1
On the thermal structure of oceanic transform faults
2
Mark D. Behn1,*, Margaret S. Boettcher1,2, and Greg Hirth1
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7
1
Department of Geology and Geophysics, Woods Hole Oceanographic Institution, Woods Hole, MA, USA
2
U.S. Geological Survey, Menlo Park, CA, USA
Abstract:
8
9
We use 3-D finite element simulations to investigate the upper mantle temperature
structure beneath oceanic transform faults.
We show that using a rheology that
10
incorporates brittle weakening of the lithosphere generates a region of enhanced mantle
11
upwelling and elevated temperatures along the transform, with the warmest temperatures
12
and thinnest lithosphere predicted near the center of the transform. In contrast, previous
13
studies that examined 3-D advective and conductive heat transport found that oceanic
14
transform faults are characterized by anomalously cold upper mantle relative to adjacent
15
intra-plate regions, with the thickest lithosphere at the center of the transform. These
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earlier studies used simplified rheologic laws to simulate the behavior of the lithosphere
17
and underlying asthenosphere.
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predicted by our calculations is directly attributed to the inclusion of a more realistic
19
brittle rheology. This warmer upper mantle temperature structure is consistent with a
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wide range of geophysical and geochemical observations from ridge-transform
21
environments, including the depth of transform fault seismicity, geochemical anomalies
22
along adjacent ridge segments, and the tendency for long transforms to break into a series
23
of small intra-transform spreading centers during changes in plate motion.
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Key Words: Oceanic transform faults, mid-ocean ridges, fault rheology, intra-transform
spreading centers
Here, we show that the warmer thermal structure
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*
Corresponding Author, Dept. of Geology and Geophysics, Woods Hole Oceanographic Institution, 360
Woods Hole Road MS #22, Woods Hole, MA 02543, email: [email protected], phone: 508-289-3637,
fax: 508-457-2187.
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1. Introduction
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Oceanic transform faults are an ideal environment for studying the mechanical
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behavior of strike-slip faults because of the relatively simple thermal, kinematic, and
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compositional structure of the oceanic lithosphere. In continental regions fault zone
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rheology is influenced by a combination of mantle thermal structure, variations in crustal
31
thickness, and heterogeneous crustal and mantle composition. By contrast, the rheology
32
of the oceanic upper mantle is primarily controlled by temperature. In the ocean basins
33
effective elastic plate thickness (e.g., Watts, 1978) and the maximum depth of intra-plate
34
earthquakes (Chen and Molnar, 1983; McKenzie et al., 2005; Wiens and Stein, 1983)
35
correlate closely with the location of the 600ºC isotherm as calculated from a half-space
36
cooling model. Similarly, recent studies show that the maximum depth of transform fault
37
earthquakes corresponds to the location of the 600ºC isotherm derived by averaging the
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half-space thermal structures on either side of the fault (Abercrombie and Ekström, 2001;
39
Boettcher, 2005). These observations are consistent with extrapolations from laboratory
40
studies on olivine that indicate the transition from stable to unstable frictional sliding
41
occurs around 600ºC at geologic strain-rates (Boettcher et al., 2006).
42
microstructures observed in peridotite mylonites from oceanic transforms show that
43
localized viscous deformation occurs at temperatures around 600–800ºC (e.g., Jaroslow
44
et al., 1996; Warren and Hirth, 2006).
