Deflection of mantle flow beneath subducting slabs and the ...people.earth.yale.edu/sites/default/files/files/Long/paczkowski_et_al... · First, the wedge and sub-slab 111 domains

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1 Deflection of mantle flow beneath subducting slabs and the origin of sub-slab 2

anisotropy 3 4 5

Karen Paczkowski1,2*, Christopher J. Thissen2, Maureen D. Long2, and Laurent G. J. Montési1 6 7 8

1Department of Geology, University of Maryland, College Park, MD USA 9 2Department of Geology and Geophysics, Yale University, New Haven, CT USA 10

11 *Corresponding author. Email: [email protected] 12

13 14 15 16 17 Abstract 18

Global compilations of sub-slab shear wave splitting parameters show a mix of trench-19 parallel and trench-perpendicular fast directions that often directly contradict predictions from 20 two-dimensional models of slab-entrained flow. Here we show that sub-slab anisotropy is 21 consistent with three-dimensional geodynamic models that feature the interaction between 22 subducting slabs and regional mantle flow. Each model represents a specific region for which 23 high-quality source-side shear wave splitting data are available. We compare the distribution of 24 finite strain in the models with shear wave splitting observations, showing that both trench-25 parallel and trench-perpendicular fast directions can be explained by deflection of regional 26 mantle flow around or beneath subducted slabs. Sub-slab maximum elongation directions 27 calculated from our models depend on a combination of geometry factors (such as slab dip angle 28 and maximum depth), mechanical parameters (such as decoupling between the slab and the 29 subjacent mantle), and the orientation and magnitude of the regional mantle flow. 30 31

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1. Introduction 32 Measurements of seismic anisotropy provide powerful observational constraints on 33 dynamic processes in the Earth’s mantle, as there is a relationship between the strain induced by 34 mantle flow and the resulting seismic anisotropy [e.g., Long and Becker, 2010]. Observations of 35 anisotropy in subduction zones worldwide, primarily from studies of shear wave splitting, have 36 yielded a rich variety of splitting behavior [e.g., Long, 2013]. However, measurements of 37 splitting due to anisotropy in the upper mantle beneath slabs (sub-slab anisotropy) have proven 38 particularly puzzling to interpret in terms of mantle flow; many subduction systems exhibit fast 39 splitting directions that are sub-parallel to the trench, contradicting the predictions of the simplest 40 flow models. A variety of conceptual models that consider three-dimensional sub-slab flow [e.g., 41 Russo and Silver, 1994; Long and Silver, 2008], slab deformation [Di Leo et al., 2014], or the 42 presence of a tilted, subducted oceanic asthenosphere layer with a strong radial anisotropy 43 component [Song and Kawakatsu, 2012] have been proposed to explain observed patterns of fast 44 splitting directions in the sub-slab mantle. 45 Recent progress has been made in modeling investigations of the three-dimensional 46 pattern of mantle flow in subduction systems, from both a numerical [e.g., Faccenda and 47 Capitanio, 2012, 2013; Di Leo et al., 2014; Li et al., 2014] and laboratory [e.g., Druken et al., 48 2011] point of view. Although these studies consider trench migration and the complex shape of 49 slabs, they do not consider that subduction zones exist within a global mantle flow field [e.g. 50 Conrad and Behn, 2010]. Interaction between subduction-induced mantle flow, the global mantle 51 flow, and trench migration affects sub-slab mantle flow [Paczkowski et al., 2014] and potentially 52 the development of anisotropy in the sub-slab mantle. Here we discuss the finite strain field that 53 develops in instantaneous three-dimensional kinematic-dynamic models of individual subduction 54

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systems that include global mantle flow, plate kinematics, and slab geometry parameters. The 55 distribution of finite strain in the sub-slab mantle predicted by each of our models provides an 56 approximation to seismic anisotropy that can be compared with high-quality source-side shear 57 wave splitting measurements that sample the sub-slab mantle. Our models demonstrate that most 58 observations of sub-slab splitting globally can be explained as a consequence of strain in a sub-59 slab mantle flow field that results from the interaction between slabs and the regional mantle 60 flow field. 61 62 2. Numerical modeling approach 63

