JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 117, B01408, doi:10.1029/2011JB008431, 2012
Small-scale convection at a continental back-arc to craton
transition: Application to the southern Canadian Cordillera
N. J. Hardebol,1,2 R. N. Pysklywec,3 and R. Stephenson4
Received 18 April 2011; revised 7 November 2011; accepted 18 November 2011; published 28 January 2012.
[1] A step in the depth of the lithosphere base, associated with lateral variations in the
upper mantle temperature structure, can trigger mantle flow that is referred to as
edge-driven convection. This paper aims at outlining the implications of such edge-driven
flow at a lateral temperature transition from a hot and thin to a cold and thick lithosphere of
a continental back-arc. This configuration finds application in the southern Canadian
Cordillera, where a hot and thin back-arc is adjacent to the cold and thick North American
Craton. A series of geodynamical models tested the thermodynamical behavior of the
lithosphere and upper mantle induced by a step in lithosphere thickness. The mantle flow
patterns, thickness and heat flow evolution of the lithosphere, and surface topography are
examined. We find that the lateral temperature transition shifts cratonward due to the
vigorous edge-driven mantle flow that erodes the craton edge, unless the craton has a
distinct high viscosity mantle lithosphere. The mantle lithosphere viscosity structure
determines the impact of edge-driven flow on crustal deformation and surface heat flow; a
dry olivine rheology for the craton prevents the edge from migrating and supports a
persistent surface heat flow contrast. These phenomena are well illustrated at the transition
from the hot Canadian Cordillera to craton that is supported by a rheological change and
that coincides with a lateral change in surface heat flow. Fast seismic wave velocities
observed in the upper mantle cratonward of the step can be explained as downwellings
induced by the edge-driven flow.
Citation: Hardebol, N. J., R. N. Pysklywec, and R. Stephenson (2012), Small-scale convection at a continental back-arc to craton
transition: Application to the southern Canadian Cordillera, J. Geophys. Res., 117, B01408, doi:10.1029/2011JB008431.
1. Introduction
[2] Present-day seismicity and vertical motions reveal
how the evolution of continental interiors is influenced by
active tectonics, despite their large distances from active
plate boundaries [Cloetingh et al., 2005; Stein and Mazzotti,
2007]. Beside plate-boundary forces that may operate over
large distances [Nielsen et al., 2007], the continental lithosphere can also be subject to various regionally derived
tectonic forces not related to plate boundaries. Vertical
loading, such as flexure under a topographic load, is a
widely observed contributor to the deformation of lithosphere [Beaumont, 1981; Nielsen et al., 2007]. The upper
mantle also introduces vertical loads that operate at the base
of the lithosphere. For instance, the temperature/seismic
velocity structure of the European upper mantle can be
linked to the deformation patterns of the continental
1
Formerly at Netherlands Research Centre for Integrated Solid Earth
Sciences, Faculty of Earth and Life Science, VU University Amsterdam,
Amsterdam, Netherlands.
2
Now at Department of Geotechnology, Faculty of Civil Engineering
and Geosciences, Delft University of Technology, Delft, Netherlands.
3
Department of Geology, University of Toronto, Toronto, Ontario,
Canada.
4
School of Geosciences, University of Aberdeen, Aberdeen, UK.
Copyright 2012 by the American Geophysical Union.
0148-0227/12/2011JB008431
lithosphere [Cloetingh et al., 2005; Hieronymus et al., 2007;
Wilson and Patterson, 2001], partly caused by buoyancy of
a hot upper mantle [Nielsen et al., 2007]. Active flow in the
sublithospheric mantle can produce “dynamic topography”
of the lithosphere. In such cases, mantle flow induces sufficiently high normal stresses on the lithosphere so that there
are surface topographic anomalies of up to several kilometers magnitude over various horizontal length scales [e.g.,
Mitrovica et al., 1989; Gurnis, 1992; Pysklywec and
Mitrovica, 2000].
[3] A specific class of mantle flow that has been invoked
to explain certain topographic/thermal perturbations to the
overlying lithosphere relates to lateral changes in temperature structure of the upper mantle. “Edge-driven convection”
has been proposed as a pattern of mantle flow that can
develop at a passive plate boundary owing to the thermal
discontinuity between an ocean and continental plate [King
and Anderson, 1995, 1998]. It has been suggested that
such flow can exert a dynamic load on the overlying lithosphere that manifests as anomalous surface topography
[Shahnas and Pysklywec, 2004]. The rheological structure of
the lithosphere will also be affected by the lateral temperature transition at the passive plate margin, especially when
coinciding with a compositional change. This thermal/rheological structure may exert a top-down influence on the
mantle flow to which the lithosphere in return responds
[Anderson, 2001].
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[4] Lateral thermal and rheological discontinuities in the
upper mantle likely also occur in the continental plate interior [e.g., van Wijk et al., 2010]. For instance, the uplift
history of the Colorado Plateau can be understood in terms
of edge-driven convection at its eastern edge, along a step in
the lithosphere at the Rio Grande rift zone [Karlstrom et al.,
2008; van Wijk et al., 2010] Many long-lived provinces of
Archean and Proterozoic lithosphere are bordered by hot and
weak regions related to Phanerozoic orogenic activity [e.g.,
Hyndman et al., 2005]. For example, the North American
Craton is bordered to its west by a hot mobile belt that
connects a long-lived and still active subduction system to
the continental interior (Figure 1). In Europe, the Eastern
European Craton is adjacent to areas with thin and hot lithosphere that were thermally perturbed in Tertiary time
[Blundell et al., 1992; Cloetingh et al., 2005].
[5] Modeling studies have considered the development of
such hot/weak regions—for example, the abrasion of continental lithosphere above a subducting slab by mantle corner
flow [Currie et al., 2004, 2008]. Mantle convection established between the subducting Juan de Fuca plate and the
overriding North American Plate initiated by a downward
traction of the cold subsiding plate and upwelling of hot
asthenosphere central underneath the Cordillera (Figures 1d
and 1e). This hot mantle upwelling is considered to have
thinned the lithosphere of the Canadian Cordillera, which
has therefore been labeled as a continental back-arc
[Hyndman et al., 2005]. The thinning must have occurred
since Eocene time with the onset of subduction of the Juan
de Fuca plate [e.g., Engebretson et al., 1985].
[6] This study considers the evolution of the other side of
such a continental back-arc where it meets the lithosphere of
the adjacent thick and cold craton. Specifically, numerical
geodynamic experiments are conducted to investigate the
dynamic consequences of the lateral temperature/rheology
heterogeneity in the uppermost mantle due to a lateral
change in thickness of the lithosphere. The thin lithosphere
may represent a hot mobile belt such as the North American
Cordillera (Figure 1) [Currie and Hyndman, 2006;
Hyndman et al., 2005] or any strongly thinned back-arc
lithosphere such as the Pannonian Basin in Europe [e.g.,
Cloetingh et al., 2005]. This study is inspired by the former.
