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JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 114, B03409, doi:10.1029/2008JB005861, 2009
for
Full
Article
How does trench coupling lead to mountain building in the Subandes?
A viscoelastoplastic finite element model
Gang Luo1 and Mian Liu1
Received 10 June 2008; revised 3 December 2008; accepted 2 February 2009; published 28 March 2009.
[1] Subduction-induced crustal shortening is believed to be the primary cause of the
Andean mountain building. The present-day crustal shortening in the Andes is clear from
the GPS measurements, but the rate (30–40 mm/a) is higher than the geological
shortening rate (<15 mm/a), suggesting that much of the present-day crustal shortening
may recover during future earthquakes in the subduction zone. Using a two-dimensional
viscoelastoplastic finite element model, we investigate here how the cyclic trench
coupling leads to long-term mountain building, which has been concentrated in the
Subandes in the past few million years. Our results show that much of the GPS-measured
crustal shortening in the Andes can be explained by the interseismic and postseismic
viscoelastic strain that does not contribute to mountain building. The apparently
discordant GPS and geological data can be reconciled in the geodynamic model with a
weakened crust in the Subandes, which allows accumulation of plastic strains that leads to
mountain building. The localized crustal weakening and mountain building in the
Subandes may have been a consequence of the uplifted High Andes, the accelerated
westward drift of the South American plate, the possible delamination of mantle
lithosphere under the Eastern Cordillera, and the increasing trench coupling.
Citation: Luo, G., and M. Liu (2009), How does trench coupling lead to mountain building in the Subandes? A viscoelastoplastic
finite element model, J. Geophys. Res., 114, B03409, doi:10.1029/2008JB005861.
1. Introduction
[2] The cause of the Andes, the second largest mountain
belt on Earth today (Figure 1), is commonly believed to be
crustal shortening that results from subduction of the
oceanic Nazca plate under the South American continent
[e.g., Allmendinger et al., 1997; Baby et al., 1997; Isacks,
1988; Schmitz, 1994; Sheffels, 1990]. The mechanics that
link subduction to mountain building, however, are not well
understood. After all, subduction of oceanic plates under
continents in other places, such as the Cascadia, does not
cause significant mountain building.
[3] Present-day crustal shortening in the Andes is shown
clearly by recent Global Positioning System (GPS) measurements (Figure 1 [e.g., Brooks et al., 2003; Kendrick et al.,
2001; Leffler et al., 1997; Norabuena et al., 1998]). However,
the 30–40 mm/a crustal shortening measured by GPS is much
higher than that estimated from geological (<15 mm/a) or
seismological (<3 mm/a) data [Kley and Monaldi, 1998;
Sheffels, 1990; Suarez et al., 1983]. Furthermore, the GPS site
velocities decrease gradually from the coast to the Subandes
(Figure 1), indicating evenly distributed crustal shortening.
The geological records, however, show concentrated crustal
1
Department of Geological Sciences, University of Missouri, Columbia,
Missouri, USA.
Copyright 2009 by the American Geophysical Union.
0148-0227/09/2008JB005861$09.00
shortening in the Eastern Cordillera and the Subandes in the
past 5 Ma [e.g., Okaya et al., 1997].
[4] Previous workers have explained this discordance by
assuming that the GPS-measured strain in the forearc and
the Altiplano plateau is interseismic transient that will be
recovered during future earthquakes, and only strain in the
Subandes will be preserved [Leffler et al., 1997; Liu et al.,
2000; Norabuena et al., 1998]. The transient interseismic
strain is consistent with the frequent large earthquakes in the
Peru-Chile trench and the associated coseismic and postseismic rebound of the Andean crust toward the trench
[Chlieh et al., 2004; Khazaradze and Klotz, 2003; Klotz
et al., 1999, 2001]. Such transient deformation raises the
question of how subduction and the associated cyclic trench
coupling lead to permanent strain and mountain building
in the overriding plate? And why is mountain building
localized in the Subandes in the past few million years?
[5] These questions cannot be adequately addressed by
previous elastic dislocation or viscoelastic models [e.g.,
Bevis et al., 2001; Hu et al., 2004; Khazaradze and Klotz,
2003], which are designed to simulate transient deformation
during seismic cycles, or by the long-term viscous and
viscoplastic models [Sobolev and Babeyko, 2005; Wdowinski
and Bock, 1994b; Yang et al., 2003], which assume permanent shortening of the overriding plate. Here we attempt to fill
in the gap between these two types of models. Using a twodimensional viscoelastoplastic finite element model, we
explore how strain is partitioned across the Andes during
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LUO AND LIU: TRENCH COUPLING AND MOUNTAIN BUILDING
Figure 1. Recent GPS velocities, large subduction earthquakes, and selected focal mechanism solutions in the
central Andes. Sources of the GPS data: red arrows, Chlieh
et al. [2004]; blue arrows, Kendrick et al. [2001]; green
arrows, Khazaradze and Klotz [2003]; brown arrows, Klotz
et al. [2001]. Yellow circles show the approximate rupture
zones of large subduction earthquakes (Mw 8.0). Focal
mechanism solutions are selected from Mw > 5.0 events
from global CMT catalogue with source depth of <50 km.
Dashed boxes R1 and R2 are the zones from which GPS
velocities are used for the profile in Figure 7. WC, Western
Cordillera; AP, Altiplano plateau; EC, Eastern Cordillera;
FTB, Subandean fold-and-thrust belt; BS, Brazilian shield.
the cycles of trench earthquakes, and how the cyclic trench
coupling leads to mountain building in the Subandes.