In order to facilitate comparison between sub-slab anisotropy observations and numerical 64 model predictions, we only model subduction systems for which uniformly processed, high-65 quality source-side shear wave splitting measurements are available. We used measurements 66 from several recent studies [Foley and Long, 2011; Lynner and Long, 2013, 2014] that directly 67 constrain anisotropy in the sub-slab mantle beneath the Tonga, Caribbean, Scotia, Alaska, 68 Aleutians, Central America, Kuril, Northern Honshu, Izu-Bonin, Ryukyu, and Sumatra 69 subduction zones. For each of these subduction zone segments, we have compiled values for slab 70 dip (αs), maximum slab penetration depth (Dslab), and estimates of trench-fixed regional mantle 71 flow velocity scaled by the convergence velocity ( ) and azimuth (θv) that combine a global 72 mantle flow model [Conrad and Behn, 2010] and observed plate motions and trench migration 73 rates [Schellart et al., 2008]. The dips (αs) and depths (Dslab) of slabs in the upper mantle (Table 74 1) are taken from a single global compilation [Lallemand et al., 2005] wherever possible (further 75 details are contained in the Supplementary Information). These estimates are derived from global 76

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mantle tomography models and necessarily involve a degree of subjectivity [Lallemand et al., 77 2005]. 78

The regional mantle flow results from global mantle flow, plate motion, and trench 79 migration [Paczkowski et al., 2014]. Therefore, our modeling approach requires estimates of 80 these quantities for each region under study. Global mantle flow was estimated using a global 81 mantle circulation model [Conrad and Behn, 2010], which combines the effects of density-driven 82 and plate-driven flow in the mantle. We calculated the vertically averaged horizontal upper 83 mantle flow velocities from Conrad and Behn [2010] in a no-net-rotation (NNR) reference frame 84 near each subduction segment (Figure 1). Trench migration velocities for each segment were 85 expressed in the NNR reference frame by combining the estimates of Schellart et al. [2008] of 86 trench-perpendicular trench migration velocity (rollback or advance) and the trench-parallel 87 component of downdip slab motion from the UNAVCO plate motion calculator to represent the 88 trench-parallel component of trench migration. Subtracting the trench migration velocity from 89 the depth-averaged global mantle flow field provides an estimate of the global mantle flow near 90 each trench in a local trench-fixed reference frame. Finally, we define the regional mantle flow 91 (Table 1) as the local trench-fixed global flow field averaged along a transect that roughly 92 corresponds to the back wall of our model. Full details of these calculations can be found in the 93 Supplementary Information. 94

For each subduction zone, we constructed a three-dimensional model of the sub-slab 95 mantle flow field for the geometry and geodynamic parameters appropriate for each subduction 96 zone (Table 1). In these models, mantle flow is driven by the motion of a planar subducting slab 97 and a mantle pressure gradient applied to the upper mantle (Figure 2a). We constructed these 98 steady-state, three-dimensional, kinematically-driven mantle flow models, assuming an 99

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incompressible, isoviscous, Newtonian fluid, using the COMSOL Multiphysics® finite element 100 modeling software, which has been shown to have excellent performance for subduction zone 101 modeling [van Keken et al., 2008]. The density is set to the low value of 10-20 kg/m3 to minimize 102 the effects of inertia, and the effects of thermal buoyancy and gravity are ignored. The slab 103 width, S, is set to 1.5D, where D is the thickness of the upper mantle (~670 km). The edges of 104 the model are located a distance W=2.5D from the edges of the subducting slab. The width of the 105 model in the subduction direction, L, is set to Dcot(αs)+2.2D, and depends on the dip of the 106 subducting plate αs. L and W are chosen to minimize any effect of the model boundaries. In some 107 models the lower mantle is included as a layer of thickness D of a Newtonian material that has 108 30 times the viscosity of the upper mantle [Čížková et al., 2012]. 109

