Geophys. J. Int. (1999) 139, 556–562
Numerical models of ductile rebound of crustal roots beneath
mountain belts
Hemin A. Koyi,1 A. Geoffrey Milnes,2,* Harro Schmeling,3 Christopher J. Talbot1,
Christopher Juhlin1 and Hermann Zeyen4
1 Hans Ramberg T ectonic L aboratory, Department of Earth Sciences, V illavägen 16, S-752 36 Uppsala, Sweden. E-mail: [email protected]
2 Department of Geology, University of Bergen, N-5007 Bergen, Norway
3 Institut für Meteorologie und Geophysik, Universität Frankfurt, Feldbergstrasse 47, 60323 Frankfurt am Main, Germany
4 Département des Sciences de la T erre Université de Paris-Sud, Bât. 504, F-91405 Orsay, cedex, France
Accepted 1999 July 27. Received 1999 June 14; in original form 1998 December 10
SU M MA RY
Crustal roots formed beneath mountain belts are gravitationally unstable structures,
which rebound when the lateral forces that created them cease or decrease significantly
relative to gravity. Crustal roots do not rebound as a rigid body, but undergo intensive
internal deformation during their rebound and cause intensive deformation within the
ductile lower crust. 2-D numerical models are used to investigate the style and intensity
of this deformation and the role that the viscosities of the upper crust and mantle
lithosphere play in the process of root rebound. Numerical models of root rebound
show three main features which may be of general application: first, with a low-viscosity
lower crust, the rheology of the mantle lithosphere governs the rate of root rebound;
second, the amount of dynamic uplift caused by root rebound depends strongly on the
rheologies of both the upper crust and mantle lithosphere; and third, redistribution of
the rebounding root mass causes pure and simple shear within the lower crust and
produces subhorizontal planar fabrics which may give the lower crust its reflective
character on many seismic images.
Key words: numerical models, root rebound, Western Gneiss complex.
IN TR O DU C TI O N
Continental crust is thickened in collisional mountain chains
by such processes as lateral shortening and partial subduction
of one continent beneath another. This formation of the crustal
roots is opposed by a corresponding increase of gravitational
(isostatic) forces, and eventually the thermally softened root
rebounds. During rebound, the deeper levels in the crust are
expected to react by penetrative–ductile deformation. This
has been proposed on theoretical grounds by several workers,
under labels such as ‘buoyancy-driven creep’ (Gratton 1989),
‘lateral extrusion’ (Bird 1991), ‘subsurface collapse’ (Avouac &
Burov 1996), ‘lower crustal spreading’ (England & Holland
1979; Platt, 199), and ‘lower crustal squeezing’ (Schmeling
& Marquart 1990). Platt (1993) and England & Holland
(1979) suggested the buoyant return of low-bulk-density,
high-pressure metamorphic rocks as a viable mechanism for
exhumation. This process has now been well documented in
the field. The Western Gneiss Complex in southern Norway
* Now at: GEA Consulting, Åsögatan 105, S-11829 Stockholm,
Sweden.
556
is interpreted as the remnant, now well exposed, of the
Caledonide crustal root (Milnes et al. 1997). The pervasive
ductile deformation attributed to root rebound in the Western
Gneiss Complex covers a huge area, making it clear that
we are dealing with an important and widespread tectonic
phenomenon.
Much attention has been focused on the lateral gravity
spreading of the upper levels of overthickened orogenic crust
beneath its free surface (Burg et al. 1984; Burchfiel & Royden
1985; Dewey et al. 1988; Dewey et al. 1989; Buck & Sokoutis
1994). Less attention has been directed towards the ‘upward
gravity spreading’ of mountain roots, our topic here.
Here, we assume that mantle flow dragging continental crust
attached to the subducting plate beneath the non-subducting
plate eventually ceases beneath the suture (Meissner 1973;
McKenzie 1984; Jones & Nur 1984; Matthews 1986; Cheadle
et al. 1987; Meissner & Kusznir 1987). Phase changes increase
the density of the root, but the subducted and/or thickened
continental crust will still be buoyant with respect to the
surrounding mantle, and will therefore rebound upwards gravitationally when continental collision and/or subduction cease
and the mantle slab has been heated or detached. Recently,
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Ductile rebound beneath mountain belts
557
root rebound after delamination of a lithospheric root. We
also use model results to define the strain patterns associated
with such ductile root rebound.
N UM ER I C A L M O DE LS
Numerical experiments were prepared using a 2-D finite
difference code (FDCONE), which solves the Navier–Stokes
equations for an initially horizontally layered multicomponent
system. The models comprised a 15-km thick upper continental
crust (density r=2700 kg m−3, viscosity m=variable between
1020 and 1023 Pa s) overlying a 15-km thick lower continental
crust (r=2900 kg m−3, m=1020 Pa s: Fig. 1a). A quarter-circle
of lower crust (adjacent to a reflective vertical boundary)
simulated an orogenic crustal root penetrating the upper mantle
to a depth of 52 km (Fig. 1a). These two layers were resting
on a 75-km thick layer simulating the denser mantle lithosphere
(r=3300 kg m−3, m=1023 Pa s), giving a maximum lithospheric thickness of 115 km. These layers, in turn, overlay a
less viscous asthenosphere (r=3300 kg m−3, m=1019 Pa s).
