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1 On the thermal structure of oceanic transform faults 2 Mark D. Behn1,*, Margaret S. Boettcher1,2, and Greg Hirth1 3 1Department of and Geophysics, Woods Hole Oceanographic Institution, Woods Hole, MA, USA 4 2U.S. Geological Survey, Menlo Park, CA, USA 5 6 7 Abstract: 8 We use 3-D finite element simulations to investigate the upper mantle temperature 9 structure beneath oceanic transform faults. We show that using a rheology that 10 incorporates brittle weakening of the generates a region of enhanced mantle 11 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 16 earlier studies used simplified rheologic laws to simulate the behavior of the lithosphere 17 and underlying asthenosphere. Here, we show that the warmer thermal structure 18 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 20 wide range of geophysical and geochemical observations from ridge-transform 21 environments, including the depth of transform 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.

24 Key Words: Oceanic transform faults, mid- ridges, fault rheology, intra-transform 25 spreading centers 26

*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. -2-

26 1. Introduction

27 Oceanic transform faults are an ideal environment for studying the mechanical 28 behavior of strike-slip faults because of the relatively simple thermal, kinematic, and 29 compositional structure of the oceanic lithosphere. In continental regions fault zone 30 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 (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 38 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). Furthermore, 42 microstructures observed in peridotite 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). 45 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 ’s crust and upper mantle (e.g., advective heat transport resulting from temperature- 48 dependent viscous flow, , 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 53 from a combination of two effects: 1) conductive cooling from the adjacent old, cold 54 lithosphere across the transform fault, and 2) decreased mantle upwelling beneath the 55 transform. Together these effects can result in up to a ~75% increase in lithospheric 56 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 -3-

57 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 59 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 61 evidence for colder upper mantle temperatures near segment ends (Ghose et al., 1996; 62 Niu and Batiza, 1994; Reynolds and Langmuir, 1997), increased fault throw and wider 63 fault spacing near segment ends (Shaw, 1992; Shaw and Lin, 1993), and the blockage of 64 along-axis flow of plume material (Georgen and Lin, 2003). 65 However, correlating the maximum depth of earthquakes on transform faults with this 66 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. Moreover, if oceanic 69 lithosphere is anomalously cold and thick beneath oceanic transform faults, it is difficult 70 to explain the tendency for long transform faults to break into a series of en echelon 71 transform zones separated by small intra-transform spreading centers during changes in 72 plate motion (Fox and Gallo, 1984; Lonsdale, 1989; Menard and Atwater, 1969; Searle, 73 1983). 74 To address these discrepancies between the geophysical observations and the 75 predictions of previous numerical modeling studies, we investigate the importance of 76 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. 79 Using a series of 3-D finite element models, we show that brittle weakening of the 80 lithosphere strongly reduces the effective viscosity beneath the transform, resulting in 81 enhanced upwelling and thinning of the lithosphere. Our calculations suggest that the 82 thermal structure of oceanic transform faults is more similar to that predicted from half- 83 space cooling, but with the warmest temperatures located near the center of the 84 transform. These results have important implications for the mechanical behavior of 85 oceanic transforms, melt generation and migration at mid-ocean ridges, and the long-term 86 response of transform faults to changes in plate motion.

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87 2. Model Setup

88 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 90 package (Figure 1). In all simulations, flow is driven by imposing horizontal velocities 91 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 93 flux without resistance from the underlying mantle. Symmetric boundary conditions are 94 imposed on the sides of the model space parallel to the spreading direction, and the 95 boundaries perpendicular to spreading are open to convective flux. The temperature

96 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. 98 To investigate the importance of rheology on the pattern of flow and thermal structure 99 at oceanic transform faults we examined four scenarios with increasingly realistic 100 descriptions of mantle rheology: 1) constant viscosity, 2) temperature-dependent 101 viscosity, 3) temperature-dependent viscosity with an pre-defined weak zone around the 102 transform, and 4) temperature-dependent viscosity with a visco-plastic approximation for 103 brittle weakening. In all models we assume a Newtonian mantle rheology. In Models 2– 104 4 the effect of temperature on viscosity is calculated by: # & exp(Qo /RT) 105 " = "o% ( (1) $ exp(Qo /RTm )'

