Download Subduction erosion modes: Comparing finite

Earth and Planetary Science Letters 287 (2009) 241–254
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Earth and Planetary Science Letters
j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / e p s l
Subduction erosion modes: Comparing finite element numerical models
with the geological record
Duncan Fraser Keppie a,⁎, Claire A. Currie b,1, Clare Warren b,2
a
b
Department of Earth and Planetary Sciences, McGill University, Montreal, Quebec, Canada
Geodynamics Research Group, Department of Oceanography, Dalhousie University, Halifax, Nova Scotia, Canada
a r t i c l e
i n f o
Article history:
Received 7 January 2009
Received in revised form 31 July 2009
Accepted 6 August 2009
Available online 6 September 2009
Editor: T. Spohn
Keywords:
subduction
subduction factory
subduction erosion
subduction angle
Andes
forearc removal
a b s t r a c t
During subduction erosion, the upper plate is tectonically eroded by the subducting plate and carried into the
mantle. The geological record suggests that subduction erosion is a fundamental process at subduction
margins; however the underlying causes are not well constrained. Finite-element numerical models of
ocean–continent subduction are used to investigate the roles of crustal frictional strength, subduction angle,
and convergence rate in subduction erosion processes.
Subduction erosion occurs in models in which the plate boundary zone is moderately strong, due to either
high frictional strength or shallow angle of subduction. The models exhibit two distinct modes of subduction
erosion: (1) steady, with slow trench migration rates (<4 km Ma− 1), subsidence in the remaining forearc,
and a decrease in the angle of subduction, in which the edge of the continental plate is eroded in small
blocks, and (2) unsteady, with fast trench migration rates (⋙15 km Ma− 1), subsidence at the end of the
process, and an increase in the angle of subduction, in which a large block of continental forearc is removed.
The unsteady mode is compatible with the sudden migration of the volcanic arc into the continental interior,
a concurrent hiatus in arc volcanic production, and geochemical signatures showing crustal (forearc)
contamination in the magma source region when arc volcanism renews in its new location. Both modes are
inhibited by the presence of a thick sediment layer within the subduction zone, and neither mode requires
the presence of topographic asperities on the lower plate.
In natural subduction zones, subduction erosion may initially occur through steady erosion at the edge of the
continental plate. As material is removed, the subduction angle may gradually decrease, increasing the
strength of the plate boundary zone. The increased strength may lead to failure in the continental interior,
unsteady removal of a large forearc block and relocation of the subduction zone into the upper plate where
the cycle may repeat. The proposed cycle may explain observed patterns in the Andean margin, including
steady and unsteady erosion recorded in the geological record and along-strike variation in present-day
subduction angles.
© 2009 Elsevier B.V. All rights reserved.
1. Introduction
Truncation of geological units in the upper plate, crustal thinning,
and relative trench migration towards the upper plate in ocean–
continent subduction zones suggest the removal of material from the
upper plate by tectonic processes. When geological candidates for the
missing material cannot be identified elsewhere, subduction erosion
processes must be considered (von Huene and Scholl, 1991; Clift
and Vannucchi, 2004). It has been suggested that more than half of
⁎ Corresponding author.
E-mail addresses: [email protected] (D.F. Keppie), [email protected]
(C.A. Currie), [email protected] (C. Warren).
1
Present address: Department of Physics, University of Alberta, Edmonton, Alberta,
Canada.
2
Present address: Department of Earth and Environmental Sciences, The Open
University, Milton Keynes, MK7 6AA, UK.
0012-821X/$ – see front matter © 2009 Elsevier B.V. All rights reserved.
doi:10.1016/j.epsl.2009.08.009
modern subduction zones undergo subduction erosion and net loss of
upper plate material (Clift and Vannucchi, 2004). The results of a
recent global survey suggest that subduction erosion is limited to
subduction zones in which trench sediments are less than 1 km thick
and where convergence is faster than 60 km Ma− 1 (Clift and
Vannucchi, 2004; Kukowski and Oncken, 2006). Beyond this, there
appears to be no obvious first-order correlation between the rate
of subduction erosion and key subduction parameters (Clift and
Vannucchi, 2004).
Despite the general consensus that tectonic subduction erosion is a
key process in the subduction factory, the controlling mechanisms are
hotly debated. Models of tectonic subduction erosion require the
mechanical entrainment of frontal and/or basal upper-plate basement
by the subducting lower (oceanic) plate (von Huene and Lallemand,
1990). Debate focuses on the causes and styles of relative mechanical
weakening of the upper plate that necessarily precede the mechanical
entrainment. Weakening may arise primarily due to elevated stresses
242
D.F. Keppie et al. / Earth and Planetary Science Letters 287 (2009) 241–254
acting across the plate interface (e.g. Uyeda and Kanamori, 1979;
Adam and Reuther, 2000; Clift and Vannucchi, 2004; Kukowski and
Oncken, 2006) or due to material softening in the upper plate above
the plate interface (e.g. Le Pichon et al., 1993; von Huene et al., 2004;
Sage et al., 2006).
Due to the wealth of data in the literature and the broad spectrum
of reported observations, the subduction of the Farallon plate and its
descendants beneath the Americas has created an ideal region in
which to formulate and test models of subduction erosion. At one end
of the spectrum, upper-plate material appears to be eroded from
the upper plate in a gradual fashion (i.e., small pieces of forearc) at
relatively slow rates (Clift and Vannucchi, 2004). For instance, trench
migration rates between 0 and 3 km Ma− 1 towards the continent
have been estimated in the central Andes due to subduction erosion
(Kukowski and Oncken, 2006). Elsewhere, higher rates of ca. 10 km
Ma− 1 have been associated with topographic asperities on the lower
plate (e.g. Clift et al., 2003). Possible mechanisms for this mode of
subduction erosion include ductile ablation of the upper plate due to
viscous drag (e.g. Tao and O'Connell, 1992; Pope, 1998), brittle and
ductile abrasion of the upper plate by topographic asperities on the
lower plate (e.g. Clift et al., 2003; Vannucchi et al., 2003; Clift and
Vannucchi, 2004; Hampel et al., 2004; Bangs et al., 2006), and brittle
hydro-fracturing arising along the base of the upper plate due to fluid
overpressures associated with dehydration of subducted sediments
and oceanic crust (von Huene et al., 2004; Sage et al., 2006).
In other localities, the geological record suggests more rapid
removal of larger blocks of forearc material, possibly due to subduction
erosion (Moran-Zenteno et al., 1996; Calvert et al., 2003; MoranZenteno et al., 2007; Malavieille and Trullenque, 2009). Minimum arc
migration rates of >12 km Ma− 1 have been associated with two
inferred episodes of forearc removal in southern Chile during the
Miocene (Kay et al., 2005), and minimum trench migration rates of ca.