2. Tectonic Background
[6] The Andean mountain ranges extend more than
3000 km along the western margin of South America. The
central Andes, the best developed section of the orogen,
includes the following units: the forearc; the Western
Cordillera, an active volcanic arc; the Altiplano-Puna Plateau
with a 4 km average elevation; the Eastern Cordillera, the
uplifted thrust belt interior; and the Subandean Zone, the
seismically active frontal part of the foreland fold-and-thrust
belt (Figure 1). The High Andes, which include the elevated
Cordilleras and the Altiplano-Puna plateau, are isostatically
supported by thick crust roots; crustal thickness is 60– 65 km
under the Altiplano-Puna plateau and 70 km under the
Western and Eastern Cordilleras [Beck and Zandt, 2002;
Beck et al., 1996]. The Subandes have 1– 2 km elevation
and intermediate crustal thickness of 43 –47 km [Beck et al.,
1996].
[7] The Andean crustal thickening and uplift have been
attributed to magma addition [e.g., Thorpe et al., 1981],
accelerated plate convergence rate 30– 25 Ma ago (Figure 2a
[e.g., Pardo-Casas and Molnar, 1987; Somoza, 1998]),
thermal weakening of the Andean lithosphere [Allmendinger
et al., 1997; Isacks, 1988; Wdowinski and Bock, 1994a,
1994b], removal of lower crust and upper mantle beneath
B03409
Altiplano-Puna plateau, including ablative subduction and
delamination [Garzione et al., 2008; Molnar and Garzione,
2007; Pope and Willett, 1998; Tao and O’Connell, 1992],
increasing trench-ward motion (westward drift) of the South
American plate [Silver et al., 1998; Wdowinski and O’Connell,
1991], and along-strike crustal flow [Yang et al., 2003].
Most workers believe that the primary cause of the crustal
thickening and Andean mountain building is crustal shortening, resulting from subduction of the Nazca plate under
the South American plate [e.g., Allmendinger et al., 1997;
Dewey and Lamb, 1992; Isacks, 1988; Sheffels, 1990].
[8] The mechanics of how subduction leads to mountain
building, however, are not fully understood. The Nazca
plate has been subducting continuously under the entire
western margin of the South American plate for the past
200 Ma [Allmendinger et al., 1997; Isacks, 1988], yet no
significant mountain building occurred until 70 Ma
[McQuarrie, 2002; McQuarrie et al., 2005]. Most of the
Andes were built in the past 25 Ma [Allmendinger et al.,
1997; Hindle et al., 2002; Isacks, 1988; Kley and Monaldi,
1998], interestingly concomitant with the deceleration of
Nazca – South American plate convergence (Figure 2a).
Such deceleration has continued in the past few million
years as indicated by the difference between recent geodetic
measurements and the NUVEL-1A velocities [Angermann
et al., 1999; Norabuena et al., 1999; Sella et al., 2002].
Some workers have also attributed the accelerated mountain
building in the past 25 Ma (Figure 2b) to stronger trench
coupling, which may have resulted from reduced sediments
in the trench along the central Andes [Lamb, 2006; Lamb and
Davis, 2003], or high normal stress on the plate interface
because of the elevated Andean mountains [Iaffaldano et
al., 2006]. Stronger trench coupling may have also resulted
from the accelerated westward drift of the overriding South
American plate during the past 25 Ma (Figure 2c [Russo
and Silver, 1996; Silver et al., 1998; Wdowinski and
O’Connell, 1991]).
[9 ] Others have attributed the late development of
Andean mountain building to thermal weakening of the
Andean lithosphere [Allmendinger et al., 1997; Isacks,
1988; Wdowinski and Bock, 1994a, 1994b]. Seismic tomography suggests delamination of the mantle lithosphere
beneath the Eastern Cordillera [Dorbath and Granet,
1996; Myers et al., 1998]. Geochemical studies suggest that
eruption of mafic magma in the Altiplano and Puna during
late Neogene is associated with removal of mantle lithosphere and lower crust [e.g., Carlier et al., 2005; Hoke et
al., 1994; Kay and Kay, 1993; Kay et al., 1994]. Garzione et
al. [2006] have used delamination of the mantle lithosphere
to explain the rapid uplift of the Eastern Cordillera during
late Miocene as suggested by oxygen isotopes (Figure 2b
[Garzione et al., 2006; Ghosh et al., 2006]).
[10] The spatiotemporal history of the Andean mountain
building remains unclear in details, but structural, geochemical, and paleoelevation studies have yield the general
patterns. The Altiplano probably began to rise as a broad
region since about 30 Ma [Allmendinger et al., 1997;
Garzione et al., 2008; Gregory-Wodzicki, 2000; Isacks,
1988]. In the past few million years crustal shortening and
mountain building have been concentrated in the Eastern
Cordillera and the Subandean fold-and-thrust belt (Figure 2d
[Allmendinger et al., 1997; Isacks, 1988; Sheffels, 1990]),
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LUO AND LIU: TRENCH COUPLING AND MOUNTAIN BUILDING
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Figure 2. (a) Relative convergence rate between the Nazca plate and the South American plate
[Somoza, 1998]. (b) Changes of elevation of the Altiplano plateau and Eastern Cordillera [after Garzione
et al., 2008]. Paleobotanic data, Gregory-Wodzicki et al. [1998] and Gregory-Wodzicki [2000]; oxygen
isotopic data, Garzione et al. [2006] and Quade et al. [2007]; D47 data, Ghosh et al. [2006] and Quade et
al. [2007]. (c) Westward drift of the South American plate [Silver et al., 1998]. (d) Crustal shortening of
Subandean fold-and-thrust belt [after Hindle et al., 2002].
where seismicity associated with thrust faulting is active
today (Figure 1 [Suarez et al., 1983]). Modeling the twostage uplift of the Andes using a viscoplastic model,
Wdowinski and Bock [1994a, 1994b] have shown that the
broad uplift of Altiplano-Puna plateau can be associated
with lithospheric thermal weakening since 25 Ma, and the
eastward migration of concentrated deformation into Subandes since 5 –10 Ma was due to gravitational buoyancy
force of uplifted high Andes.