Furthermore,
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While a half-space cooling model does a good job of predicting the maximum depth
46
of transform earthquakes, it neglects many important physical processes that occur in the
47
Earth’s crust and upper mantle (e.g., advective heat transport resulting from temperature-
48
dependent viscous flow, hydrothermal circulation, and viscous dissipation). Numerical
49
models that incorporate 3-D advective and conductive heat transport indicate that the
50
upper mantle beneath oceanic transform faults is anomalously cold relative to a half-
51
space model (Forsyth and Wilson, 1984; Furlong et al., 2001; Phipps Morgan and
52
Forsyth, 1988; Shen and Forsyth, 1992). This reduction in mantle temperature results
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from a combination of two effects: 1) conductive cooling from the adjacent old, cold
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lithosphere across the transform fault, and 2) decreased mantle upwelling beneath the
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transform. Together these effects can result in up to a ~75% increase in lithospheric
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thickness beneath the center of a transform fault relative to a half-space cooling model, as
Behn et al: Thermal Structure of Oceanic Transform Faults, Submitted to Geology March 2006
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well as significant cooling of the upper mantle beneath the ends of the adjacent spreading
58
centers. This characteristic ridge-transform thermal structure has been invoked to explain
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the focusing of crustal production toward the centers of ridge segments (Magde and
60
Sparks, 1997; Phipps Morgan and Forsyth, 1988; Sparks et al., 1993), geochemical
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evidence for colder upper mantle temperatures near segment ends (Ghose et al., 1996;
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Niu and Batiza, 1994; Reynolds and Langmuir, 1997), increased fault throw and wider
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fault spacing near segment ends (Shaw, 1992; Shaw and Lin, 1993), and the blockage of
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along-axis flow of plume material (Georgen and Lin, 2003).
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However, correlating the maximum depth of earthquakes on transform faults with this
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colder thermal structure implies that the transition from stable to unstable frictional
67
sliding occurs at temperatures closer to ~350ºC, which is inconsistent with both
68
laboratory studies and the depth of intra-plate earthquakes.
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lithosphere is anomalously cold and thick beneath oceanic transform faults, it is difficult
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to explain the tendency for long transform faults to break into a series of en echelon
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transform zones separated by small intra-transform spreading centers during changes in
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plate motion (Fox and Gallo, 1984; Lonsdale, 1989; Menard and Atwater, 1969; Searle,
73
1983).
Moreover, if oceanic
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To address these discrepancies between the geophysical observations and the
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predictions of previous numerical modeling studies, we investigate the importance of
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fault rheology on the thermo-mechanical behavior of oceanic transform faults. Earlier
77
studies that incorporated 3-D conductive and advective heat transport used simplified
78
rheologic laws to simulate the behavior of the lithosphere and underlying asthenosphere.
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Using a series of 3-D finite element models, we show that brittle weakening of the
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lithosphere strongly reduces the effective viscosity beneath the transform, resulting in
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enhanced upwelling and thinning of the lithosphere. Our calculations suggest that the
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thermal structure of oceanic transform faults is more similar to that predicted from half-
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space cooling, but with the warmest temperatures located near the center of the
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transform. These results have important implications for the mechanical behavior of
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oceanic transforms, melt generation and migration at mid-ocean ridges, and the long-term
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response of transform faults to changes in plate motion.
Behn et al: Thermal Structure of Oceanic Transform Faults, Submitted to Geology March 2006
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2. Model Setup
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To solve for coupled 3-D incompressible mantle flow and thermal structure
89
surrounding an oceanic transform fault we use the COMSOL 3.2 finite element software
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package (Figure 1). In all simulations, flow is driven by imposing horizontal velocities
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parallel to a 150-km transform fault along the top boundaries of the model space
92
assuming a full spreading rate of 6 cm/yr. The base of the model is open to convective
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flux without resistance from the underlying mantle. Symmetric boundary conditions are
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imposed on the sides of the model space parallel to the spreading direction, and the
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boundaries perpendicular to spreading are open to convective flux. The temperature
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across the top and bottom of the model space is set to Ts = 0ºC and Tm = 1300ºC,
97
respectively. Flow associated with temperature and compositional buoyancy is ignored.