The model is meshed with free tetrahedra in two steps. First, the wedge and sub-slab 110 domains are meshed at high-resolution (element size between 0.05D to 0.1D). Then, the mesh in 111 the surrounding mantle edges and the lower mantle is generated by matching the sub-slab and 112 wedge meshes at the boundaries, but with progressively coarser elements away from the slab. 113 Free slip is imposed on the bottom model boundary at a depth of 1340 km or, when no lower 114 mantle is included, at a depth of 670 km (the base of the transition zone). The top surface of the 115 model at the base of the overriding plate is fixed with a no-slip boundary condition as 116 appropriate for the trench-fixed reference frame of our calculations. The subducting plate and the 117 downgoing slab are moving at the trench-perpendicular convergence velocity Vc. 118

Coupling between the slab and the surrounding mantle is implemented with the help of a 119 coupling factor C such that the velocity imposed on the mantle in contact with the slab and the 120 subducting plate is CVc The interface between the slab and the overlying mantle wedge 121 transitions from fully decoupled (C=0) at depths shallower than 80 km to fully coupled (C=1) 122

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below 80 km [Wada and Wang, 2009]. The coupling factor is uniform along the interface 123 between the subducting slab and the mantle beneath it. The effect of changing the sub-slab 124 coupling factor has been explored systematically in our models. (In contrast to our modeling 125 approach, Conrad and Behn [2010] effectively assume full coupling between slabs and the sub-126 slab mantle when considering global density-driven flow; the implications of this are discussed 127 in the Supplementary Information.) 128

Our models feature a background mantle flow that represents global mantle flow and 129 trench migration. In our local trench-fixed reference frame, a subduction system with strong 130 trench rollback corresponds to a model with a strong background flow field coming from the 131 back-arc side. The background flow is generated by imposing on the model sides a pressure field 132 that varies linearly with horizontal distance. The magnitude and azimuth θv, (counted positive 133 clockwise from the convergence direction) of the background flow are calculated a posteriori by 134 averaging the model mantle velocity along the upper mantle section of the wall behind the 135 subducting slab [Paczkowski et al., 2014]. For each subduction zone segment of interest, the 136 magnitude and azimuth of the pressure gradient are iterated until the background flow field in the 137 model matches the regional mantle flow field evaluated from global convection models and 138 observed trench migration rate, as described above. 139 140 3. Finite strain calculations 141

Our models are evaluated by comparing finite strain ellipsoids (FSEs) in our models with 142 observations of sub-slab seismic anisotropy. The anisotropy dataset is limited to source-side 143 shear wave splitting measurements [Lynner and Long, 2013], thus avoiding complications due to 144

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complex anisotropy in the mantle wedge. Histograms of the observed seismic fast directions for 145 each subduction zone segment are shown in Figure 3. 146

We calculated finite strain ellipsoids (FSEs) by integrating the velocity gradient field 147 along particle streamlines [McKenzie, 1979] using a 5th order Runge-Kutta integration method 148 with adaptive step-size [Press et al., 2007]. The orientation of the maximum elongation of the 149 FSEs can be used as a proxy for the geometry of anisotropy [Ribe, 1992; Becker et al., 2003; Lev 150 and Hager, 2008] for most olivine lattice preferred orientation (LPO) scenarios [Karato et al., 151 2008; Long and Becker, 2010]. As the FSE may not always align with the local mantle flow 152 trajectory [e.g., Li et al., 2014], this approach improves on our previous work, which only 153 considered mantle flow, not strain [Paczkowski et al., 2014]. The effects of inherited fabrics, 154 which may be significant [e.g., Skemer et al., 2012], are ignored here, but our approach should 155 be a good approximation for regions with relatively large amounts of accumulated strain (stretch 156 ratios greater than ~3). 157

We examine the FSEs in a volume corresponding to the sub-slab region sampled by 158 source-side shear wave splitting measurements [Foley and Long, 2011] (160 km to 435 km 159 depth, approximately 200 km to 67 km behind the slab, and 670 km along the strike of the slab; 160 Figure 2a) and containing 1331 FSEs. Further details of these calculations, along with videos 161 showing the accumulation of finite strain along particle streamlines for several example models, 162 can be found in the Supplementary Material. 163

The horizontal projection of maximum elongation directions of the finite strain ellipsoids 164 were compared with the fast directions obtained from source-side shear wave splitting. To 165 facilitate the comparison, both datasets are converted to probability density functions by 166

