Supplementary Information Text
S1. Calculating Regional Mantle Flow Fields
We calculated the regional mantle flow in the trench-fixed reference frame for each of the
15 subduction zone segments of interest using the global flow model of Conrad and Behn
[2010], trench migration data from Schellart et al. [2008] and the UNAVCO plate motion
calculator (http://sps.unavco.org). This framework allows us to incorporate trench migration
without needing to rely on an arbitrarily chosen reference frame; we are effectively considering
trench migration with respect to global mantle flow in each subduction system. We report the
amplitude 𝑉 of the regional mantle flow, scaled by the convergence velocity and its azimuth v.
Our sign convention is such that the trench-perpendicular component is positive towards the
trench from the sub-slab side and the parallel component is positive 90° clockwise from the
positive perpendicular direction.
S1.1 Global Flow Model
We used the global flow field [Conrad and Behn, 2010] in a no-net-rotation (NNR)
reference frame [Kreemer et al., 2003] to calculate an average global flow field, 𝑣⃗𝐴𝐺 , by taking a
weighted average of the velocity at a depth equivalent to the midpoint the asthenosphere, 𝑣⃗𝑎 , and
that of the upper mantle, 𝑣⃗𝑢𝑚 , such that
𝑣⃗𝐴𝐺 =
(𝑣⃗𝑎 𝐻𝑎 ) + (𝑣⃗𝑢𝑚 𝐻𝑢𝑚 )
2(𝐻𝑎 + 𝐻𝑢𝑚 )
(S.1)
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where 𝐻𝑎 is the thickness of the asthenosphere (200 km) and 𝐻𝑢𝑚 is the thickness of the upper
mantle (370 km). These values were further averaged laterally along a trench-parallel transect,
as described in Section S1.3 and visualized in Figure 1 and supplementary Figures S1 to S4. The
averaged global flow is then decomposed into the trench-perpendicular component, 𝑉┴𝐺 , and
parallel component, 𝑉‖𝐺 , shown in Table 2 of Paczkowski et al. [2014].
S1.2 Trench Migration
We calculated the trench-perpendicular and trench-parallel trench migration velocities for
each subduction zone to express the global mantle flow field into a local, trench-fixed reference
frame.
S1.2.1 Trench-Perpendicular Migration
We estimated the average perpendicular trench migration velocity [Schellart et al., 2008],
𝑉┴𝑇 , along the 15 trench segments in the NNR reference frame (Table 2 in Paczkowski et al.
[2014]). Note that in the Schellart et al. [2008] compilation the convention is such that trench
retreat is positive. Here we report the perpendicular component as positive towards the trench
from the sub-slab side, and retreating velocities are negative.
S1.2.2 Trench-Parallel Migration
Since trench-parallel trench migration velocities are not well documented by geodetic
measurements and are not reported by Schellart et al. [2008], we assumed the trench moves
along strike with the subducting plate and approximated 𝑉||𝑇 as equivalent to the trench-parallel
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component of the subducting plate velocity. We estimated this component using the UNAVCO
Plate Motion Calculator in the NNR reference frame with the NUVEL-1A plate motion model.
The model of Conrad and Behn [2010] used in Section S1.1 to calculate the global flow field is
expressed in the same reference frame. We specified the latitude and longitude of a point on the
subducting plate close to the trench and used the UNAVCO plate velocity in N-E coordinates.
We then calculated the trench-parallel migration, 𝑉‖𝑇 , (Table 2 in Paczkowski et al. [2014]) using
𝑉‖𝑇 = 𝑉𝑁 cos(𝛽) + 𝑉𝐸 sin(𝛽)
(S.2)
where 𝛽 is the strike of the trench from north. We assumed that the lateral variation in this
velocity component is negligible.
S1.3 Trench-Fixed Reference Frame Mantle Flow
We then expressed the global mantle flow field, 𝑣⃗𝐴𝐺 , in a local trench-fixed reference
frame by subtracting the trench migration velocity components, 𝑉‖𝑇 and 𝑉┴𝑇 , for each subduction
zone. Using Generic Mapping Tools [Wessel and Smith, 1991] we plotted the resulting trenchfixed reference frame velocity field overlaid with the topography from the General Bathymetric
Chart of the Oceans (GEBCO) (http://www.gebco.net/) at each subduction zone segment
(Figures S1-S4). Note that Figures S1-S4 have the same topographic scale bars as Figure 1. We
calculated the regional mantle flow by averaging along a linear transect that has the same strike,
, and approximately 3 times the length of each trench segment (Figures S1-S4).
S1.4 Convergence Velocity
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The final estimates of the regional mantle flow, 𝑉 and v (Table S1), for each subduction
system were normalized by the local (trench-normal) convergence velocity, Vc, as determined by
the UNAVCO plate velocity calculator.
Using the UNAVCO plate velocities in a N-E
coordinate system, we found the trench-perpendicular component of motion for each plate using
𝑉┴𝑃 = 𝑉𝑁 sin(𝛽) − 𝑉𝐸 cos(𝛽).
(S.3)
We then calculated the convergence velocity as the difference between the trench-perpendicular
velocity of the subducting plate and the overriding plate [Paczkowski et al., 2014].
S2. Boundary Conditions
S2.1 Slab geometry
Data for slab dip parameters (𝛼𝑠 ) for each subduction segment were taken from the
compilation of Lallemand et al. [2005]. Lallemand et al. [2005] do not report slab dip at depths
for the N., C., and S. Caribbean subduction zone segments, so we use recent estimates from
Syracuse and Abers [2006]. Estimates of maximum slab penetration depth (𝐷max ) into the
mantle were derived from seismic tomography models and were taken from the compilation of
Lallemand et al. [2005].