18–75 km Ma− 1 are implied for the late Oligocene/early Miocene
forearc removal from southern Mexico (Moran-Zenteno et al., 1996,
2007).
Along the Andean margin, geological evidence suggests that both
gradual and rapid subduction erosion may have operated in the past
or still be operating today (e.g. Kay et al., 2005; Clift and Hartley,
2007). More than one mechanism may therefore control subduction
erosion and in any one place the mode may also change over time.
In this study, finite element numerical models are used to investigate
possible mechanisms that may lead to the mechanical failure, entrainment and eventual subduction of upper-plate material. The models
focus on parameters that have previously been suggested to be
important in subduction erosion processes: subduction angle, convergence rate, sediment cover on the oceanic plate, and the brittle strength
of the upper plate. The aim is to address the following questions:
1. What is the relative importance of various parameters to the failure
and subsequent entrainment of upper-plate material?
2. What are the key mechanisms of failure and entrainment associated with these parameters?
3. What are the kinematic expressions of these processes? Does
upper plate material fail and entrain in relatively small or large
blocks? What are the rates of trench migration and/or material
removal? Does the remaining forearc undergo subsidence in
response to subduction erosion processes?
2. Numerical modelling methodology
2.1. Basic principles
The numerical modelling approach closely follows previous work
(Currie et al., 2007; Warren et al., 2008b). Ocean–continent subduction is modelled using a 2-dimensional thermal–mechanical finite
element code (SOPALE) that assumes vertical cross-section plane
strain (Fullsack, 1995). The Arbitrary Lagrangian Eulerian (ALE) methodology (Fullsack, 1995) calculates large-deformation flows with free
upper surfaces on an Eulerian finite-element grid that stretches
vertically to conform to the material domain. A Lagrangian grid and
passive tracking particles, advected with the model velocity field, are
used to update the mechanical and thermal property distributions on
the Eulerian grid.
Conservation equations for mass assuming incompressibility
(Eq. (1)), momentum assuming creeping (Stokes) flow (Eq. (2)),
and (heat) energy (Eq. (3)) are solved in the model domain.
∂νi
= 0 i = 1; 2
∂xi
∂σij′
∂xi
ρcp
−
∂P
+ ρg = 0 i; j = 1; 2
∂xj
∂T
∂T
∂ ∂T
+ A + ν2 αgTρ
=k
+ νi
∂t
∂xi
∂xi ∂xi
ð1Þ
ð2Þ
ð3Þ
where xi,j are spatial coordinates, νi are the components of velocity, σ ij′
is the deviatoric stress tensor, P is dynamic (mean stress) pressure, ρ
is density, g is the gravitational acceleration, cp is the specific heat, T is
the absolute temperature, t is time, k is thermal conductivity, A is
radioactive heat production per unit volume, and α is the volumetric
thermal expansion coefficient. The last term in the heat balance
equation is the temperature correction for adiabatic heating when
material moves vertically at velocity ν2.
The mechanical computation calculates the velocity field, strain
rate, deformation, and stress, subject to specified velocity boundary
conditions and internal buoyancy forces (associated with compositional and thermal density variations). The thermal computation
solves the heat balance equation on the Eulerian grid subject to
the mechanical velocity field in the model domain and the thermal
boundary conditions.
2.2. Model setup and mechanical and thermal boundary conditions
The 2000 km × 660 km model domain is represented by a 200 ×
115 Eulerian grid. Eulerian cell dimensions are 10 km × 2 km in the
upper 120 km and 10 km × 10 km below (Fig. 1). Oceanic lithosphere
is separated from continental lithosphere by an inclined weak seed
used to initiate subduction.
Mechanical boundary conditions are stress-free (upper), no-slip
(sides) and free-slip (base). A uniform velocity boundary is applied
to the oceanic lithosphere (VP, Fig. 1); the continental lithosphere
boundary is held stationary (VR, Fig. 1). Material fluxed into the model
domain by the specified convergence is balanced by a small uniform
leakage flux out of the sides of the model domain beneath the
lithosphere (VF, Fig. 1, after Currie et al., 2007). Material is not permitted to flow through the base of the model. The current models do
not include surface processes.
The initial steady-state two-dimensional temperature field is
calculated for a fixed surface temperature (273 K), insulated side
boundaries, and a fixed basal temperature (1833 K) (Fig. 1). Initial
oceanic and continental lithosphere geotherms are illustrated in Fig. 1
and corresponding thermal parameters are listed in Table 1. In the
sublithospheric mantle, convective heat transport is modelled conductively (52 W m− 1 K− 1) by scaling the conductivity by the Nusselt
number for marginally supercritical upper mantle convection (Pysklywec and Beaumont, 2004) using an adiabatic temperature gradient
of 0.4 K km− 1. The current models do not include shear heating
(Warren et al., 2008b) or viscous strain weakening.
D.F. Keppie et al. / Earth and Planetary Science Letters 287 (2009) 241–254
243
Fig. 1. Finite element numerical model setup showing mechanical and thermal boundary conditions. Ocean lithosphere reflects the thermal structure of a 70 Ma oceanic plate
(Parsons and Sclater, 1977; Ranalli, 1987; Stein and Stein, 1992). Continental lithosphere reflects the thermal structure of average 120 km thick non-cratonic continental lithosphere
(Vitorello and Pollack, 1980) including the combined effects of lithospheric thermal conductivity (W m− 1 K− 1) and crustal radioactive heat production (µW m− 3).
2.3. Model materials
invariant of deviatoric strain. Frictional strength is reduced from
′
ϕeff = 15° to ϕeff = 2°–6° through the strain range 0:5 < ðI2 Þ < 1:5
for all model materials except the weak seed and ocean sediment
(Table 1).
Viscous flow deformation is specified by thermally-activated
power law creep (Eq. (6)).
1
2
Both frictional-plastic and viscous flow rheologies are specified for
each model material. Frictional-plastic failure deformation (loosely
termed brittle) is specified by a pressure-dependent Drucker–Prager
yield criterion (Eq. (4)).
′ 12
ð4Þ
J2 = P sinϕeff + C; with
v
P sin ϕeff = ðP−Pf Þ sin ϕ
ð5Þ
where J 2′ is the second invariant of deviatoric stress, ϕeff is an effective
internal angle of friction, C is the cohesion, P is the dynamic (mean
stress) pressure, Pf is the pore fluid pressure, and ϕ is the internal
angle of friction. Frictional-plastic strain softening is implemented
through a linear decrease in ϕeff with ðI2′ Þ , where I 2′ is the second
1
2
⁎
ðð1−nÞ = 2nÞ
ηeff = f ðB ÞI˙2′
Q + PV ⁎
nRT
ð6Þ
e
where ηveff is an effective viscosity, f is a linear scaling factor, B⁎ is the
pre-exponential factor converted from uniaxial experiments to plane
strain, İ2′ is the second invariant of deviatoric strain rate, n is the stress
exponent, Q is the activation energy, V ⁎ is the activation volume and
R is the universal gas constant (Table 1).
