α s ~ 0) when abyssal-hill faults strike at α h > 25°. B: Reactivation of abyssalhill faults occurs when α h < 25° from trench parallel. © 2007 The Geological Society of America. For permission to copy, contact Copyright Permissions, GSA, or [email protected]. GEOLOGY, September 2007 Geology, September 2007; v. 35; no. 9; p. 819–822; doi: 10.1130/G23847A.1; 4 figures; 1 table. 819 faults. The transition angle is the angle at which the type of fault active in the trench transitions from reactivated abyssal-hill faults to new faults that crosscut the abyssal-hill fabric. Here we first present observations of the transition angle and dip of newly formed and reactivated faults in the outer slopes of trenches. We then use these observations with a three-dimensional Mohr Circle–type failure analysis to determine the coefficient of friction on reactivated abyssal-hill faults. Because the orientations of stresses in the outer slope can be confidently related to bending of the oceanic plate, reactivation of abyssal-hill faults provides a rare opportunity to investigate the frictional properties of the oceanic crust subject to a triaxial stress state. OBSERVATIONS OF OUTER-SLOPE FAULTING Outer-slope faults begin to accommodate extension in the subducting plate in the outer rise at distances of 45–75 km from the trench axis (Masson, 1991; Kobayashi et al., 1998; Massell, 2002; Ranero et al., 2003). Reactivated abyssal-hill faults are identified by their orientation, which is parallel to the abyssal-hill fabric or magnetic lineations seaward of the subduction zone. Observations of the strike relative to the trench (α) of outer-slope faults and abyssalhill orientation are compiled in Table 1 for 13 regions where the subducting plate has a simple structure and the subduction direction is dominantly perpendicular to the trench. We have excluded regions in which active or aseismic ridges or seamounts are subducting or there is a large component of oblique convergence, because the local stress state associated with these complexities may affect the angle at which outer-slope faulting occurs (Massell, 2002; Mortera-Gutierrez et al., 2003). This worldwide data set shows that the transition angle from reactivation of abyssal-hill faults to formation of new faults is ~25° (Fig. 2). The abrupt transition observed across subduction zones is also seen along individual trenches, where there is a rapid change in trench axis orientation (not included Table 1), such as at the junction of the northern Japan and Kurile Trenches (Kobayashi et al., 1998), or the northern end of the Tonga Trench (Massell, 2002). In both these regions, the transition from new trench-parallel faults to reactivation of abyssal-hill faults occurs over a distance of <50 km along the trench. Although the best method for determining fault dip is seismic imaging, outer-slope faults have only been directly imaged in seismic reflection profiles in the Middle America Trench, where reactivated abyssal-hill faults dip at ~45° (Ranero et al., 2003). There are no direct observations of the dip of new faults that form in the outer rise. Estimates on the dip of outer-slope faults in other regions are limited to fault scarp 820 TABLE 1. FAULT ORIENTATIONS Trench Region Reactivated Abyssal-Hill Faults Kuril (2) 41.0°–42.3°N Aleutians (5) 179°E–170°W 157°–170°W Middle 9.5°–11.8°N America (3) 11.8°–14.0°N N. Peru (2) 10.0°–14.0°S C. Peru (4) 17.5°–19.5°S S. Peru (4) 19.5°–21.5°S New Outer-Slope Faults Japan (1) 35.5°–38.5°N 38.5°–39.0°N 39.0°–41.0°N Java (4) 108°–120°W N. Chile (3,4) 22.0°–24.5°S C. Chile (3) 28.0°–31.5°S Kermadec (4) 26.0°–36.0°S Tonga (4) 20.7°–25.5°S Strike Fault αh αs dip 10° 10° N.D.* 1.0° 3.5° N.D. 0–23° 0–23° N.D. 0° 2° N.D. 24° 24° 45° 12.5° 12.5° N.D. 15° 15° 30–60° 20° 20° 30–60° 40° 24° 64° 30° 35° 59° 73° 89° 0° 38° 0° 38° 0° 38° 2.5° N.D. 4° 30–60° 5–10° N.D. 4° 30–50° 3° 30–50° Note: Observations of outer-slope faulting in regions free from structural complexity and oblique convergence. Strike of the fault plane with respect to the trench axis, assuming the feature dips trenchward (αh —abyssal-hill faults, αs —outer-slope faults; see Fig. 1). Numbers in parentheses are references: 1— Kobayashi et al., 1998; 2—Masson, 1991; 3—Ranero et al., 2005; 4—Massell, 2002; 5—Mortera-Gutierrez et al., 2003. N.D. = no data morphology, and range from 30° to 60° (Table 1). However, the range in the actual fault dips may be smaller due to the limited resolution of the