-
*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.
On the thermal structure of oceanic transform faults 1 Mark D.
Behn1,*, Margaret S. Boettcher1,2, and Greg Hirth1 2 1Department of
Geology and Geophysics, Woods Hole Oceanographic Institution, Woods
Hole, MA, USA 3 2U.S. Geological Survey, Menlo Park, CA, USA 4 5 6
Abstract: 7 We use 3-D finite element simulations to investigate
the upper mantle temperature 8
structure beneath oceanic transform faults. We show that using a
rheology that 9
incorporates brittle weakening of the lithosphere generates a
region of enhanced mantle 10
upwelling and elevated temperatures along the transform, with
the warmest temperatures 11
and thinnest lithosphere predicted near the center of the
transform. In contrast, previous 12
studies that examined 3-D advective and conductive heat
transport found that oceanic 13
transform faults are characterized by anomalously cold upper
mantle relative to adjacent 14
intra-plate regions, with the thickest lithosphere at the center
of the transform. These 15
earlier studies used simplified rheologic laws to simulate the
behavior of the lithosphere 16
and underlying asthenosphere. Here, we show that the warmer
thermal structure 17
predicted by our calculations is directly attributed to the
inclusion of a more realistic 18
brittle rheology. This warmer upper mantle temperature structure
is consistent with a 19
wide range of geophysical and geochemical observations from
ridge-transform 20
environments, including the depth of transform fault seismicity,
geochemical anomalies 21
along adjacent ridge segments, and the tendency for long
transforms to break into a series 22
of small intra-transform spreading centers during changes in
plate motion. 23
Key Words: Oceanic transform faults, mid-ocean ridges, fault
rheology, intra-transform 24 spreading centers 25
26
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1. Introduction 26
Oceanic transform faults are an ideal environment for studying
the mechanical 27
behavior of strike-slip faults because of the relatively simple
thermal, kinematic, and 28
compositional structure of the oceanic lithosphere. In
continental regions fault zone 29
rheology is influenced by a combination of mantle thermal
structure, variations in crustal 30
thickness, and heterogeneous crustal and mantle composition. By
contrast, the rheology 31
of the oceanic upper mantle is primarily controlled by
temperature. In the ocean basins 32
effective elastic plate thickness (e.g., Watts, 1978) and the
maximum depth of intra-plate 33
earthquakes (Chen and Molnar, 1983; McKenzie et al., 2005; Wiens
and Stein, 1983) 34
correlate closely with the location of the 600ºC isotherm as
calculated from a half-space 35
cooling model. Similarly, recent studies show that the maximum
depth of transform fault 36
earthquakes corresponds to the location of the 600ºC isotherm
derived by averaging the 37
half-space thermal structures on either side of the fault
(Abercrombie and Ekström, 2001; 38
Boettcher, 2005). These observations are consistent with
extrapolations from laboratory 39
studies on olivine that indicate the transition from stable to
unstable frictional sliding 40
occurs around 600ºC at geologic strain-rates (Boettcher et al.,
2006). Furthermore, 41
microstructures observed in peridotite mylonites from oceanic
transforms show that 42
localized viscous deformation occurs at temperatures around
600–800ºC (e.g., Jaroslow 43
et al., 1996; Warren and Hirth, 2006). 44
While a half-space cooling model does a good job of predicting
the maximum depth 45
of transform earthquakes, it neglects many important physical
processes that occur in the 46
Earth’s crust and upper mantle (e.g., advective heat transport
resulting from temperature-47
dependent viscous flow, hydrothermal circulation, and viscous
dissipation). Numerical 48
models that incorporate 3-D advective and conductive heat
transport indicate that the 49
upper mantle beneath oceanic transform faults is anomalously
cold relative to a half-50
space model (Forsyth and Wilson, 1984; Furlong et al., 2001;
Phipps Morgan and 51
Forsyth, 1988; Shen and Forsyth, 1992). This reduction in mantle
temperature results 52
from a combination of two effects: 1) conductive cooling from
the adjacent old, cold 53
lithosphere across the transform fault, and 2) decreased mantle
upwelling beneath the 54
transform. Together these effects can result in up to a ~75%
increase in lithospheric 55
thickness beneath the center of a transform fault relative to a
half-space cooling model, as 56
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well as significant cooling of the upper mantle beneath the ends
of the adjacent spreading 57
centers. This characteristic ridge-transform thermal structure
has been invoked to explain 58
the focusing of crustal production toward the centers of ridge
segments (Magde and 59
Sparks, 1997; Phipps Morgan and Forsyth, 1988; Sparks et al.,
1993), geochemical 60
evidence for colder upper mantle temperatures near segment ends
(Ghose et al., 1996; 61
Niu and Batiza, 1994; Reynolds and Langmuir, 1997), increased
fault throw and wider 62
fault spacing near segment ends (Shaw, 1992; Shaw and Lin,
1993), and the blockage of 63
along-axis flow of plume material (Georgen and Lin, 2003).
