PreprintPDF Available

Abstract and Figures

Tectonic plate motions predominantly result from a balance between the potential energy change of the subducting slab and viscous dissipation in the mantle, bending lithosphere, and slab-upper plate interface. A wide range of observations from active subduction zones and exhumed rocks suggest that subduction interface shear zone rheology is sensitive to the composition of subducting crustal material-for example, sediments versus mafic igneous oceanic crust. Here we use 2-D numerical models of dynamically consistent subduction to systematically investigate how subduction interface viscosity influences large-scale subduction kinematics and dynamics. Our model consists of an oceanic slab subducting beneath an overriding continental plate. The slab includes an oceanic crustal layer that controls the rheology of the interface. We implement a range of slab and interface strengths and explore how the kinematics respond for an initial upper mantle slab stage, and subsequent quasi-steady-state ponding near a viscosity jump at the 660-km-discontinuity. If material properties are suitably averaged, our results confirm the effect of interface strength on plate motions as based on simplified viscous dissipation analysis: a ∼ 2 order of magnitude increase in interface viscosity can decrease convergence speeds by ∼ 1 order of magnitude. However, the full dynamic solutions show a range of interesting behavior including an interplay between interface strength and overriding plate topography and an end-member weak interface-weak slab case that results in slab breakoff/tearing. Additionally, for models with a spatially limited, weak sediment strip embedded in regular interface material, as might be expected for the subduction of different types of oceanic crust through Earth's history, the transient response of enhanced rollback and subduction velocity is different for strong and weak slabs. Our work substantiates earlier suggestions as to the importance of the plate interface, and expands the range of quantifiable links between plate reorganizations, the nature of the incoming and overriding plate, and the potential geological record.
Content may be subject to copyright.
Geophys. J. Int. (2022) 00, 1–17 https://doi.org/10.1093/gji/ggac075
Advance Access publication 2022 Feb r uar y 22
GJI Geodynamics and Tectonics
The effects of plate interface rheology on subduction kinematics
and dynamics
Whitney M. Behr ,
1 Adam F. Holt,
2 Thorsten W. Becker
3 , 4 , 5 and Claudio Faccenna
6 , 7
1
Geological Institute, Department of Earth Sciences, ETH Zurich, Sonneggstrasse 5 , 8092 Zurich, Switzerland. E-mail: wbehr@ethz.ch
2
Rosenstiel School of Marine and Atmospheric Science, University of Miami, 4600 Ric kenbac ker Cause w ay Miami, FL 33149-1031, USA
3
Institute for Geophysics, Ja ckson School of Geosciences, The University of Texas at Austin, J .J . Pickle Research Campus, Bldg. 196 10100 Burnet Road,
Austin, TX 78758-4445, USA
4
Department of Geological Sciences, Jackson School of Geosciences, The University of Texas at Austin, 2275 Speedway Stop C9000, Austin,
TX 78712-1722, USA
5
Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, 201 E. 24th Street, Austin, Texas 78712-1229, USA
6
Dipartimento Scienze, Laboratory of Experimental Tectonics, University of Roma Tre, L.S.L. Murialdo 1, Roma 00146, Italy
7
Helmholtz Centre Potsdam GFZ, German Research Centre for Geosciences Potsdam (Germany), Telegrafenberg D-14473 Potsdam, Germany
Accepted 2022 Feb r uar y 19. Received 2022 Febr uar y 13; in original form 2021 September 22
S U M M A R Y
Tectonic plate motions predominantly result from a balance between the potential energy
change of the subducting slab and viscous dissipation in the mantle, bending lithosphere
and slab–upper plate interface. A wide range of observations from active subduction zones
and exhumed rocks suggest that subduction interface shear zone rheology is sensitive to the
composition of subducting crustal material—for example, sediments versus mafic igneous
oceanic crust. Here we use 2-D numerical models of dynamically consistent subduction to
systematically investigate how subduction interface viscosity influences large-scale subduction
kinematics and dynamics. Our model consists of an oceanic slab subducting beneath an
overriding continental plate. The slab includes an oceanic crustal/weak layer that controls the
rheology of the interface. We implement a range of slab and interface strengths and explore how
the kinematics respond for an initial upper mantle slab stage, and subsequent quasi-steady-state
ponding near a viscosity jump at the 660-km-discontinuity. If material properties are suitably
averaged, our results confirm the effect of interface strength on plate motions as based on
simplified viscous dissipation analysis: a 2 order of magnitude increase in interface viscosity
can decrease convergence speeds by 1 order of magnitude. However, the full dynamic
solutions show a range of interesting behaviour including an interplay between interface
strength and overriding plate topography and an end-member weak interface-weak slab case
that results in slab break-of f/tearing. Additionall y, for models with a spatially limited, weak
sediment strip embedded in regular interface material, as might be expected for the subduction
of different types of oceanic materials through Earth’s history, the transient response of
enhanced rollback and subduction velocity is different for strong and weak slabs. Our work
substantiates earlier suggestions as to the importance of the plate interface, and expands the
range of quantifiable links between plate reorganizations, the nature of the incoming and
overriding plate and the potential geological record.
Key words: Fault zone rheology; Rheology and friction of fault zones; Dynamics of litho-
sphere and mantle; Rheology: crust and lithosphere; Subduction zone processes.