Table 1
Finite element numerical model parameters.
A. Parameters varied in the model experiments
Parameter
Description
Units
Value
ZS
ϕS
θP
VP
Sediment thickness
Strain-softened ϕeff
Subduction angle
Convergence rate
km
deg
deg
km Ma− 1
0, 4
2, 3, 4, 5, 6
10, 15, 20, 25, 30
25, 50, 75, 100, 125, 150
B. Mechanical and thermal material properties
Parameter
Units
Ocean sediment
Ocean crust
Continent crust
(upper)
Continent crust
(lower)
Mantle lithosphere
Sub-lithospheric
mantle
Thickness
km
Zs
8
24
12
To 660 km
2800
473
2900
–
8−1
0
Wet quartzite
1
4
2.92 × 106
223
0
750
2.25
1.0 × 10− 6
3.0 × 10− 5
1.15
2900
273
3300
–
15 − ϕS
0
Dry diabase
0.1
4.7
1.91 × 105
485
0
750
2.25
1.0 × 10− 6
3.0 × 10− 5
0
2800
473
2850
2900
15 − ϕS
2
Wet quartzite
5
4
2.92 × 106
223
0
750
2.25
1.0 × 10− 6
3.0 × 10− 5
1.15
2950
773
3100
–
15 − ϕS
0
Dry diabase
0.1
4.7
1.91 × 105
485
0
750
2.25
1.0 × 10− 6
3.0 × 10− 5
0.55
82 (ocean)
84 (cont.)
3250
1609
–
–
15 − ϕS
0
Wet olivine
10
3
1.92 × 104
430
1.0 × 10− 5
1250
2.25
0.6 × 10− 6
3.0 × 10− 5
0
Ref density
Ref density T
HP density
UHP density
ϕeff − ϕS
Cohesion
Flow lawa
f
n
B⁎
Q
V⁎
Heat capacity
Thermal conductivity
Thermal diffusivity
Thermal expansion
Heat production
a
−3
kg m
K
kg m− 3
kg m− 3
deg
MPa
1
Pa sN
kJ mol− 1
m3 mol− 1
J kg− 1 K− 1
W m− 1 K− 1
m2 s− 1
K− 1
μW m− 3
Flow law references in text.
3250
1609
–
–
15 − ϕS
0
Wet olivine
1
3
1.92 × 104
430
1.0 × 10− 5
1250
52
1.4 × 10− 5
3.0 × 10− 5
0
244
D.F. Keppie et al. / Earth and Planetary Science Letters 287 (2009) 241–254
The overall nonlinear solution for each timestep is solved using ηveff
(Eq. (6), viscous flow) when the local flow stress is less than the
Drucker–Prager yield stress and ηPeff (Eq. (7), frictional-plastic flow)
when the Drucker–Prager yield stress is exceeded. Setting
1
P
ηeff =
J2′ 2
ð7Þ
1
2
2ðI˙2 Þ
′
1
in regions that are on frictional-plastic yield (stress equals J2′ 2) and
deforming at ðI˙2′ Þ allows the velocity field to be determined from the
finite element solution for viscous creeping flows (Fullsack, 1995;
Willett, 1999).
Rheological parameters for viscous deformation in Eq. (6) (B⁎, n,
Q , V ⁎) are based on experimental results for wet quartz (Gleason and
Tullis, 1995), dry Maryland diabase (Mackwell et al., 1998), and wet
olivine (Karato and Wu, 1993). Viscous flow laws for rocks that are
stronger or weaker than the base set are constructed by linearly
scaling the values of ηveff by f (Eq. (6)) (Beaumont et al., 2006). The use
of a small set of reference materials permits some variation in flow
properties but simplifies the interpretation of model results. This
approach acknowledges inherent uncertainties in extrapolating
laboratory results to natural settings (Patterson, 2001) but does not
imply that corresponding Earth materials have the same composition
as materials whose flow laws were used.
Representative densities are specified for model materials at
reference temperatures close to their average initial temperatures;
densities are adjusted for thermal expansion during model evolution
(Table 1). Sediment parameters follow Currie et al. (2007). Density
changes for model materials are specified for eclogite (HP) and ultrahigh pressure (UHP) facies metamorphism (Table 1, following Warren
et al. (2008b)). Phase-change densities are estimated by considering
upper continental crust to contain 10% mafic and 90% felsic by volume
(Walsh and Hacker, 2004); density changes correspond to 100%
metamorphic transformation of the mafic component and 20% of the
felsic component based on observations from natural UHP terranes
(Krabbendam et al., 2000). Density changes are reversible.
For density changes accompanying phase changes, the incompressibility equation (Eq. (1)) is modified for mass conservation. The
associated volume change is calculated numerically by applying an
δρ
additional isotropic stress (pressure), δP =
where βv is the
1
2
δρ
βv ⁎ρ
viscous bulk modulus and is the fractional density change, to finite
ρ
elements only at the moment of phase-related density change. This
mitigates the long-term effect of over/under estimation of buoyancy
forces due to fractional error in material volumes (Warren et al.,
2008a).
2.4. Model evolution and parameter variation
Prior to assessing model evolution for subduction processes, two
stages prepare the models (Currie et al., 2007; Warren et al., 2008a,b).
A first stage allows oceanic and continental domains to adjust
isostatically. A second stage applies 500 km convergence at 25 km
Ma− 1 to initiate subduction. Model times referred to below include
the second preparation stage. The third stage investigates variations
in shear traction on the plate boundary subduction shear zone by
varying the effective angle of internal friction, the initial angle of the
weak seed used to initiate subduction, the presence of sediment on
the oceanic crust and the convergence velocity.
In the models, shear traction in the brittle regime is primarily
controlled by the effective angle of internal friction (ϕeff, Eq. (4)).
Frictional-plastic strain-softening in nature is poorly constrained, but
geological processes, including changes in mineralogical composition,
foliation development and/or the impact of fluid-assisted processes,
may contribute to a reduction in frictional strength in strongly
deformed regions (Bos and Spiers, 2002; Huismans and Beaumont,
2003, 2007; Selzer et al., 2007; ). We implement frictional strainsoftening by varying the strain-softened effective internal angle of
friction, ϕS, over a range of values (2° to 6°, Table 1) consistent with
similar studies (Huismans and Beaumont, 2003; Ellis et al., 2004;
Huismans and Beaumont, 2007).