64
However, correlating the maximum depth of earthquakes on
transform faults with this 65
colder thermal structure implies that the transition from stable
to unstable frictional 66
sliding occurs at temperatures closer to ~350ºC, which is
inconsistent with both 67
laboratory studies and the depth of intra-plate earthquakes.
Moreover, if oceanic 68
lithosphere is anomalously cold and thick beneath oceanic
transform faults, it is difficult 69
to explain the tendency for long transform faults to break into
a series of en echelon 70
transform zones separated by small intra-transform spreading
centers during changes in 71
plate motion (Fox and Gallo, 1984; Lonsdale, 1989; Menard and
Atwater, 1969; Searle, 72
1983). 73
To address these discrepancies between the geophysical
observations and the 74
predictions of previous numerical modeling studies, we
investigate the importance of 75
fault rheology on the thermo-mechanical behavior of oceanic
transform faults. Earlier 76
studies that incorporated 3-D conductive and advective heat
transport used simplified 77
rheologic laws to simulate the behavior of the lithosphere and
underlying asthenosphere. 78
Using a series of 3-D finite element models, we show that
brittle weakening of the 79
lithosphere strongly reduces the effective viscosity beneath the
transform, resulting in 80
enhanced upwelling and thinning of the lithosphere. Our
calculations suggest that the 81
thermal structure of oceanic transform faults is more similar to
that predicted from half-82
space cooling, but with the warmest temperatures located near
the center of the 83
transform. These results have important implications for the
mechanical behavior of 84
oceanic transforms, melt generation and migration at mid-ocean
ridges, and the long-term 85
response of transform faults to changes in plate motion. 86
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2. Model Setup 87
To solve for coupled 3-D incompressible mantle flow and thermal
structure 88
surrounding an oceanic transform fault we use the COMSOL 3.2
finite element software 89
package (Figure 1). In all simulations, flow is driven by
imposing horizontal velocities 90
parallel to a 150-km transform fault along the top boundaries of
the model space 91
assuming a full spreading rate of 6 cm/yr. The base of the model
is open to convective 92
flux without resistance from the underlying mantle. Symmetric
boundary conditions are 93
imposed on the sides of the model space parallel to the
spreading direction, and the 94
boundaries perpendicular to spreading are open to convective
flux. The temperature 95
across the top and bottom of the model space is set to Ts = 0ºC
and Tm = 1300ºC, 96
respectively. Flow associated with temperature and compositional
buoyancy is ignored. 97
To investigate the importance of rheology on the pattern of flow
and thermal structure 98
at oceanic transform faults we examined four scenarios with
increasingly realistic 99
descriptions of mantle rheology: 1) constant viscosity, 2)
temperature-dependent 100
viscosity, 3) temperature-dependent viscosity with an
pre-defined weak zone around the 101
transform, and 4) temperature-dependent viscosity with a
visco-plastic approximation for 102
brittle weakening. In all models we assume a Newtonian mantle
rheology. In Models 2–103
4 the effect of temperature on viscosity is calculated by:
104
!