1 INTRODUCTION
The subduction interface is a shear zone of varying thickness that
defines the boundary between a subducting slab and the overriding
lithosphere. The thermal and mechanical properties of these shear
zones affect a wide range of tectonic processes such as the transport
of volatiles from Earth’s surface to its deep interior (e.g. Kerrick
& Connolly 2001 ; Wad a et al. 2008 ; Bebout 2013 ), the growth of
continents and topography (e.g. Vo n Huene & Scholl 1991 ; Foley
et al. 2002 ; Bassett & Watts 2015 ) and the amounts and rates of
return flow of subducted material back to the surface (e.g. Gerya
et al. 2002 ; Burov et al. 2014 ).
C
The Author(s) 2022. Published by Oxford University Press on behalf of The Royal Astronomical Society. This is an Open Access
article distributed under the terms of the Creative Commons Attribution License ( https://cr eativecommons.or g/licenses/by/4.0/ ), which
permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.
1
2 W. M . Behr et al .
Observations from modern and exhumed subduction complexes
suggest that subduction interfaces exhibit quite different character-
istics from place to place and over geological time. Modern sub-
duction zones, for example, show a wide variation in the types of
materials entering the trench, with some blanketed by sediments
sourced from local seafloor depocentres and/or nearby terrestrial
landmasses (Von Huene & Scholl 1991 ; Rea & Ruff 1996 ; Clift
2017 ); and others that are sediment-poor and dominated by oceanic
crustal seamounts or other forms of seafloor topography (Cloos
1993 ; Abercrombie et al. 2001 ; Laursen et al. 2002 ). These differ-
ences appear to produce variations in the state of stress, fluid pres-
sure and seismic coupling along the subduction interface within
and around the seismogenic layer (Cloos 1992 ; Scholz & Small
1997 ; Gulick et al. 2011 ; Heuret et al. 2012 ; Barnes et al. 2020 ),
which suggests that differences in the types of material delivered
to the trench are correlated with differences in interface rheological
properties. This notion is also supported by laboratory friction ex-
periments on materials collected from seafloor drilling sites (Kurza-
wski et al. 2018 ; Boulton et al. 2019 ; Seyler et al. 2020 ), as well
as geological observations from accretionary complexes that are
exposed onshore (Fagereng & Sibson 2010 ; Kitamura & Kimura
2012 ; Clarke et al. 2018 ; Phillips et al. 2020 ; Braden & Behr 2021 ).
Data from ancient exhumed subduction complexes fur ther more
suggest that the heterogeneity we see in materials entering trenches
may also persist with pro gressi ve subduction along the interface
to significant depth. Remnants of subduction interface shear zones
exhumed from below seismogenic depths, for example, can show
quite variable protolith compositions along strike and/or at different
structural levels (see the compilation of fossil subduction interfaces
in Agard et al. 2018 ). These commonly range from metasedimentary
rocks (representing sediment cover), to metabasalts and metagab-
bros (representing mafic oceanic crust), to serpentinites and peri-
dotites (potentially representing subducted oceanic mantle). Where
these different protolith rock types are juxtaposed, they exhibit
geolo gical e vidence for significant variations in their rheological
properties, such as boudin–matrix relationships, sharp strain gradi-
ents or differences in deformation mode (brittle versus ductile) or
mechanism (diffusion versus islocation creep, St
¨
ockhert et al. 1999 ;
Angiboust et al. 2011 ; Grigull et al. 2012 ; Kotowski & Behr 2019 ;
Tewksbury-Christle et al. 2021 ). Seismic images of the deep forearc
region also suggest that the thicknesses and mechanical properties
of the deep subduction interface vary among different subduction
zones or within individual subduction zones along-strike (Nedi-
movi
´
c et al. 2003 ; Han et al. 2017 ; Audet & Schaeffer 2018 ; Calvert
et al. 2020 ; Delph et al. 2021 ; Tewksbury-Christle & Behr 2021 ).
Sev eral workers hav e used these observations of mechanical con-
trast of subducting materials on both the shallow and deep interface
to hypothesize that subducting sediments have the propensity to act
as a lubricant to interplate sliding. Cloos ( 1985 ), for example, first
suggested that sediment-dominated melange could define a narrow,
low viscosity channel between the downgoing and overriding plates.
Lamb & Davis ( 2003 ) raised the prospect of sediment lubrication as
an explanation for temporal variations in upper plate topography in
the Andes, based on the inference that sediments increase megath-
rust pore fluid pressures and decrease friction, and thereby control
coupling between the slab and the upper plate. Recently, Behr &
Becker ( 2018 ) demonstrated that viscous sections of subduction
interfaces should also be sensitive to sediment subduction because
metasedimentary protoliths are two to three orders of magnitude
weaker than mafic protoliths based on experimentall y deri ved vis-
cous creep laws (e.g. Jin et al. 2001 ; Hirth et al. 2001 ; Zhang et al.
2006 ; Tokle et al. 2019 ). Behr & Becker ( 2018 ) used a simplified
energy balance for plate speeds based on constant geometry, simpli-
fied subduction from Conrad & Hager ( 1999 ) to show that interface
viscosity variations could significantly influence plate convergence
rates. Sobolev & Brown ( 2019 ) invoked this mechanism to sug-
gest that sedimentation at continental margins, dri ven b y erosion
during global deglaciation events, could explain the onset of fast
subduction rates characteristic of modern plate tectonics.