[11] The present-day crustal shortening delineated by the
GPS measurements (Figure 1) provides a glimpse of active
mountain building in the Andes, or does it? The 30– 40 mm/a
crustal shortening rates indicated by the GPS data are much
higher than the <15 mm/a geological rates (Figure 2d
[Hindle et al., 2002; Kley and Monaldi, 1998; Schmitz,
1994; Sheffels, 1990]) or the 1 – 3 mm/a estimated from the
seismic moments [Suarez et al., 1983]. The evenly distributed present-day crustal shortening across the Andes,
indicated by the gradual decrease of the GPS site velocities,
also contradicts with geological and seismic evidence of
concentrated crustal shortening in the Subandes.
[12] In this study we reconcile the apparent discordance
between the GPS and geological data in a geodynamic
model. By simulating strain partitioning across the Andes
during the cycles of trench earthquakes, we explore how
subduction leads to mountain building in the Andes.
3. Model Setup
[13] To explore how cyclic trench coupling leads to longterm mountain building in the Andes, we have developed a
two-dimensional viscoelastoplastic finite element model
(Figure 3). The model domain is 300 km deep and 1400 km
long to include part of the Nazca plate and the entire width
of the central Andes. The Nazca – South America plate
convergence is simulated, in most cases, by fixing the right
side of the model domain (stable South America) and
imposing the relative subduction rate on the subducting
Nazca plate at the left side and on the bottom of the model
domain (Figure 3). In some cases we use velocity boundary
conditions on both plates to study the impacts of the
westward drift of the South American plate relative to
the mantle [Russo and Silver, 1996; Silver et al., 1998;
Wdowinski and O’Connell, 1991]. Spring elements are used
at the surface of the model domain to simulate the topographic loading [Desai, 1979; Williams and Richardson,
3 of 16
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LUO AND LIU: TRENCH COUPLING AND MOUNTAIN BUILDING
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Figure 3. Finite element mesh and boundary conditions. Both plates include two rheological layers.
The top layer is elastic for the Nazca plate and elastic or elastoplastic for the South American plate; the
lower layer for both plates is viscoelastic. The blow-ups show details of the subduction zone and the
decollement and the thrust in the Subandes.
1991]. The bottom of the model domain can move freely
horizontally except near the subduction zone where the
velocity boundary condition is applied to the subducting
slab (Figure 3).
[14] We use two layers of special finite elements to
represent the seismogenic segment of the subduction zone:
a bottom viscous layer with low viscosity to accommodate
interseismic creep, and a top elastoplastic layer to simulate
interseismic strain accumulation and coseismic slip (Figure 3).
In most cases the updip and downdip limits of the seismogenic zone are set at 10 km and 50 km depths, respectively
[Oleskevich et al., 1999]. Varying the downdip limit from
35 to 55 km depth has no significant impact on our
model results. The other part of the subduction interface
is modeled as a viscous layer with relatively low viscosity
to accommodate the subduction. The geometry of the
subduction interface is based on depth contours of the
Wadati-Benioff zone beneath the central Andes [Cahill
and Isacks, 1992].
[15] The model simulates lithospheric deformation by
solving the equation of force balance:
crust for the South American plate. The lower crust and the
upper mantle of both plates are represented by Maxwell
viscoelastic media, whose constitutive relation can be
written as:
@sij
þ rgi ¼ 0;
@xj
where {_e} is the strain rate vector, {s}
_ is the stress rate
vector, {s} is the stress vector, [D] and [Q] are the material
matrices related to elastic modulus E, Poisson’s ratio n, and
viscosity h. Here {} and [] represent the vector (3 1) and
the matrix (3 3), respectively. The plastic deformation is
simulated with the Mohr-Coulomb yield criterion and
nonassociated flow rule [Dunne and Petrinic, 2005;
Zienkiewicz and Taylor, 2005]:
ð1Þ
where sij is the stress tensor (i, j = 1, 2); r is the density;
gi is the gravitational acceleration. Because deformation is
mainly caused by nonlithostatic tectonic force, the
lithostatic pressure is included only in a few selected
cases where we examine the impact of lithostatic pressure
on plastic strain, which is pressure dependent. We consider
a top 30-km-thick elastic layer for the Nazca plate [Watts
and Burov, 2003] and a 20-km-thick elastoplastic upper
fe_ g ¼ ½D
1 fs_ g þ ½Q
1 fsg
0
½ D
¼
B
B
E
B
ð1 þ n Þð1 2n Þ B
@
1n
n
0
n
1n
0
0
0
0:5 n
0
1
1
B 4
4
1B
B
½Q
1 ¼ B 1 1
hB 4 4
@
0
4 of 16
F ðs; kÞ ¼
ð2Þ
0
0
1
C
C
C
C
A
ð3Þ
1
C
C
C
0C
C
A
ð4Þ
1
s 1 s2 s 1 þ s2
þ
sin f C cos f Hk
2
2
ð5Þ
LUO AND LIU: TRENCH COUPLING AND MOUNTAIN BUILDING
B03409
B03409
Table 1. Model Cases and Parameter Valuesa
Plate Couplingb
Overriding Platec
Case Number and
Associated Figures
Cs (MPa)
fs (°)
(Figures 4 and 5)
(Figure 6)
(Figure 7)
(Figure 8)
(Figures 9 and 10)
40
30
30
40
40
10
10
10
10
10
6 (Figures 11 and 12)
30
10
7f (Figure 13)
30
10
8 (Figure 14)
9 (Figure 15a)
10 (Figure 15b)
11 (Figure 15c)
12 (Figure 15d)
30
40
50
40
40
10
30
35
30
30
1
2
3
4
5
Co (MPa)
–
–
–
20
20
60
10
60
10
60
30
–
–
–
–
(S)d
(P)d
(D)e
(P)e
(D)e
(P)e
(T)e
fo (°)
–
–
–
20
0 (S)d
30 (P)d
20 (D)e
30 (P)e
20 (D)e
30 (P)e
10 (T)e
–
–
–
–
Plastic Strain on
Overriding Plate
no
no
no
yes
yes
yes
yes
yes
no
no
no
no
a
In all cases, elastic modulus is 8.25 1010 Pa for elastic/elastoplastic layers and 1.1 1011 Pa for viscoelastic layers;
Poisson’s ratio is 0.25 and Crustal density is 2.8 103 kg/m3.