" ="oexp Qo /RT( )exp Qo /RTm( )
#
$ %
&
' ( (1) 105
where ηo is the reference viscosity of 1019 Pa⋅s, Qo is the
activation energy, and R is the 106
gas constant. In all simulations we assume an activation energy
of 250 kJ/mol. This 107
value represents a reduction of a factor of two relative to the
laboratory value as a linear 108
approximation for non-linear rheology (Christensen, 1983). The
maximum viscosity is 109
not allowed to exceed 1023 Pa⋅s. 110
3. Influence of 3-D Mantle Flow on Transform Thermal Structure
111
Figure 2 illustrates the thermal structure calculated at the
center of the transform fault 112
from Models 1–4, as well as the thermal structure determined by
averaging half-spacing 113
cooling models on either side of the transform. Because the
thermal structure calculated 114
from half-space cooling is equal on the adjacent plates, the
averaging approach predicts 115
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the same temperature at the center of the transform fault as for
the adjacent intra-plate 116
regions. This model, therefore, provides a good reference for
evaluating whether our 3-D 117
numerical calculations predict excess cooling or excess heating
below the transform. The 118
temperature solution for a constant viscosity mantle (Model 1)
was determined 119
previously by Phipps Morgan and Forsyth (1988); our results
agree with theirs to within 120
5% throughout the model space. The coupled temperature, mantle
flow solution predicts 121
a significantly colder thermal structure at the center of the
transform than does half-space 122
cooling, with the depth of the 600ºC isotherm increasing from ~7
km for the half-space 123
model to ~12 km for the constant viscosity flow solution (Figure
2A). As noted by 124
Phipps Morgan and Forsyth (1988) this reduction in temperature
is primarily the result of 125
decreased mantle upwelling beneath the transform fault relative
to enhanced upwelling 126
under the ridge axis. Shen and Forsyth (1992) showed that
incorporating temperature-127
dependent viscosity (e.g., Model 2) produces enhanced upwelling
and warmer 128
temperatures beneath the ridge axis relative to a constant
viscosity mantle (Figure 3). 129
However, away from the ridge axis the two solutions are quite
similar and result in 130
almost identical temperature-depth profiles at the center of the
transform (Figures 2A & 131
3). 132
4. Influence of Fault Zone Rheology on Transform Thermal
Structure 133
Several lines of evidence indicate that oceanic transform faults
are significantly 134
weaker than the surrounding lithosphere. Comparisons of abyssal
hill fabric observed 135
near transforms to predictions of fault patterns from numerical
modeling suggest that the 136
mechanical coupling across the fault is very weak on geologic
time scales (Behn et al., 137
2002; Phipps Morgan and Parmentier, 1984). Furthermore, dredging
in transform valleys 138
and valley walls frequently returns serpentinized peridotites
(Cannat et al., 1991; Dick et 139
al., 1991), which may promote considerable frictional weakening
along the transform 140
(Escartín et al., 2001; Moore et al., 1996; Rutter and Brodie,
1987). Finally, in 141
comparison to continental strike-slip faults, seismic moment
studies show that oceanic 142
transforms have high seismic deficits (Boettcher and Jordan,
2004; Okal and 143
Langenhorst, 2000), suggesting that oceanic transforms may be
characterized by large 144
amounts of aseismic slip. 145
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In Model 3 we simulate the effect of a weak fault zone, by
setting the viscosity to 1019 146
Pa⋅s in a 5-km wide region surrounding the transform that
extends downward to a depth 147
of 20 km. This results in a narrow fault zone that is 3–4 orders
of magnitude lower 148
viscosity than the surrounding regions. Our approach is similar
to that used by Furlong et 149
al. (2001) and van Wijk and Blackman (2004), though these
earlier studies modeled 150
deformation in a visco-elastic system in which the transform
fault was simulated as a 151
shear-stress-free plane using the slippery node technique of
Melosh and Williams (1989). 152
Our models show that the incorporation of a weak fault zone
produces slightly warmer 153
conditions along the transform than for either a constant
viscosity mantle (Model 1) or 154
temperature-dependent viscosity without an imposed fault zone
(Model 2). However, the 155
predicted temperatures from the fault zone model remain colder
than those calculated by 156
the half-space cooling model (Figures 2A & 3). Varying the
maximum depth of the 157
weak zone does not significantly influence the predicted thermal
structure. 158
Representing the transform as a pre-defined zone of uniform
weakness clearly over-159
simplifies the brittle processes occurring within the
lithosphere. In Model 4, we 160
incorporate a more realistic formulation for fault zone behavior
by using a visco-plastic 161
rheology to simulate brittle weakening (Chen and Morgan, 1990).