The hypothesis that interface ef fecti ve rheolo gy is sensiti ve to
sediment subduction, and by corollary that sediment subduction
may influence large-scale subduction dynamics is intriguing be-
cause it implies a potential feedback between the processes that
control seafloor sedimentation (e.g. climate-driven terrestrial sup-
ply and/or organically driven seafloor deposition) and tectonic plate
motions (Lamb & Davis 2003 ; Behr & Becker 2018 ; Sobolev &
Brown 2019 ; Chen et al. 2022 ). However, the impact of plate inter-
face viscosity on subduction dynamics is relati vel y underexplored
in dynamically consistent numerical subduction models and, in par-
ticular, the impact of interface strength on near-surface subduction
properties like topography and upper plate stress is unclear. Some
recent time-dependent modelling studies show that interface viscos-
ity can indeed impact slab dynamics significantl y; particularl y slab
rollback rates, plate velocities and slab interactions with the viscos-
ity jump at the 660-km-seismic discontinuity (Andro vi
ˇ
co v
´
a et al.
2013 ;
ˇ
C
´
ıˇ
zkov
´
a & Bina 2013 ; Ratnaswamy et al. 2015 ; Pokorn
`
y et al.
2021 ). More typicall y, howe ver, the interface is implemented as a
constant viscosity region, or a constant shear stress fault, in large-
scale subduction simulations and is set to be weak enough to permit
steady-state subduction at Earth-like convergence rates (King &
Hager 1990 ; Zhong & Gurnis 1995a ; Billen & Gurnis 2001 ). The
formulation by Conrad & Hager ( 1999 ), utilized in Behr & Becker
( 2018 ), does not take into account the time-dependent evolution of
the subducting slab or the potential influence of power law creep rhe-
ologies in the mantle, nor did that study permit the examination of
different kinematic components of the subduction system (e.g. sub-
ducting plate v elocity, ov erriding plate retreat rate and convergence
rates). Thus, several open questions remain, including the following:
(i) How does interface viscosity influence subduction kinematics,
including both the early transient (pre-660) and later, steady-state
(post-660) rates of slab sinking, overriding plate retreat and plate
convergence?
(ii) How and over what timescales do slab kinematics respond to
sudden changes in interface viscosity?
(iii) How do variations in interface viscosity affect overriding
plate stress state and topography?
(iv) What is the relative importance of oceanic crust and overrid-
ing plate buoyancy in subduction plate speeds compared to interface
viscosity?
In this paper, we address these questions using fully dynamic
2-D numerical models of subduction of oceanic lithosphere beneath
a continental overriding plate. We systematically investigate slab
kinematics and morphology for varying slab strengths, interface
viscosities, and density structures and discuss the implications for
linkages between subduction dynamics and surface processes.
2 MODELLING APPR O ACH
2.1 Model framework
We use the finite element code ASPECT (v. 2.1.0; Kronbichler
et al. 2012 ; Heister et al. 2017 ) to solve the equations that govern
interface rheology effects on subduction 3
convection in an incompressible viscous fluid with negligible inertia
and no internal heating. This includes the conservation of mass:
·v = 0 (1)
momentum:
−∇ ·(
2 η˙)
+ p = ρg (2)
and energy:
ρC
p
T
t + v ·∇T
k
2
T = 0 , (3)
where v is velocity, ˙the strain-rate tensor, ηviscosity, p pressure,
ρdensity, g gravitational acceleration, C
p
specific heat capacity, T
temperature and k thermal conductivity Ta bl e 1 .
Our general set-up follows that of, for example, Holt et al. ( 2015 )
in that a compositionally controlled, crustal layer with properties
that can be varied between models allows for dynamic subduction
within a thermochemical convection system with a freely moving
subducting and overriding plate. The composition is advected as a
compositional field. The details of the rheology and density structure
are provided below, but our model set-up is similar to that outlined
in Holt & Condit ( 2021 ) with a domain size that is 2900 km deep
(whole mantle) and 11 600 km wide (Fig. 1 ). The model is initi-
ated with two flat-lying lithospheric plates of different ages. The
subducting plate is 6000-km-long, 80 Ma old, and is placed next to
a 2500-km-long, 60 Ma old overriding plate. The overriding plate
is compositionally buoyant and stiff relative to the subducting plate
so as to approximate a continental-affinity upper plate. Both plates
are bounded on the outer model margins by ridge segments and are
separated from each other by a thin crustal layer (discussed further
below). The subducting plate is pre-bent with a radius of curvature
of 250 km and extends to an initial depth of 200 km. All model
mechanical boundaries are free slip.
Our models are self-consistent in that all dynamics and deforma-
tion are driven by internally generated forces and without imposed
kinematics. Ho wever , it should be noted that this does not necessar-
ily mean that they are regionally realistic. For example, our models
are 2-D, which means that they are most applicable in the centre of
wide slabs. Moreov er, re gional tectonics on Earth may be affected
by far-field plate forces, for example, and along-strike variations in
various slab/trench/upper plate properties; those are not included
in our study in order to be able to isolate the local dynamics and
effects of rheology.