swath bathymetry data and clear evidence of mass wasting (e.g., sediment-filled horst-graben structures) and rotation of fault blocks to shallower dips due to continued extension down the outer slope (Massell, 2002). In most regions there are both trenchward- and seaward-facing fault scarps, but the accumulated fault throw is larger by a factor of 2–3 for trenchward- facing scarps (Masson, 1991). In a few locations, seismic moment tensor solutions of outer-slope events also delimit fault dip to 30°–60°, with a peak near 45° for a data set dominated by reactivated abyssal-hill faults (Thatcher and Hill, 1995). THREE-DIMENSIONAL FAILURE ANALYSIS FOR FAULT FRICTION To determine the friction on reactivated faults, we first choose the form of the failure criteria for new and reactivated faults. The failure analysis then proceeds by defining the stress state due to bending in the outer slope and defining the relative magnitudes of the principal stresses. From the principal stresses and orientations of reactivated faults we determine the normal and shear components of stress on the fault planes, which are then used to calculate the coefficient of friction. Failure Criteria for New and Reactivated Faults For the following analysis it is necessary to first consider the type of failure criteria used to characterize failure of new and reactivated Figure 2. Observations of outer-slope fault orientation versus orientation of abyssal-hill (AH) fault orientation from Table 1. When abyssal-hill faults trend <~25°, the trend of outer-slope faults equals the trend of the abyssal-hill faults, while at larger trends new faults form subparallel to the trench. faults. The failure of new faults can be viewed as fracture of intact rock, in which failure is described by Mohr-Coulomb fracture criteria, σs = μiσn + Co, where Co is the cohesion (0–10 MPa) and μi is the coefficient of internal friction (0.5–1.0). In particular, μi = 0.8 for gabbros, dunites, eclogites, and granites for σn < 1000 MPa (Shimada and Cho, 1990). Similarly, frictional slip on preexisting faults is described by Byerlee’s Law, σs = μσn + C; here μ = 0.85 and C = 0 at shallow depths (σn ≤ 200 MPa; Byerlee, 1978). However, on the length scale of crustal faulting, it may be more appropriate to consider the brittle crust as a pervasively fractured rock, in which new faults form through slip on optimally oriented fractures that coalesce to form a new fault. In this case, formation of new faults would also obey Byerlee’s Law. Because both physical models for formation of new faults take the form of a linear failure law with similar values for the failure slope and intercept, either model can be applied for the current analysis. Therefore, we adopt the notation of μf and μs for the failure slope on new and reactivated faults, respectively, and we assume that there is no cohesion (C = 0). Stress State on the Trench Outer Slope We begin by establishing a trench-oriented coordinated system in which the x1 axis is vertical, the x2 axis is trench parallel, and the x3 axis is trench perpendicular (Fig. 1). For comparison of observations of outer-slope faults and abyssal-hill orientations, it is convenient to describe the fault orientation by the fault dip, θ, and the fault strike, α, relative to the trench axis (Fig. 1). The stress state in the outer slope is dominated by bending of the subducting plate along an axis parallel to the trench; therefore, the principal stresses can be approximated as a superposition of the overburden stress and an applied tectonic stress, in the x2-x3 plane, due to bending. In this case, the maximum principal stress is vertical and is given by the overburden stress, σ1 = ρgh, (1) GEOLOGY, September 2007 where ρ, g, and h are the rock density, gravitational acceleration, and depth to a point on the plane, respectively. Bending of the plate at the trench introduces a tectonic stress in both the bending-parallel and bending-perpendicular directions. Assuming plane strain bending of the plate, extension will align the minimum principal stress, σ3, with the direction of bending (x3, trench perpendicular). Along the trenchparallel bending axis (x2), the intermediate principal stress is given by the bending-induced stress for plane strain deformation, σ 2 = ν( σ1 + σ 3 ) (2) (Jaeger and Cook, 1979). The magnitude of the bending-induced extensional stress in the x3 direction is unknown; however, the magnitude of σ3 can be defined relative to σ1 by using