In this formulation, 162
brittle strength is approximated by defining a frictional
resistance law (e.g., Byerlee, 163
1978): 164
!
"max
= Co
+ µ#gz (2) 165
in which Co is cohesion (10 MPa), µ is the friction coefficient
(0.6), ρ is density (3300 166
kg/m3), g is the gravitational acceleration, and z is depth.
Following Chen and Morgan 167
(1990), the maximum effective viscosity is then limited by:
168
!
" =#
max
2˙ $ II
(3) 169
where
!
˙ " II is the second-invariant of the strain-rate tensor. The
effect of adding this brittle 170
failure law is to limit viscosity near the surface where the
temperature dependence of 171
Equation 1 produces unrealistically high mantle viscosities and
stresses (Figure 2B). 172
The inclusion of the visco-plastic rheology results in
significantly warmer thermal 173
conditions beneath the transform than predicted by Models 1–3 or
half-space cooling 174
(Figures 2A & 3). The higher temperatures result from the
brittle weakening of the 175
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lithosphere, which reduces the effective viscosity by up to 2
orders of magnitude in a 10-176
km wide region surrounding the fault zone. Unlike Model 3 the
width of this region is 177
not predefined and develops as a function of the rheology and
applied boundary 178
conditions. The zone of decreased viscosity enhances passive
upwelling beneath the 179
transform, which in turn increases upward heat transport,
warming the fault zone and 180
further reducing viscosity (Figure 4). The result is a
characteristic thermal structure in 181
which the transform fault is warmest at its center and cools
towards the adjacent ridge 182
segments (Figures 2C). Moreover, rather than the transform being
a region of 183
anomalously cold lithosphere relative to a half-space cooling
model and the surrounding 184
intra-plate mantle, the center of the transform is warmer than
adjacent lithosphere of the 185
same age. 186
Although we have not explicitly modeled the effects of
non-linear rheology, several 187
previous studies have examined the importance of a non-linear
viscosity law on mantle 188
flow and thermal structure in a segmented ridge-transform system
(Furlong et al., 2001; 189
Shen and Forsyth, 1992; van Wijk and Blackman, 2004). Without
the effects of brittle 190
weakening, these earlier studies predicted temperatures below
the transform that were 191
significantly colder than a half-space cooling model. Thus, we
conclude that the 192
inclusion of a visco-plastic rheology is the key factor for
producing the warmer transform 193
fault thermal structure illustrated in Model 4. 194
5. Implications for the Behavior of Oceanic Transform Faults
195
Our numerical simulations indicate that brittle weakening plays
an important role in 196
controlling the thermal structure beneath oceanic transform
faults. Specifically, 197
incorporating a more realistic treatment of brittle rheology (as
shown in Model 4), results 198
in an upper mantle temperature structure that is consistent with
a wide range of 199
geophysical and geochemical observations from ridge-transform
environments. The 200
temperatures below the transform fault predicted in Model 4 are
similar to the half-space 201
cooling model, indicating that the maximum depth of transform
fault seismicity is indeed 202
limited by the ~600ºC isotherm as shown by Abercrombie and
Ekström (2001). This 203
temperature is consistent with the transition from
velocity-weakening to velocity-204
strengthening frictional behavior extrapolated from laboratory
experiments (Boettcher et 205
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al., 2006) and the depth of oceanic intra-plate earthquakes
(McKenzie et al., 2005). In 206
addition, a combination of microstructural and petrological
observations indicate that the 207
transition from brittle to ductile processes occurs at a
temperature of ~600ºC in oceanic 208
transform faults. Microstructural analyses of peridotite
mylonites recovered from 209
oceanic fracture zones indicate that strain localization results
from the combined effects 210
of grain size reduction, grain boundary sliding and second phase
pinning (Warren and 211
Hirth, 2006). Jaroslow et al. (1996) estimated a minimum
temperature for mylonite 212
deformation of ~600ºC, based on olivine-spinel geothermometry.