2.2 Temperature and density structure
The two lithospheric plates are defined using half-space cooling
profiles for lithosphere of 80 (subducting plate) and 60 Ma (over-
riding plate), a thermal dif fusi vity of 10
6 m
2
s
–1 and a mantle
potential temperature of 1300 C. Density is temperature depen-
dent with different reference densities for the background mate-
rial (oceanic lithosphere and sublithosphere mantle), the overriding
plate lithosphere and the oceanic crust. In the reference case, the
crust and overriding plate material (both tracked by separate com-
positional fields) have densities that are reduced relative to that of
the oceanic lithosphere/mantle (3175 kg m
–3
reference density, rel-
ative to 3300 kg m
–3
). This is to approximate the lower density of
basaltic crust, and to ensure the upper plate is positi vel y buoyant and
hence remains at the surface. In the upper plate, this compositional
component extends to an initial depth of 100 km.
2.3 Rheology
2.3.1 Asthenosphere and lower mantle.
The rheology of the mantle in our models is governed by a composite
creep law with diffusion creep, dislocation creep and plastic yielding
in order to capture the first-order controls on subduction-induced
flow and deformation (e.g. Billen & Hirth 2005 ; Garel et al. 2014 ).
The dislocation and diffusion creep laws are parametrized as:
ηdiff/ disl
= A
1
n
˙
1 n
n
II
exp
E + P V
nRT , (4)
where ηis the composite viscosity, A is a pre-factor, ˙II
is the second
invariant of the strain rate tensor, n is the stress exponent, R is the
gas constant, P is the lithostatic pressure and T is the temperature.
The stress exponents ( n ) (dislocation creep = 3.5, diffusion creep =
1), acti v ation volumes ( V ) and energies ( E ) are consistent with the
range of values derived from laboratory experiments on wet olivine
(Hirth & Kohlstedt 2004 ). Despite assuming incompressibility in
our models, we add a 0.3
C km
–1 adiabatic temperature gradient
to the temperature used in eq. ( 4 ). The diffusion and dislocation
creep pre-factors are set to give ηdiff = ηdisl = 5 ×10
20 Pa s at
a transition strain rate of 5 ×10
5 s
1 and depth of 330 km ( cf .
Billen & Hirth 2005 ). The lower mantle is more viscous than the
upper mantle and is set to only deform via diffusion creep. The
lower mantle diffusion creep pre-factor is computed to produce an
upper-to-lower mantle diffusion creep viscosity increase of factor
20. This factor of 20 increase in viscosity allows us to test the effect
of a reduction in slab sinking rates and the resulting ’anchoring’,
similar to numerous prior studies. While exact values for and the
depth of such an increase are unclear (e.g. King & Masters 1992 ),
geoid and slab sinking rate studies indicate that the lower mantle has
a higher viscosity than the upper mantle (e.g. Hager 1984 ; Ricard
et al. 1993 ).
The equi v alent plastic ‘viscosity’ is defined as:
ηyield
=
min
τyield
, 0.5 GPa
2 ˙II
(5)
and τyield
is approximated by a Coulomb friction criterion for opti-
mally oriented faults:
τyield
= ( aσn
+ b) λ(6)
in which a is the friction coefficient (0.6), b is the cohesion (60 MPa),
λis a pore fluid factor defined as λ= 1 P
fluid
P
rock = 0 . 15 and σn is
assumed to equal the lithostatic pressure P . This value of λresults in
significant plastic weakening, yet does not weaken the trench region
completely, and is comparable to that required to produce coherent
downwellings/slabs in previous convection/subduction modelling
studies [e.g. Enns et al. ( 2005 ): 0.1, Moresi & Solomatov ( 1998 ):
0.03–0.13].
The ef fecti ve model viscosity is then calculated as:
ηeff =
1
ηdiff +
1
ηdisl +
1
ηyield
1
(7)
and is capped with upper and lower limits of, respecti vel y,
2.5 ×10
18 and 2.5 ×10
23 Pa s in the reference model set-up.
In regions without plastic yielding, our rheological parameters pro-
duce a reference viscosity of 2.5 ×10
20
Pa s (at ˙II
= 5 ×10
5
s
1
,
depth = 330 km).
4 W. M . Behr et al .
Tab le 1. Model parameters.