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smoothing with a Gaussian kernel using a Gaussian optimal bandwidth [Bowman and Azzalini, 167 1997], as shown in Figure 3. 168 169 4. Results 170

Figure 2c illustrates the generation of FSEs elongated parallel to the trench in the sub-171 slab domain of a model that represents the Tonga subduction zone, which exhibits a well-defined 172 pattern of trench-parallel fast splitting directions [Foley and Long, 2011]. Tonga has a steeply 173 dipping, deep slab (αs = 56°, Dslab = 670 km) and rapid trench rollback [Schellart et al., 2008]. 174 Accordingly, the background mantle flow enters the model domain flowing in a trench-175 perpendicular direction ( =1.76Vc, θv = -7°), but is abruptly deflected in a trench-parallel 176 direction by the slab. The slab acts as an obstruction and directs mantle flow toward escape paths 177 around the slab edge [Paczkowski et al., 2014]. 178

The FSEs associated with this flow field are elongated in a trench parallel direction 179 (Figure 2c, Figure 3) in the region sampled by source-side shear wave splitting measurements 180 (Figure 2a), even though the background mantle flow is trench-perpendicular (Figure 1). A 181 model with full coupling also shows dominantly trench-parallel maximum elongation directions, 182 although slightly less than for the decoupled model (Figure 3). The FSE maximum elongation 183 horizontal azimuths show good agreement with shear wave spilling observations, especially for 184 the coupled model (Figure 3), suggesting that the approximately trench-parallel seismic 185 anisotropy directions beneath Tonga may result from the deflection of the regional mantle flow 186 field around the slab. 187

Figure 2d illustrates the generation of FSEs elongated perpendicular to the trench in the 188 sub-slab domain of a model that represents the Alaska subduction zone, which has a relatively 189

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moderately dipping, short slab (αs = 40°, Dslab = 300 km). The background mantle flow enters 190 the model domain flowing in a trench-perpendicular direction ( = 0.49Vc, θv = 17°). The slab 191 again acts as an obstruction to the background mantle flow, but with this subduction zone 192 geometry, the flow is deflected underneath the slab and its azimuth remains largely unchanged 193 [Paczkowski et al., 2014]. The maximum elongation directions of the FSEs, unlike the Tonga 194 model, are dominantly trench-perpendicular through the region for both fully decoupled and 195 fully coupled models,, in agreement with observations of sub-slab seismic anisotropy (Figure 3 196 and Supplementary Information). This suggests deflection of mantle flow is also a plausible 197 geodynamic explanation for trench-perpendicular fast directions in the sub-slab mantle, as 198 observed in the Alaska subduction zone. 199

We have developed similar regional geodynamic models for each of the subduction zone 200 segments in the source-side shear wave splitting database (Table 1). The results of each 201 subduction zone model are summarized and the distribution of FSE maximum elongation 202 horizontal azimuths are compared to the measured fast splitting directions in Figure 3. We 203 include results for both fully decoupled and fully coupled models. With the exception of the 204 model representing the Aleutians subduction zone, the amount of coupling has relatively minor 205 effects on the distribution of maximum elongation azimuths. The effect of including a lower 206 mantle in our model is minimal (Supplementary Information; see also Paczkowski et al. [2014]). 207 In general, this comparison demonstrates that in most subduction systems, observations of sub-208 slab anisotropy can be explained by the interactions among subducting slabs, plate motions, 209 trench migration, and global mantle flow, as discussed further below. 210

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5. Discussion 213 Our analysis reveals that the orientation of the mantle flow deflection and the resulting 214

maximum elongation directions are highly sensitive to subduction zone geometry, the direction 215 and magnitude of the regional mantle flow in a trench-fixed reference frame, and (in some cases) 216 the coupling between the subducting plate and the underlying mantle. A more systematic study 217 that investigates the effect of different model parameters on sub-slab mantle flow (although not 218 FSEs) is described in Paczkowski et al., [2014]. 219