Variations in the angle of subduction may play a role in determining the onset of subduction erosion processes (Pilger, 1981; Pope,
1998; Gutscher, 2002; Kay et al., 2005; Clift and Hartley, 2007). If
subduction erosion does not occur, the evolution of slab dip at crustal
depths does not vary much through model time. Varying the angle of
the weak seed used to initiate subduction (from 10° to 30°, Table 1) is
therefore a useful proxy for subduction angle at shallow (i.e., crustal)
depths until subduction erosion processes modify the subduction
zone.
Subduction erosion appears in nature to be limited to those
margins where trench sediments are less than 1 km thick (e.g. Clift
and Vannucchi, 2004; Kukowski and Oncken, 2006). We have run a
set of numerical models both with and without a 4 km (2-element
thick) layer of weak oceanic sediment to test the potential effect of
trench sediment on subduction erosion processes. This thickness
represents the upper limit of sediment supplied to natural subduction
zones (e.g. Mishra et al., 2004; Currie et al., 2007).
Erosive margins appear to be limited to those at which convergence
is faster than 60 km Ma− 1 (Clift and Vannucchi, 2004; Kukowski and
Oncken, 2006). We test a possible dependence on convergence rate by
varying orthogonal convergence rates over a range of values consistent
with Cenozoic subduction of the Farallon plate and its descendents
beneath the Americas (25 km Ma− 1 to 150 km Ma− 1 Table 1) (Müller
et al., 2008).
3. Results
3.1. Tectonic modes
Four tectonic modes are observed in the numerical models (Fig. 2).
Models where the plate boundary subduction shear zone is weak (i.e.,
low maximum shear traction) show no subduction erosion. In these
models, the subduction zone remains stable throughout model
evolution, i.e., no forearc is removed, the trench doesn't migrate and
no change in subduction angle is evident. In models where the plate
boundary subduction shear zone is strong (i.e., high maximum shear
traction), plate convergence is accommodated through repeated
failure of the oceanic plate in a manner inconsistent with modern
plate tectonics. Numerical models where the strength of the plate
boundary subduction shear zone is intermediate show two distinct
modes of subduction erosion.
(1) The term edge-weakening subduction erosion (EWSE) is
introduced in this paper to describe the steady and gradual
removal of upper plate (continental) material from the edge of
the upper plate; both lower (Fig. 3A) and upper (Fig. 3B) crustal
material is removed. Initially, the ductile lower continental
lithosphere of the upper plate is carved away by the subducting
plate (Fig. 3A), possibly due to viscous drag (Tao and O'Connell,
1992). This results in a shallowing of the subduction angle at
depth. Subsequently, the brittle upper continental lithosphere of
the upper plate at the continent edge adjacent to the plate
boundary may deform and strain-soften and will ultimately
fail when the frictional-plastic yield stress is achieved. It is then
entrained with the lower plate and subducted (Fig. 3B).
Subducted continental material may transiently underplate
the continental lithosphere before being subducted into the
deep mantle (Fig. 3C). Trench migration rates are generally
<4 km Ma− 1 (Fig. 2A and C). Rates >4 km Ma− 1 are observed
only for very shallow and relatively fast subduction zones
(Fig. 2C). Over time, the subduction angle generally shallows.
D.F. Keppie et al. / Earth and Planetary Science Letters 287 (2009) 241–254
245
Fig. 2. Numerical model results showing tectonic styles for variations in (A-series) strain-softened internal angle of friction and subduction seed angle (no sediment), (B-series)
strain-softened internal angle of friction and subduction seed angle (4 km sediment), and (C-series) orthogonal convergence rate and subduction seed angle (no sediment). Example
numerical models from A-series discussed in the text are MA1(ϕS = 4°, θP = 30°) for edge-weakening subduction erosion and MA2(ϕS = 3°, θP = 15°) for internal-weakening
subduction erosion.
(2) The term internal-weakening subduction erosion (IWSE) is
introduced in this paper to describe when the upper (continental) plate weakens within the orogenic zone (Fig. 4A) and
eventually fails (Fig. 4B). During failure, the plate boundary
relocates from the ocean–continent interface to the shear zone
formed in the continental interior. Rapid, unsteady removal of
continental forearc happens as the forearc between the old and
new subduction zones is entrained with the lower plate and
subducted (Fig. 4C). The trench (or ocean–continent interface)
migrates towards the upper plate at the orthogonal convergence rate. Some of the subducted forearc underplates the
upper plate at depth (Fig. 4D). For models converging slowly
with shallow angles of subduction, some of the underplated
forearc subsequently exhumes up the subduction channel. The
subduction angle of the new subduction zone is generally
steeper (ca. 30° to 40°) than the abandoned subduction zone
(ca. 10° to 30°).
The internal-weakening subduction erosion mechanism observed
in our numerical models occurs when moderate strength on the active
subduction shear zone promotes bending (and thickening) in the
orogenic zone of the upper plate (Fig. 5A). Bending (and thickening)
deformation triggers brittle strain-softening which progressively
weakens this region (Fig. 5A). Given sufficient weakening, failure
initiates on several, variously oriented, shear zones (Fig. 5B) which
then connect and form a new subduction zone across the weakened
continental interior (Fig. 5C). Continental forearc trapped between
the old and new subduction zones is entrained with the lower plate
and subducted (Fig. 5D).
3.2. Effect of parameter variation on tectonic modes
Fig. 2A shows the distribution of tectonic modes for variations
in the strain-softened frictional angle and subduction angle for a
convergence rate of 25 km Ma− 1 and no oceanic plate sediment. As
the strain-softened internal angle of friction (ϕS) is increased, the
strength or maximum shear traction on the plate boundary
subduction shear zone increases. The tectonic mode shown by the
models changes from stable subduction through edge-weakening
subduction erosion to internal-weakening subduction erosion. At
large ϕS, the plate boundary subduction shear zone is so strong that
convergence is accommodated through failure of the oceanic plate.
This behaviour is also dependent on subduction angle (θP). For larger
θP, boundaries between the modes are shifted to larger ϕS. For cases in
which internal-weakening subduction erosion occurs, the distance
between the old and new subduction shear zones changes with the
subduction angle such that the width of the removed forearc
block decreases from ~ 300 km-wide for θP = 10° to ~50 km-wide for
θP = 30°.