S2.2 Boundary condition on the slab/mantle interface and degree of coupling
The sub-slab boundary condition in our model is imposed kinematically, as described in
the main text. Specifically, we prescribe a velocity boundary condition defined by the subducting
slab velocity multiplied by a constant coupling factor, C, which is varied from fully coupled (C =
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1) to fully decoupled (C = 0). In the fully decoupled limit, this kinematic boundary condition
becomes no-slip. While a free-slip boundary condition would be a more physically realistic
representation for a fully decoupled slab, we have chosen to use a velocity boundary condition in
all cases because it allows us to investigate partial coupling (that is, intermediate values of C). In
contrast, using a stress boundary condition for the fully decoupled case and a velocity boundary
condition for the fully coupled case would not allow for an investigation of partial coupling. It is
possible to include a thin low-viscosity layer beneath the slab as a more physically realistic way
to incorporate decoupling; however, our models do not have sufficient resolution to capture the
dynamic of such a layer accurately in three dimensions. Furthermore, many of the subduction
zones considered in this study demonstrate a good match with observations for fully coupled
models, which suggests that our main conclusions do not rely on the no-slip approximation to the
fully decoupled case.
S2.3 Background pressure and flow field
Flow in our models is generated by the motion of the slab (as explained in section S2.2)
and by a pressure field applied on the side of the model:
P(x,y)=P0+Gp [cos (p x) +sin (p y)],
where P0 is an arbitrary constant, typically taken as 0, and Gp and p control the magnitude of
and orientation of the background pressure gradient. We calculate a posteriori the amplitude and
azimuth of the mantle flow averaged over the upper mantle portion of the back wall of our
simulation to characterize the background flow field. We then iterate over Gp and p until the
background flow field matches the regional flow field of the subduction zone of interest.
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S3. Finite Strain Calculations
Finite strain ellipsoids were calculated following the method outlined by Malvern [1969]
and McKenzie [1979], using
𝑑𝑭
= 𝑳𝑭
𝑑𝑡
(S.4)
where F is the deformation gradient tensor and L is the velocity gradient tensor. Equation (S.4) is
integrated along particle streamlines using a 5th order Runge-Kutta method with Dormand-Prince
coefficients and an adaptive stepsize routine [Press et al., 2007]. To calculate the finite strain in
the same spatial averaging box beneath the slab used in Paczkowkski et al. [2014], we start our
integration inside the averaging box and integrate the particles backwards in time through the
inverse velocity field until the particles either leave the model domain or accumulate significant
strain (maximum elongation greater than 5) [e.g., Zhang and Karato, 1995]. The deformation
gradient tensor at this final position is inverted to obtain the finite strain in the averaging box. In
practice, our results are not sensitive to whether the particles leave the model domain or reach
our specified deformation magnitude, or to the parameters in the adaptive stepsize routine.
S4. Effects of the Lower Mantle and Fixed Trench Width
In order to demonstrate the sensitivity of our finite strain results to the presence or
absence of a high-viscosity lower mantle in our model, we show histograms equivalent to Figure
3 in the main text, but for models that do not include a lower mantle, in Figure S1. The absence
of a lower mantle makes a significant difference only in models of the W. Sumatra subduction
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zone and the N. Scotia subduction zone. In those cases, the models that include a viscous lower
mantle match the observations slightly better than the models without.
Our modeling framework includes a fixed trench length (that is, slab width) for all
models; for simplicity, we do not vary the trench length and keep this parameter fixed. This
represents a significant simplification, as slab width has been shown to influence anisotropy
development in subduction systems [e.g., Li et al., 2014]. However, our approach is justified
based on previous studies of the effect of slab width on subduction dynamics. Specifically, Li et
al. [2014] found that the primary influence of slab width was on subduction kinematics, as has
been noted previously [e.g., Stegman et al., 2006; Schellart et al., 2007]. In particular, Li et al.
[2014] found that larger slab widths are correlated with faster plate velocity and slower trench
retreat velocity. They further found that wider subduction zones experience less trench parallel
finite strain, which is a direct result of the reduced magnitude of trench retreat. Retreat velocity is
imposed in our models, so our models already indirectly take into account the effect of slab
width on subduction kinematics. The slab width in our modeling framework was chosen such
that for a given retreat velocity (or regional mantle flow), our results are independent of slab
width, as we are in the long slab regime limit. It may be possible to improve the fit between
model predictions and anisotropy observations in some regions by considering a shorter trench
length in future studies.
S5. Implications of Sub-Slab Decoupling for Global Flow Models
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Our modeling results (Figure 3 in the main text) suggest that in some subduction systems,
the downgoing slab may be partially or fully mechanically decoupled from the mantle beneath
them. In contrast, global flow models such as that of Conrad and Behn [2010], which provides
the estimates of global mantle flow used in our study, essentially assume that slabs are fully
coupled to the mantle around them in their treatment of density-driven mantle flow. In our
models, slabs are fully coupled to the ambient mantle above the slab (at depths greater than 80
km), consistent with the idea of entrained flow driven by density anomalies. Furthermore, many
of the model cases considered in our study show good agreement with splitting observations for
cases with full sub-slab coupling, again consistent with the implementation of density-driven
flow in Conrad and Behn [2010]. Therefore, our use of the Conrad and Behn [2010] model to
estimate global mantle flow should generally be a good approximation. However, our finding
that some degree of decoupling beneath some subduction systems may be required suggests that
future studies of global mantle flow that incorporate partial decoupling beneath downgoing slabs
may be warranted. Such studies would enable a more self-consistent framework for the type of
regionally specific models considered here.
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