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Appendix A. Thermal structure of the Eurasian plate
Figure A1. Maps showing initial thermal field (200 C contour intervals) at various
depths for two reference models for the southern Ryukyu subduction zone.
1
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Appendix C. Influence of model parameters
C1. Slab depth and dip, and trench geometry: Models VIII-XI
The generation of trench-normal flow components and ISA directions are
facilitated by a deeper slab, a steeper slab dip angle, and a linear trench. Results for a
model with a deeper slab and a relatively shallow slab dip angle show stronger
rollback-induced mantle circulation (model VIII) (Figures C1a and C1b). In the
models with a steep slab dip, the magnitudes of the velocity vectors for both the
poloidal motion and toroidal component are compatible with the plate velocity in
general (models IX and XI) (Figures C1c, C1d, C1g and C1h). The strength of the
mantle circulation is considerably lower (models IX and XI), compared with those in
the models with a shallower slab dip angle (models VIII and X). The trench-parallel
flow components could be significantly stronger if significant variations in trench
geometry in regions close to the subduction zone edge are present (models X and XI)
(Figures C1f and C1h). The ISA orientations for each model vary correspondingly
(Figure C2). The trench-parallel components for the ISA orientations become
considerably weaker for models with a deeper slab (models VIII, IX and XI), but
could be significantly enhanced for models with trench curvature variations near the
subduction zone edge (models X and XI).
C2. Plate motion, strengths of slab and continent, and lithospheric structure: Models
X-XIII
Moderate change in plate motion at the surface does not change the overall
patterns of mantle circulation (model XII) (Figures C3a and C3b). Figure C3d shows
substantial deformation of the bottom of the continental edge in a model for a thick
neighboring lithosphere with lower minimum strength due to the combined effects of
higher temperature and strain rate (model XIII) (Figures C3c and C3d). The minimum
viscosity of the continent is not specified in the model. The westward flow in the
mantle wedge is slightly weaker than that in a model (model XII) with a stronger
continental root. The convective vigor and the degree of slab rollback are significantly
higher for a model with a weaker slab (model XIV) (Figures C3e and C3f), while the
overall flow pattern is similar to that of the reference model (model VI). For models
with lower maximum slab viscosity (5x102-103r), the flow pattern is similar to that
in model XIV. The along-arc flow component is considerably smaller in a model with
smaller lateral thickness variations (model XV) (Figures C3g and C3h). The toroidal
2
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circulation due to rollback subduction predominates in the mantle wedge near the
subduction zone edge.
C3. Mantle rheology and degree of locking between plates: Models XVI-XIX
The mantle rheology controls the convective vigor, but does not change the
overall flow pattern in the mantle wedge (models XVI and XVII) (Figures C4a-C4d).
The collision between the subducting plate and the neighboring plate does not alter
the flow field in general (models XVIII and XIX) (Figures C4e-C4h). Increased
degree of the locking between the subducting plate and the neighboring lithosphere
only affects the flow field locally near the subduction zone edge (model XVIII)
(Figures C4e and C4f). The locking between the plates (friction) is controlled by the
higher viscosity between the plates next to the mantle wedge where the slab starts to
bend downward in the numerical experiment (Figures C4e and C4f). To further test
the effects of locking between plates, a narrow thin plate of the neighboring
lithosphere is defined adjacent to the subduction zone edge, so that there is no contact
between the subducting plate and the neighboring lithosphere in the depth range of ~
50-100 km (Figures C4g and C4h). The thickness for most of the neighboring
lithosphere is set to be ~ 160 km (model XIX). The overall flow pattern in the shallow
mantle remains.
3
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Figure C1. Influence of various physical parameters on mantle wedge flow. Thin
black lines depict the thermal field with 200 C contour intervals. The left and the
right columns display the vertical cross sections of thermal and flow fields along the
N-S direction and the E-W direction, respectively. (a, b) Results for a model with a
deeper slab and a relatively shallow slab dip angle (model VIII). (c, d) Results for a
model with a deeper slab and a steep slab dip angle (model IX). (e, f) Results for a
model with variation in trench curvature for the region close to the subduction zone
edge (model X). (g, h) Results for a model with a deeper slab, a steep slab dip angle,
and variation in trench curvature (model XI).
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Figure C2. Maps of thermal and flow fields at 75 km depth and ISA orientations for
models of Figure C1. (a, b, c, d) Thin black lines depict the thermal field with 100 C
contour intervals. Flow field within the slab is not shown for clarity. (e, f, g, h)
Comparisons between seismic data and ISA orientations. Black lines depict the
thermal field at 50 km depth.
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Figure C3. Cross sections of thermal and flow fields. (a, b) Results for a model with
plate motion in the direction of N 48 W at surface (model XII). (c, d) Results for a
model with a weaker continental lithosphere (model XIII). The minimum viscosity of
the continent is not specified. (e, f) Results for a model with a weaker slab (model
XIV). (g, h) Results for a model with thinner neighboring lithosphere (model XV).