The above experiments were repeated for a model with a 4 km
layer of sediment on top of the oceanic plate (Fig. 2B). The addition of
rheologically weak sediment inhibits subduction erosion, and field
boundaries for internal-weakening subduction erosion shift towards
increased friction and shallowed subduction. Edge-weakening
246
D.F. Keppie et al. / Earth and Planetary Science Letters 287 (2009) 241–254
Fig. 3. An example of edge-weakening subduction erosion. Key observations include: (1) the initial entrainment and subduction of the lower continental crust followed by the
entrainment and subduction of the upper continental crust, and (2) the decrease in subduction angle at crustal depths over time. See discussion in text.
subduction erosion is not observed in any of the models with
sediment. Our numerical models examined only one possible
sediment model; future work will address variations in sediment
thickness and sediment rheology.
Fig. 2C shows the results for variations in orthogonal convergence
rate and subduction angle for a strain-softened friction angle of 2° and
no sediment. At lower subduction angles, internal-weakening
subduction erosion is the stable tectonic mode. At higher subduction
angles, no subduction erosion is seen at low convergence rates, and
edge-weakening subduction erosion is seen at higher convergence
rates.
3.3. Trench migration and forearc subsidence for subduction erosion
modes
The migration of the trench towards the continent and the subsidence of the forearc may be tracked during model evolution, to allow
comparison with data from natural subduction zones. For tracking
purposes, we define the position of the model trench as the left-most
surficial Eulerian cell containing continental material. Fig. 6 shows
plots of the position of this Eulerian cell over time for models showing
edge-weakening subduction erosion (Fig. 6A) and internal-weakening
subduction erosion (Fig. 6B). The horizontal (migration) and vertical
(subsidence) components of trench/forearc motion are shown in the
left and right plots, respectively.
For edge-weakening subduction erosion, the trench migrates
steadily towards the continent at rates typically <4 km Ma− 1, and
subsides during the subduction erosion process (Fig. 6A). The trench
migration rate due to edge-weakening subduction erosion scales with
the orthogonal convergence rate for a set of models with the same
initial subduction angle (Fig. 2C). The scaling relationship is greatest
for the set of models with the smallest initial subduction angle (10°)
where trench migration rates are observed to be roughly 10% of the
orthogonal convergence rate (Fig. 2C).
For internal-weakening subduction erosion, subduction erosion
occurs during a 2 to 10 Ma event. During this event, the trench
migrates towards the upper plate at the orthogonal convergence rate
and subsides at the end of the subduction erosion process (Fig. 6B).
Fig. 6B (left plot) also shows trench migration back towards the
oceanic plate during exhumation/unroofing of previously subducted
material.
3.4. Fate of tectonically eroded continental crust for subduction erosion
modes
Subducted crustal material is tracked in the models as it is transported into the mantle. During edge-weakening subduction erosion,
most of the crustal material is transported into the deeper mantle
(Fig. 3). In contrast, following internal-weakening subduction erosion,
a significant proportion of tectonically eroded material underplates
D.F. Keppie et al. / Earth and Planetary Science Letters 287 (2009) 241–254
247
Fig. 4. An example of internal-weakening subduction erosion. Key observations include: (1) the formation of a new subduction shear zone across the deformed and softened
continental interior, (2) the entrainment and subduction of a wide forearc block in a single event, and (3) the net effect of subduction angle steepening at crustal depths. See
discussion in text. Legend as in Fig. 3.
the upper-plate lithosphere (Fig. 4). In some of the models, most
notably those which have shallow subduction and converge at slow
rates, subducted crustal material may subsequently be exhumed up
the subduction channel (Fig. 6B).
4. Discussion
4.1. The relative strength of subduction shear zones
The numerical models show that plate convergence is accommodated by lithosphere-scale shear zones which operate at the weakest
section of lithosphere at any time, i.e., subduction at the ocean–
continent interface (plate boundary zone), failure in the continental
crust (leading to subduction erosion) or oceanic plate failure. These
variations may be explained by theoretical calculations of the strength
of potential shear zones across each section of model lithosphere.
Fig. 7A shows Brace–Goetze strength envelopes for the continental
and oceanic plates and the plate boundary zone assuming a strain
rate of 1 Ma− 1 (3.17 10− 14 s− 1); details of the calculations are in
Appendix A. These theoretical profiles are in good agreement with
strength profiles extracted from the numerical models (Fig. 7B).
Integration of each strength profile over the surface area of the shear
zone provides a measure of the total strength of the lithosphere.
The behaviour of the subduction system is governed by the relative
strengths of the plate boundary zone, oceanic and continental lithospheres. In the models, a weak plate boundary arises with a low
effective internal angle of friction of 2° (Fig. 7A). Plate convergence is
accommodated through localized deformation along the narrow shear
zone. This is the stable subduction mode.
The strength of the plate boundary zone will increase with either a
larger strain-softened effective angle of internal friction (Fig. 7C) or a
decrease in subduction zone angle, which increases the length of the
shear zone and increases the effective frictional strength of the shear
zone materials (Fig. 7D). At low subduction angles and high internal
friction angles, the oceanic plate is the weakest lithosphere section in
the system and geologically-unreasonable oceanic plate failure occurs
(Fig. 7A).
Between these two modes, the plate boundary has moderate
strength, and subduction erosion is observed. Edge-weakening subduction erosion occurs for a plate boundary zone that is slightly
stronger than the stable subduction case (e.g., higher internal angle of
friction). Enhanced shear traction from the plate margin induces
viscous drag and brittle failure and entrainment of the adjacent
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D.F. Keppie et al. / Earth and Planetary Science Letters 287 (2009) 241–254
Fig. 5. Evolution of cumulative strain in the internal-weakening subduction erosion mechanism. Bending in the continental interior causes sufficient strain to trigger strain-softening.
The strain-softened region in the continental interior ultimately fails as a new subduction shear zone. See discussion in text. Velocity arrows as in Fig. 3.
continental crust. The rate at which continental material is removed
through edge-weakening depends on the magnitude of shear traction,
which is related to the subduction angle and the orthogonal
convergence rate (Fig. 7A).
An even stronger plate boundary zone exhibits internal-weakening
subduction erosion, as increased shear traction promotes bending and
thickening in the interior region of the continental plate in a broad
region from 50 to 500 km inboard of the plate margin depending on
the geometry of the subduction zone (e.g., Fig. 5A). This region
undergoes frictional-plastic strain-softening, which reduces its
strength (Fig. 7C). Once this section of lithosphere is weaker than
the plate boundary zone, it begins to fail (Figs. 7B and 5C). The locus of
subduction shifts landward a distance of 50 to 300 km depending on
model geometry when continued failure in the orogenic zone forms a
new subduction zone (Fig. 5C). Continental forearc trapped between
the old and new subduction zones is entrained with the lower plate
and subducted (Fig. 5D). Strain softening is one mechanism by which
the continental interior may be weakened. Natural weakening
mechanisms could also include thermal weakening due to arc
magmatism and activation of pre-existing weak planes.