b
Cs and fs are respectively the cohesion and the angle of internal friction for plastic yield on the seismogenic plate interface.
c
Co and fo are respectively the cohesion and the angle of internal friction for plastic yield in the overriding plate.
d
S, Subandean upper crust; P, other part of the Andean upper crust.
e
D, Subandean decollement; P, other part of the Andean upper crust; T, Subandean thrust.
f
Case 7 includes effects of lithostatic pressure on plastic deformation, but case 6 does not.
where s1 and s2 are maximal and minimal principal
stresses, C is cohesion, f is internal frictional angle, H is the
hardening modulus (H = 0 for perfect plastic deformation;
H < 0 for strain softening plastic deformation), k is effective
plastic strain. The effects of lithostatic pressure on plastic
failure are shown by the term (s1 + s2)/2 in equation (5).
Note that when the angle of internal frictional is zero (f = 0),
lithostatic pressure has no impact on plastic yield.
[16] The plastic strain increments are given as [Dunne
and Petrinic, 2005; Zienkiewicz and Taylor, 2005]:
@G
;
fde g ¼ dl
@s
p
ð6Þ
where {dep} is incremental plastic strain vector (3 1),
dl is the plastic multiplier, and G = (s1 s2)2/4 is the
plastic potential function. The values of material parameters
are given in Table 1.
[17] The displacement, strain, and stress fields are determined by the finite element method. We developed the finite
element codes using the commercial package FEPG (http://
www.fegensoft.com). The codes are parallelized and all
cases were run on a 16-node dual-processor PC cluster. To
avoid the unwanted influence of arbitrary initial conditions,
we run the model until it reaches a quasisteady state, which
provides the background stress field. We then calculate strain
partitioning and stress evolution during the cycles of trench
earthquakes.
4. Model Results
[18] We have run a suite of numerical experiments to
explore answers to these questions: (1) How is strain
partitioned across the Andes during the cycles of trench
earthquakes? (2) How does the cyclic trench coupling lead
to mountain building in the Andes? (3) Why has mountain
building been localized in the Subandes during the past few
million years?
4.1. Strain Partitioning in the Andes During the Cycles
of Trench Earthquakes
[19] As suggested by previous studies [Leffler et al.,
1997; Liu et al., 2000; Norabuena et al., 1998] and
indicated by frequent large earthquakes in the Peru-Chile
trench [Comte and Pardo, 1991; Nishenko, 1991], much of
the GPS-measured crustal shortening in the Andes is
transient that will be restored during future trench earthquakes [Chlieh et al., 2004; Hu et al., 2004; Khazaradze
and Klotz, 2003; Klotz et al., 1999, 2001]. Understanding
the partitioning and evolution of the short-term strain is
hence logically the first step to study how such strain
eventually leads to mountain building in the Andes.
[20] To simulate strain partitioning and evolution during
the cycles of trench earthquakes, we started with a simple
model, in which the Andean lithosphere is viscoelastic and
laterally homogeneous. In this case the right side of the
model domain (stable South America) is fixed, and the
Nazca plate moves toward the South American plate at
65 mm/a [Kendrick et al., 2003]. We adjusted the viscosity
(to 1.4 1019 Pa s) of the bottom layer of the seismogenic
subduction fault (Figure 2) so that 30 mm/a of plate
convergence is accommodated by aseismic creeping in the
subduction zone and 35 mm/a is absorbed by crustal
shortening on the overriding plate, as indicated by the
GPS data in the central Andes (Figure 1). We also adjusted
the plastic yield strength in the subduction zone and the
stress drop of trench earthquakes (in a few MPa) such that
the recurrence interval of the trench earthquakes is about
130 years, and the average coseismic slip is about 4 m,
similar to the values of the large earthquakes in the central
segments of the Peru-Chile trench [Comte and Pardo, 1991;
Nishenko, 1991].
5 of 16
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LUO AND LIU: TRENCH COUPLING AND MOUNTAIN BUILDING
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Figure 4. Predicted displacement (vectors) and horizontal strain ex (background color) across the plate
boundary during one cycle of trench earthquakes. (a) Accumulative interseismic displacement and strain
for 130 years. (b) Coseismic displacement and strain. (c) Accumulative postseismic displacement and
stain due to 130 years of viscous relaxation. Black heavy lines show the subduction interface. White lines
in the overriding plate show the bottom of the elastic or elastoplastic upper crust. The strain is capped at
±105 for the scale bar; positive strain is compressive.
[21] Figure 4 shows the displacement and strain during one
of the seismic cycles. The entire Andean crust is under compression during the 130-year interseismic phase (Figure 4a).