Quantity Symbol Units Value(s)
Temperature/density
Surface temperature T
s K 273
Potential temperature T
m K 1573
Adiabatic temperature gradient d
z
T K km
1 0.3
Reference density (slab/mantle) ρ0 kg m
3 3300
Reference density (crust/overriding plate) ρC kg m
3 3175
Thermal expansion coefficient αK
1 3 ×10
5
Thermal dif fusi vity κm
2
s
1 10
6
Lithosphere properties
Subducting plate age t
SP Myr 80
Subducting plate viscosity (core) ηcore Pa s 2.5 ×10
24
Subducting plate viscosity (non-core) ηSP Pa s 2.5 ×10
22
; 2.5 ×10
23
Overriding plate age t
OP Myr 60; 120
Overriding plate viscosity ηOP Pa s 2.5 ×10
24
Overriding plate compositional thickness h
OP km 100; 150
Crust viscosity ηcrust Pa s 2.5 ×10
18
;10
19
;10
20
;10
21
Dislocation creep (upper mantle)
Acti v ation energy E kJ mol
1 540
Acti v ation volume V cm
3
mol
1 12
Prefactor A Pa
n
s
1 8.5 ×10
15
Exponent n –3.5
Diffusion creep (upper and lower mantle)
Acti v ation energy E kJ mol
1 300 (UM, LM)
Acti v ation volume V cm
3
mol
1 4 (UM), 2.5 (LM)
Prefactor A Pa
1
s
1 10
10
(UM); 5.8 ×10
13
(LM)
Exponent n –1
Plastic yielding
Friction coefficient a –0.6
Cohesion b MPa 60
Pore fluid factor λ–0.1
Maximum yield stress τmax MPa 500
2.3.2 Lithospheric mantle and crust
Aside from where plastic yielding is acti v ated, in the bending region
of the slab, this upper viscosity limit (2.5 ×10
23
Pa s) dictates the
lithospheric strength. In the overriding plate, we increase this upper
limit to by an order of magnitude (2.5 ×10
24
Pa s) to mimic a stiff
overriding plate. As detailed in Section 2.5, we also test the effects
of a strong slab core ( cf . Capitanio et al. 2007 ; Buffett & Becker
2012 ) by increasing the upper viscosity limit within a 12.5-km-thick
layer in the centre of the subducting lithosphere. Like the crust and
overriding plate, this slab core region is tracked using a distinct
compositional field. The crust is a 7.5-km-thick oceanic crustal
layer (in some cases referred to as an `oceanic weak lay er’), w hich
is placed along the curved slab top and is prescribed a constant
viscosity (Fig. 1 ).
2.4 Numerical parameters
Adaptive mesh refinement (AMR) is set to occur for the Q
2
P
1
finite elements associated with high viscosity gradients, high tem-
perature temperature, and/or non-zero compositions (Bangerth et al.
2018 ). This enables us to highly resolve our (compositional) crust
while also capturing large-scale mantle flow and slab dynamics. In
models with a slab core, and hence another compositional field, we
also refine the mesh within this core. The AMR parameters produce
a maximum level of refinement corresponding to 2.8-km-wide finite
elements (in the crust and core). This maximum refinement corre-
sponds to three levels of adaptive mesh refinement on top of seven
le vels of globall y unifor m refinement (Banger th et al.
2018 ). See
Holt & Condit ( 2021 ) for numerical accuracy and mesh resolution
tests for comparable model set-ups.
2.5 Model analysis and varied parameters
For each model run, we quantitati vel y track: (i) the slab kinematics,
including subducting plate velocity ( V
sp
), overriding plate veloc-
ity ( V
op
), and convergence velocity ( V
c
); (ii) slab dip (extracted at
200 km depth); (iii) viscosity, stress and temperature distributions
and (i v) topo graphic e volution. We compute surface topo graphy
from the vertical normal stress ( σxx
) at the free slip upper bound-
ary. This assumes the corresponding free surface, with zero normal
stress, would deflect according to this normal stress (e.g. Zhong
& Gurnis 1994 ).We also qualitati vel y examine the slab morphol-
ogy near the 660-km-discontinuity and the interface shear zone
thickness and geometry near the trench. We vary the following
parameters between different model runs:
(i) Sla b avera ge strength. We explore three dif ferent ef fecti ve
slab strengths. The strongest slab case is implemented with a high-
viscosity (unyielding) core in the centre of the slab (2.5 ×10
24
Pa s)
and relati vel y high pre-yield viscosity else where in the lithosphere
(2.5 ×10
23 Pa s); whereas the other two have no slab core and
variable pre-yield viscosities (2.5 ×10
23 Pa s, 2.5 ×10
22 Pa s).
In subsequent sections, we refer to the three slab types as strong,
intermediate and weak.
interface rheology effects on subduction 5
Figure 1. Model set-up with initial viscosity field and zoomed in view of the subduction interface region. White text boxes and arrows point to parts of the
model that are varied (see text for details). Dashed white lines show the regions over which slab viscosity is averaged both within and away from the bending
region.
(ii) Oceanic crustal/weak layer viscosity and thickness. The
oceanic crustal/weak layer viscosity is varied from 2.5 ×10
18
to 10
21
Pa s. In some models the whole crustal layer is assigned the same
viscosity, whereas in others a lower viscosity section is implemented
as a 500-km-wide low-viscosity strip embedded within higher vis-
cosity crust. Physically, the low viscosity crustal/w eak la yer could
correspond to, for example, layers of particularly weak sediments
(e.g. Vrolijk 1990 ; Tobin & Saffer 2009 ), exhumed seafloor serpen-
tinite (e.g. Minshull 2009 ; Guillot et al. 2015 ), or patches of excep-
tionally altered/weak oceanic crustal igneous rock (e.g. Braden &
Behr 2021 ). We also vary the thickness of the oceanic weak layer
from 7.5 to 10 to 12.5 km in some models.