Subduction of rheologically weak sediments will modify the
behaviour of the plate boundary (Fig. 2B). At steep subduction angles,
sediments act to localize deformation within the plate boundary zone
and inhibit subduction erosion. This behaviour is consistent with
observations that significant subduction erosion does not occur where
trench sediments are greater than 1 km thick (Clift and Vannucchi,
2004). At shallower subduction angles, shear traction along the
interface increases, and internal-weakening subduction erosion may
occur for conditions that allow stress to be transmitted into the plate
interior (e.g., higher internal angle of friction). At large values of
internal friction, the continent becomes too strong to deform, leading
to oceanic plate failure.
4.2. Comparing the numerical modelling results with natural subduction
zones
4.2.1. Trench migration rates
In nature, trench migration is inferred from changes in volcanic arc
position (e.g. Moran-Zenteno et al., 1996; Kay et al., 2005) and from
estimates of forearc removal from forearc subsidence records and
other proxies (e.g. Clift and Vannucchi, 2004; Clift and Hartley, 2007).
Rates of trench migration towards the upper plate estimated for
natural examples fall into two categories:
1. slow, ca. 0–3 km Ma− 1 (ranging up to 10 km Ma− 1 when topographic asperities on the lower plate appear to enhance forearc
removal), for which several subduction erosion mechanisms have
been proposed including ductile ablation (e.g. Tao and O'Connell,
D.F. Keppie et al. / Earth and Planetary Science Letters 287 (2009) 241–254
249
Fig. 6. Representative behaviour for the change in trench/forearc position and elevation through time in numerical models of subduction erosion. (A) An example of edge-weakening
subduction erosion (EWSE, Model MA1, Fig. 3). (B) An example of internal-weakening subduction erosion (IWSE, Model MA2, Fig. 4).
1992), topographic abrasion (e.g. Clift and Vannucchi, 2004) and
hydro-fracturing due to fluid over-pressures (e.g. von Huene et al.,
2004), and
2. fast, ca. 10–100+ km Ma− 1, for which subduction erosion
processes have been invoked (Moran-Zenteno et al., 1996; Kay
et al., 2005; Moran-Zenteno et al., 2007) but mechanisms were not
discussed.
We suggest that the edge-weakening and internal-weakening
subduction erosion mechanisms may provide explanations for the
slow and fast mode of natural subduction erosion respectively.
Rates of trench migration due to edge-weakening subduction
erosion in the numerical models are generally slow, ca. 0–4 km Ma− 1,
for most of the tested parameters. Critically, this erosion mechanism
does not require the presence of topographic asperities on the lower
plate. Model trench migration rates in excess of 10 km Ma− 1 are
observed for crustal subduction angles <15° and convergence rates
>100 km Ma− 1 (Fig. 2C). There is currently not enough data in the
literature for natural examples to test whether this prediction is also
the case in nature. The current numerical models are not designed to
address the details of magmatic processes at the volcanic arc, but it is
expected that edge-weakening subduction erosion should be accompanied by landward migration of the volcanic arc at approximately
the trench migration rate.
In the models, internal-weakening subduction erosion occurs
during a short (2 to 10 Ma) event during which a large (50 to 300 km
wide) forearc block is subducted. During this period, model trench
migration rates are generally equivalent to the imposed model
convergence rate (i.e., 25–150 km Ma− 1).
4.2.2. Forearc subsidence records
Our numerical models show that for margins experiencing edgeweakening subduction erosion, subsidence takes place during the
process (Fig. 6A). This result matches the correlation between forearc
subsidence and inferred slow subduction erosion inferred along the
Middle American and Andean subduction zones (e.g. Vannucchi et al.,
2003; Clift and Vannucchi, 2004; Clift and Hartley, 2007).
In models that experience an internal-weakening subduction
erosion event, subsidence occurs suddenly at the end of the process
(Fig. 6B). This result is similar to the record in southern Mexico where
250 m of forearc subsidence has been suggested to have taken place
between 23 Ma and 19.5 Ma (Clift and Vannucchi, 2004). The subsidence in southern Mexico took place just after the inferred removal of
a ca. 250 km wide forearc block (Moran-Zenteno et al., 1996; Keppie
and Morán-Zenteno, 2005). Constraints on the size and timing of
forearc removal in southern Mexico come from the concurrent hiatus
and migration of the volcanic arc from the coast to the Mexican interior
at the end of the Oligocene (Keppie and Morán-Zenteno, 2005; MoranZenteno et al., 2007; Gomez-Tuena et al., 2008).
4.2.3. Where does tectonically eroded crust end up?
The fate of subducted continental crust has important implications
for crustal recycling processes at convergent margins. The models
suggest that subducted material may be transported into the deep
mantle, may underplate the continental lithosphere or may be
subsequently exhumed up the subduction channel.
Crustal material returned to the deep mantle will affect the Earth's
chemical fractionation through time (e.g. Clift and Vannucchi, 2004;
Hawkesworth and Kemp, 2006). Underplated material may be
returned to the surface through arc magmatism and will affect the
chemistry of the magma source region (e.g. Kay et al., 2005; Currie
et al., 2007). Although most exhumed UHP material is thought to be
sourced from the subducting plate (Warren et al., 2008a), the results
of this and other studies suggest that exhumed material may also be
sourced from subducted upper plate continental crust (Gerya et al.,
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D.F. Keppie et al. / Earth and Planetary Science Letters 287 (2009) 241–254
Fig. 7. A: Calculated profiles for non-softened ocean, non-softened continent and a softened subduction zone dipping at 15°. These profiles represent reference estimates for the
corresponding sections of lithosphere in the numerical models initiated with a 15°-dipping subduction zone
just prior to varying parameters in order to study their effect on
′
1
subduction zone evolution(i.e., at the end of setup stage). The calculations assume a constant strain rate of ð˙I2 Þ2 = 3:17 × 10−14 s−1 (see Appendix A for details). B: Strength profiles
for different sections of lithosphere obtained in Model MA2 (θ = 15°, ϕeff = 3°, Fig. 2A). Profiles shown are for non-softened ocean, non-softened continent, softened subduction zone,
and softened continent obtained from vertical, vertical, 15° inclined, and the weakest non-linear trajectory through the softened orogenic zone starting at the surface of the model at
300 km, 1700 km, 600 km and 800 km model distance for 22 Ma, 22 Ma, 22 Ma, and 30 Ma model time, respectively. C: Changes in subduction zone strength and continental
lithosphere strength as a function of the effective angle of internal friction given a constant angle of shearing with respect to the horizontal (37.5° for the continental lithosphere and
15° for the subduction zone, See Appendix A for details). D: Changes in subduction zone strength as a function of upper slab subduction angle given the effective angle of internal
friction used in the setup stage (2°).