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Figure C4. Cross sections for thermal and flow fields (a, c), and for viscosity structure
(b, d) for models with (a, b) Newtonian rheology (model XVI) and (c, d) dislocation
creep deformation mechanism (model XVII) for the ductile flow for the upper mantle
rheology. (e, f) Thermal and flow fields for a model with increased degree of locking
between plates (model XVIII). (g, h) Thermal ad flow fields for a model without
contact between plates in the depth range of ~ 50-100 km (model XIX).
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Table C1. Model Parameters
Edf
r
Eds
Vds
480
11x10-6
IX
335 4x10
-6
480
11x10
-6
250
10
X
335 4x10-6
480
11x10-6
250
XI
335 4x10
-6
480
11x10
-6
XII
335 4x10-6
480
11x10-6 250
XIII
335 4x10
-6
480
11x10
-6
250
10
XIV
335 4x10-6
480
11x10-6
250
XV
335 4x10
-6
480
11x10
-6
XVI
300 4x10-6
-----
--------
VIII
Vdf
335 4x10-6
dref
D210
1020 310
45∘
6 (N 43 W)
310
68∘
6 (N 43 W)
1020 210
45∘
6 (N 43 W)
310
68∘
6 (N 43 W)
1020 210
45∘
6 (N 48 W)
210
45∘
6 (N 43 W)
1020 310
68∘
6 (N 48 W)
210
45∘
6 (N 48 W)
150 2x1019 210
45∘
6 (N 43 W)
210
45∘
6 (N 48 W)
1020 210
45∘
6 (N 48 W)
45∘
6 (N 48 W)
250
250
480
8x10
XVIII 335 4x10-6
480
11x10-6 250
480
-6
XIX
335 4x10
-6
11x10
10
250
-6
XVII 335 4x10
-6
Sd
20
20
20
10
250
20
10
250
10
20
20
Pm : Plate motion (cm yr-1)
Sd : Slab depth (km)
Edf : Activation energy (diffusion creep) (KJ mol-1)
Vdf : Activation volume (diffusion creep) (m3 mol-1)
Eds : Activation energy (dislocation creep) (KJ mol-1)
Vds : Activation volume (dislocation creep) (m3 mol-1)
dref : Reference depth for the reference viscosity (km)
r : Reference viscosity (Pa s)
D210: Slab dip angle at 210 km depth
8
210
Pm
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Appendix D. Limitations on ISA prediction for the instantaneous flow model
In the calculation of the ISA and the GOL parameter (  ISA/flow), we follow
the formulation of Kaminski and Ribe [2002]. The ISA depends on the inverse of the
absolute value of the largest eigenvalue of the strain rate tensor (  1 ). The flow is
defined as
flow
D

Dt
1
(D1)
where D/Dt  /t + u  is the material derivative and  represents the angle
between the local flow direction and the local ISA. The values of flow depend both on
position and on time for the time-dependent flow field. In most of our calculations for
flow, assuming /t = 0, only the spatial contribution is considered due to limitations
of the instantaneous model. This assumption would contradict the time-varying flow
field in the dynamically evolving systems like subduction zones.
The a axis rotates toward ISA for 1.0  1  t  3.0  1 for dry olivine (Kaminski
and Ribe, 2002). The mantle wedge material deforms at rates of ~ 2.5 x 10-13 - 4 x
10-15 s-1 in our models. The characteristic timescales are ~ 0.1-10 Myr. To evaluate the
ISA changes over time, we have calculated the evolving flow field for ~1.1 Myr for a
selected
southern
Ryukyu
model
(Model
VI).
The
time-dependent
heat
advection-diffusion equation is solved for the entire calculation domain using
numerical approaches described in Lin et al. [2005, 2010]. The quantity of
time-dependent contribution in  is evaluated with an approach introduced in Conrad
et al. [2007], by differencing measurements of  across more than 50 time steps (t
of ~ 1.1 Myr), and dividing by t.
The result suggests that ISAs may significantly change with time at greater
depths, but most ISAs roughly remain the same at shallow depths due to the blocking
effect of the thick lithosphere adjacent to the subduction zone (Figure D1). The
time-dependent contribution in the lag parameter is generally small (< 1) at shallow
depths (Figure D1b), and the quantity is typically compatible in magnitude to the
advective term (Figure D1c). Our seismic data sample the shallow mantle (~ 50-100
km depths), where the ISA changes are small. The result indicates that the ISA
orientations might provide good approximations for the LPOs in the shallow mantle
for the southern Ryukyu and the comparisons between the seismic data and the ISAs
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would help to constrain the regional dynamics. Nonetheless, the ISA changes may be
greater than those predicted in this model since evolution of the southern Ryukyu
subduction system may be more complex. Numerical modeling for the evolving
mantle flow field, calculations for the corresponding time-dependent LPO formation
and syntheses for amplitude and directions of seismic anisotropy would be necessary
in future investigations.
Figure D1. (a) Cross section showing the initial thermal field (0 Myr) and the ISA
orientations at snapshots of 0 Myr (blue) and ~1.1 Myr (yellow) at 50 km depth for an
evolving flow model. Thin black lines depict the thermal field with 100 C contour
intervals. (b) Map showing time-dependent contribution in  due to time-dependent
changes in  at 50 km depth. (c) Map showing the spatial contribution of  in  at
snapshot of 1.1 Myr at 50 km depth.
10