19 106 where ηo is the reference viscosity of 10 Pa⋅s, Qo is the activation energy, and R is the 107 gas constant. In all simulations we assume an activation energy of 250 kJ/mol. This ! 108 value represents a reduction of a factor of two relative to the laboratory value as a linear 109 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

112 Figure 2 illustrates the thermal structure calculated at the center of the transform fault 113 from Models 1–4, as well as the thermal structure determined by averaging half-spacing 114 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 -5-

116 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 119 temperature solution for a constant viscosity mantle (Model 1) was determined 120 previously by Phipps Morgan and Forsyth (1988); our results agree with theirs to within 121 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 123 cooling, with the depth of the 600ºC isotherm increasing from ~7 km for the half-space 124 model to ~12 km for the constant viscosity flow solution (Figure 2A). As noted by 125 Phipps Morgan and Forsyth (1988) this reduction in temperature is primarily the result of 126 decreased mantle upwelling beneath the transform fault relative to enhanced upwelling 127 under the ridge axis. Shen and Forsyth (1992) showed that incorporating temperature- 128 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). 130 However, away from the ridge axis the two solutions are quite similar and result in 131 almost identical temperature-depth profiles at the center of the transform (Figures 2A & 132 3).

133 4. Influence of Fault Zone Rheology on Transform Thermal Structure

134 Several lines of evidence indicate that oceanic transform faults are significantly 135 weaker than the surrounding lithosphere. Comparisons of abyssal hill fabric observed 136 near transforms to predictions of fault patterns from numerical modeling suggest that the 137 mechanical coupling across the fault is very weak on geologic time scales (Behn et al., 138 2002; Phipps Morgan and Parmentier, 1984). Furthermore, dredging in transform valleys 139 and valley walls frequently returns serpentinized peridotites (Cannat et al., 1991; Dick et 140 al., 1991), which may promote considerable frictional weakening along the transform 141 (Escartín et al., 2001; Moore et al., 1996; Rutter and Brodie, 1987). Finally, in 142 comparison to continental strike-slip faults, seismic moment studies show that oceanic 143 transforms have high seismic deficits (Boettcher and Jordan, 2004; Okal and 144 Langenhorst, 2000), suggesting that oceanic transforms may be characterized by large 145 amounts of aseismic slip.

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146 In Model 3 we simulate the effect of a weak fault zone, by setting the viscosity to 1019 147 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 150 al. (2001) and van Wijk and Blackman (2004), though these earlier studies modeled 151 deformation in a visco-elastic system in which the transform fault was simulated as a 152 -stress-free plane using the slippery node technique of Melosh and Williams (1989). 153 Our models show that the incorporation of a weak fault zone produces slightly warmer 154 conditions along the transform than for either a constant viscosity mantle (Model 1) or 155 temperature-dependent viscosity without an imposed fault zone (Model 2). However, the 156 predicted temperatures from the fault zone model remain colder than those calculated by 157 the half-space cooling model (Figures 2A & 3). Varying the maximum depth of the 158 weak zone does not significantly influence the predicted thermal structure. 159 Representing the transform as a pre-defined zone of uniform weakness clearly over- 160 simplifies the brittle processes occurring within the lithosphere. In Model 4, we 161 incorporate a more realistic formulation for fault zone behavior by using a visco-plastic 162 rheology to simulate brittle weakening (Chen and Morgan, 1990). In this formulation, 163 brittle strength is approximated by defining a frictional resistance law (e.g., Byerlee, 164 1978):

165 " max = Co + µ#gz (2)

166 in which Co is cohesion (10 MPa), µ is the friction coefficient (0.6), ρ is density (3300 167 kg/m3), g is the gravitational acceleration, and z is depth. Following Chen and Morgan ! 168 (1990), the maximum effective viscosity is then limited by: # 169 " = max (3) 2$˙ II