2002; Gerya and Stockhert, 2006). Further study will assess the
relative importance of subduction erosion mode to other factors, such
as material density, in determining the fate of subducted material.
Where the subduction and possible underplating of large forearc
blocks have been inferred in nature, arc magmatism is observed to
experience a hiatus of several million years before resuming in a
position farther into the continental interior (Kay et al., 2005; MoranZenteno et al., 2007). Geochemical signatures from the earliest
magmas produced after the hiatus show spikes in trace element
signatures (Kay et al., 2005) as well as adakitic signatures (GomezTuena et al., 2008). One explanation of the geochemical signatures
could be large amounts of crustal material supplied to the magma
source region after subducted forearc blocks underplate the upper
plate (Kay et al., 2005).
4.3. Subduction erosion cyclicity
The two subduction erosion modes represent end-members in a
kinematic continuum (Fig. 8A). Sizes of continental forearc blocks
removed from the upper plate range from less than the model resolution
(i.e., 10 × 2 km2) up to roughly 300 × 15 km2 in cross-section. Rates of
trench migration range from <1 km Ma− 1 up to the model convergence
rate (25 to 150 km Ma− 1). Removal of small forearc blocks and slow
trench migration is characteristic of edge-weakening subduction
erosion, whereas removal of a large forearc block and rapid trench
migration is characteristic of internal-weakening subduction erosion.
In the Andean forearc, several studies suggest that periods of
steady (slower) subduction erosion have been interrupted by periods
of non-steady (faster) subduction erosion (Kay et al., 2005; Clift and
Hartley, 2007). Variations in subduction angle have also been
observed along the Andes. Subduction geometry has been linked to
plate velocity (e.g. Lallemand et al., 2005), distance from a symmetry
plane inferred for the Central Andes (Gephart, 1994), resistance to
bending in the middle of large oceanic plates, (Schellart et al., 2007;
Schellart, 2008) and topographic asperities on the subducting slab
(Gutscher, 2002). These explanations, however, do not always hold
for the whole Andean subduction system (Fig. 9).
We propose a conceptual model linking the two numerical model
modes and use this conceptual model to propose an explanation for the
observed cyclicity in subduction erosion and variation in subduction
D.F. Keppie et al. / Earth and Planetary Science Letters 287 (2009) 241–254
251
Fig. 8. A: Edge-weakening and internal-weakening subduction erosion are end-members in a possible kinematic continuum of subduction erosion modes. B: A conceptual model of
subduction erosion cyclicity predicts alternation between edge-weakening and internal-weakening subduction erosion modes. See discussion in text.
angle in the Andes (Fig. 8B). This model is based on the observation that
edge-weakening subduction erosion is the preferred mode for steeper
subduction angles but acts to shallow the subduction system, whereas
internal-weakening subduction erosion is favoured for shallow subduction angles but acts to steepen the subduction system.
The cyclical model starts with a subduction system showing little to
no subduction erosion. Over time, external boundary forces such as
plate velocity (Lallemand et al., 2005) or resistance to plate bending
(Schellart et al., 2007; Schellart, 2008) may cause the subduction angle
to shallow. Edge-weakening subduction erosion is initiated, resulting
in tectonic erosion of the side and basal edges of the upper plate and a
decrease in subduction angle. The combination of shallowing and
cooling by the subducting plate acts to increase the strength of the
plate boundary shear zone. Once the strength of the active subduction
shear zone exceeds the strength of the continental interior, internalweakening subduction erosion is triggered. A large block of forearc
material is subducted and the plate margin relocates inboard to a new
subduction zone which initiates at moderate angles of 35° to 45°. The
external forcing of the shallow subduction angles governs ongoing
evolution, re-engaging edge-weakening subduction erosion and the
sequence repeats. The numerical models themselves show partial
cyclicity, from edge-weakening to internal-weakening back to edgeweakening subduction erosion, in the absence of an external control
renewing shallow subduction angles.
The proposed cycle may explain, in part, the present-day alongstrike variation of near-surface subduction angle observed in the
Andean margin (~15° to ~ 40°, Fig. 9). At a given time, different
segments of the margin could be at different stages in the proposed
cycle. Segments of the system may progress through the cycle at
different rates depending where factors such as supply of sediment to
the trench and pulses of arc magmatism vary along strike (e.g. Ernst,
2004; Kukowski and Oncken, 2006).
Cascadia (Calvert et al., 2003), a forearc block subducted beneath the
Luzon arc (e.g. Chemenda et al., 1997; Malavieille and Trullenque,
2009), and the forearc removed from southern Mexico during the late
Oligocene/early Miocene (Moran-Zenteno et al., 1996, 2007). Further
evidence comes from the rapid step-wise shift of arc magmatism into
the continental interior as inferred in the Andes and in southern
Mexico (Kay et al., 2005; Moran-Zenteno et al., 2007). Proposed
explanations for the observations include the removal of the forearc by
strike-slip tectonics in the southern Mexico example (e.g. Pindell et al.,
1988; Silva-Romo, 2008) and slab shallowing causing arc migration in
the Andean example (e.g. Clift and Hartley, 2007). Subduction erosion
is an alternative possibility that should be explored.
In the numerical models, internal-weakening subduction erosion
occurs above relatively strong shallowly-dipping subduction zones
(Fig. 2). Early stages of the process include thrust-sense shearing in
the weakened continental interior on several disconnected and
variously oriented shear zones (Fig. 4).
The global CMT earthquake catalogue (Global-CMT-Catalog, 2008),
filtered for thrust-sense earthquake focal mechanisms (i.e., rake > 45°)
along the Andean margin, suggests that thrust-sense earthquakes in
the continental interior are apparently restricted to the segments of
relatively shallow subduction (i.e., from 0°–14° S and from 27°–32° S,
Fig. 9). It is important to note that earthquake focal mechanisms do not
discriminate between subduction-synthetic and subduction-antithetic thrusts. These earthquakes may be explained by thin-skinned foldand-thrust belts (e.g. Kley et al., 1999) or subduction-antithetic thrusts
where the South American craton is underthrusting the Andes.
However, they may also indicate that internal-weakening subduction
erosion is incipient above the Andean shallow subduction zone
segments, where the shallow subduction angle results in a strong
plate boundary where stress can be transmitted inboard to the weaker
orogenic zone.