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To investigate the importance of rheology on the pattern of flow and thermal structure
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at oceanic transform faults we examined four scenarios with increasingly realistic
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descriptions of mantle rheology: 1) constant viscosity, 2) temperature-dependent
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viscosity, 3) temperature-dependent viscosity with an pre-defined weak zone around the
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transform, and 4) temperature-dependent viscosity with a visco-plastic approximation for
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brittle weakening. In all models we assume a Newtonian mantle rheology. In Models 2–
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4 the effect of temperature on viscosity is calculated by:
# exp(Q /RT ) &
o
" = "o %
(
exp
Q
$ ( o /RTm ) '
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where ηo is the reference viscosity of 1019 Pa⋅s, Qo is the activation energy, and R is the
106
107
108
(1)
!
gas constant. In all simulations we assume an activation energy of 250 kJ/mol. This
value represents a reduction of a factor of two relative to the laboratory value as a linear
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approximation for non-linear rheology (Christensen, 1983). The maximum viscosity is
110
not allowed to exceed 1023 Pa⋅s.
111
3. Influence of 3-D Mantle Flow on Transform Thermal Structure
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Figure 2 illustrates the thermal structure calculated at the center of the transform fault
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from Models 1–4, as well as the thermal structure determined by averaging half-spacing
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cooling models on either side of the transform. Because the thermal structure calculated
115
from half-space cooling is equal on the adjacent plates, the averaging approach predicts
Behn et al: Thermal Structure of Oceanic Transform Faults, Submitted to Geology March 2006
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the same temperature at the center of the transform fault as for the adjacent intra-plate
117
regions. This model, therefore, provides a good reference for evaluating whether our 3-D
118
numerical calculations predict excess cooling or excess heating below the transform. The
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temperature solution for a constant viscosity mantle (Model 1) was determined
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previously by Phipps Morgan and Forsyth (1988); our results agree with theirs to within
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5% throughout the model space. The coupled temperature, mantle flow solution predicts
122
a significantly colder thermal structure at the center of the transform than does half-space
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cooling, with the depth of the 600ºC isotherm increasing from ~7 km for the half-space
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model to ~12 km for the constant viscosity flow solution (Figure 2A). As noted by
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Phipps Morgan and Forsyth (1988) this reduction in temperature is primarily the result of
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decreased mantle upwelling beneath the transform fault relative to enhanced upwelling
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under the ridge axis. Shen and Forsyth (1992) showed that incorporating temperature-
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dependent viscosity (e.g., Model 2) produces enhanced upwelling and warmer
129
temperatures beneath the ridge axis relative to a constant viscosity mantle (Figure 3).
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However, away from the ridge axis the two solutions are quite similar and result in
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almost identical temperature-depth profiles at the center of the transform (Figures 2A &
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3).
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4. Influence of Fault Zone Rheology on Transform Thermal Structure
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Several lines of evidence indicate that oceanic transform faults are significantly
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weaker than the surrounding lithosphere. Comparisons of abyssal hill fabric observed
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near transforms to predictions of fault patterns from numerical modeling suggest that the
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mechanical coupling across the fault is very weak on geologic time scales (Behn et al.,
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2002; Phipps Morgan and Parmentier, 1984). Furthermore, dredging in transform valleys
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and valley walls frequently returns serpentinized peridotites (Cannat et al., 1991; Dick et
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al., 1991), which may promote considerable frictional weakening along the transform
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(Escartín et al., 2001; Moore et al., 1996; Rutter and Brodie, 1987).
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comparison to continental strike-slip faults, seismic moment studies show that oceanic
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transforms have high seismic deficits (Boettcher and Jordan, 2004; Okal and
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Langenhorst, 2000), suggesting that oceanic transforms may be characterized by large
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amounts of aseismic slip.
Finally, in
Behn et al: Thermal Structure of Oceanic Transform Faults, Submitted to Geology March 2006
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In Model 3 we simulate the effect of a weak fault zone, by setting the viscosity to 1019
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Pa⋅s in a 5-km wide region surrounding the transform that extends downward to a depth
148
of 20 km. This results in a narrow fault zone that is 3–4 orders of magnitude lower
149
viscosity than the surrounding regions. Our approach is similar to that used by Furlong et
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al. (2001) and van Wijk and Blackman (2004), though these earlier studies modeled
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deformation in a visco-elastic system in which the transform fault was simulated as a
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shear-stress-free plane using the slippery node technique of Melosh and Williams (1989).