It is broadly agreed that the central belts of the Canadian
Cordillera mark a zone of substantially thinned lithosphere
related to mantle upwelling [Gough, 1986; Hyndman et al.,
2005]. The thin and hot Cordillera lithosphere here exhibits
a high surface heat flow (Figure 1b) and a high electrical
conductivity [e.g., Jones and Gough, 1995; Lewis et al.,
1992] that stand in contrast to the relatively low values for
the nearby North American Craton. Our numerical experiments replicate this lateral thermal change in coupled mantle
and lithosphere models and consider how the geodynamics
influence the thickness evolution of the thermal and
mechanical lithosphere, sub-lithospheric mantle flow, and
heat flow and surface topography.
2. Numerical Model
2.1. Governing Principles
[7] The numerical experiments use the plane strain viscous-plastic finite element code SOPALE that solves the
governing system of equations of conservation of mass,
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momentum and energy [Fullsack, 1995; Pysklywec et al.,
2002]. The governing equations are:
r⇀
u ¼ 0;
ð1Þ
r s′ij rp þ rg ¼ 0 ⋯ ⋯ i; j ¼ 1; 2;
ð2Þ
rcp
∂T ⇀
þ u rT ¼ kr2 T þ A:
∂t
ð3Þ
This system of equations (in addition to an equation of state)
u), pressure
iteratively solves for temperature (T), velocity (⇀
(p), and density (r), while assuming incompressible flow
and ignoring inertial forces. The deviatoric stress tensor is
given by s′ij and g, cp, k, A and t are gravitational acceleration, heat capacity, thermal conductivity, radioactive heat
production (per unit mass) and time. Density is a function of
temperature:
r ¼ r0 ð1 aðT T0 ÞÞ;
ð4Þ
Where a is the coefficient of thermal expansivity, r0 is the
reference material density, and T0 is the reference
temperature.
[8] SOPALE incorporates viscous-plastic behavior by
determining the point-wise deviatoric stress as the lesser of a
calculated viscous or yield stress (i.e., the yield stress for
plastic strain or viscous stress for creep mechanisms).
SOPALE calculates viscous stress (sviscous = he ɛ̇) from a
power law creep expression in which the effective viscosity
varies as function of strain rate and temperature as given by
[see also Pysklywec et al., 2002]:
1
ðn þ 1Þ 1 n
ð1
n 1Þ
2
A n ɛ̇
he ðɛ̇; T Þ ¼ 3
:eQ=nRT :
2n
n
ð5Þ
The variables A, n, Q are the viscosity parameter, power
exponent and activation energy from uniaxial laboratory
experiments, R is the ideal gas constant, and ɛ̇ is the second
invariant of the strain rate tensor. The first bracketed term on
the right-hand side of equation (5) is necessary for the conversion of the uniaxial laboratory experimental data to a state
of stress that is independent of the choice of coordinate
system.
[9] The frictional plastic yield stress is described by the
Drucker-Prager yield criterion, which is equivalent to the
Coulomb yield criterion for plane strain [Fullsack, 1995] and
with the standard-representation given by:
syield ¼ snormal sinFeff þ C0 :
ð6Þ
The shear stress at which brittle yielding occurs is a function
of the normal stress (snormal), i.e., the confining pressure,
and the material parameters Feff and C0, which are the
internal friction coefficient and the material cohesion. The
internal friction angle sets the slope of the brittle yield curve
and limits the maximum stress level that the lithosphere can
sustain through viscous deformation before plastic yielding
occurs.
[10] The two-dimensional temperature structure is governed by the conservation of energy equation that contains
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Figure 1. The case of the Canadian temperature and rheological lateral temperature transition in the
upper mantle beneath the Cordilleran Foreland Belt. (a) The main tectonic features of the southern
Canadian Cordillera, with the Juan de Fuca plate subduction and the active Insular and Coastal belts in
the west. The Cordillera interior comprises the Intermontane and Omineca belts, the latter contain several
core complexes. The Foreland Belt forms the Cordillera’s eastern border, marked by Cretaceous-Paleocene
contractional tectonics and some extensional features of Eocene-Oligocene age. (b) Heat flow data across
the belts of the southern Canadian Cordillera after Currie and Hyndman [2006] and based on data from
Lewis et al. [1992]. (c) Lithosphere structure across the Cordillera derived from geophysical probing [after
Clowes et al., 1995]. (d) Postulated upper mantle flow scenarios in explanation of mantle lithosphere thinning and: (I) edge-driven mantle flow, this study; (II) Subduction-related corner flow [see Currie et al.,
2004, 2008]; (III) mantle upwelling central underneath the Cordillera [e.g., Jones and Gough, 1995] possibly related to presence of a relic subducted slab which sinking through the 660-km discontinuity (IV)
may cause large-wavelength uplift [e.g., Mitrovica et al., 1989; Pysklywec and Mitrovica, 2000]. (e) Outline of P wave velocity anomalies (dVp/Vp%) beneath the Cordillera along a transect following the
U.S.-Canada border (adopted after Sigloch et al. [2008]). Positive P wave anomalies point to bodies with
higher velocities and typically low temperatures whereas negative anomalies to lower velocity and typically hotter bodies. The Juan de Fuca plate is imaged with a +3 dVp/Vp% in the upper 200 km and
connected with a large +1–2 dVp/Vp% at 400 km depth beneath the Cordillera. Also the cold craton
to the east is depicted with a positive 2–3 dVp/Vp% velocity anomaly. In strong contrast stands the upper
mantle beneath the Cordillera with a negative 3–4 dVp/Vp% P wave anomaly.
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Figure 2. Numerical model setup showing the mesh specifications and initial-stage and boundary conditions. The initial stage temperature structure is constrained by surface
temperature and heat flow (I) and temperature profile (II)
and define the depth to the base of the lithosphere (III).
The crustal thickness is 35 km. The rheological properties
of the crust, mantle lithosphere and asthenospheric mantle
are given in Table 1.
conductive, advective and heat production terms. Conduction dominates in the lithosphere due to low internal material
velocities, whereas temperature in the sub-lithospheric
mantle is controlled by heat advection. Shear heating is not
included in the model.
[11] SOPALE solves the governing system of equations
using coupled Lagrangian and Eulerian meshes in the arbitrary Lagrangian-Eulerian scheme [Fullsack, 1995]. The
Eulerian mesh remains essentially undeformed (it is allowed
to dilate vertically) and acts as a solver grid, whereas the
Lagrangian mesh acts as a tracker grid that moves along with
the deforming material. This technique is useful when
dealing with large deformation, like mantle convection, and
for tracking moving material interfaces like the free-surface
and internal boundaries. Previous numerical experiments
[e.g., Fullsack, 1995] with SOPALE have extensively verified the accuracy of the computational code by an extensive series of benchmarking models that also include tests
to Rayleigh-Taylor instabilities in agreement with other
numerical and analytical studies [e.g., Houseman and
Molnar, 1997; van Keken et al., 1997].
2.2. Model Setup
[12] Figure 2 shows the setup of the model with a solution
space of 3000 km width and 660 km depth. The 660 km
seismic discontinuity is chosen as the base for the models as
it corresponds to a viscosity increase [Forte and Mitrovica,
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1996] related to a phase-change of olivine [e.g., Korenaga
and Jordan, 2004]. The Eulerian and Lagrangian computational meshes have 201 101 and 601 301 nodes in
the x and y directions, respectively. The top 200 km of each
mesh has a higher resolution in order to increase the stability and accuracy of the calculations in the lithosphere and
topmost mantle (Figure 2).