the observation that new faults form parallel to the bending axis. Relative Magnitude of the Minimum Principal Stress New faults on the outer slope form approximately parallel to the bending axis (x2) and therefore these faults can be analyzed using only the two-dimensional state of stress (σ1 – σ3) and the fault dip. We assume that failure occurs at the critical stress; therefore, on a Mohr diagram the failure plane is the point on the Mohr circle that is tangent to the failure criterion (e.g., squares in Fig. 3). The differential stress (σD = σ1 – σ3) at failure can be determined geometrically for a linear failure criterion, σs = μf σn + C, where μf = tan φ and C = 0, such that ⎛ 1 − sin ϕ ⎞ σ 3 = σ1 ⎜ . ⎝ 1 + sin ϕ ⎟⎠ (3) Therefore, we can use the observation that new faults form parallel to the bending axis to determine the relative magnitude of σ3 with respect to σ1 in the trench outer slope. In addition, substitution of σ3 into equation 2 shows that σ2 is also proportional to σ1. Coefficient of Friction on Reactivated Faults The derivation here makes three assumptions that allow us to delimit the magnitudes of the principal stresses in the trench outer slope. The normal and shear stress on a fault plane are determined by projecting the stress state, defined by the principal stresses given in equations 1–3, onto the fault plane with an orientation given by the fault plane normal [n = (n1, n2, n3) = (cos θ, sin θ sin α, sin θ cos α)], σ n = σ1 ( n12 + An22 + Bn32 ) (4) and σs = σ1 n12n22(1− A) + n12n32(1− B) + n22 n32(A − B) , (5) 2 2 2 where σ2 = Aσ1, σ3 = Bσ1, A = ν(1 + B), and B = (1 – sin φ)/(1 + sin φ). In a Mohr diagram, the normal and shear stresses on a plane are given by a point on or between the three circles defined by the principal stresses (Fig. 3). The stress components for the observed orientations of outer-slope faults are calculated using equations 4 and 5 and are plotted in Figure 3 for dips of 30°, 45°, and 60°. The faults oriented at the transition angle (αt = 25°) are marked by the location at which the reactivated faults (circles) meet the nonreactivated faults (triangles) for each dip. The maximum value of μs is found by either locating the failure line that passes through the points corresponding to faults at the transition angle on the Mohr diagram or by substituting equations 4 and 5 into μs = σs /σn, ficient of friction for the surrounding crust (μf), and the dip of the reactivated faults (Fig. 4). Increasing the assumed strength of new faults predicts higher values of μs, but weaker reactivated faults relative to the surrounding crust. For example, for a dip of 45°, as observed in the Middle America Trench, reactivated abyssalhill faults at the transition angle (α = 25°) are ~30% weaker than the surrounding crust if μf = 0.85 (μs = 0.61), but are only 17% weaker if μf = 0.6 (μs = 0.5). Uncertainty in the fault dip also has a significant effect on the fault friction estimates. For μf = 0.85, reactivated faults are predicted to be only 10% weaker (μs = 0.77) for θ = 60°, while they are more than 50% weaker (μs = 0.4) if θ = 30°. Without the observation of a transition angle, reactivation of faults dipping at 45° would result in an estimate of μs = 0.64 (μf = 0.85, Figs. 3 and 4), which is not very different from the estimates at the transition angle. However, the observation that only faults striking at less than the transition angle are reactivated constrains the minimum value of μs. For example, if abyssal-hill faults dipping at 45° were 50% weaker than the surrounding crust, then outer-slope faults of all orientations would be reactivated (Figs. 3 and 4). Therefore, the small observed transition angle of 25° is consistent with only a moderate strength reduction (<30%) on abyssal-hill faults in the oceanic crust. DISCUSSION AND CONCLUSIONS Bending of subducting crust along the outer slope of trenches provides a relatively simple environment in which to address the frictional properties of rocks at a large scale: the history of deformation is known (extension at the ridge followed by quiescence), the rock type μs = Figure 3. Three-dimensional Mohr Circle for stress state, in which relative magnitudes of σ2 and σ3 with respect to σ1 are constrained by equations 2 and 3 (see text); ν = 0.3, and C = 0, and μ f = 0.85 for new faults. Stress components (σn , σs ) on the outer-slope and abyssal-hill faults listed in Table 1 are plotted with observed strike angles (cos β 3 = sin θ cos α) and