The forearc moves eastward at 35 mm/a, and the velocity
gradually decreases landward, similar to the GPS site velocities in the central Andes (Figure 1). When earthquake occurs,
the Andean crust moves trench-ward by elastic rebound
(Figure 4b). In the forearc, the coseismic rebound causes
intensive extensional strain, which may have contributed to
the pervasive trench-parallel extensional structures in the
Andean forearcs [e.g., Delouis et al., 1998]. The trench-ward
rebound continues by postseismic viscous relaxation after
the earthquake (Figure 4c), as evidenced from GPS measurements around the epicenters of the 1960 great Chilean
earthquake [Klotz et al., 2001] and the 1995 Antofagasta
earthquake [Khazaradze and Klotz, 2003; Klotz et al.,
2001]. Postseismic rebound occurs across the entire Andes
(Figure 4c); its rate depends on the viscosity of the lower
crust and the mantle, as also shown in previous studies [Hu
et al., 2004; Klotz et al., 2001].
[22] The displacement and strain near the surface are
directly relevant to the GPS and geological observations
of crustal shortening. Their evolutions during the seismic
cycle are shown in Figure 5. The predicted interseismic
surface displacement is evenly distributed across the central
Andes (Figure 5a), similar to the GPS site velocities (Figure 1).
Near the end of the 130-year interseismic period, about 5 m
displacement is accumulated in the forearc (i.e., at 38 mm/a).
More than half of that is recovered by coseismic slip; the rest
is gradually recovered by postseismic viscous relaxation.
Whereas the predicted transient strain is partitioned over
the entire Andean orogen, most of the coseismic and postseismic strains are in the forearc, and all the accumulated
interseismic shortening is recovered in a few hundred years
(Figure 5b). In this case, trench coupling in the subduction
zone does not lead to mountain building in the overriding
plate.
[23] The lateral variations of lithospheric rheology can
affect the spatial partitioning of the transient strain (Figure 6).
More interseismic strain is predicted over the High Andes if
the underlying lower crust and mantle lithosphere there
have a lower viscosity than those under the Subandes and
the Brazilian shield. Nonetheless, the strain evolution is
similar to Figure 5: most coseismic and postseismic strains
are found in the forearc, and all compressive strain accumulated during the interseismic period is restored in a few
hundred years.
[24] Such transient strain partitioning and evolution can
explain much of the GPS measurements in the central
Andes (Figure 7). The trench between 19°S and 23°S has
not ruptured since 1877 (Figure 1), thus the GPS velocities
in the corresponding latitudes represent mainly interseismic
deformation, and their general trend can be fit by the
predicted interseismic surface velocity of a viscoelastic
model with a homogeneous viscosity. Around the epicenter
of the 1995 Antofagasta earthquake (Mw 8.0), the GPS
velocities are still affected by postseismic relaxation [Chlieh
et al., 2004; Khazaradze and Klotz, 2003; Klotz et al.,
2001], which can be reasonably fit with a homogeneous
viscosity of 8 1018 Pa s in the model lower crust and mantle
6 of 16
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LUO AND LIU: TRENCH COUPLING AND MOUNTAIN BUILDING
Figure 5. Predicted evolution of (a) horizontal displacement Ux and (b) horizontal strain ex on the
surface across the central Andes for the trench earthquake cycle shown in Figure 4. Note the nonlinear
scale in the strain axis. The interseismic curves show accumulated displacement and strain during the
130-year interseismic period. The coseismic curves show the cumulative displacement and strain
immediately after a trench earthquake. The curves labeled P-50 yr are results for 50 years into the
postseismic relaxation; the labels are similar for other curves. Positive displacement is toward the stable
South America (right side); positive strain is compressive.
Figure 6. Predicted evolution of (a) horizontal displacement Ux and (b) horizontal strain ex on the
surface during one seismic cycle with laterally heterogeneous lithospheric viscosities: 8 1018 Pa s
under the High Andes, 3 1021 Pa s under the Subandes, and 2 1022 Pa s under the Brazil shield.
Note the nonlinear scale in the strain axis. Labels are explained in Figure 5. Positive displacement is
toward the stable South America (right side).
7 of 16
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LUO AND LIU: TRENCH COUPLING AND MOUNTAIN BUILDING
B03409
Figure 7. Comparison of predicted surface velocities (Vx) and GPS velocities across the central Andes.
Interseismic and postseismic GPS velocities are collected from regions labeled R1 and R2 in Figure 1,
respectively. These GPS velocities are projected onto the direction of plate convergence (N77°E).
Interseismic GPS data are from Kendrick et al. [2001]. Postseismic GPS data are from Chlieh et al.
[2004], Khazaradze and Klotz [2003], and Klotz et al. [2001]. Model predicted velocity is along the
direction of plate convergence (N77°E) toward the fixed Brazilian shield. Viscosity of the South
American plate is 8 1018 Pa s. Other material parameters are shown in Table 1.
lithosphere (Figure 7). Here we do not consider possible
afterslip and poroelasticity, which have much smaller spatiotemporal scales than postseismic viscous relaxation [Piombo
et al., 2005; Uchida et al., 2003; Yagi et al., 2003].
4.2. Plastic Deformation: The Link Between Trench
Coupling and Mountain Building
[25] Our results reaffirm that most of the GPS-measured
crustal shortening in the Andes is transient. For crustal
shortening to lead to mountain building in the Andes, some
of the GPS-measured shortening must be permanent (plastic),
and such permanent shortening needs to accumulate through
the cycles of trench earthquakes.
[26] To simulate the plastic strain and explore its controlling factors, we modified the model to include plasticity in
the Andean crust. Using the model in Figure 4 as the
reference model, we now allow the Andean crust to deform
plastically when the stress reaches the Mohr-Coulomb yield
criterion. The predicted plastic strain is concentrated in the
forearc-Western Cordillera region, although the rheological
structure of the Andean lithosphere is assumed to be
laterally homogeneous (Figure 8). The plastic deformation
causes the interseismic surface velocities to deviate from the
linear trend predicted by the viscoelastic model (see
Figure 4a), but only slightly because of the relatively large
viscoelastic components (Figure 8a). The plastic strain
shows up more prominently in the calculated strain evolution (Figure 8b). During the cycles of trench earthquakes,
the viscoelastic strain is restored by coseismic slip and
postseismic rebound, but the plastic strain is preserved
and accumulated.