Finite strain accumulates gradually throughout the sub-slab mantle in our models, 220 reaching the largest magnitudes close to the slab (see Videos MS1-MS4 and Figures FS6-FS9 in 221 the Supplementary Information). For fully decoupled long slabs where flow is deflected around 222 the slab edges, the maximum elongation directions also develop trench-parallel directions 223 consistently throughout the sub-slab mantle. For fully coupled long slabs, however, a component 224 of trench-perpendicular maximum elongations develops just beneath the slab (Figures 3 and 225 FS06-07), which increases the width of the distribution of FSE azimuths. In contrast, for short 226 slabs where the regional mantle flow is deflected beneath the slab, trench-perpendicular 227 maximum elongation directions accumulate gradually for both fully decoupled and fully coupled 228 cases (Figures 3 and FS08-09). 229

The finite strain patterns we predict are generally similar to those found by fully dynamic 230 models of subduction with a retreating trench [Faccenda and Capitanio, 2012, 2013; Li et al., 231 2014], which confirms the validity of our approach of including slab retreat as part of a regional 232 mantle flow. These studies found that sub-slab shear wave splitting should generally be 233 influenced by both entrained flow directly beneath the plate and deeper toroidal flow due to 234

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trench retreat. Our study explicitly explores how slab geometry, trench migration, and global 235 mantle flow interact to produce such variable finite strain patterns. 236

The maximum elongation directions of the FSEs predicted by our models generally agree 237 well with source-side shear wave splitting fast directions for many of the subduction zones 238 examined in this study. This suggests that the regional mantle flow and its interaction with slab-239 entrained flow are captured adequately in our models, and that this interaction provides a 240 plausible explanation for both trench-parallel and trench-perpendicular shear wave splitting 241 directions. In systems with a trench-parallel regional mantle flow field (e.g. Izu-Bonin), this flow 242 continues unaltered through the sub-slab domain and produces trench-parallel maximum 243 elongation directions, even with a relatively high coupling factor. For deep, steeply dipping slabs 244 (e.g., Tonga, E. Sumatra, Kuril, Scotia, Caribbean), an originally trench-perpendicular regional 245 mantle flow is deflected around the slab edges, creating trench-parallel maximum elongation 246 directions in the sub-slab mantle. Subduction zones with deep, steeply dipping slabs but that 247 exhibit primarily trench-perpendicular fast splitting directions may be explained by partial 248 coupling between the subducting slab and the subjacent mantle that entrains trench-perpendicular 249 flow (Ryukyu) or by weak regional mantle flow field magnitudes relative to the convergence 250 velocity (W. Sumatra). For subduction zones with shallow slabs (e.g., Aleutian, Alaska, Central 251 America), trench-perpendicular regional mantle flow fields are deflected beneath the slab, 252 preserving the original regional mantle flow direction and creating trench-perpendicular 253 maximum elongation directions. 254

The model comparisons are less satisfactory for three of our fifteen cases: the Kuril, N. 255 Honshu, and S. Caribbean subduction zones. All three cases include complexity in their tectonic 256 setting that is not captured by our relatively simple models. The seismic anisotropy fast 257

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directions for the Kuril subduction zone transition from primarily trench-perpendicular to 258 primarily trench-parallel along the length of the trench, whereas the FSE are consistently trench 259 parallel or at 45° from the trench direction, depending on the degree of coupling. It may be that 260 the degree of coupling between the slab and the subjacent mantle changes along the strike of the 261 subduction zone in relation to lithospheric age [Lynner and Long, 2014]. The global mantle flow 262 field near the N. Honshu subduction zone has variable direction and low magnitude, which 263 suggests that the fairly uniform background mantle flow present in the models may not 264 accurately represent the ambient conditions for this subduction zone. Improved models with 265 spatially variable background mantle flow may agree more completely with the seismic 266 anisotropy observations from that region. Seismic data from the S. Caribbean subduction zone 267 are principally derived from events located close to the thick continental lithosphere of South 268 America, which may influence the sub-slab anisotropy in a way not captured by our model 269 [Miller and Becker, 2012; Lynner and Long, 2013]. 270