[13] The initial crust in the models has a uniform thickness
of 35 km and a wet quartzite composition [Gleason and
Tullis, 1995] (Table 2). The plastic rheology (Feff and C0)
of the crust has a cohesion of 1.0 MPa and strain softening
controlled by a decrease in friction angle (15° to 2°) with
accumulating strain [Braun et al., 1999; Pysklywec et al.,
2002] (Table 2). The sub-lithospheric mantle has a wet
olivine viscous creep rheology representative of nondehydrated mantle [Hirth and Kohlstedt, 1996]. The base of
the lithosphere may be defined as a thermal/rheological
boundary (at 1600 K) without a compositional contrast
between the mantle lithosphere and the rest of the mantle.
The “craton” has no compositional distinctiveness in models for which the base of the lithosphere is defined as a
thermal boundary layer, and simply refers to the right part
of the model domain that exhibits a thicker thermal lithosphere. In addition, we test models with a distinct dry
olivine rheology [Hirth and Kohlstedt, 1996] for the mantle
lithosphere at the right of the box, i.e., the “craton”-part of
the model. This simulates viscosity variations along the
western North American Craton [Dixon et al., 2004] and the
higher viscous strength of cratons [Doin et al., 1997;
Lenardic et al., 2003]. The plastic rheology of the mantle
under high confining pressures is defined by a high material
cohesion and no internal friction angle (Table 2). All
materials have a temperature dependent density structure
with reference densities of 2800 kg/m3 and 3300 kg/m3 for
the crust and mantle respectively (Table 2). The thermal
rock parameters are summarized in Tables 1 and 2 and
specifications of the different model runs are shown in
Table 3.
[14] The models in this study are defined (at onset) by a
hot and thin upper mantle lithosphere (“Cordilleran”) to the
left and a cool and much thicker mantle lithosphere
(cratonic) to the right of the model domain (Figure 3a).
This initial temperature structure is based on a conductive
Table 2. Definition of Material Dependent Parameter Values
Parameter
Crust
Mantle Lithosphere
Mantle
Thermal
w
k (W.m1.K1)
1136
2.5
1212
3.5
1212
3.5
Value
C0 (MPa)
Feff
1.0
15° to 2°
Plastic Rheology
1200
0°
1e24a
0°
Parameter
Wet Quartziteb
A (Pa-n s1)
n
Q (kJ mol1)
Viscous Rheology
1.10e–28
4.85e-17
4
3.5
223
515
Table 1. Definition of Parameter Values Common to All Models
Definition
r0 (crust)
r0 (mantle)
g
R
General Parameters
crustal reference density
mantle reference density
gravity acceleration
gas constant
2800 kg/m3
3300 kg/m3
10 m/s2
8.314 JK1 mol1
a
k
T0
Thermal Parameters
thermal expandability
thermal diffusivity
reference temperature
3.0 105 K1
1.0 106 m2/s
293 K
a
Dry Olivinec
Wet Olivinec
4.89e-15
3.5
498
Cohesion of mantle is set high to enforce viscous response.
After Gleason and Tullis [1995].
c
After Hirth and Kohlstedt [1996].
b
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Table 3. List of Numerical Experiments Describing the Variations in Model Setupa
Model
TempModel1
TempModel2
TempModel3
TempModel4
Thermal Parameters
BTL for craton: 160 km
BTL for back-arc 100 km
BTL for craton: 200 km
BTL for back-arc: 60 km
same as model TempModel1
same as TempModel1,
except of crustal heat production
RheoModel1
same as TempModel1
RheoModel2
RheoModel3
RheoModel4
same as model TempModel2
same as TempModel1
same as TempModel1
Rheological Compositions
Model Variants
Variant Temperature Structures
crust: wet quartzite; mantle: wet olivine
visco-range: 1020–1023 Pas; no shear
same as TempModel1
no shear; visco-range: 1020–1023 Pas
same as TempModel1
same as TempModel1
3.2 cm/yr shear; visco-range: 1020–1023 Pas
same as TempModel1
Variant Rheological Structures
crust: wet quartzite; craton ML: dry olivine;
mantle: wet olivine
same as RheoModel1
same as RheoModel1
same as RheoModel1
visco-range: 1020–1025 Pas; no shear
visco-range: 1020–1025 Pas; no shear
visco-range: 1020–1023 Pas; no shear
visco-range: 1020–1027 Pas; no shear
a
The rheological parameters are listed in Table 2.
temperature profile for the lithosphere and an adiabatic
gradient for the asthenosphere (Figure 3b) of 0.5 K/km
and with a thermal expansion coefficient (a) of
3.0 105 K1 and a heat capacity (cp) of 1212 J.kg1.K1.
The temperature boundary conditions are defined by a fixed
293 K top surface and fixed temperature bottom boundary
determined as described above. There is a zero heat flux
condition imposed on the sidewalls of the box.
[15] The interface between the conductive lithosphere and
underlying convecting mantle is defined by the 1600 K
isotherm and referred to as base of the thermal lithosphere
(BTL) [Doin et al., 1997; Jaupart and Mareschal, 1999].
For a BTL at 160 km, the mantle adiabat gives a temperature
of 1800 K at the base of the model domain at 660 km
depth (Figure 3c). A series of tests performed to determine
what BTL depth produced a semi-stable cratonic lithosphere
indicated that initial lithosphere thicknesses of 150–200 km
are stable over sufficiently long time-scales (at least
200 Myr). These values also comply with global estimates of
cratonic lithosphere thicknesses in the range of 175–
185 km [Artemieva and Mooney, 2001].
[16] The mechanical boundary conditions include a free
top surface. The bottom boundary of the box is, by default,
free-slip, except when a basal shear velocity is applied in a
few selected models. The sidewalls are free-slip boundaries,
which means that they allow for vertical motion while being
horizontally fixed and are impermeable to material flow
normal to them. The models omit horizontal displacements
whereby any geodynamic response results purely from the
mantle flow and lithospheric response to the lateral thermal
and rheological transition in the upper mantle.
3. Modeling Results
[17] In a first series of models (TempModels) the size of
the step in the BTL depth between the craton and the backarc region is varied. A second series (RheoModels) takes
into account a lateral change from hydrated to dry mantle
lithosphere. Table 3 lists the various TempModels and
RheoModels.
3.1. “Temperature” Models
[18] The first model, TempModel1 (Figure 4), has an initial temperature structure defining a lithosphere of 100 km
thickness to the left of the model and a 160 km thick
Figure 3. (a) The initial (zero-stage) stage temperature
structure specifying the hot upper mantle and thin lithosphere to model left and colder upper mantle thicker lithosphere to model right. (b) Definition of the base of the
thermal lithosphere located at the intersection of the conductive geotherm and mantle adiabatic gradient. The thermal
boundary layer forms a zone where the conductive gradient
transits to the mantle adiabat, above which conduction prevails and below which convection takes over [e.g., Jaupart
and Mareschal, 1999]. (c) One-dimensional temperature
profiles of a 660-km vertical slice through the modeldomain, with a conductive gradient for the thermal lithosphere and the mantle adiabat for the underlying convective
mantle.
