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Journal of Geophysical Research: Solid Earth
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Supporting Information for
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Revisiting visco-elastic effects on interseismic deformation and locking degree: a
case study of the Peru - North Chile subduction zone
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Shaoyang Li1, Marcos Moreno1, Jonathan Bedford1, Matthias Rosenau1 and Onno
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Oncken1
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1Helmholtz
Centre Potsdam, GFZ German Research Centre for Geosciences,
Telegrafenberg, Potsdam 14473, Germany
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Contents of this file
Text S1
Figures S1 to S12
Table S1
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Introduction
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This supporting information provides: one text related to Subducting Plate modeling
results, 12 supporting figures for the main and supporting text, and one table listing the
material properties used in our FEM modeling.
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Text S1.
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In the following text, we include our interseismic deformation modeling results for the
alternative kinematic subduction model known as the Subducting Plate model [Kanda
and Simons, 2010]. This model considers deformation in the subducting and overriding
plates taking into account the elastic thickness of the slab. In the Subducting Plate
Model, the slip rate is applied on the deep part of the slab-top fault and on the whole
slab-bottom fault as shown in Figure S1, while the respective plate motion at the
seismogenic plate interface remains at zero. While the model may predict similar
interseismic elastic deformation as back-slip model [Kanda and Simons, 2010], the
differences in predicted interseismic viscoelastic deformation remains unexplored until
now.
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Similar to the strategy of investigating the viscoelastic effects of back-slip model in the
main text, we used 2-D synthetic modeling to clarify the different features of deformation
for Back-slip and Subducting Plate models. Here, the direction, magnitude and location
of the specified fault slip rate were determined according to which approach (back-slip or
Subducting Plate) was used to simulate the interseismic deformation. We applied the full
plate convergence rate of 68 mm/yr [Ruegg et al., 2009] along the slab top fault from 0
to 50 km depth in the back-slip model. Therefore in the case of the Subducting Plate
model, we applied the plate convergence rate along the slab top fault below 50 km depth
and the entire slab bottom fault, thereby leaving the interface nodes above 50 km
without slip constraints (Figure S1). Note that the only difference between the back-slip
and Subducting Plate model is the kinematic configuration of the prescribed interseismic
slip while their fault interface locking are equivalent.
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We compare the effects between the two subduction modeling approaches: (1) backslip and (2) Subducting Plate models. The predictions of surface deformation from both,
elastic and viscoelastic, models are shown in Figure S2. In general, the back-slip and
Subducting Plate models produce qualitatively similar deformation patterns and
quantitatively similar displacement magnitudes in both horizontal (Figure S2a-b) and
vertical (Figure S2c-d) directions. Specifically, in the horizontal direction, the Subducting
Plate models have a slightly larger displacement (with roughly 1 mm/yr out of a
convergence rate of 68 mm/yr) than those of back-slip models (green curves in Figure
S2a and S2b). Also, the Subducting Plate model has a slightly broader deformation than
the back-slip model: The horizontal displacement of the Subducting Plate model extends
a little further inland. In the vertical direction, both the elastic and viscoelastic Subducting
Plate models, induce slightly less subsidence in the area close to the trench (between 0
to 50 km from the trench), with a magnitude difference of roughly 5 mm/yr (green curves
in Figure S2c and S2d).
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In summary, the differences in surface deformation predicted by the back-slip or
Subducting Plate models are minor compared to the differences between the elastic and
viscoelastic model predictions (10 times smaller, when backslip and Subducting plate
models are compared with the same rheological constraints; see Figure 2 in main text).
Therefore, for simplification, it is reasonable in the main text to use only the back-slip
model because of its easier and more elegant kinematic configuration.
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Figure S1. Schematic plot of two typical kinematic interseismic subduction zone models.
The so-called “back-slip” model assumes the seismogenic zone creeps in the opposite
sense of coseismic rupture in the interseismic period (as shown with red vectors). The
so-called “Subducting Plate” model assumes the seismogenic zone is locked while the
deep part of the slab-top fault and slab-bottom fault are creeping steadily with the plate
convergence rate (as showed with purple vectors).
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Figure S2. The model effects on surface deformation from both elastic and viscoelastic
models. Note that both continental and oceanic mantle were assigned viscoelastic
behaviors in viscoelastic models. The red curves represent the results of Subducting
Plate models. The blue curves represent the results of back-slip models. The green
curves show the difference between Subducting Plate and back-slip models, thus
representing the differences in modeling approaches. (a) Horizontal displacement
profiles of elastic models. (b) Horizontal displacement profiles of viscoelastic models. (c)
Vertical displacement profiles of elastic models. (d) Vertical displacement profiles of
viscoelastic models.
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Figure S3. Horizontal velocities of different points from four kinds of models (i.e. Backslip elastic, back-slip viscoelastic, Subducting Plate elastic, and Subducting Plate
viscoelastic model) without a previous earthquake. (a) Point 53 km away from the
trench. (b) Point 148 km away from the trench. (b) Point 202 km away from the trench.
