Supplementary information
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Quantifying the energy dissipation of overriding plate
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deformation in three-dimensional subduction models
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Zhihao Chen*, Wouter P. Schellart and João C. Duarte
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School of Earth, Atmosphere and Environment, Monash University, Melbourne, VIC
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3800, Australia
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*Corresponding author: Z. Chen, School of Earth, Atmosphere and Environment,
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Monash University, Melbourne, VIC 3800, Australia. (zhihao.chen@monash.edu)
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Journal of Geophysical Research: Solid Earth
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This PDF file includes:
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Figs. S1-S3
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0.76
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0.38
Overriding plate extensional rate
(×10-5) [s-1 ]
0
0
-0.38
-1
0
1
2
3
4
5
6
7
8
9
-0.76
10 11 12 13
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Exp.4 (ηOP/ηUM = 155)
Exp.6 (ηOP/ηUM = 208)
Exp.3 (ηOP/ηUM = 345)
Exp.2 (ηOP/ηUM = 557)
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2.28
1.90
4
1.52
3
1.14
2
0.76
1
0.38
0
1
2
3
4
5
6
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t'
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9
10 11 12 13
0
5
d
Exp.13 (TOP = 1.0 cm)
Exp.10 (TOP = 2.0 cm)
Exp.18 (OP-Fixed)
2.28
1.90
4
1.52
3
1.14
2
0.76
1
0.38
0
0
-0.38
-1
-2
t'
Exp.17 (TOP = 0.5 cm)
Exp.16 (TOP = 1.5 cm)
Exp.11 (TOP = 2.5 cm)
0
1
2
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Scaled Overriding plate shear rate
(× 10-16) [s-1 ]
1.14
0
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1.52
3
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-0.76
10 11 12 13
t'
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Exp.17 (TOP = 0.5 cm)
Exp.16 (TOP = 1.5 cm)
Exp.11 (TOP = 2.5 cm)
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Exp.13 (TOP = 1.0 cm)
Exp.10 (TOP = 2.0 cm)
Exp.18 (OP-Fixed)
2.28
1.90
4
1.52
3
1.14
2
0.76
1
0.38
0
0
1
2
3
4
5
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0
10 11 12 13
Scaled Overriding plate extensional rate
(× 10-16) [s-1 ]
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1.90
b
Overriding plate shear rate
(× 10-5) [s-1 ]
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-2
c
2.28
Exp.4 (ηOP/ηUM = 155)
Exp.6 (ηOP/ηUM = 208)
Exp.3 (ηOP/ηUM = 345)
Exp.2 (ηOP/ηUM = 557)
Overriding plate extensional rate
(× 10-5) [s-1]
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Scaled Overriding plate extensional rate
(×10-16) [s-1 ]
Overriding plate shear rate
(× 10-5) [s-1 ]
a
Scaled Overriding plate shear rate
(× 10-16) [s-1 ]
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t'
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Figure S1. Diagram illustrating the progressive development of overriding plate
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shear rate (a, b) and extensional rate (c, d) with progressive non-dimensional time (t’)
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for (a, c) the experiments with a different overriding plate to upper mantle viscosity
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ratio (ηOP/ηUM) and (b, d) the experiments with different overriding plate thickness
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(TOP). Additionally, an experiment with a fixed overriding plate was included in the
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set of experiments with different TOP. The shear and extensional strain rates were
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measured as shown in Figure 1b. Note that t’= t/t(bottom). t’=1 corresponds to the
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moment the slab tip first touches the bottom of the tank. Maximum error in
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measurement for shear rate is ±10% and for extensional rate is ±5%.