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Figure 4. The evolution of TempModel1 shown in five time-slices at 1, 10, 30, 50 and 100 Myr. The
temperature and displacement fields are shown for each time-slice and the BTL is outlined as the
1600 K temperature contour. The initial lateral temperature contrast (1 Myr) is marked by a lithospheric
thickness of 100 km to the left and 160 km to the right.
lithosphere to the right with a 250 km wide transition at
x = 500 km (Figure 3a). The thermal and velocity fields
show how mantle flow is initiated at the lateral temperature
transition, with initial upwelling beneath the thin lithosphere
and downwelling at the temperature discontinuity (i.e., in a
style of edge-driven convection). The base of the lithosphere
is a pure thermal boundary layer for TempModel1 (located
between 1000 and 1600 K isotherms) and shows in the first
10 Myr the transient effect as it adjusts from the initial conditioned temperature structure to a new quasi-equilibrium.
Small-scale convection migrates to areas beneath the thicker
cratonic lithosphere. Through the model progression this
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Figure 5. The evolution of (a) TempModel2 and (b) TempModel3 at 1, 10, 30, 50 and 100 Myr.
Differences in evolution are the result of an enhanced lateral temperature transition (TempModel2)
and of the shear at lower left of the model domain (TempModel3).
small-scale flow is quite strongly time-dependent as the
lithospheric thermal boundary layer instabilities grow and
diminish in variable locations through the 100 Myr evolution of the model (Figure 4).
[19] The step in BTL depth is larger in TempModel2; a
60 km thick lithosphere is adjacent to a 200 km thick cratonic lithosphere (Figure 5a). As a result, the TempModel2
model develops much stronger edge-driven convection,
involving a stronger ascent of hot mantle under the thin
lithosphere and descent at the edge of the craton. The edgedriven flow erodes the craton edge (500 km cratonward
migration after 30 Myr) whereby hot mantle replaces the
cold mantle. After 100 Myr, the edge has moved 1000 km
cratonward, while the vertical contrast at the step between
the 80 km-thick domain of thin and hot lithosphere and the
150 km thick craton is maintained.
[20] TempModel3 (Figure 5b) has the same initial temperature structure as TempModel1 but has a shear velocity
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imposed at the lower left base of the model (Table 3). The
imposed basal velocity triggers a counter-clockwise convection cell (Figure 5b; at 1 Myr)., opposite to the edgedriven flow that resembles the flow pattern of models [e.g.,
Currie and Hyndman, 2006; Currie et al., 2008] that
account for a subducting slab to the left of the back-arc
region. TempModel4 addresses the effects of crustal heat
production with 1.7 mW/m3 and 0.8 mW/m3 for the upper and
lower crust respectively. While the heat flow through the
crust increases with 45 mW/m2, the overall temperature
structure and mantle flow patterns are not significantly different from models of the same setup but without heat
production.
[21] The different TempModels all generate an initial
convection cell at the lateral temperature transition after a
few Myr that consequently spreads to small-scale convection
cells through the entire model domain (Figures 4 and 5). The
convection cells comprise wide zones of hot mantle
upwelling and narrow zones of cold descending mantle that
have an aspect ratio of 1 and are 500 km in size. The upper
mantle flow shapes the temperature structure and the BTL
evolves from the interplay between conductive heat transfer
in lithosphere and mantle dynamics (i.e., convective flow
and instabilities).
3.1.1. Crustal Deformation and Topographic Response
[22] The free-surface deflection predicted by the models
are the response of the upper boundary surface to changes in
the density structure (e.g., by changes in crustal thickness)
and to stresses induced by mantle flow [e.g., Boutilier and
Keen, 1999; Pysklywec and Shahnas, 2003].
[23] The models predict a relative positive elevation above
the hot and thin lithosphere and a negative elevation for the
cold cratonic lithosphere (Figures 4 and 5). The relative,
rather than absolute, values of the topography are important
here since the absolute deflections integrated over the model
domain remain essentially equal to zero as result of conservation of mass and incompressibility of the material. A
first-order topographic contrast of 1300 m develops in
TempModel1 with positive elevation above the hot lithosphere relative to the craton (Figure 4). This topographic
contrast establishes immediately after onset (i.e., 1 Myr) as
result of the imposed initial temperature structure. In later
stages, sensible deviations develop on top of this first-order
trend with positive and negative topography respectively
correlating to zones of hot mantle rise and cold mantle
descent.
[24] For comparison, models with a lithosphere of uniform
thickness of 140–160 km were tested in which the convection cells produced free-surface deflections with amplitudes
of up to 100 m and horizontal wavelengths that correspond
to the width of the convection cell (500 km). Much higher
free-surface deflections of 300–600 m (Figures 4 and 5) are
formed in the TempModels because of strong mantle convection that results from the lateral temperature transition. In
addition, the free-surface deflection profiles in TempModel2
are affected by the particularly strong mantle flow at the
craton edge.
[25] The surface response to mantle flow and instabilities
at the BTL is outlined in more detail in Figure 6 in which a
time series of surface-deflection profiles (Figure 6a) are
plotted for TempModel1 along with profiles of the evolution
of the BTL (Figure 6b), crustal thickness (Figure 6c) and
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horizontal surface strain (Figures 6d). The depth to the BTL
(Figure 6b) evolves when downwellings are formed that
entrain lithosphere material and displace the 1600 K isotherm deep into the mantle. After 100 Myrthe average lithosphere thickness to the left is 90 km versus a lithosphere
thickness of 120–130 km to the right in the model domain.
Furthermore, in these models the lithosphere deformation
(reflected in crustal thickness changes and surface deflection) seems affected more by mantle flow around the lateral
temperature transition than by the short wavelength high
amplitude instabilities at the BTL (Figure 6b).
[26] The crust at the left side of the domain continues to
thin while it thickens below the craton. The changes in
crustal thickness are isostatically compensated and therefore
incorporated in the free-surface deflection response. The
thinning of the back-arc crust is related to tensile stresses
exerted from the base of the lithosphere and reflected in the
horizontal strain rates distribution at surface (Figure 6d).
Tensile stresses occur above the strong upward mantle flow
central underneath the thin lithosphere with horizontal flow
in opposite directions at the interface with the thermal lithosphere base. At the surface the horizontal extensional strain
rate is 1.0–2.0 1016 s1. This induces crustal thinning of
20–30% in about 30–50 Myr. The crust of the craton lithosphere thickens under the influence of strong mantle flow
around the step in the BTL and is augmented by the feeding
of drips and instabilities at the base of the craton lithosphere.
3.1.2. Lithosphere and Surface Heat Flow
[27] The surface heat flow is 30 mW/m2 higher in the
hot and thin lithosphere region than in the craton for
TempModel1 (Figure 4) at 30 Myr. The mantle flow has
fully established at this time and mantle heat has conducted
into the lithosphere. The surface heat flow consequently
reflects the lateral temperature transition and shape of the
BTL. Furthermore, TempModel2 (Figure 5a) shows how the
lateral change in surface heat flow shifts cratonward in time
and follows the migrating step at the base of the lithosphere.