[27] The predicted concentration of permanent crustal
shortening in the forearc-volcanic arc region is consistent
with the early phase of Andean mountain building (70 –
30 Ma) inferred from sedimentary records and foreland
basin evolution [e.g., Horton and DeCelles, 1997; Horton
et al., 2001], but since the Late Neogene crustal shortening
and mountain building have been concentrated in the
Eastern Cordillera and the Subandes [e.g., Allmendinger et
al., 1997; Isacks, 1988; Okaya et al., 1997]. The Subandean
fold-and-thrust system and the decollement zone under the
Subandes [Allmendinger et al., 1997; Baby et al., 1992;
Isacks, 1988] may have reduced the plastic yield strength in
the Andean upper crust. Modifying the model to include a
weak upper crust in the Subandes, we can reproduce the
localized plastic shortening there (Figures 9 and 10). Such
strain localization happens despite the relatively stiff lower
crust and upper mantle under the model Subandes [Beck
and Zandt, 2002].
[28] Similar results are predicted when the model includes
a decollement under the Subandes (Figures 11 and 12),
simulated with a low-strength elastoplastic layer (Figure 3).
The low-strength decollement (<15 MPa) in Subandes has
been suggested by previous studies through force balance
analysis [e.g., Lamb, 2006] and could be explained by
lubrication of sediments [Babeyko et al., 2006; Lamb,
2006]. With the decollement, the model simulates the
effects of continuous plastic creep in the fold-and-thrust
belt. We also tested effects of lithostatic pressure on plastic
deformation by adding lithostatic pressure into the mean
stress term in equation (5). Assuming the same plastic yield
strength, adding the lithospheric pressure would reduce
plastic strain on the decollement (Figure 13).
[29] To further explore the link between cyclic trench
coupling and crustal shortening in the Subandes, we run
another model with a stick-slip thrust fault in the Subandes
(Figure 1), and simulate cycles of earthquakes both in the
trench and on this Subandean fault (Table 1, case 8). The
prescribed average coseismic slip on the Subandean thrust is
1 m, consistent with moderate-sized Subandean earthquakes
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Figure 8. Predicted evolution of (a) horizontal displacement Ux and (b) horizontal strain ex on the
surface during one seismic cycle with viscoelastoplastic strain in the overriding plate. Note the nonlinear
scale in the strain axis. The model assumes laterally constant plastic yield strength (Table 1) and viscosity
of 8 1018 Pa s for the overriding plate. Labels are explained in Figure 5.
Figure 9. Predicted horizontal strain ex during one trench earthquake cycle with a weak Subandean
upper crust. (a) Interseismic horizontal strain accumulated for 130 years. (b) Coseismic deformation
superimposed on the strain field in Figure 9a. (c) Total strain field at 130 years after the trench
earthquake, showing the effects of postseismic relaxation. Note the compressive strain (blue) in the
Subandean crust survives through coseismic and postseismic crustal rebound. White solid lines show the
bottom of the elastoplastic upper crust. White dashed lines are the rheological boundaries. The strain is
capped at ±105 for the scale bar.
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Figure 10. Predicted evolutions of (a) horizontal displacement Ux and (b) horizontal strain ex for the
model in Figure 9. Note the nonlinear scale in the strain axis. Labels are explained in Figure 5.
[e.g., Funning et al., 2005; Suarez et al., 1983]. Figure 14
shows the evolution of horizontal strain during one cycle of
trench earthquake. During the interseismic period of trench
earthquakes, the Subandean thrust slips, leading to permanent strain there (Figure 14). The results are similar to that
with the decollement (Figures 11 – 13).
4.3. Why Has Crustal Shortening Been Localized in
the Subandes?
[30] We have shown that mechanical weakening of the
Subandean crust can lead to concentrated permanent shortening and mountain building there. However, why is crustal
weakening localized in the Subandes?
Figure 11. Predicted horizontal strain ex during one trench earthquake cycle with the decollement under
the Subandes. (a) Interseismic horizontal strain accumulated for 130 years. (b) Coseismic deformation
superimposed on the strain field in Figure 11a. (c) Total strain field at 130 years after the trench
earthquake, showing the effects of postseismic relaxation. Other labels are similar to those in Figure 9.
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Figure 12. Predicted evolution of (a) horizontal displacement Ux and (b) horizontal strain ex for the case
shown in Figure 11. Note the nonlinear scale in the strain axis. Labels are explained in Figure 5.
[31] A number of mechanisms have been proposed for
the localized mountain building in the Subandes [e.g.,
Allmendinger et al., 1997; Babeyko et al., 2006; Garzione
et al., 2008; Isacks, 1988; Wdowinski and Bock, 1994b].
Here we explore some of the mechanisms by calculating
their effects on the quasi steady state differential stress,
which is directly responsible for plastic strain and mountain
building. We have shown that, for a flat and laterally
homogeneous overriding plate, the differential stress is
compressive (sxx > szz) across the overriding plate; the
highest compression is found in the forearc-volcanic arc
region, as indicated by the resulting plastic strain (Figure 8).
[32] Uplift of the High Andes can have a significant
impact on the stress pattern in the Andean crust. As shown
in Figure 15a, topographic loading of the uplifted landmass
tends to cause extension in the High Andes while intensify
compression near the foothills. The results are similar to
those of previous analytic studies [Molnar and Lyon-Caen,
1988] and numerical modeling [Liu et al., 2000; Wdowinski
and Bock, 1994a, 1994b; Wdowinski and O’Connell, 1991],
and consistent with the stress state indicated by geological
structures [Mercier et al., 1992] and seismicity (Figure 1).