Perhaps the most poorly constrained parameter in our models is the degree of coupling 271 between the subducting slab and the underlying sub-slab mantle, as other subduction zone 272 parameters and regional mantle flow can be estimated independently of regional shear wave 273 splitting measurements. In many subduction zones (Tonga, W. Sumatra, Izu-Bonin, Alaska, N. 274 Caribbean, C. Caribbean, S. Caribbean, N. Scotia, S. Scotia, Central America, and N. Honshu), 275 sub-slab maximum elongation directions (and thus splitting directions) are largely insensitive to 276 the coupling factor and are instead controlled by slab geometry and kinematics. Seismic 277 observations of fast directions at subduction zones in which sub-slab maximum elongation 278 directions are sensitive to the coupling factor suggest nearly full coupling in some cases (E. 279 Sumatra and Aleutians) and partial coupling (Ryukyu) or spatially variable coupling (Kuril) 280

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[Lynner and Long, 2014] in other cases. When the slab and mantle are well coupled, a boundary 281 layer of entrained mantle flow develops beneath the slab [Paczkowski et al., 2014], favoring 282 trench-perpendicular maximum elongation directions. 283

Physically, partial coupling may result from a thin layer of low-viscosity material, such 284 as a layer of entrained buoyant, weak asthenosphere [Phipps Morgan et al., 2007; Long and 285 Silver, 2009], partial melt [Kohlstedt, 2002; Katz et al., 2006; Kawakatsu et al., 2009; Schmerr, 286 2012], or solidified wet gabbro [Karato, 2012], and may be facilitated by shear heating [Larsen 287 et al., 1995; Long and Silver, 2009] or the onset of small-scale convection [Lynner and Long, 288 2014]. Alternatively, a non-Newtonian rheology may also thin the mechanical boundary layer at 289 the base of the slab and partially decouple the slab and the subjacent mantle [Parmentier et al., 290 1976; Tovish et al., 1978; McKenzie, 1979; Faccenda and Capitanio, 2013]. While our models 291 cannot discriminate among these different scenarios, some level of decoupling appears necessary 292 for the Ryukyu and Kuril subduction zones, whereas the Tonga and E. Sumatra subduction zones 293 are better explained by fully coupled models. Improved constraints on the level of coupling in 294 each location may shed new light on the nature of the oceanic lithosphere-asthenosphere 295 boundary and its relation to the geologic history of oceanic plates. Furthermore, our results 296 suggest that global circulation models may need to be revisited by including very high viscosity, 297 potentially rigid slabs that are only partially coupled with the subjacent mantle. 298 299 6. Summary 300

We developed a suite of instantaneous three-dimensional kinematic-dynamic models of 301 individual subduction systems that consider the interaction between slab geometry and a regional 302 mantle flow that represents a combination of global mantle flow, trench migration, and plate 303

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motion. In these experiments, the subducting slab acts as a barrier that deflects regional mantle 304 flow either around or beneath the slab. Deflections around the sides of deep slabs create trench 305 parallel maximum elongation directions behind the slab. Deflections beneath shorter slabs 306 preserve the regional mantle flow direction, making it possible to have trench-perpendicular 307 maximum elongation directions in the sub-slab mantle. In some cases, coupling between the 308 subducting slab and the underlying mantle influences the maximum elongation directions, with 309 coupling producing more trench-perpendicular directions. Comparisons between the horizontal 310 azimuth of the maximum elongations and the orientations of source-side shear wave splitting fast 311 directions for specific subduction zones are generally successful. Including complexities in the 312 regional flow field, the degree of coupling, and/or the presence of continental lithosphere may 313 further improve the agreement between models and seismic observations. Nevertheless, the 314 models shown here suggest that deflection of regional mantle flow is a geodynamically plausible 315 explanation for the global distribution of sub-slab seismic anisotropy directions. 316 317 Acknowledgements 318

Data supporting Figure 3 can be found in Foley and Long [2011] and Lynner and Long 319 [2013, 2014]. 320 We are grateful to Clint Conrad, Dave Bercovici, Shun Karato, Mark Brandon, Chris 321 Kincaid, and Colton Lynner for discussions and comments. This work was funded by NSF grants 322 EAR-0911286 (M.D.L.), EAR-0911151 and OCE-1060878 (L.G.J.M. and K.P.). M.D.L. 323 acknowledges additional support from an Alfred P. Sloan Research Fellowship, and C.J.T. 324 acknowledges support from an NSF Graduate Research Fellowship under grant DGE-1122492. 325