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Our models show that the incorporation of a weak fault zone produces slightly warmer
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conditions along the transform than for either a constant viscosity mantle (Model 1) or
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temperature-dependent viscosity without an imposed fault zone (Model 2). However, the
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predicted temperatures from the fault zone model remain colder than those calculated by
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the half-space cooling model (Figures 2A & 3). Varying the maximum depth of the
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weak zone does not significantly influence the predicted thermal structure.
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Representing the transform as a pre-defined zone of uniform weakness clearly over-
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simplifies the brittle processes occurring within the lithosphere.
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incorporate a more realistic formulation for fault zone behavior by using a visco-plastic
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rheology to simulate brittle weakening (Chen and Morgan, 1990). In this formulation,
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brittle strength is approximated by defining a frictional resistance law (e.g., Byerlee,
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1978):
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" max = Co + µ#gz
166
167
168
!
173
kg/m3), g is the gravitational acceleration, and z is depth. Following Chen and Morgan
(1990), the maximum effective viscosity is then limited by:
"=
# max
2˙$II
(3)
where "˙II is the second-invariant of the strain-rate tensor. The effect of adding this brittle
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172
(2)
in which Co is cohesion (10 MPa), µ is the friction coefficient (0.6), ρ is density (3300
169
171
In Model 4, we
!
!
failure law is to limit viscosity near the surface where the temperature dependence of
Equation 1 produces unrealistically high mantle viscosities and stresses (Figure 2B).
The inclusion of the visco-plastic rheology results in significantly warmer thermal
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conditions beneath the transform than predicted by Models 1–3 or half-space cooling
175
(Figures 2A & 3). The higher temperatures result from the brittle weakening of the
Behn et al: Thermal Structure of Oceanic Transform Faults, Submitted to Geology March 2006
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lithosphere, which reduces the effective viscosity by up to 2 orders of magnitude in a 10-
177
km wide region surrounding the fault zone. Unlike Model 3 the width of this region is
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not predefined and develops as a function of the rheology and applied boundary
179
conditions. The zone of decreased viscosity enhances passive upwelling beneath the
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transform, which in turn increases upward heat transport, warming the fault zone and
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further reducing viscosity (Figure 4). The result is a characteristic thermal structure in
182
which the transform fault is warmest at its center and cools towards the adjacent ridge
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segments (Figures 2C).
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anomalously cold lithosphere relative to a half-space cooling model and the surrounding
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intra-plate mantle, the center of the transform is warmer than adjacent lithosphere of the
186
same age.
Moreover, rather than the transform being a region of
187
Although we have not explicitly modeled the effects of non-linear rheology, several
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previous studies have examined the importance of a non-linear viscosity law on mantle
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flow and thermal structure in a segmented ridge-transform system (Furlong et al., 2001;
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Shen and Forsyth, 1992; van Wijk and Blackman, 2004). Without the effects of brittle
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weakening, these earlier studies predicted temperatures below the transform that were
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significantly colder than a half-space cooling model.
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inclusion of a visco-plastic rheology is the key factor for producing the warmer transform
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fault thermal structure illustrated in Model 4.
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5. Implications for the Behavior of Oceanic Transform Faults
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Thus, we conclude that the
Our numerical simulations indicate that brittle weakening plays an important role in
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controlling the thermal structure beneath oceanic transform faults.
Specifically,
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incorporating a more realistic treatment of brittle rheology (as shown in Model 4), results
199
in an upper mantle temperature structure that is consistent with a wide range of
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geophysical and geochemical observations from ridge-transform environments.