Furthermore, the 213
randomization of pre-existing lattice preferred orientation
(LPO) in the finest grained 214
areas of these mylonites indicates the grain size reduction
promotes a transition from 215
dislocation creep processes to diffusion creep, consistent with
extrapolation of 216
experimental olivine flow laws to temperatures of 600–800ºC.
217
While the inclusion of a visco-plastic rheology results in
significant warming beneath 218
the transform fault, the temperature structure at the ends of
the adjacent ridge segments 219
changes only slightly relative to the solution for a constant
viscosity mantle. In 220
particular, both models predict a region of cooling along the
adjacent ridge segments that 221
extends 15–20 km from the transform fault (Figure 2C). This
transform “edge effect” 222
has been invoked to explain segment scale variations in basalt
chemistry (Ghose et al., 223
1996; Niu and Batiza, 1994; Reynolds and Langmuir, 1997) and
increased fault throw 224
and fault spacing toward the ends of slow-spreading ridge
segments (Shaw, 1992; Shaw 225
and Lin, 1993). In addition, this along-axis temperature
gradient provides an efficient 226
mechanism for focusing crustal production toward the centers of
ridge segments (Magde 227
and Sparks, 1997; Phipps Morgan and Forsyth, 1988; Sparks et
al., 1993). 228
The elevated temperatures near the center of the transform in
Model 4 may also 229
account for the tendency of long transform faults to break into
a series of intra-transform 230
spreading centers during changes in plate motion (Fox and Gallo,
1984; Lonsdale, 1989; 231
Menard and Atwater, 1969). This “leaky transform” phenomenon has
been attributed to 232
the weakness of oceanic transform faults relative to the
surrounding lithosphere (Fox and 233
Gallo, 1984; Lowrie et al., 1986; Searle, 1983). However, the
leaky transform hypothesis 234
is in direct conflict with the thermal structure predicted from
Models 1–3, which show 235
the transform to be a region of anomalously cold, thick
lithosphere. In contrast, the 236
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thermal structure predicted by Model 4 indicates that transforms
are hottest and weakest 237
near their centers (Figure 2C). Thus, perturbations in plate
motion, which generate 238
extension across the transform, should result in rifting and
enhanced melting in these 239
regions. 240
The incorporation of the brittle rheology also promotes strain
localization on the plate 241
scale. In particular, if transforms were regions of thick, cold
lithosphere (as predicted by 242
Models 1–3) then over time deformation would tend to migrate
outward from the 243
transform zone into the adjacent regions of thinner lithosphere.
However, the warmer 244
thermal structure that results from the incorporation of a
visco-plastic rheology will tend 245
to keep deformation localized within the transform zone on
time-scales corresponding to 246
the age of ocean basins. 247
In summary, brittle weakening of the lithosphere along oceanic
transform faults 248
generates a region of enhanced mantle upwelling and elevated
temperatures relative to 249
adjacent intra-plate regions. The thermal structure is similar
to that predicted by a half-250
space cooling model, but with the warmest temperatures located
at the center of the 251
transform. This characteristic upper mantle temperature
structure is consistent with a 252
wide range of geophysical and geochemical observations, and
provides important 253
constraints on the future interpretation of microseismicity
data, heat flow, and basalt and 254
peridotite geochemistry in ridge-transform environments. 255
Acknowledgements 256
We thank Jeff McGuire, Laurent Montési, Trish Gregg, Jian Lin,
Henry Dick, and Don 257
Forsyth for fruitful discussions that helped motivate this work.