Although the effects of topographic loading is symmetric on
both sides of the high land, in the forearc the compressive
stress is reduced by trench-ward crustal motion induced by
coseismic slips and postseismic relaxation associated with
the repeated trench earthquakes (Figure 4). The Subandes,
on the other hand, has high compressive stress from
combined effects of tectonic compression and topographic
loading. Thus uplift of the High Andes to near its presentday elevation by 5– 10 Ma may have contributed to the
tectonic change from broad uplift of the Andean orogen to
localized crustal shortening in the Subandes [Allmendinger
et al., 1997; Isacks, 1988; Wdowinski and Bock, 1994b].
[33] The uplifted High Andes would also increase the
mechanical coupling at the trench by exerting high normal
stress on the plate interface, a mechanism proposed for the
accelerated mountain building in the past few million years
[Iaffaldano et al., 2006; Lamb, 2006] (Figure 2). Stronger
trench coupling may also result from the reduced sediments
in the trench [Lamb, 2006; Lamb and Davis, 2003]. Using
the model in Figure 15a as a reference, we increased the
trench coupling by raising the Mohr-Coulomb yield strength
on the seismogenic subduction zone. The results are intensified compression across the entire Andean lithosphere
(Figure 15b); in the High Andes the extension is weakened.
[34] Delamination of the mantle lithosphere under the
Eastern Cordillera, another process proposed for the accelerated mountain building in the Eastern Cordillera and
the Subandes [Garzione et al., 2006, 2008; Molnar and
Garzione, 2007], could also contribute to localized crustal
shortening in the Subandes. Relative to the model in Figure
15a, we simulated the impact of the delamination by
reducing the density and viscosity of the mantle lithosphere
beneath the Eastern Cordillera. In addition to a rapid uplift,
more deviatoric stress is concentrated within the upper
crust, hence amplifies extension within the plateau and
compression in the Subandes (Figure 15c).
[35] Finally, we explored the impact of the accelerated
westward drift of the South American plate relative to the
mantle (Figure 2b [Russo and Silver, 1996; Silver et al.,
1998; Wdowinski and O’Connell, 1991]). For this test, we
changed the model from the South America – fixed reference
frame to the mantle-fixed reference frame, and changed the
boundary conditions accordingly. We applied 30 mm/a
westward motion to the overriding South American plate
at the right boundary, and 35 mm/a eastward motion at the
left side and the tip of the Nazca plate, so the relative plate
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Figure 13. Predicted horizontal strain ex during one trench earthquake cycle. Including lithostatic
pressure in this case reduces plastic strain in the deeper part of the decollement under the Subandes (see
Figure 11). (a) Evolution of horizontal strain on the surface. (b) Interseismic horizontal strain
accumulated for 130 years. (c) Coseismic deformation superimposed on the strain field in Figure 13b.
(d) Total strain field at 130 years after the trench earthquake. Other labels are similar to those in Figures 5
and 9.
convergence rate remains at 65 mm/a. Comparing with
Figure 15a shows that the westward drift of the South
American plate tends to increase compressive stress in the
Subandes while decrease it in the forearc (Figure 15d). The
results are similar to those of Sobolev and Babeyko [2005].
5. Discussion
[36] The viscoelastoplastic model of the Andean subduction system presented here allows us to explore the link
between the short-term crustal deformation measured by
GPS and the long-term mountain building in the Andes. Our
results show that most of GPS-measured crustal shortening
in the Andes can be explained by transient deformation, as
suggested previously [Leffler et al., 1997; Liu et al., 2000;
Norabuena et al., 1998]. Most of crustal shortening accumulated during the interseismic period will be restored by
future trench earthquakes and the associated postseismic
processes. Such transient crustal shortening explains the
apparently contradicting high GPS (30 – 40 mm/a) and low
geological (<15 mm/a) shortening rates, and the evenly
distributed shortening across the Andes indicated by the
GPS data versus the geologically localized crustal shortening
in the Subandes [Liu et al., 2000].
[37] Our results show that crustal shortening in the
overriding plate of a subduction zone does not necessarily
lead to mountain building. To do so requires permanent
(plastic) compressive strain to be produced and accumulated
through the cycles of trench earthquakes. In a separate study
we show that all proposed mechanisms for the Andean
mountain building boil down to two factors: (1) the strength
of mechanical coupling on the plate interface, which
modulates the tectonic compressive stress transmitted to
the overriding plate, and (2) the yield strength of the
overriding plate. The contribution of various geological
processes to the Andean mountain building can be better
understood in light of these two factors. For example, the
plate convergence rate has shown both positive and negative
correlation with the Andean mountain building, but the
convergence rate itself does not directly contribute to
mountain building unless it affects either mechanical coupling in the subduction zone or thermal state of the
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Figure 14. Predicted horizontal strain ex during one trench earthquake cycle with the stick-slip
Subandean thrust. (a) Evolution of horizontal strain on the surface. (b) Interseismic horizontal strain
accumulated for 130 years. (c) Coseismic deformation superimposed on the strain field in Figure 14b.
(d) Total strain field at 130 years after the trench earthquake, showing the effects of postseismic
relaxation. Other labels are similar to those in Figures 5 and 9.
overriding plate. The positive correlation between the
accelerating plate convergence and the initiation of the main
phase of the Andean mountain building around 30 Ma
may be understood if fast plate convergence changed either
mechanical coupling at the plate interface or weakened the
Andean lithosphere, or both. Conversely, the negative
correlation between the deceleration of the Nazca – South
America plate convergence and the apparent acceleration of
the Andean mountain building in the past 25 Million years
(Figures 2a and 2b) may be explained by the increased
normal stress on the plate interface due to the elevated
Andes [Iaffaldano et al., 2006; Lamb, 2006; Meade and
Conrad, 2008]; the resulting strong coupling in the trench
also slows the subduction of the Nazca plate [Iaffaldano et
al., 2006; Meade and Conrad, 2008].