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temperatures below the transform fault predicted in Model 4 are similar to the half-space
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cooling model, indicating that the maximum depth of transform fault seismicity is indeed
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limited by the ~600ºC isotherm as shown by Abercrombie and Ekström (2001). This
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temperature is consistent with the transition from velocity-weakening to velocity-
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strengthening frictional behavior extrapolated from laboratory experiments (Boettcher et
The
Behn et al: Thermal Structure of Oceanic Transform Faults, Submitted to Geology March 2006
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al., 2006) and the depth of oceanic intra-plate earthquakes (McKenzie et al., 2005). In
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addition, a combination of microstructural and petrological observations indicate that the
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transition from brittle to ductile processes occurs at a temperature of ~600ºC in oceanic
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transform faults.
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oceanic fracture zones indicate that strain localization results from the combined effects
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of grain size reduction, grain boundary sliding and second phase pinning (Warren and
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Hirth, 2006). Jaroslow et al. (1996) estimated a minimum temperature for mylonite
213
deformation of ~600ºC, based on olivine-spinel geothermometry.
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randomization of pre-existing lattice preferred orientation (LPO) in the finest grained
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areas of these mylonites indicates the grain size reduction promotes a transition from
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dislocation creep processes to diffusion creep, consistent with extrapolation of
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experimental olivine flow laws to temperatures of 600–800ºC.
Microstructural analyses of peridotite mylonites recovered from
Furthermore, the
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While the inclusion of a visco-plastic rheology results in significant warming beneath
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the transform fault, the temperature structure at the ends of the adjacent ridge segments
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changes only slightly relative to the solution for a constant viscosity mantle.
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particular, both models predict a region of cooling along the adjacent ridge segments that
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extends 15–20 km from the transform fault (Figure 2C). This transform “edge effect”
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has been invoked to explain segment scale variations in basalt chemistry (Ghose et al.,
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1996; Niu and Batiza, 1994; Reynolds and Langmuir, 1997) and increased fault throw
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and fault spacing toward the ends of slow-spreading ridge segments (Shaw, 1992; Shaw
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and Lin, 1993). In addition, this along-axis temperature gradient provides an efficient
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mechanism for focusing crustal production toward the centers of ridge segments (Magde
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and Sparks, 1997; Phipps Morgan and Forsyth, 1988; Sparks et al., 1993).
In
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The elevated temperatures near the center of the transform in Model 4 may also
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account for the tendency of long transform faults to break into a series of intra-transform
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spreading centers during changes in plate motion (Fox and Gallo, 1984; Lonsdale, 1989;
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Menard and Atwater, 1969). This “leaky transform” phenomenon has been attributed to
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the weakness of oceanic transform faults relative to the surrounding lithosphere (Fox and
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Gallo, 1984; Lowrie et al., 1986; Searle, 1983). However, the leaky transform hypothesis
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is in direct conflict with the thermal structure predicted from Models 1–3, which show
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the transform to be a region of anomalously cold, thick lithosphere. In contrast, the
Behn et al: Thermal Structure of Oceanic Transform Faults, Submitted to Geology March 2006
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thermal structure predicted by Model 4 indicates that transforms are hottest and weakest
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near their centers (Figure 2C). Thus, perturbations in plate motion, which generate
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extension across the transform, should result in rifting and enhanced melting in these
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regions.
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The incorporation of the brittle rheology also promotes strain localization on the plate
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scale. In particular, if transforms were regions of thick, cold lithosphere (as predicted by
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Models 1–3) then over time deformation would tend to migrate outward from the
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transform zone into the adjacent regions of thinner lithosphere. However, the warmer
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thermal structure that results from the incorporation of a visco-plastic rheology will tend
246
to keep deformation localized within the transform zone on time-scales corresponding to
247
the age of ocean basins.
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In summary, brittle weakening of the lithosphere along oceanic transform faults
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generates a region of enhanced mantle upwelling and elevated temperatures relative to
250
adjacent intra-plate regions. The thermal structure is similar to that predicted by a half-
251
space cooling model, but with the warmest temperatures located at the center of the
252
transform. This characteristic upper mantle temperature structure is consistent with a
253
wide range of geophysical and geochemical observations, and provides important
254
constraints on the future interpretation of microseismicity data, heat flow, and basalt and
255
peridotite geochemistry in ridge-transform environments.