4.4. Does internal-weakening subduction erosion occur in nature?
5. Conclusions
The evidence for the entrainment and subduction of large forearc
blocks at ocean–continent subduction zones is only sparsely preserved in the geological record, and thus has not yet been fully
recognized in subduction margin evolution. Candidate examples
include a forearc block interpreted in seismic images beneath
Finite-element numerical models of ocean–continent subduction
have been used to investigate the roles of crustal frictional strength,
subduction angle, and convergence rate in subduction erosion processes. The models exhibit two distinct modes of subduction erosion,
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D.F. Keppie et al. / Earth and Planetary Science Letters 287 (2009) 241–254
Fig. 9. The Nazca Plate and the South American Andes and the Cocos Plate and the Mexican Sierra Madres are shown in (A) plan view, and (B) for several vertical sections constructed
orthogonal to the subduction zones. The Global GMT earthquake catalogue filtered for thrust-sense earthquakes (i.e., rake > 45°) (Global-CMT-Catalog, 2008), slab-top contours (in
km, Syracuse and Abers, 2006)), and topography (Farr et al., 2007) are plotted. Regions of shallow thrust-sense earthquakes in the continental interior occur above shallow
subduction angle segments.
neither of which require topographic asperities on the subducting
plate.
1. Steady, with slow trench migration rates (<0–4 km Ma− 1) and a
decrease in subduction angle, in which most tectonically eroded
material moves in small blocks that are principally transported
into the deep mantle. During this process, the forearc undergoes
progressive subsidence and the volcanic arc may migrate inland at
the trench migration rate.
2. Unsteady, with fast trench migration rates (⋙15 km Ma− 1) and
an increase in subduction angle to moderate values (ca. 35°–45°),
in which a large (50 to 300 km wide) block of continental forearc is
removed in a single tectonic event. The remaining forearc may
record evidence of thrust deformation at the beginning of this
process and sudden subsidence timed with the end of this process.
After the unsteady removal of a large forearc block, the volcanic arc
may relocate inland into the upper plate a distance approximately
equal to the width of the removed forearc block. The volcanic arc
may appear to jump to its inland position since migration may
coincide with a hiatus in the production of arc volcanics. The first
arc volcanics produced in the new location may also show
geochemical signatures consistent with forearc material in the
arc magma source region.
The occurrence of subduction erosion is governed by the relative
strength of the plate boundary zone and the interior of the upper
(continental) plate. If the plate boundary is weak due to low frictional
strength or the presence of rheologically weak sediments, subduction
erosion does not occur. A moderate increase in plate boundary
strength (e.g., increased frictional strength, decreased subduction
angle or increased convergence rate) will increase shear traction on
the continental plate, initiating subduction erosion. The steady mode,
termed edge-weakening subduction erosion, is characterized by the
entrainment of small blocks of continental material adjacent to the
plate boundary. The non-steady mode, termed internal-weakening
subduction erosion, occurs at stronger plate boundary zones where
plate convergence induces failure within the interior continental
orogenic zone. Subduction erosion behaviour in the numerical models
is compatible with geological evidence from the Mexican and Andean
subduction zones.
D.F. Keppie et al. / Earth and Planetary Science Letters 287 (2009) 241–254
A cyclical model has been proposed in which the two subduction
erosion modes alternate. If regional tectonics favour shallowlydipping subduction zones, then repeated internal-weakening subduction erosion events, which temporarily increase the subduction angle,
may occur in response to edge-weakening subduction erosion, which
acts to continually shallow and strengthen the active subduction zone.
This cycle may provide an explanation for the observed alternation
between steady and non-steady subduction erosion as well as alongstrike variation in subduction angle at natural subduction zones such
as along the Andean margin.
Acknowledgements
DFK acknowledges support from a Canada Graduate Scholarship
from the Natural Sciences and Engineering Research Council of Canada.
Chris Beaumont of the Geodynamics Research Group at Dalhousie
University is thanked for his generosity, guidance and support, without
which this work would not have been possible. Douglas Guptill
(Geodynamics Research Group, Dalhousie University) is acknowledged
for technical support. Two anonymous reviewers are acknowledged for
their constructive feedback.
Appendix A. Strength profile calculations
Strength profiles plotting differential stress with depth (e.g. Ranalli,
1987) are produced to illustrate the strength of different sections of
lithosphere in the numerical models for the case of failure on thrustsense shear zones (Fig. 7). In Fig. 7B, values for the differential stress
are extracted directly from the numerical models. In Fig. 7A, B, and D,
we calculate values for the differential stress using a theoretical
calculation and some simplifying assumptions. Details of this approach
are as follows.
For principal stress axes, we assume σ1 is horizontal and σ2 is
vertical and equal to the lithostatic pressure. This represents simple
stress conditions compatible with thrust-sense shearing (Anderson,
1951; Sibson, 1974). For strain rate, we assume a constant value of
1 Ma− 1 (i.e., 3.17 ⁎ 10− 14 s− 1). This represents a geologically reasonable strain rate for the purposes of illustration (Ranalli, 1987),
although it is understood that strain rate is variable in the numerical
models and nature. For differential stresses, at each depth, we calculate
the differential stress that would be sustained on a thrust-sense shear
zone inclined at a constant angle with respect to the horizontal. For
each material, differential stress for frictional-plastic (Eq. (4)) and
viscous (Eq. (6)) rheological equations of state are calculated and the
minimum value of the two is used (Ranalli, 1987).
Brittle anisotropy occurs in the numerical models because the
subduction zone is initiated at a given angle with weak material and
model materials strain-soften in dynamically produced shear zones.
The finite element method handles brittle anisotropy directly. In the
1
theoretical calculations, we use Eq. (4) ⁎sinð2θ + ϕeff Þ to account for
brittle anisotropy, where θ is the angle of the shear plane with respect
to σ1 and ϕeff is the effective angle of internal friction. For isotropic
materials, brittle failure occurs on the optimal failure plane which
satisfies the condition 2θ + ϕeff = 90°. The required differential stress
will be larger for deformation along planes at other orientations
unless the material is anisotropic and the effective frictional strength
is sufficiently low for weak planes with non-optimal orientations
(Jaeger, 1960).
For potential shear zones crossing undeformed oceanic and continental lithosphere, we assume the same initial rheological and thermal
profiles as in our numerical experiments (Fig. 1) and ϕeff = 15°. If these
sections of lithosphere were to fail and shear, the Drucker–Prager yield
criterion (Eq. (4)) for material with ϕeff = 15° predicts failure planes at
an angle of θ = 37.5° from the horizontal maximum stress, σ1. A value of
θ = 37.5° is used in the calculations to illustrate the strength of shear
zones crossing initially undeformed oceanic and continental litho-
253
sphere, and for simplicity, it is assumed that the shear zone maintains
this angle, even if the material undergoes strain softening. We approximate the differential stress in the subduction zone as half the sum of a
continental lithosphere calculation and an oceanic lithosphere calculation with a depressed geotherm of 10 °C km− 1, and the parameters
θ = 15°, ϕeff = 2° consistent with the setup stage of models initiated
with a subduction angle of 15°.
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