[38] The present-day crustal shortening in the Andes is
reproduced by the subduction of the Nazca plate under the
South American plate. This short-term crustal shortening
would be reconciled with the localized mountain building in
the Subandes as shown by seismological and geological
records, if the short-term crustal shortening is transient across
the Andes except in the Subandes, where the GPS-measured
crustal shortening is largely plastic. The mechanically
weakened crust in the Subandes, probably by the foldand-thrust system and the decollement, could cause localized plastic shortening. The predicted shortening rates
depend on model parameters, mainly the mechanical coupling in the trench, viscosity of Andean lower crust and
upper mantle, and plastic yield strength of the Andean crust.
When these parameters are proper for the short-term crustal
deformation (Figures 9 – 14), the predicted plastic shortening in the Subandes is in the range of 4 – 11 mm/a,
comparable with the geologically estimated shortening rate
in the Subandes (<15 mm/a) [Hindle et al., 2002; Kley and
Monaldi, 1998; Schmitz, 1994; Sheffels, 1990].
[39] Our focus in this study is on the dynamic link
between plate coupling in the trench and localized mountain
building in the Subandean zone during the past few million
years. We avoided the question of what cause the broad
uplift of the High Andes, the Altiplano and the Western and
Eastern Cordilleras. Geological evidence shows limited
crustal shortening and seismicity within the Altiplano
[Allmendinger et al., 1997; Isacks, 1988; Suarez et al.,
1983], hence the thick crust there requires ductile thickening
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Figure 15. Predicted differential stress (sxx szz) with (a) topographic loading of a 4-km plateau alone,
(b) strengthened trench coupling, (c) delamination under the Eastern Cordillera (simulated by reducing
mantle density by 0.02 g/cm3 and viscosity by two orders of magnitude in the region outlined by the
magenta dashed lines), and (d) with 30 mm/a westward drift of the South American plate. Black dashed
lines show the model Moho. Elevation is exaggerated five times. Stress is capped at ±100 MPa for the
scale bar; positive stress is compressive.
in the lower crust. The possible processes may involve
magma addition [Thorpe et al., 1981], gravity-driven lower
crustal flow by Western and Eastern Cordilleras [Husson
and Sempere, 2003], compression of the ductile lower crust
by the underthrusting of the Brazilian shield [Vietor and
Oncken, 2005], and along-strike flow of the ductile crustal
material from the limbs of the Andes to the central Andes
[Yang et al., 2003]. Thus the Altiplano may not be caused
by crustal shortening alone.
[40] Once the High Andes has reached to the presentmean elevation, it may become easier to grow wider than
higher, because going higher requires overcoming the
gravitational potential energy that increases with the square
of the elevation [Molnar and Lyon-Caen, 1988]. Our results
show that the uplifted High Andes plays a major role in
concentrating compressive stress in the Subandes, consistent with previous studies [e.g., Allmendinger et al., 1997;
Isacks, 1988; Wdowinski and Bock, 1994a, 1994b]. A
number of geological processes that may have operated in
the past few million years, including the increased trench
coupling [Hindle et al., 2002; Lamb and Davis, 2003], the
accelerated westward drift of the South American plate
[Russo and Silver, 1996; Silver et al., 1998; Wdowinski
and O’Connell, 1991], and the delamination of the mantle
lithosphere under the Eastern Cordillera [Garzione et al.,
2006, 2008; Molnar and Garzione, 2007], may have further
localized strain in the Subandes.
6. Conclusions
[41] Using a two-dimensional viscoelastoplastic finite
element model, we have investigated how the short-term
crustal shortening in the Andes associated with the cyclic
trench coupling and earthquakes leads to the concentrated
mountain building in the Subandes. Our main conclusions
from this study include the following:
[42] 1. The present-day crustal shortening across the
Andes, as indicated by the GPS measurements, results from
the Nazca –South American plate convergence. However,
the GPS-measured crustal shortening is largely transient and
will be restored by future earthquakes in the subduction
zone, and by the associated postseismic relaxations. Only in
the Subandes is the crustal shortening plastic that will lead
to permanent crustal shortening and hence mountain building.
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[43] 2. Mechanical weakening of the upper crust in the
Subandes, as evidenced by the development of the fold-andthrust system and the decollement, can cause localized
plastic strain in the Subandes. The localized crustal weakening in the Subandes results from topographic loading of
the High Andes and other processes, including increased
plate coupling, accelerated westward drift of the South
American plate, and possible delamination of the mantle
lithosphere under the Eastern Cordillera in the past few
million years.
[44] Our results support the notion that crustal shortening
induced by the subduction of the Nazca plate under South
American is the primary cause of the Andean mountain
building in the past few million years. However, our model
does not simulate the broad uplift of the Altiplano and other
parts of the High Andes, where shortening in the upper crust
is limited, thus ductile thickening of the lower crust is
required. Further studies are needed to illuminate the
mechanics that change the Andean mountain building from
broad uplift of the orogen to localized and laterally migrating
crustal shortening near its eastern margin.
[45] Acknowledgments. We benefited from discussions with Seth
Stein and Paco Gomez. Constructive comments from A.E. Tim Dixson
and reviewers Shimon Wdowinski and Andy Newman improved the paper.
We thank Huai Zhang for providing the parallel viscoelastic FEM codes on
which our models are developed. Support for this work was provided by
NASA grant NNX08AF97G and the Huggins Scholarship from the
University of Missouri to Gang Luo.
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