(iii) Overriding plate thickness and density. Moti v ated b y the
occurrence of different upper plate tectonic histories (e.g. cratonic
versus thinned continental lithosphere versus oceanic), we explore
the impact of variable upper plate thickness/density. In addition
to the reference parametrization (60 Ma upper plate with 100-km-
thick compositonally buoyant/stiff portion), we consider a thickened
upper plate model (120 Ma age, 150 km compositional thickness),
and a 60 Ma upper plate case with the compositionally buoyant/stiff
component eliminated.
(iv) Oceanic crustal density. While most models contain crusts
and overriding plates that are lighter ( ρ0
= 3175 kg m
–3
) than the
surrounding material ( ρ0
= 3300 kg m
–3
), we also examine the ef-
fects of removing this computational buoyancy from both elements.
This is to ensure first-order model behaviour holds in the presence
of eclogitized oceanic crust and/or oceanic upper plates.
(v) Crustal cut-off depth. In all models, we remove the crust at
a certain depth in the mantle. In most of our models, we gradually
taper the weak and buoyant crust from full thickness at 200 km
depth to zero thickness at 300 km depth in order to reduce stress
discontinuities. Because the persistence of weak material to mid-
mantle depths creates an overly thickened cold forearc region (e.g.
Kincaid & Sacks 1997 ), which conflicts with petrological and heat
flow evidence for a warm mantle wedge (e.g. Furukawa 1993 ; Wad a
& Wang 2009 ) we test the effect of discretely cutting the crust off at
a shallo wer , 100 km depth [which eliminates this issue in dynamic
models: e.g. Holt & Condit ( 2021 )].
3 RESULTS
3.1 Effect of varying slab strength
Fig. 2 illustrates the effects of variable slab strength for uniform,
10
20
Pa s plate interface strength. Plotted are four time steps for the
strongest and weakest slab end-members (Figs 2 a and b) along with
the subducting plate, overriding plate, and conv ergence v elocities
for the three slab types (Figs 2 c–e) implemented here. The general
dynamics of these self-consistent subduction models are compara-
ble to earlier wo rk (e.g. Garel et al. 2014 ; Holt & Becker 2016 ) and
can be considered as ‘typical’ of such self-consistent upper mantle
scenarios with diffusion/dislocation creep viscoplastic rheologies.
All three slab types show plastic yielding in the bending region
at the start of model run ( cf . Enns et al. 2005 ; Stegman et al. 2006 ).
Fig. 3 shows the computed average (geometric mean) viscosity
both away from and near the bending region of the plate (see Fig. 1
for averaging locations) for the three slab strength categories. The
average viscosity in the bending region for the weak and strong
slab end-members differ by slightly more than one order of magni-
tude. Our ef fecti ve slab viscosities are a fe w orders of magnitude
6 W. M . Behr et al .
Figure 2. Model snapshots and kinematics for end-member slab strengths.(a and b) Pre- and post-660 snapshots of model runs with a strong slab (a) and
a weak slab (b) for the same subduction interface strength. (c–e) Kinematics of models for various slab strengths (strong, intermediate and weak) and two
different interface viscosities.
larger than the background asthenosphere; this is lower than what
would be expected from application of laboratory constraints for
oli vine dif fusion and dislocation creep. Howe ver, such moderate
strength slabs are consistent with a range of observations includ-
ing: low elastic thickness at the trench (Billen & Gurnis 2005 );
large strain-rates within slabs (Holt 1995 ); tomo graphicall y imaged
slab morphologies, which indicate low viscosity fluid deformation,
likel y accommodated b y plastic yielding (e.g.
ˇ
C
´
ıˇ
zkov
´
a et al. 2002 ;
Garel et al. 2014 ); and more indirect inferences from plate driving
force and slab dynamics considerations (e.g. Funiciello et al. 2008 ;
Wu et al. 2008 ; Buffett & Beck er 2012, cf . Billen 2008 ; Beck er &
Faccenna 2009 ).
interface rheology effects on subduction 7
Figure 3. Slab average viscosities over time away from the bending region
(solid lines) and within the bending region (dashed lines) for the four slab
types implemented in this model suite. See Fig. 2 for locations of averaging
regions.
All three models show an early transient peak in convergence
v elocities driv en primaril y b y rapid subducting plate motion ( V
sp
)
as the slab sinks rapidly through the relatively weak upper man-
tle (Fig. 2 ). Upon approaching the 660 km viscosity increase, the
sinking velocity for the strong and intermediate slab strength cases
decelerates rapidly, whereas deceleration is slower for the weaker
slab due to more prolonged slab stalling in the transition zone. At the
same time, ho wever , the weakest slab exhibits lower overriding plate
velocities post-660. Because deformation in the overriding plate is
negligible in all model runs (due to it being compositionally stiff),
V
op is approximatel y equi v alent to the rate of trench retreat/slab
rollback. Despite small V
sp
and V
op
differences between the weak-
est slab case and the other slab strengths, all three slab strengths
exhibit similar post-660 convergence velocities after 15 Myr. Sim-
ilar kinematic patterns are observed for the case of a weaker (10
19
Pa s) subduction interface and equi v alentl y v ariable slab strengths
(green lines, Figs 2 c–e).
These results suggest that slab strength, within the moderate
ranges of contrast to the asthenosphere ( cf . Billen 2008 ; Becker
& Faccenna 2009 ) that we explore here, does not substantially af-
fect conv ergence v elocities, as e xpected (Conrad & Hager 1999 ).