170 where "˙ II is the second-invariant of the strain-rate tensor. The effect of adding this brittle 171 failure law is to limit viscosity near the surface where the temperature dependence of ! 172 Equation 1 produces unrealistically high mantle viscosities and stresses (Figure 2B). ! 173 The inclusion of the visco-plastic rheology results in significantly warmer thermal 174 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 -7-

176 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 178 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 180 transform, which in turn increases upward heat transport, warming the fault zone and 181 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 183 segments (Figures 2C). Moreover, rather than the transform being a region of 184 anomalously cold lithosphere relative to a half-space cooling model and the surrounding 185 intra-plate mantle, the center of the transform is warmer than adjacent lithosphere of the 186 same age. 187 Although we have not explicitly modeled the effects of non-linear rheology, several 188 previous studies have examined the importance of a non-linear viscosity law on mantle 189 flow and thermal structure in a segmented ridge-transform system (Furlong et al., 2001; 190 Shen and Forsyth, 1992; van Wijk and Blackman, 2004). Without the effects of brittle 191 weakening, these earlier studies predicted temperatures below the transform that were 192 significantly colder than a half-space cooling model. Thus, we conclude that the 193 inclusion of a visco-plastic rheology is the key factor for producing the warmer transform 194 fault thermal structure illustrated in Model 4.

195 5. Implications for the Behavior of Oceanic Transform Faults

196 Our numerical simulations indicate that brittle weakening plays an important role in 197 controlling the thermal structure beneath oceanic transform faults. Specifically, 198 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 200 geophysical and geochemical observations from ridge-transform environments. The 201 temperatures below the transform fault predicted in Model 4 are similar to the half-space 202 cooling model, indicating that the maximum depth of transform fault seismicity is indeed 203 limited by the ~600ºC isotherm as shown by Abercrombie and Ekström (2001). This 204 temperature is consistent with the transition from velocity-weakening to velocity- 205 strengthening frictional behavior extrapolated from laboratory experiments (Boettcher et

Behn et al: Thermal Structure of Oceanic Transform Faults, Submitted to Geology March 2006 -8-

206 al., 2006) and the depth of oceanic intra-plate earthquakes (McKenzie et al., 2005). In 207 addition, a combination of microstructural and petrological observations indicate that the 208 transition from brittle to ductile processes occurs at a temperature of ~600ºC in oceanic 209 transform faults. Microstructural analyses of peridotite mylonites recovered from 210 oceanic zones indicate that strain localization results from the combined effects 211 of grain size reduction, grain boundary sliding and second phase pinning (Warren and 212 Hirth, 2006). Jaroslow et al. (1996) estimated a minimum temperature for 213 deformation of ~600ºC, based on olivine-spinel geothermometry. Furthermore, the 214 randomization of pre-existing lattice preferred orientation (LPO) in the finest grained 215 areas of these mylonites indicates the grain size reduction promotes a transition from 216 dislocation creep processes to diffusion creep, consistent with extrapolation of 217 experimental olivine flow laws to temperatures of 600–800ºC. 218 While the inclusion of a visco-plastic rheology results in significant warming beneath 219 the transform fault, the temperature structure at the ends of the adjacent ridge segments 220 changes only slightly relative to the solution for a constant viscosity mantle. In 221 particular, both models predict a region of cooling along the adjacent ridge segments that 222 extends 15–20 km from the transform fault (Figure 2C). This transform “edge effect” 223 has been invoked to explain segment scale variations in chemistry (Ghose et al., 224 1996; Niu and Batiza, 1994; Reynolds and Langmuir, 1997) and increased fault throw 225 and fault spacing toward the ends of slow-spreading ridge segments (Shaw, 1992; Shaw 226 and Lin, 1993). In addition, this along-axis temperature gradient provides an efficient 227 mechanism for focusing crustal production toward the centers of ridge segments (Magde 228 and Sparks, 1997; Phipps Morgan and Forsyth, 1988; Sparks et al., 1993). 229 The elevated temperatures near the center of the transform in Model 4 may also 230 account for the tendency of long transform faults to break into a series of intra-transform 231 spreading centers during changes in plate motion (Fox and Gallo, 1984; Lonsdale, 1989; 232 Menard and Atwater, 1969). This “leaky transform” phenomenon has been attributed to 233 the weakness of oceanic transform faults relative to the surrounding lithosphere (Fox and 234 Gallo, 1984; Lowrie et al., 1986; Searle, 1983). However, the leaky transform hypothesis 235 is in direct conflict with the thermal structure predicted from Models 1–3, which show 236 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 -9-