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0.8
0.8
0.4
0.4
0
1
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3
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Exp.4 (ηOP/ηUM = 155)
Exp.6 (ηOP/ηUM = 208)
Exp.3 (ηOP/ηUM = 345)
Exp.2 (ηOP/ηUM = 557)
1.2
1.2
0.8
0.8
0.4
0.4
0
0
1
2
3
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d
2.0
1.6
1.6
0
9 10 11 12 13
Exp.13 (TOP = 1.0 cm)
Exp.10 (TOP = 2.0 cm)
Exp.18 (OP-Fixed)
2.0
1.6
1.2
1.2
0.8
0.8
0.4
0.4
0
t'
2.0
1.6
FOPD(EXT) (× 10-2) [N]
0
9 10 11 12 13
Exp.17 (TOP = 0.5 cm)
Exp.16 (TOP = 1.5 cm)
Exp.11 (TOP = 2.5 cm)
0
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Scaled FOPD(SH) (× 1018) [N]
1.2
2.0
0
9 10 11 12 13
t'
2.0
Exp.17 (TOP = 0.5 cm)
Exp.16 (TOP = 1.5 cm)
Exp.11 (TOP = 2.5 cm)
1.6
Exp.13 (TOP = 1.0 cm)
Exp.10 (TOP = 2.0 cm)
Exp.18 (OP-Fixed)
2.0
1.6
1.2
1.2
0.8
0.8
0.4
0.4
0
0
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Scaled FOPD(EXT) (×1018) [N]
1.2
0
c
1.6
FOPD(EXT) (× 10-2) [N]
FOPD(SH) (×10-2) [N]
1.6
b
2.0
FOPD(SH) (×10-2) [N]
Exp.4 (ηOP/ηUM = 155)
Exp.6 (ηOP/ηUM = 208)
Exp.3 (ηOP/ηUM = 345)
Exp.2 (ηOP/ηUM = 557)
Scaled FOPD(SH) (× 1018) [N]
2.0
Scaled FOPD(EXT) (× 1018) [N]
a
0
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Figure S2. Diagrams illustrating the progressive development of the overriding plate
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deformation force (FOPD(SH) – shear force and FOPD(EXT) – extensional force) with
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progressive non-dimensional time (t’) for (a, c) the experiments with different
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overriding plate to upper mantle viscosity ratio (ηOP/ηUM) and (b, d) the experiments
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with different TOP. Note that FOPD(SH), and FOPD(EXT) were calculated using equations
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(6) and (5) in the text. t’= t/t(bottom). t’=1 corresponds to the moment the slab tip
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first touches the bottom of the tank.
t'
t'
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a
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3
2
Exp.17 ( TOP = 0.5 cm)
Exp.16 ( TOP = 1.5 cm)
Exp.11 (TOP = 2.5 cm)
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0
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0
10 11 12 13
0
1
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Exp.17 ( TOP = 0.5 cm)
Exp.16 ( TOP = 1.5 cm)
Exp.11 (TOP = 2.5 cm)
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FOPD(EXT)/ FBu (%)
FOPD(EXT)/ FBu (%)
d
Exp.4 (ηOP/ηUM = 155)
Exp.6 (ηOP/ηUM = 208)
Exp.3 (ηOP/ηUM = 345)
Exp.2 (ηOP/ηUM = 557)
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3
2
1
0
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10 11 12 13
t'
t'
c
Exp.13 ( TOP = 1.0 cm)
Exp.10 ( TOP = 2.0 cm)
Exp.18 (OP-Fixed)
1
1
0
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FOPD(SH)/ FBu (%)
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FOPD(SH)/ FBu (%)
b
Exp.4 (ηOP/ηUM = 155)
Exp.6 (ηOP/ηUM = 208)
Exp.3 (ηOP/ηUM = 345)
Exp.2 (ηOP/ηUM = 557)
Exp.13 ( TOP = 1.0 cm)
Exp.10 ( TOP = 2.0 cm)
Exp.18 (OP-Fixed)
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Figure S3. Diagrams illustrating the evolution of the ratio of overriding plate shear
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force to slab negative buoyancy force (FOPD(SH)/FBU) and extensional force to slab
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negative buoyancy force (FOPD(EXT)/FBU) for (a, c) the experiments with different
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ηOP/ηUM and (b, d) the experiments with different TOP with progressive non-
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dimensional time (t’). Note that FOPD(SH), FOPD(EXT) and FBU were calculated using
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equations (6), (5) and (8) in the text, respectively. t’= t/t(bottom). t’=1 corresponds to
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the moment the slab tip first touches the bottom of the tank.
t'
t'
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