on the thermal structure of oceanic transform faults9 structure beneath oceanic transform faults. we...

*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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Behn et al: Thermal Structure of Oceanic Transform Faults, Submitted to Geology March 2006

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

on the thermal structure of oceanic transform faults9 structure beneath oceanic transform faults. we...

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