[28] Even when the lateral transition in the BTL and surface heat flow stays in place, time-variations in the surface
heat flow values occur. The models display an increase in
surface heat flow in time that is, in part, caused by mantle
heat entering the lithosphere once mantle convection is
established (Figure 7). This is not significantly changed by
incorporating crustal heat production (TempModel4).
TempModel4 contains a constant radiogenic heat production
of 1.5 mW/m3 to a depth of 20 km, both in the construction
of the initial temperature profile and for the subsequent
model evolution. The bottom panels (Figure 7, panels I)
show the vertical heat flow distribution in the upper 260 km
and shows for TempModel1 after 30 Myr the highest values
in the lower part of the thermal lithosphere (within the thermal boundary layer between the 1000–1600 K isotherms).
The top panels (Figure 7, panels II) show the vertical heat
flow at different depths in the models. After 30 Myr heat
flow values of 55 mW/m2 at 60 km depth are found for
the hot mantle lithosphere to the left in TempModel1. At
this time, the hot upper mantle has convected heat into the
conductive lithosphere, but this has not reached surface
since surface heat flow values are only 35–40 mW/m2
(Figure 7a; TempModel1 at 30 Myr). In the case of steady
state thermal lithosphere conditions, the observed surface
heat flow would equal the sum of heat flow coming from
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Figure 6. Profiles at selected times for model TempModel1, showing the evolution over the horizontal
box domain [x = 0→3000 km] of (a) surface deflection, (b) depth to base thermal lithosphere (i.e.,
1600 K isotherm), (c) crustal thickness, and (d) horizontal surface strain rate.
the mantle and crustal heat production. Since TempModel1
contains no crustal heat production, the strong contrast
between mantle and surface heat flow values is the result of
profound nonsteady state temperature conditions (i.e., transient) in the conductive lithosphere. Consequently, it takes
up to 60 Myr before the mantle heat has reached the
surface. The effect of crustal heat production is included in
TempModel4 (Figure 7b). The surface heat flow after
30 Myr is 40 mW/m2 higher for this model than for the
model without crustal heat production.
[29] The side-panels (labeled III) of Figure 7 depict vertical temperature profiles that show a steep temperature
gradient in the lower part of the mantle lithosphere shortly
after the onset of the model evolution. Temperature rises at
the base of the BTL after initiation of mantle convection,
which steepens the temperature gradient and produces the
high vertical heat flow (50 mW/m2) through the mantle
lithosphere. At the same time, heat has not yet transferred
upward in the lithosphere, resulting in a still smaller average
temperature gradient for the lithosphere (i.e., only 8 K/km
for the craton lithosphere at 30 Myr of TempModel1,
Figure 7a, panels III) and a lower heat flow of 35 mW/m2
through the crust overlying the hot mantle lithosphere to the
left. Crustal heat flow at 30 km depth (15 mW/m2) is notably
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Figure 7. Temperature and heat flow evolution from base conductive lithosphere to surface for
(a) TempModel1 at 30, 50 and 100 Myr without crustal heat production and (b) with heat production
(TempModel 4). The bottom panels (I) give the distribution in vertical heat flow for the upper 260 km
of the model domain. The top panels (II) show the vertical heat flow distribution for three horizontal
slices at 10, 30 and 60 km depth through the model domain. The panels to the right (III) depict the vertical temperature profile for three zones in the model domain (left, central, right).
lower for the craton lithosphere to the right of the model
domain. Over time, the surface heat flow increases to 50–
60 mW/m2 for the hot lithosphere and 25 mW/m2 for the
craton lithosphere. A similar pattern in crustal and surface
vertical heat flow distribution is shown for TempModel4
(Figure 7b) with crustal heat production.
[30] To summarize, the surface heat flow increases both
for the hot back-arc and craton over a time interval of 30–
100 Myr. However, the contrast in crustal heat flow (e.g.,
25–35 mW/m2 at 30 km depth) between the hot back-arc and
craton remains a dominant feature after 30–100 Myr.
3.2. “Rheological” Models
[31] The base of the lithosphere may represent a pure
thermal boundary layer (TempModels). Alternatively the
lithosphere can be considered to be compositionally distinct
from the convective mantle owing to differences in water
content by dehydration or chemical depletion of older
mantle lithosphere [Jordan, 1978]. A dry olivine rheology
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Figure 8. (a) Compositional and rheological setup of the RheoModels with the base of the lithosphere
(1600 K) of RheoModel1. (b) Viscosity structure for four different rheologies as described in Table 2 over
a linear temperature profile of 200–1600 K.
assigned to the cratonic mantle lithosphere increases the
effective viscosity contrast with the underlying convecting
mantle [Currie et al., 2004; Lenardic et al., 2003] and
amplifies the rheological contrast that occurs at the lateral
temperature transition.
[32] Figure 8 shows the compositional and rheological
structure of the RheoModels. The models contain a dry
olivine mantle lithosphere for the craton lithosphere
(Figure 8a), while the hot upper mantle to the left maintains
the wet olivine composition similar to the sub-lithospheric
mantle. Figure 8b outlines the viscosity as function of
temperature for different crustal and mantle compositions.
The upper viscosity limit is increased to 1025 Pas for the
RheoModels (1023 Pas in the TempModels) and its brittle
failure is defined by a cohesion of 120 MPa (Table 3). The
temperature structure of the RheoModels is similar to their
TempModel counterparts. RheoModel1 and RheoModel2
allow viscosities to reach 1025 Pas and, as result, support
higher deviatoric stresses compared to the TempModels.
[33] When the craton lithosphere is rigid (RheoModel1,
Figure 9a), it does not erode easily and the lateral temperature gradient is preserved over longer time scales. The
30 Myr time slice shows an overall mantle convection pattern across the model domain, comparable to TempModel1
(Figure 4), including edge-driven flow along the lateral
temperature transition. However, while the transition
migrates cratonward for TempModel1, the transition stays in
place in RheoModel1 (Figure 9a) as a result of the added
strength from a dry olivine composition for the craton lithosphere. This is well illustrated by the lateral temperature
transition, which has not shifted nor reduced in amplitude
after 50 and 100 Myr compared to the initially imposed
temperature structure (Figure 9a; 1 Myr).
[34] Figure 9b outlines the evolution of RheoModel2,
which contains a similar initial temperature structure as
TempModel2 (Figure 5a). Both models are characterized by
an enhanced temperature contrast, which leads to much
stronger edge-driven convection and overall mantle flow
compared to RheoModel1 and TempModel1. The higher
viscosities in RheoModel2 for the mantle lithosphere prevent erosion of the craton (over 100 Myr). The high viscosity of the craton mantle lithosphere also mitigates the
crustal deformation and surface deflection. However, the hot
mantle upwelling along with the edge-driven flow at the
transition still tends to thin the crust in the overlying
back-arc. Crustal deformation in RheoModel1 is negligible,
whereas the crust in RheoModel2 thins as result of stronger
mantle flow (Figure 9b). Consequently, free-surface undulations develop on top of the first-order >2 km topography
above the hot lithosphere and are related to deformation of
crust.
