Download Determination of fault friction from reactivation of

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.
ACKNOWLEDGMENTS
Discussions with Rob Twiss, Margarete Jadamec,
and Roland von Huene and thorough reviews by
Ray Fletcher and Juliet Crider greatly improved the
manuscript.
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Manuscript received 12 March 2007
Revised manuscript received 20 April 2007
Manuscript accepted 28 April 2007
Printed in USA
GEOLOGY, September 2007