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435 Figure Captions 436

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Figure 1. Mantle flow and splitting observations for the Tonga subduction zone. Bathymetry 437 (color field) and vertically averaged horizontal velocity in the upper mantle (black arrows) 438 predicted for the Tonga subduction zone, where the Pacific Plate subducts to the west beneath 439 the Australia Plate. Individual source-side shear wave splitting measurements for the sub-slab 440 mantle [white, Foley and Long, 2011] are available for a segment of the boundary of length 441 Ltrench (blue double-ended arrows). The global mantle flow [Conrad and Behn, 2010], depth-442 averaged over the upper mantle, is expressed in a reference frame fixed with the trench (black 443 arrows) and average along a trench-parallel transect (red arrows) to provide an estimate of the 444 regional flow field. Plate boundaries are indicated in brown [Bird, 2003]. Similar figures for each 445 subduction zone segment used here are available in the Supplementary Information. 446 447 Figure 2. Schematic model setup and results for two subduction zones. a) Side-view schematic 448 diagram of the basic model setup, with the subducting plate in brown. The dip, αs, and depth, 449 Dslab, of the subducting plate, the coupling factor between the subducting plate and the 450 underlying mantle, , the depth of the upper mantle and lower mantle (when present), , and the 451 boundary conditions are shown. The region where finite strain ellipsoids are calculated is shown 452 in red and corresponds to the region sampled by source-side shear wave splitting observations 453 [Foley and Long, 2011]. b) Perspective view of the model geometry. The arrows indicate plate 454 motion, the convergence velocity Vc, and the background mantle flow (magnitude scaled by the 455 convergence velocity, and azimuth θv positive clockwise from the convergence direction). c) 456 Finite strain ellipsoids and streamlines (black lines) for a fully decoupled model representing the 457 Tonga subduction zone. The finite strain ellipsoids are colored by the horizontal azimuth of the 458 maximum elongation direction, and show dominantly trench-parallel maximum elongation 459

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directions as the background mantle flow is directed around the edges of the slab. d) Same as c 460 but for the Alaska subduction zone. The finite strain ellipsoids show dominantly trench-461 perpendicular maximum elongation directions as the background mantle flow is deflected 462 underneath the short Alaska slab. Videos of finite strain development for c) and d) are available 463 in the Supplementary Information. 464 465 Figure 3. Numerical model predictions and seismic anisotropy observations. Distributions of 466 horizontal azimuth of the maximum elongation directions and the seismic anisotropy fast 467 direction are shown for each subduction zone segment (0° is trench-perpendicular and 90° is 468 trench-parallel). The horizontal projection of the maximum elongation directions of the finite 469 strain ellipsoids is shown for both fully coupled models (red lines) and fully decoupled models 470 (blue lines). Models include a viscous lower mantle with a Newtonian viscosity 30 times greater 471 than the viscosity of the upper mantle. The distribution of seismic anisotropy fast directions for 472 the subduction zone of interest are shown as both probability density (grey lines) and as the 473 histogram of raw data, binned in 10 degree intervals, and normalized to unit mass (grey bars). 474 Seismic anisotropy directions are shown as deviations from the trench-perpendicular direction, 475 defined as perpendicular to the transect used to calculate the regional mantle flow 476 (Supplementary Information). 477 478 Tables 479 Table 1: Geometry and regional mantle flow parameters for subduction zone segments. 480 Additional details of these calculations can be found in the Supplementary Information. Errors 481 are two standard deviations of the magnitude and orientation of the regional mantle flow and 482

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include errors propagated from trench migration velocity estimates [Schellart et al., 2008]. For 483 simplicity the slab depth is set to 670 km for all slabs that clearly reach the base of the transition 484 zone and 335 km otherwise. The regional mantle flow is calculated over a transect of length 3 485 Ltrench (Figures 1, S1-S4). 486

176˚

176˚

−180˚

−180˚

−176˚

−176˚

−172˚

−172˚

−168˚

−168˚

−164˚

−164˚

−160˚

−160˚

−40˚ −40˚

−36˚ −36˚

−32˚ −32˚

−28˚ −28˚

−24˚ −24˚

−20˚ −20˚

−16˚ −16˚

−12˚ −12˚

−8˚ −8˚

−4˚ −4˚

15.00 cm/yr

N. Tonga

300 km

a)

b)