Funding was provided by 258
NSF grants EAR-0405709 and OCE-0443246. 259
260
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Figure Captions 260
Figure 1: Model setup for numerical simulations of mantle flow
and thermal structure at 261
oceanic transform faults. All calculations are performed for a
150-km long transform and 262
a full spreading rate of 6 cm/yr. Locations of cross-sections
used in Figures 2–4 are 263
shown in grey. 264
Figure 2: (A) Thermal structure and (B) stress calculated versus
depth calculated at the 265
center of a 150-km long transform fault assuming a full
spreading rate of 6 cm/yr. (C) 266
Location of the 600ºC and 1200ºC isotherms along the plate
boundary for the half-space 267
model (grey), Model 1 (black), and Model 4 (red). 268
Figure 3: Cross-sections of mantle temperature at a depth of 20
km for (A) Model 1: 269
constant viscosity of 1019 Pa⋅s, (B) Model 2:
temperature-dependent viscosity, (C) Model 270
3: temperature-dependent viscosity with a weak fault zone, and
(D) Model 4: 271
temperature-dependent viscosity with a frictional failure law.
Black arrows indicate 272
horizontal flow velocities. Grey lines show position of plate
boundary. Location of 273
horizontal cross-section is indicated in Figure 1. Note that
Model 4 incorporating 274
frictional resistance predicts significantly warmer temperatures
along the transform than 275
Models 1–3. 276
Figure 4: Vertical cross-sections through the center of the
transform fault showing (left) 277
strain-rate, and (right) temperature and mantle flow for Models
1–4. The location of the 278
cross-sections is indicated in Figure 1. Note the enhanced
upwelling below the transform 279
results in warmer thermal structure for Model 4 compared to
Models 1–3. 280
281
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382 383
-
250 km
150 km
50 km
100 km
100 km
3 cm/yr
3 cm/yr Ts = 0ºC
Tm = 1300ºC
Fig. 4
Fig. 3
Figure 1
-
0 100 200 300Stress (MPa)
B)Center ofTransform
Temperature (oC)
Dep
th (k
m)
Half−Space ModelModel 1: Constant ηModel 2: η(T)Model 3: η(T) +
FaultModel 4: η(T, friction)
A)Center ofTransform
0 500 1000−35
−30
−25
−20
−15
−10
−5
0
Distance Along Plate Boundary (km)
Dep
th (k
m)
Transform FaultRidge RidgeAxis Axis
600oC Isotherm ~ B/D Transition
1200oC Isotherm ~ Solidus
C)
Figure 2
−100 −75 −50 −25 0 25 50 75 100
−30
−20
−10
0
-
Alon
g−R
idge
Dis
tanc
e (k
m)
A. Model 1: Constant η
−40
−20
0
20
40 B. Model 2: η(T)
Along−Transform Distance (km)
C. Model 3: η(T) + Fault
−100 −50 0 50 100−40
−20
0
20
40
Along−Transform Distance (km)
D. Model 4: η(T, friction)
Figure 3
−100 −50 0 50 100
Temperature (oC)1000 1100 1200 1300
-
Dep
th (k
m)
A. Model 1: Constant η
−80
−60
−40
−20
0
Dep
th (k
m)
B. Model 2: η(T)
−80
−60
−40
−20
0
Dep
th (k
m)
C. Model 3: η(T) + Fault
−80
−60
−40
−20
0
Dep
th (k
m)
D. Model 4: η(T, friction)
log10 srII (1/s)
−40 −20 0 20 40−80
−60
−40
−20
0
−15 −14 −13 −12
Across−Transform Distance (km)
Temperature (oC)
Figure 4
−40 −20 0 20 40
0 400 800 1200