Figs 2 (a) and (b), ho wever , agrees with previous modelling studies
that show slab strength has a strong effect on the morphology of the
slab when it reaches an upper-to-lower mantle viscosity increase; the
strong slab exhibits earl y buckling, followed b y ponding, whereas
the weaker slab shows much tighter-wavelength folding and con-
tinuous sinking through the transition zone with limited ponding
( cf . Davies 1995 ; Christensen 1996 ; Ribe et al. 2007 ; Billen 2008 ;
Garel et al. 2014 ).
3.2 Effects of varying interface viscosity
Fig. 4 shows model snapshots and kinematics for interfaces varying
over four orders of magnitude for a single (strong) slab strength. For
the strongest interface case (10
21
Pa s), subduction is extremely slow
with convergence rates less than 5 mm yr
–1
. This lo w P eclet num-
ber setting results in substantial thermal diffusion of the slab within
the upper mantle prior to it reaching the 660-km-discontinuity,
which results in its viscosity structure being dominated by the stiff,
compositional core (Fig. 4 a). Thus an end-member emerges that
represents ef fecti ve subduction stalling, so in subsequent discus-
sions, we focus on the three lower viscosity interface cases (strong
= 10
20
Pa s, weak = 10
19
Pa s, very weak = 2.5 ×10
18
Pa s).
As in the variable slab strength models discussed in Section 3.1,
all three models first show an early increase in convergence velocity
( V
c
) associated primarily with rapid slab sinking through the rela-
ti vel y weak upper mantle (Fig. 4 e). The magnitude and timescale of
this transient phase of fast subducting plate velocities and plate con-
vergence scales with interface viscosity, with the weakest interface
e xhibiting conv ergence rates of up to 13 cm yr
–1
ov er a 2 Myr time
interval, and the moderately strong interface peaking at 7 cm yr
–1
over a 7 Myr pulse (Fig. 4 g). Overriding plate velocity ( V
op
),
w hich is appro ximately equal to trench velocity, also scales with
interface viscosity, with fastest trench retreat for the very weak in-
terface case (Fig. 4 f). In addition to being in direct response to the
viscosity reduction (and hence shear stress reduction) at the deep
plate interface, subducting plate velocities within the weak and very
weak interface models are further enhanced by local decreases in
upper mantle viscosity around the slab due to the the dominance of
dislocation creep within these high strain rate regions ( cf . Figs 4 c
and d)
Upon reaching the 660, V
sp immediately decreases due to the
increase of mantle viscosity for all three interface cases, whereas
V
op
reaches an approximately constant velocity, with faster rates of
trench retreat for the weaker interfaces, after a steady decrease dur-
ing the pre-660 phase. With time, the fast rollback associated with
the two weakest interfaces causes the slab dip to shallow resulting in
a repartitioning of the slab pull force. The strong interface case, by
contrast, exhibits slower overriding plate retreat and retains a steeper
dip and an approximately constant subducting plate velocity such
that there is both more slab penetration through the 660 and, due to
the low convergence rates, more accumulation of thermally thick-
ened slab in the 300-km-thick region surrounding the viscosity
increase. P ost-660 con vergence rates reach an approximate steady
state for all models, with V
c remaining fastest for the very weak
interface case and slowest for the strong interface case (Fig. 4 g).
The interface viscosity variations also result in differences in the
morphology of the trench and interface shear zone itself after the
slab reaches the 660. The fast rollback and shallower dip of the slab
in the weak interface cases produces a longer and thicker interface
shear zone.
In addition to exploring the effects of plate interface strength
on the strong slab models (i.e. with a core), we also conducted
equi v alent tests for the other two, relati vel y weaker, slab strength
cases. Fig. 5 summarizes V
sp
, V
op and V
c computed both before
(maximum) and after (time-average) the slab reaches the 660 for
all model runs as a function of interface viscosity and colour-coded
by slab strength. This shows that the first-order effects of varying
plate interface strength on subduction kinematics hold for variable
slab strengths, and that convergence velocities and related subduc-
tion kinematics both pre-and post-660 can vary by more than one
order of magnitude depending on the strength of the interface (ef.
ˇ
C
´
ıˇ
zkov
´
a & Bina 2013 ;
ˇ
c
´
ıˇ
zkov
´
a & Bina 2019 ). Interestingly, an ad-
ditional behavioural end-member emerges here when both the slab
and interface are set to the weakest end-member cases; this model
exhibits slab break-off within 1 Myr of the model run, prior to the
slab reaching the 660. That is, the combination of weak slab (low
bending resistance) and weak interface (low mantle resistance) man-
ifest as high slab pull transmission to the shallow slab and hence
‘plastic’ yielding throughout the entire lithosphere for our chosen
yield stress parameters.
8 W. M . Behr et al .
Figure 4. Effects of varying interface viscosity for a single (strong) slab strength. (a–d) Snapshots of the viscosity profile through models with different
interface viscosity. (e–g) Kinematics of the models colour-coded by interface viscosity. ( V
sp
for the strongest interface viscosity is not shown in (e) because it
is lower than 0.1 cm yr
–1
.) See text for detailed description, and supporting information for videos of these model runs.