237 thermal structure predicted by Model 4 indicates that transforms are hottest and weakest 238 near their centers (Figure 2C). Thus, perturbations in plate motion, which generate 239 extension across the transform, should result in rifting and enhanced melting in these 240 regions. 241 The incorporation of the brittle rheology also promotes strain localization on the plate 242 scale. In particular, if transforms were regions of thick, cold lithosphere (as predicted by 243 Models 1–3) then over time deformation would tend to migrate outward from the 244 transform zone into the adjacent regions of thinner lithosphere. However, the warmer 245 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. 248 In summary, brittle weakening of the lithosphere along oceanic transform faults 249 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.

256 Acknowledgements

257 We thank Jeff McGuire, Laurent Montési, Trish Gregg, Jian Lin, Henry Dick, and Don 258 Forsyth for fruitful discussions that helped motivate this work. Funding was provided by 259 NSF grants EAR-0405709 and OCE-0443246.

260

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260 Figure Captions

261 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.

265 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) 267 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).

269 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: 272 temperature-dependent viscosity with a frictional failure law. Black arrows indicate 273 horizontal flow velocities. Grey lines show position of plate boundary. Location of 274 horizontal cross-section is indicated in Figure 1. Note that Model 4 incorporating 275 frictional resistance predicts significantly warmer temperatures along the transform than 276 Models 1–3.

277 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

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281 References

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Behn et al: Thermal Structure of Oceanic Transform Faults, Submitted to Geology March 2006 F 3 cm/yr ig . 4 150 km

5 0 1 k 0 m 0 k m Fig. 3 3 cm/yr Ts = 0ºC

100 km Tm = 1300ºC

250 km

Figure 1 A) B) 0 Center of Center of −5 Transform Transform

−10

−15

−20 Depth (km) Half−Space Model −25 Model 1: Constant η Model 2: η(T) −30 Model 3: η(T) + Fault Model 4: η(T, friction) −35 0 500 1000 0 100 200 300 Temperature (oC) Stress (MPa)

Ridge Ridge Axis Transform Fault Axis 0 600oC Isotherm ~ B/D Transition −10

−20 1200oC Isotherm ~ Solidus Depth (km)

−30 C) −100 −75 −50 −25 0 25 50 75 100 Distance Along Plate Boundary (km)

Figure 2 Along−Ridge Distance (km) −40 −20 −40 −20 20 40 20 40 −100 0 0 Along−Transform Distance(km) −50 C.Model3 A.Model1 0 : : Constant η (T) +Faul 1000 50

η t 1100 Temperature 100 −100 1200 ( o C) Along−Transform Distance(km) −50 D.Model4 B.Model2 1300 : 0 η (T, friction) : η Fi (T ) g 50 ure 3 100 Depth (km) Depth (km) Depth (km) Depth (km) −80 −60 −40 −20 −80 −60 −40 −20 −80 −60 −40 −20 −80 −60 −40 −20 −40 0 0 0 0 −15 −20 lo −14 g 10 Across−Transform Distance(km) srII(1/s 0 −13 C.Model3 D.Model4 A.Model1 B.Model2 20 −12 ) 40 : : : Constant η η −40 (T) +Faul (T, friction) : η Temperature 0 (T −20 ) 400

η t 0 800 20 1200 ( Figure 4 o C) 40