three possible dips: 30° (2β 1 = 60°), 45° (2β 1 = 90°), and 60° (2β 1 = 120°). New faults (squares) are assumed to fail at critical stress for coefficient of friction of μ f = 0.85. Transition angle of 25° corresponds to point where nonreactivated (triangles) meet reactivated (circles) abyssal-hill faults. Straight lines are failure curves for range of possible μ s values for reactivated faults. GEOLOGY, September 2007 n12 n22 (1− A) + n12 n32 (1− B) + n22n32 (A − B) . (6) n12 + An22 + Bn32 2 2 2 Because σ2 and σ3 are proportional to σ1, μs is independent of the absolute magnitude of the stress and depends only on the ν, μf, and the orientation of the fault plane. The Poisson ratio for the crust is usually in the range of 0.25–0.3 and has only a small effect (<2%) on the estimates of μs. For the observed transition angle (25°), the two parameters that have the largest effect on the estimate of the fault friction are the coef- Figure 4. Friction on reactivated abyssal-hill faults (ν = 0.3) as a function of the strength of new faults, the dip of reactivated faults (θ = 30°, 45°, 60°), and the transition angle (dashed, α t = 0°; solid, α t = 25°; dash-dot, α t = 45°). 821 is grossly uniform, and the stress state during reactivation can be quantified with a limited set of assumptions. By combining the observations that new faults form parallel to the trench, and the transition angle for reactivation of abyssalhill faults in the outer slope is 25°, we are able to determine the strength of abyssal hill faults relative to the surrounding crust independent of the absolute magnitude of the principal stresses. The main limitations of the analysis are that the assumed stress state in the outer slope does not account for local variations due to interaction of faults, variations in crustal structure, or variations in the magnitude or orientation of stress with depth in the subducting plate (Mueller et al., 1996). Therefore, the analysis provides a first-order constraint assuming these other processes do not have a significant effect on the average orientation of faults. We find that for a dip of 45°, consistent with observations, a range in the strength of surrounding crust of μf = 0.5–1.0 translates into a range in sliding friction on preexisting faults of 0.44–0.66, or a 12%–34% decrease in the relative strength of abyssal-hill faults. While the values at the low end of the predicted range for μs are consistent with a low coefficient of friction expected for clays or serpentinites that may have formed on fault surfaces at the ridge, the values at the high end suggest that either incomplete healing (e.g., lithification or mineralization that removes clays or serpentine) occurs as the crust moves from the ridge to the outer slope, or the strength reduction is due to some other process, such as smoothing of the fault surface during displacement. However, unless reactivated faults have a very shallow dip (<30°), or the surrounding crust is quite weak, reactivated faults will only be ~30% weaker than the surrounding crust. Our result is consistent with the observation that abyssal-hill fault reactivation is uncommon outside the outer-slope region, as very weak abyssal-hill faults would be easily reactivated, leading to significant intraplate deformation. Such intraplate fault reactivation has only been observed in the central Indian Ocean (Bull and Scrutton, 1990). We conclude that while hydrothermal alteration at the ridge may weaken faults through formation of serpentinites or clays (e.g., μs < 0.2–0.5), these faults do not remain significantly weaker than the surrounding crust. This conclusion suggests that widespread serpentinization of the mantle 822 portion of the oceanic lithosphere, thought to be responsible for transporting fluids to the mantle (e.g., Ranero et al., 2003), may predominantly occur along the outer slope of trenches, after new faults form or abyssal-hill faults are reactivated in the outer rise. 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Zoback, M.D., Zoback, M.L., Mount, V.S., Suppe, J., Eaton, J.P., Healy, J.H., Oppenheimer, D., Reasenberg, P., Jones, L., Raleigh, C.B., Wong, I.G., Scotti, O., and Wentworth, C., 1987, New evidence on the state of stress of the San Andreas fault: Science, v. 238, p. 1105–1111, doi: 10.1126/science.238.4830.1105. Manuscript received 12 March 2007 Revised manuscript received 20 April 2007 Manuscript accepted 28 April 2007 Printed in USA GEOLOGY, September 2007