Ope

n Bo

unda

ryO

pen

Boun

dary

Ope

n Bo

unda

ry

Free Slip

No Slip

Ope

n Bo

unda

ry

Lower Mantle(when present)

Region for finite strain calculation

Free Slip(no lower mantle)

Depth of shallowslabs = 0.5D

Depth of deepslabs = D

Subducting

Plate top boundary

Subducting

Plate top boundary

c) Tonga

Alaskad)

trench trench

0 10 20 30 40 50 60 70 80 90

Maximum Elongation Horizontal Azimuth

Figure 2

Fully Coupled Model

Seismic Fast DirectionsFully Decoupled Model

Maximum Elongation Horizontal Azimuth

Deviation From Trench Perpendicular (°) Deviation From Trench Perpendicular (°)Deviation From Trench Perpendicular (°)

,

Figure 3

-150 -100 -50 -0 50 100 150

-90° 90°0°

dens

ity

-150 -100 -50 -0 50 100 150

-90° 90°0°

dens

ity-150 -100 -50 -0 50 100 150

-90° 90°0°

dens

ity

-150 -100 -50 -0 50 100 150

-90° 90°0°

dens

ity

-150 -100 -50 -0 50 100 150

-90° 90°0°

dens

ity

-150 -100 -50 -0 50 100 150

-90° 90°0°

dens

ity

-150 -100 -50 -0 50 100 150

-90° 90°0°

dens

ity

-150 -100 -50 -0 50 100 150

-90° 90°0°

dens

ity

-150 -100 -50 -0 50 100 150

-90° 90°0°de

nsity

-150 -100 -50 -0 50 100 150

-90° 90°0°

dens

ity

-150 -100 -50 -0 50 100 150

-90° 90°0°

dens

ity

-150 -100 -50 -0 50 100 150

-90° 90°0°

dens

ity

-150 -100 -50 -0 50 100 150

-90° 90°0°

dens

ity

-150 -100 -50 -0 50 100 150

-90° 90°0°

dens

ity

-150 -100 -50 -0 50 100 150

-90° 90°0°

dens

ity

Tonga W. Sumatra E. Sumatra

Kuril Izu-Bonin Ryukyu

Aleutians Alaska N. Caribbean

C. Caribbean S. Caribbean N. Scotia

S. Scotia Central America N. Honshu

0.02

0.01

0.02

0.01

0.03

0.015

0.01

0.005

0.03

0.015

0.25

0.01

0.02

0.01

0.014

0.007

0.04

0.02

0.03

0.015

0.02

0.01

0.01

0.005

0.04

0.02

0.014

0.007

0.03

0.015

# Subduction zone Slab

dip

Slap

depth

Trench

length

Regional mantle flow

s Dslab

(km)

Ltrench

(km) v (°)

1 Tonga 56° 670 3000 1.76±0.06 -6.5°±1.2°

2 W. Sumatra 45° 670 3500 0.18±0.03 3.9°±1.6°

3 E. Sumatra 68° 670 4200 0.64±0.06 -49.9°±1.7°

4 Kuril 40° 670 2600 0.63±0.13 51.6°±1.7°

5 Izu – Bonin 65° 670 2000 0.89±0.24 83.5°±2.4°

6 Ryukyu 60° 670 2200 0.80±0.21 -7.1°±6.0°

7 Aleutians 60° 335 5400 0.84±0.05 40.7°±5.2°

8 Alaska 40° 335 2700 0.49±0.13 16.6°±3.1°

9 N. Caribbean 49° 670 2200 6.55±0.87 2.9°±2.1°

10 C. Caribbean 51° 670 1500 3.21±0.13 -25.2°±0.4°

11 S. Caribbean 42° 670 1200 2.55±0.21 -41.7°±0.9°

12 N. Scotia 72° 670 1450 16.00±0.10 0.9°±0.5°

13 S. Scotia 65° 670 1250 24.42±1.20 -11.4°±0.5°

14 Central America 60° 335 3400 0.22±0.07 -12.7°±6.9°

15 N. Honshu 30° 670 2400 0.15±0.09 7.7°±26.1°

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