Figure 5. Summary plots of key parameters as a function of interface viscosity, colour-coded by slab strength, with symbols showing metrics computed prior
to (circles) and after (squares) the slab reaches the 660. Pre-660 velocities plotted are maxima whereas post-660 velocities plotted are time-averages.
interface rheology effects on subduction 9
3.3 Kinematic response to transient changes in interface
rheology
All pre viousl y described model runs had a constant viscosity as-
signed to the oceanic weak layer on top of the subducting slab. Here
we examine the kinematic responses to a sudden change in interface
viscosity. Fig. 6 shows the kinematic indicators for models in which
the oceanic crustal layer exhibits a high viscosity (strong interface
case = 10
20
P a s), e xcept for the presence of a 500-km-long-strip in
the centre of the downgoing plate (initially 500 km from the trench).
Fig. 6 shows the results from two model cases, one in which the
strip is weak (10
19 Pa s) and the other in which the strip is very
weak (2.5 ×10
18
Pa s) relative to the ambient crust (10
20
Pa s). In
both models the strip enters the trench just after the slab begins to
interact with the 660. The immediate response to the low viscosity
strip in both model runs is an increase in slab rollback velocity
( V
op
) and an associated increase in convergence rate. The pulse
of fast rollback is then followed by a period of faster slab sinking
for both model runs. For the weak strip tests conducted for slab
strength set at the weak end-member, the peak in early V
op
velocity
(rollback) is closely spaced in time to the peak in subducting plate
velocity ( V
sp
, cf . Fig. 6 b). This produces a single pulse-like increase
in conv ergence v elocity, of about a factor of two over 15 Myr, as-
sociated with the low viscosity strip subduction (Fig. 6 h). Fig 6 (b)
shows that the peak conv ergence v elocity achiev ed during weak
strip subduction for the weak slab case reaches the same velocity
as the uniformly weak interface model case. For the strong slab
models with a weak strip, the behaviour is quite different. In these
models the early slab rollback peak is distinctly separated in time
from a later peak in slab sinking velocity ( cf . Figs 6 c and e). This
results in a much broader-wa velength, low er-amplitude increase in
conv ergence v elocity, with V
c ele v ated b y a factor of 1.5 over
50–60 Myr. The peak convergence velocities for these models re-
main lower than for the equi v alent, uniform weak interface models
because the length of the low viscosity strip is insufficient to al-
low the subducting plate to accelerate to its maximum convergence
velocity.
3.4 Effects on upper plate stresses and topography
We also examined how the strength of the interface affects upper
plate stress regime and topography. The upper boundary of our
models is free slip and so dynamic topography is calculated to be
that which would support the ver tical nor mal stresses produced at
the surface (e.g. Zhong & Gurnis 1994 ). Fig. 7 shows the spatial
distribution of topography and horizontal deviatoric stress across
the trench for two interface models (strong versus very weak in-
terface) and a strong slab, both before and after the slab reaches
the 660. Prior to the slab reaching the 660, both models exhibit
a topographic high seaward of the bending region of the slab that
represents viscous flexure associated with slab bending (e.g. Zhong
& Gurnis 1994 ; Crameri et al. 2017 ). Both also show an ove rall
increase in topography across the trench region and into the up-
per plate, which is due to the isostatic effect of a relati vel y light
overriding plate being juxtaposed against the dense subducting
plate.
The two models show a distinctive difference in the near-
trench/forearc region ( < 200 km from the trench), however; the
strong interface model shows compressional stresses (Fig. 7 b) and
a pronounced topographic low ( cf . Billen & Gurnis 2001 ), whereas
the weaker interface exhibits neutral to extensional stresses and
continuously increasing topography from the trench to the upper
plate. This dif ference likel y occurs for two reasons: (i) in the strong
interface case, the slab and forearc are strongly coupled across the
interface such that the slab more ef fecti vel y pulls down on the upper
plate; (ii) flow in the mantle wedge corner is more vigorous in the
weak interface case (Fig. 7 c) such that there is more of a contribu-
tion from dynamic pressure effects. After the slab reaches the 660,
the forearc stresses remain mostly compressional in the strong inter-
face case (Fig. 7 e), but the stress magnitudes are lower due to slab
stalling and hence reduced plate velocities; the associated local to-
pographic low in the forearc is less pronounced (Fig. 7 d, Chen et al.
2017 ). In the weak interface case, shallowing of the slab dip after the
slab reaches the 660 (Fig. 7 f) results in reduced viscous flexure such
that the topographic profile is approximately flat across the trench
(Fig. 7 d).
3.5 Effects of b uoy anc y, overriding plate thickness, weak
layer thickness and crustal cut-off variations
All models discussed thus far included a compositionally light
oceanic crust and overriding plate ( ρ0 = 3175 kg m
–3
), relative
to the subducting lithosphere ( ρ0
= 3300 kg m
–3
), a constant over-
riding plate compositional thickness (100 km), a constant subduct-
ing crust thickness, and crustal material that is gradually tapered
out at depths beyond 200 km. In Fig. 8 , we illustrate the effects
of relaxing these assumptions on convergence velocities. The re-
moval of the oceanic crust compositional buoyancy (i.e. setting
ρ0
= 3300 kg m
–3
, Fig. 8 a) results in fa