(b) Point 304 km away from the trench.
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Figure S4. Similar to Figure S3 but for Vertical velocities. (a) Point 53 km away from the
trench. (b) Point 148 km away from the trench. (b) Point 202 km away from the trench.
(b) Point 304 km away from the trench.
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Figure S5. Horizontal velocities of different points from four kinds of models (i.e. Backslip elastic, back-slip viscoelastic, Subducting Plate elastic, and Subducting Plate
viscoelastic model) with a previous earthquake. The earthquake releases the full slip
deficiit of 6.8 m from the trench to a depth of 50 km, which has been accumulated over
100 years. If we assume the earthquake ruptures a segment of 200 km, it is identical to
an Mw 8.6 great earthquake. (a) Point 53 km away from the trench. (b) Point 148 km
away from the trench. (b) Point 202 km away from the trench. (b) Point 304 km away
from the trench.
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Figure S6. Similar to Figure S5 but for Vertical velocities. (a) Point 53 km away from the
trench. (b) Point 148 km away from the trench. (b) Point 202 km away from the trench.
(b) Point 304 km away from the trench.
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Figure S7. Example of 3 non-overlapping fault patches for inversion approach. The
nodes located in one patch are applied same slip and all the other nodes on the fault are
applied zero slip when calculating the surface deformation from this patch.
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Figure S8. Investigating how different viscosities in the continental mantle affect the
fitting of backarc GPS data in Peru - North Chile. (a) The wrms value as a function of
uniform locking depth for different viscosity models. The letter V and E stand for
viscoelastic and elastic model, respectively. The numbers on the x axis show multiples
of 1019 Pa*s, representing the tested viscosity values. (b) Average wrms value of
physical uniform locking depths (from 40 to 55 km) as a function of viscosity value. The
blue line is from the wrms value of elastic model.
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Figure S9. Model spin-up effects on viscoelastic interseismic model. We applied the
same configurations and boundary conditions as the models of section 3 in main text
except we ran additional “earthquake” cycles for viscoelastic model. Here we defined a
characteristic “earthquake” releasing the same amount of slip deficit that would
accumulate in the entire interseismic period (150 years). The fault creeps throughout
the entire simulation. (a) Model spin-up effects on horizontal direction. For the legend,
the letter “V” stands for the viscoelastic model and the number means the year time for
calculating surface velocity. The blue curve is from elastic model. The green curve
represents the viscoelastic effects in last “earthquake cycle”. The magenta curve
represents the spin-up effects from the first to the last “earthquake cycle”. (b) Model
spin-up effects on vertical direction. The legend is same as Figure S10a.
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Figure S10. Checkerboard tests for inversions of elastic and viscoelastic models. (a)
The recovered patches from elastic inversion of input locked patches. (b) The input
locked patches are about 30 km2 in size and assigned with 68 mm/yr back-slip rate.
These parameterizations of the input backslip are used for both elastic and viscoelastic
inversion tests. (c) The recovered patches from viscoelastic inversion of input locked
patches.
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Figure S11. FEM-inversion of total slip of main shock and aftershock of 2014 Iquique
earthquake. Note that here we use the same FEM-derived Green’s Functions as for
elastic interseismic locking inversion. The blue vectors are GPS observations same as
those used in [Schurr et al., 2014]. The red vectors are predicted by our inverted slip.
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Figure S12. Time series of the JRGN cGPS (located on Mejillones Peninsula). Left: EW
accumulated displacements. Right: NS accumulated displacements.
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Table S1. Material Properties Used in Elastic and Viscoelastic Models
Density,
(Kg/m3)i
2700

Shear
wave Young’s Module, Poisson
velocity, vs (m/s)ii E (Pa)iii
 iii
3826.1
1.00*e+11
0.265
ratio, Viscosity,  (Pa S)iv
Continental
None
plate
Oceanic slab 3300
3739.8
1.20*e+11
0.3
None
Viscoelastic
3300
4403.9
1.60*e+11
0.25
4.0*e+19
continental
mantle
Viscoelastic
3500
4276.2
1.60*e+11
0.25
1.0*e+20
oceanic
mantle
i
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: Reference source: [Andrés Tassara and Echaurren, 2012; A. Tassara et al., 2006]
ii
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: Calculated from density, Young’s Module and Poisson ratio.
iii
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: Reference source: [Christensen, 1996; Hu et al., 2004; Khazaradze et al., 2002;
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Moreno et al., 2011; Wang et al., 2007]
iv
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: Note that “Viscoelastic continental mantle” and “Viscoelastic continental mantle”
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were specified with no viscosity in purely elastic models. Reference source: [Hu et al.,
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2004; Moreno et al., 2011; Wang et al., 2007]
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