[35] In addition to the change to dry olivine composition
for the upper mantle of the craton, the impact of the effective
viscosity range has also been tested (Figure 8b). In addition
to RheoModel1 and RheoModel2 with upper viscosity limit
set to 1025 Pas, the effect of an upper viscosity limit of
1023 Pas (RheoModel3; similar to the TempModels) and of
1027 Pas (TempModel4) was tested (Table 3). The results
(not shown) indicate that models with a dry olivine rheology
produce effective viscosities above 1023 Pas, while occasional peak values above 1025 Pas introduce numerical
instabilities (RheoModel4). An effective viscosity range of
1020-1025 Pas gives the models sufficient stability and
freedom to generate both a low viscous upper mantle and
high viscous lithosphere at the lateral temperature transition.
[36] Figure 10 summarizes the evolution of the surface
deflection pattern in time for RheoModel1 with respect to
the shape of the BTL, the crustal thickness, and horizontal
strain rate. This model produces, similar to TempModel1
(Figure 6a), high topography above the back-arc from the
isostasy and additional dynamic support from the upward
flow in the mantle that stands in contrast with low topography across the craton (Figure 10a). The topographic contrast
between the back-arc and the craton of RheoModel1 is more
stable in its location because of the well-preserved temperature transition in the upper mantle. The crustal thickness
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Figure 9. The evolution of (a) RheoModel1 and (b) RheoModel2 for five time-slices at 1, 10, 30, 50 and
100 Myr. The model corresponds to TempModel1 and TempModel2, respectively (Figure 4) except for a
dry olivine rheology for the craton mantle lithosphere.
profiles (Figure 10d) show how the RheoModel1 preserves
the uniform 35 km thick crust along the model domain
over 100 Myr. Another important difference with the
TempModels is the absence of small topographic undulations
of few hundred meters amplitude and a wavelength of 400–
600 km across the craton. These free-surface deflections
that correlated well with the general mantle convection cells
in the TempModels are inhibited in the RheoModels as
result of the more rigid mantle lithosphere of the craton.
[37] Figure 11 compares the rheology structure and
consequent deformation patterns of RheoModel1 and
RheoModel2 with TempModel1 at 30 Myr. Panel I of
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Figure 10. Profiles at selected times for RheoModel1, showing the evolution over the horizontal box
domain [x = 0->3000 km] of (a) surface deflection, (b) depth to base thermal lithosphere, i.e.,
1600 K isotherm, (c) crustal thickness, and (d) horizontal surface strain rate.
Figure 11a depicts the crustal thickness and surface strain
rate for TempModel1 and panel II outlines the mantle flow
patterns and lithosphere displacement field. They confirm,
as shown above, how the lithosphere deforms significantly
for TempModel1 and how, in particular, the crust extends
and thins above the hot upper mantle domain and contracts
and thickens in a distributed manner across the cratonic
lithosphere. In contrast, in RheoModel1, the displacement
field in the lithosphere displays no significant deformation
(Figure 11b, panel II) and the crust retains a constant
thickness of 35 km (Figure 11b, panel I).
[38] The difference in deformation response can be better
understood by comparing the viscosity structure and strain
rate distributions (Figure 11, panels III and IV, respectively).
The low viscosity asthenosphere results in high flow rates of
1012-1015 s1 for both models (Figures 11a and 11b). The
overlying lithosphere exhibits strain rates of 10151017 s1 for TempModel1. The vector field for the lithosphere of TempModel1 (Figure 11a, panel II) shows large
horizontal displacements above the transition and directed
toward the craton that gradually decreases in amplitude (i.e.,
a converging vector field) across the craton lithosphere,
reflected in the contractional surface strain rate and crustal
thickness evolution. The lithosphere in RheoModel1 exhibits strain rates that are 100 times smaller (i.e., 10171019 s1) than TempModel1 and displays negligible
(crustal) deformation, due to the higher viscous upper mantle
despite the same initial temperature structure and similar
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Figure 11. Rheological structure, stresses and deformation of the lithosphere for (a) TempModel1 compared with (b) the new RheoModel1 and (c) the RheoModel2 at 30 Myr with (I) the crustal thickness and
horizontal surface strain rate, (II) compositional structure and displacement field for the upper 250 km of
the model domain, (III) viscosity structure, and (IV) strain rate distribution across the upper 250 km of the
model domain.
overall mantle flow pattern. The more vigorous mantle flow
around the lateral temperature transition of RheoModel2
initiates higher strain rates of 1016-1018 s1 in the lithosphere (Figure 11c, panel IV) compared to RheoModel1,
despite the same strong mantle lithosphere rheology for the
craton. RheoModel2 also shows substantial localized thinning of the crust above the lateral transition (Figure 11c,
panel I) that, as the surface strain rates illustrate, is caused by
extension on the back-arc side (versus compression on the
craton side) of the step.
[39] These results show how edge-driven flow can generate viable strain rates of 1016-1018 s1 typical of intraplate
lithosphere away from active plate margins, depending on
the existence of strong lateral temperature gradient in the
upper mantle and on the compositional structure of the
mantle lithosphere.
4. Discussion
4.1. Edge-Driven Flow in the Back-Arc of an Active
Margin
[40] Edge-driven flow can occur at lateral temperature
transitions of the lithosphere and the process has been well
studied for passive margin transitions [e.g., King and
Anderson, 1995, 1998]. The occurrence of edge-driven
flow has only recently been discussed within continental
interiors, such as the Colorado Plateau [Karlstrom et al.,
2008; van Wijk et al., 2010]. The models presented here
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address for the first time the development of such flow for
transitions from hot and thin back-arc lithosphere to cratonic
lithosphere. Edge-driven convection needs no active plate
boundary forcing but can start after such a transition has
been established. A scenario for the formation of continental
back-arcs [Hyndman et al., 2005] is described by models
that include a cold oceanic subducting plate and account for
its traction and the release of water [Arcay et al., 2006;
Currie and Hyndman, 2006; Currie et al., 2008]. In the case
of a continental back-arc, presumed subduction-driven
corner flow first needs to etch out a sharp lateral change at
the BTL [Arcay et al., 2006] and may later be supported
by additional edge-driven convection.
[41] In the outline of the models (Figure 1), corner and
edge-driven flow are depicted by two convection cells
with a counter-clockwise (II) and clockwise (I) directed
flow, respectively and with a central zone of upwelling.
TempModel3 shows that when a counter-clockwise convection cell is imposed by boundary conditions to the left
(i.e., a vertical shear velocity of 3.2 cm/yr), a clockwise
convection cell still develops toward the right edge of the
back-arc. TempModel 3 (and other models) shows that a
back-arc of 500 km is sufficiently wide to host both a
clockwise edge-driven convection cell and counter-clockwise
cell that together produce the upwelling central underneath
the back-arc.
[42] Subduction-driven models can account for lithosphere thinning underneath the continental back-arc [Currie
et al., 2004, 2008], but also indicate the difficulty in producing simultaneously high temperatures in the overriding
mantle lithosphere close to the subducting slab and at larger
distances in order to sustain a wide and thin back-arc [Currie
et al., 2004]. The results of the present study suggest that
edge-driven flow is also a mechanism at play once a lateral
temperature transition has formed at the base of the thermal
lithosphere.