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Acknowledgements
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We thank Jeff McGuire, Laurent Montési, Trish Gregg, Jian Lin, Henry Dick, and Don
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Forsyth for fruitful discussions that helped motivate this work. Funding was provided by
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NSF grants EAR-0405709 and OCE-0443246.
260
Behn et al: Thermal Structure of Oceanic Transform Faults, Submitted to Geology March 2006
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Figure Captions
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Figure 1: Model setup for numerical simulations of mantle flow and thermal structure at
262
oceanic transform faults. All calculations are performed for a 150-km long transform and
263
a full spreading rate of 6 cm/yr. Locations of cross-sections used in Figures 2–4 are
264
shown in grey.
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Figure 2: (A) Thermal structure and (B) stress calculated versus depth calculated at the
266
center of a 150-km long transform fault assuming a full spreading rate of 6 cm/yr. (C)
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Location of the 600ºC and 1200ºC isotherms along the plate boundary for the half-space
268
model (grey), Model 1 (black), and Model 4 (red).
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Figure 3: Cross-sections of mantle temperature at a depth of 20 km for (A) Model 1:
270
constant viscosity of 1019 Pa⋅s, (B) Model 2: temperature-dependent viscosity, (C) Model
271
3: temperature-dependent viscosity with a weak fault zone, and (D) Model 4:
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temperature-dependent viscosity with a frictional failure law. Black arrows indicate
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horizontal flow velocities. Grey lines show position of plate boundary. Location of
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horizontal cross-section is indicated in Figure 1. Note that Model 4 incorporating
275
frictional resistance predicts significantly warmer temperatures along the transform than
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Models 1–3.
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Figure 4: Vertical cross-sections through the center of the transform fault showing (left)
278
strain-rate, and (right) temperature and mantle flow for Models 1–4. The location of the
279
cross-sections is indicated in Figure 1. Note the enhanced upwelling below the transform
280
results in warmer thermal structure for Model 4 compared to Models 1–3.
281
Behn et al: Thermal Structure of Oceanic Transform Faults, Submitted to Geology March 2006
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.
Fig
3 cm/yr
4
150 km
50
km
k
100
m
3 cm/yr
Fig. 3
Ts = 0ºC
Tm = 1300ºC
100 km
250 km
Figure 1
0
A)
B)
Center of
Transform
−5
Center of
Transform
Depth (km)
−10
−15
−20
Half−Space Model
Model 1: Constant η
Model 2: η(T)
Model 3: η(T) + Fault
Model 4: η(T, friction)
−25
−30
−35
Depth (km)
0
0
500
1000
Temperature (oC)
Ridge
Axis
0
100
200
Stress (MPa)
300
Ridge
Axis
Transform Fault
600oC Isotherm ~ B/D Transition
−10
1200oC Isotherm ~ Solidus
−20
−30
C)
−100
−75
−50
−25
0
25
50
Distance Along Plate Boundary (km)
75
100
Figure 2
40
A. Model 1: Constant η
B. Model 2: η(T)
C. Model 3: η(T) + Fault
D. Model 4: η(T, friction)
Along−Ridge Distance (km)
20
0
−20
−40
40
20
0
−20
−40
−100
−50
0
50
Along−Transform Distance (km)
1000
100 −100
−50
0
50
Along−Transform Distance (km)
1100
1200
Temperature (oC)
1300
Figure 3
100
A. Model 1: Constant η
Depth (km)
0
−20
−40
−60
−80
B. Model 2: η(T)
Depth (km)
0
−20
−40
−60
−80
C. Model 3: η(T) + Fault
Depth (km)
0
−20
−40
−60
−80
D. Model 4: η(T, friction)
Depth (km)
0
−20
−40
−60
−80
−40 −20
0 20 40 −40 −20 0 20
Across−Transform Distance (km)
−15 −14 −13 −12
log10 srII (1/s)
40
0 400 800 1200
Temperature (oC)
Figure 4