4.2. Lateral Temperature Transition and Heat Flow
Evolution
[43] Comparison of TempModel1 and TempModel2
shows how a different vertical step size at the BTL affects
the upper mantle flow and consequent thermal evolution.
TempModel1 shows flattening and cratonward migration of
the temperature transition from 10 to 50 Myr (Figure 4).
While the temperature transition has widened and diminished in amplitude, it has not entirely dissipated over
100 Myrs (Figure 4). The position and amplitude of
the temperature transition is much better maintained in
TempModel2 owing to enhanced edge-driven flow accompanying the more pronounced transition in lithosphere
thickness. The stronger edge-driven flow better preserves
the thin lithosphere at one side by stronger upwelling and
thick lithosphere at the other side due to enhanced downwelling. This shows the ability of mantle dynamics to support a lateral temperature transition at the base of the
lithosphere during long periods during which time it would
otherwise widen and diminish in amplitude by heat conduction [Schmeling and Marquart, 1993; Hieronymus et al.,
2007].
[44] The evolution of the upper mantle temperature structure and the differences among the TempModels and
RheoModels also result in different heat flow responses
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through the overlying lithosphere and at the surface. TempModel1 (Figure 4) and TempModel2 (Figure 5a) show a
lateral change in surface heat flow from high to low values
from above the thin to thick lithosphere, respectively, that
widens and shifts cratonward in time. This is in contrast to
the RheoModels, for which the sharp transition from high
surface heat flow above the hot mantle and low values above
the craton lithosphere remain in place over a time-span of
100 Myr (Figure 9). The results (Figure 7) also point to the
transience between mantle and surface heat flow; the latter
only fully reflect changes in mantle (heat) flow patterns after
60 Myr.
4.3. Surface Topographic and Deformational Response
to Mantle Flow
[45] The RheoModels show the effects of a lateral compositional change for the mantle lithosphere on the evolution
of the lateral temperature transition in the upper mantle. The
rheological transition from wet to dry olivine enhances the
corner flow effect, supports the hot back-arc anomaly and
maintains its positive elevation, even at 100 Myr. Especially
RheoModel2, with its enhanced edge-driven convection that
lead to a strong migration of the step in TempModel2, shows
how the more rigid upper mantle of the craton preserves
the temperature and rheological transition and maintains
the corner flow and lithosphere response at their initial
positions.
[46] The viscosity structure of the upper mantle lithosphere determines how far edge-driven mantle flow transmits deformation into the overlying lithosphere and is
inhibited for an effective viscosity above 1024 Pas. Therefore, a compositionally distinct lithosphere for the craton can
have a significant impact on the interplay between mantle
flow dynamics and lithosphere response.
[47] Topographic undulations from small-scale mantle
convection are mostly absent in the RheoModels, except
where the edge-driven flow induces a positive topography
signal on the back-arc side of the transition (Figure 10c; at
x = 1000 km) and a negative signal on the craton side.
Consequently, the positive topographic contrast of the thin
and hot back-arc lithosphere relative to the craton is combined with a smaller wavelength additional topographic
contrast and with a width of 500 km is the result of the
descending mantle beneath the lateral temperature transition.
The amplitude of this signal is dependent on the viscosity of
the mantle lithosphere and is as much as 300–400 m for the
models presented.
[48] The models reveal the tendency of the crust to thin
above the hot upper mantle as a result of traction at the
lithosphere base from edge-drive mantle flow at the transition. The thinning of the crust is triggered solely by the
presence of a hot upper mantle and the lateral temperature
transition because the models explicitly exclude horizontal
tectonic forcing of the lithosphere. The transfer of edgedriven traction into the overlying lithosphere and the magnitude of crustal deformation depend on the viscosity of the
mantle lithosphere. The RheoModels indicate that a lateral
temperature transition at the BTL can migrate cratonward
under the influence of edge-driven flow until it meets a
rheological transition that keeps the transition in place.
Furthermore, the RheoModels exhibit a lithosphere that is
more decoupled from convective instabilities in the upper
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mantle [e.g., Jordan, 1978; Shapiro et al., 1999; Lenardic
et al., 2003].
5. Application to the Southern Canadian
Cordillera
[49] The geodynamics of a lateral temperature transition in
the upper mantle has application to the southern Canadian
Cordillera (Figure 1). The crustal and upper mantle architecture of the Canadian Cordillera and North American
Craton has been extensively studied [Clowes et al., 1995;
Cook, 1995; Zelt et al., 1996; Burianyk et al., 1997; Bouzidi
et al., 2002]. The high upper mantle temperatures beneath
the Cordillera that were first inferred from high surface heat
flow (Figure 1b) and high electrical conductivities [Gough,
1986; Jones and Gough, 1995; Lewis et al., 1992] have
been recently confirmed by high resolution tomography
studies [van der Lee and Frederiksen, 2005; Mercier et al.,
2009; Sigloch et al., 2008]. The studies outline a first-order
transition, roughly following the deformation front in the
southern Canadian Cordillera, from lower seismic velocities
beneath the Cordillera to much higher seismic velocities
(Figure 1e) in the upper mantle of the North American
Craton [Frederiksen et al., 2001; van der Lee and
Frederiksen, 2005].
[50] While previous modeling studies addressed lithosphere thinning underneath the central Cordillera [e.g.,
Currie et al., 2004, 2008] as well as the significance of a hot
upper mantle adjacent to the cold lithosphere of the North
American Craton [Hyndman and Lewis, 1999; Hyndman,
2010; Lowe and Ranalli, 1993], the geodynamic implication of the transition was not previously addressed. Edgedriven flow may only complement earlier proposed
mechanisms that initiated continental back-arc thinning
[e.g., England and Houseman, 1989; Jones and Gough,
1995; Arcay et al., 2006; Currie and Hyndman, 2006;
Currie et al., 2008]. Edge-driven flow in the Canadian
Cordillera may have started in the Eocene after the onset
and development of subduction of the Juan de Fuca plate,
with mantle flow established and the overriding North
American plate thinned beneath the Cordillera. Since the
initial state of the presented models corresponds with the
time of establishment of a back-arc to continental edge
transition and the start of edge-driven flow, the 30–50 Myr
model time slices reflect the present-day.
[51] The present study outlines cratonward migration of a
temperature transition for hydrated mantle lithosphere, until
the transition faces a drier mantle lithosphere. This can
explain why the lateral temperature transition under the
Canadian Cordillera is currently located beneath the eastern
Foreland Belt. The upper mantle of the Cordillera is considered to have a low viscosity wet olivine rheology due to a
long history of subduction-related hydration of the upper
mantle beneath the Intermontane and Omineca Belts [Arcay
et al., 2006; Dixon et al., 2004; Hyndman et al., 2005]. A
lateral compositional and, consequently, rheological transition must be located beneath the Foreland Belt, since the
mantle lithosphere of the North American Craton reportedly
has a dry, high viscosity rheology [Dixon et al., 2004; Doin
et al., 1997]. Consequently, edge-driven flow could have
readily consumed mantle lithosphere at a lateral temperature
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transition since the Eocene, until it reached its current position under the Foreland Belt.
[52] Comparison of the 30–50 Myr time slices of the
RheoModels 1 and 2 with present-day upper mantle
structure (i.e., seismic velocities after Sigloch et al. [2008];
Figure 1e) shows that some features correlate. The models
produce a zone of descending colder mantle at x = 900–
1000 km about 200 km cratonward of the edge that correspond well with the +3% DVp beneath the Foreland. Similar
drops of descending mantle by edge-driven flow are found
beneath the cratons adjacent to the thinned lithosphere of the
Colorado plateau [van Wijk et al., 2010].
[53] Furthermore, the tendency of the lithosphere and
overlying crust to thin as a result of edge-driven traction
at the lateral temperature transition (e.g., TempModel1)
reflects some large-scale deformation patterns in the
Cordillera. The models portray tensional forcing and viscous creep activation of the crust that fit well with the formation of core complexes and half-grabens in the Cordillera
in Eocene-Oligocene time [e.g., Parrish et al., 1988;
Gordon et al., 2008] (Figure 1a). The formation of core
complexes is sometimes described by collapse of an overthickened crust and lithosphere that fails after far-field
compressional forces ceased, for the Canadian Cordillera by
the establishment of a more westerly subduction system of
the Juan de Fuca plate [e.g., Constenius, 1996; Liu, 2001].
Instead, the presented models contain no thickened crust
and no tectonic forcing on the side boundaries of the model.
Crustal thinning occurs as result of local edge-driven flow
in the mantle underneath an already thinned Cordillera
lithosphere.
[54] The deformation in the RheoModels is more subtle
compared to the TempModels since the mantle lithosphere
of the craton is more rigid and therefore reflects a more
realistic lateral lithosphere transition. This is reflected in the
surface deflection response, for which the RheoModels display a subtle short wavelength topographic high and low
(300 m) above the lateral temperature transition in addition
to the broad isostatic uplift above the hot back-arc
(Figure 10). The position of the deflection corresponds to the
location of the Canadian Foreland Belt (Figure 1a) and has a
similar wavelength as lithosphere flexure and could have
added to the strong flexural deflections from the build-up
and later removal of an orogenic surface load [Beaumont,
1981]. The surface deflection in this study did not exhibit
any >1000 km wavelength signals to explain post-orogenic
Eocene uplift and exhumation that not only affected the
Cordillera, but also the adjacent craton at large distance
[Hardebol et al., 2009]. Beaumont [1981] already pointed
out that the Cretaceous foreland subsidence in southern
Canada was too wide in extent to be attributed only to continental flexure under the Cordilleran orogenic load (see also
Peper, 1994 and references therein). Deep-rooted mantle
flow, deeper than the upper 660 km that this study considers,
would be required to explain such large wavelength epeirogenic surface deflections [Mitrovica et al., 1989; Pysklywec
and Mitrovica, 2000].
[55] Finally, the surface deflection and heat flow effects of
the lateral transition occur especially above the transition
from hot Cordillera lithosphere to cold North American
Craton, i.e., the location of the Foreland Belt (Figure 1a).
High surface heat flow values for the Cordillera (>80 mW/m2;
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Figure 1b) decrease eastward to values typical for cratonic
lithosphere (50 mW/m2) and are well represented by the
model with crustal heat flow in combination with a dry
olivine mantle rheology for the craton. These models exhibit
a lateral change in surface heat flow of 30 mW/m2 with
lithosphere thickness for the back-arc of 80–90 km and
craton lithosphere thickness of 140–170 km, 30–50 Myr
after the temperature transition establishes (Figure 7).
Mantle flow modeling can help to constrain basal heat flow,
an important input in basin modeling studies for the temperature and petroleum history evolution of the foreland belt
and adjacent basin. It is shown here that the lateral (near
surface) heat flow distribution (input for basin models) is
critically controlled by the upper mantle temperature structure and the evolution of a lateral transition at the base of
the lithosphere. Lateral changes in the heat flow distribution
can migrate or stay fixed, depending on mantle flow
dynamics and upper mantle rheology.
6. Summary and Conclusions
[56] This study addresses the interaction between lithosphere deformation and small-scale convection at a significant upper mantle lateral temperature transition in the
absence of any plate boundary or other external forces. The
lateral temperature transition constitutes a major change of
depth to the base of the thermal lithosphere and can be found
between any two distinct continental regions of different
thermal regime. The present numerical experiments show
that the effect from edge-driven convection at a temperature
transition at the base of lithosphere is large enough to produce a noticeable response in the lithosphere deformation
and heat flow pattern. Edge-driven mantle flow at the lateral
transition can trigger deformation in the overlying lithosphere that results in crustal thinning, producing significant
temporal and lateral changes in surface heat flow and
deflection patterns.
[57] The surface heat flow response, while entailing a
significant transient component, reflects the lateral temperature transition over time. A distinct transition with a
30 mW/m2 contrast between the hot back-arc and cold
craton is found which follows the lateral temperature transition when it migrates cratonward. The amount of crustal
thinning by edge-driven traction depends on the rheology of
the upper mantle lithosphere that, for a distinct dry olivine
composition and high viscosity, inhibits deformation
induced by mantle flow. The vertical step size at the base of
the lithosphere influences the vigor of the edge-driven flow
and the amount of traction along the base of the lithosphere
near the transition. A larger step increases the traction of the
mantle flow, accentuating the step and increasing the tendency of the lateral transition to migrate cratonward. Edgedriven flow maintains the step by upward flow underneath
the thin and downward flow underneath the thick lithosphere sides of the transition. The step at the base of the
lithosphere is preserved and is not eroded when the mantle
lithosphere of the craton has a more viscous dry olivine
composition. Upper mantle flow and mantle lithosphere
rheology hence work together in maintaining long-term
stability between adjacent tectonic provinces of distinct
lithosphere thickness for at least 60 Myr.
B01408
[58] The models are applied to the Canadian Cordillera,
which hot and thin lithosphere is adjacent to the much colder
and thicker North American Craton. The temperature transition is positioned beneath the Cordilleran Foreland Belt at
the boundary between the hydrated back-arc and the
depleted craton mantle lithosphere. Edge-driven convection
at the lateral transition is important for understanding basement heat flow fluctuations and surface deflection below the
Foreland Belt. The models predict cold downwelling that
may correspond to fast seismic wave velocities below the
craton edge, as well as erosion of the craton edge 30–50 Myr
after thinning of the Cordillera lithosphere and initial
development of a lateral temperature transition.
[59] Acknowledgments. This work was conducted under the program of the Netherlands Research Centre for Integrated Solid Earth Science
(ISES). Research visits of N.J.H. were (financially) supported through a
travel grant from the VU University FALW promovendifonds (PhD student
support) and by the Natural Sciences and Engineering Research Council
(NSERC) of Canada. We like to thank J. van Wijk and C. Matyska for their
very useful reviews and suggestions. N.J.H. acknowledges J.-P. Callot (IFP
Energies nouvelles) for stimulating research toward mantle flow modeling
and appreciates the opportunity for using the numerical facilities and
SOPALE code at the University of Toronto. SOPALE was originally developed by Philippe Fullsack.
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N. J. Hardebol, Department of Geotechnology, Faculty of Civil
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R. Stephenson, School of Geosciences, University of Aberdeen, King’s
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