A passive grid was introduced to all layers to act as strain
markers to monitor strain during deformation.
A Newtonian rheology was assumed for all four units (upper
and lower crust, mantle lithosphere and asthenosphere). Since
the emphasis is mainly on the first-order controls of ductile
root rebound, our models did not take into account any effects
of erosion or thermal disturbance, which would accelerate and
localize the deformation, as would non-linear rheologies. All
the models were assigned a free-slip bottom boundary and
non-flexible top boundary. A series of models systematically
explored the effects of changing the viscosities of the upper
crust and mantle lithosphere with respect to the constant
viscosities of the lower crust and the asthenosphere (both
1020 Pa s). The viscosity ratio of the upper crust relative to
the lower crust (constant at 1020 Pa s) was increased to give
viscosity ratios of 1, 10, 100 and 1000. For each case, four
models were run, with the viscosity of the mantle lithosphere
varying between 1020 and 1023 Pa s. It was assumed that the
root was a 2-D feature, extending infinitely along-strike in
the third dimension. In our models we assumed that, as long
as a heavy lithospheric root drags the crust down, a crustal
root cannot rebound. Our model simulates crustal root
rebound that occurs after delamination of the lithospheric root.
R ES U LTS
Models with the above initial geometry were allowed to evolve
under the effect of gravity (Fig. 1a). In all realizations, the
Moratta et al. (1998) used numerical models to study the
conditions that lead to lithospheric unrooting. Herein, we
explore the effect of the viscosity variation of the upper crust
and mantle lithosphere on the mechanisms and rates of crustal
© 1999 RAS, GJI 139, 556–562
Figure 1. (a) Initial configuration of the model. All boundaries are
free slip. Complete root rebound is shown ( b) after 390 Ma in a model
with stiff upper crust (viscosity=1023 Pa s), and (c) after 135 Ma with
a less stiff upper crust (viscosity=1021 Pa s). In both cases, channel
flow in the distal lower crust shears both its upper and lower
boundaries due to viscous drag during the lateral spreading of the
rebounding root mass. In ( b), only the lower crust deforms internally
since the stiff upper crust acts as a lid, whereas in (c) the less stiff
upper crust is also deformed with the lower crust. The depression in
the upper crust above the root area in (c), indicates isostatic readjustment of the upper crust to the diminishing root and stretching of the
upper crust by the laterally spreading root mass within the lower crust.
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H. A. Koyi et al.
lower crustal root rebounds and deforms internally as it rises
buoyantly. Because the mantle lithosphere has to fill the void
generated by the rising lower crustal root, the rate of root
rebound is controlled by the rebounding layer with highest
viscosity, that is, the mantle lithosphere. When the viscosity of
the mantle lithosphere is decreased by one order of magnitude,
the rate of rebound increases by almost one order of magnitude
(Figs 2a and b). For cases in which the root rebound takes
place within a realistic time window of 10–100 Ma, the viscosity
of mantle lithosphere is expected to range between 1022 and
1023 Pa s (Figs 2a and b). However, the viscosity of the upper
crust has little influence on the rate of rebound if it is more
viscous than the lower crust (Figs 2a and b). Model results
also show that changing the rheology of the mantle lithosphere
has a much greater effect on the rate of root rebound than
changing its thickness (Fig. 2c) (note that the viscosity is
changed by three orders of magnitude, and the thickness by a
factor of <2). For example, for the same viscosity, a crustal
root in a thinner lithosphere (80 km) rebounds five times faster
than a crustal root in a thicker lithosphere (135 km) (Fig. 2c).
As the root mass rebounds, it displaces and shears the lower
crust on its flanks. Our models suggest the formation of two
types of fabric within the lower crust during root rebound:
(1) a subhorizontal fabric above the root, formed due to
vertical shortening by the rebounding mass; and (2) inclined
fabrics formed on either side of the root area. The latter fabrics
form when the rebounding mass induces channel flow within
the lower crust, resulting in viscous drag along the boundaries
between the lower and upper crust and lower crust and mantle.
The resultant simple shear produces inclined fabrics with
opposing senses of shear along each boundary (Figs 1b and c).
Away from the root, the effect of the root rebound decreases
and the fabric weakens. The fabrics produced within the lower
crust by the spreading root mass could explain the reflective
character of the lower crust on seismic images. Deep crustal
reflections elsewhere have been ascribed to lithological layering
and/or overpressured fluids trapped in intergrain cracks and
fractures (Cheadle et al. 1987; Jones & Nur 1984; Matthews
1986; McKenzie 1984; Meissner 1973; Meissner & Kusznir
1987), petrophysical layering related to tectonometamorphic
processes and mylonitization (Fountain et al. 1984; Hurich
et al. 1985; Reston 1987; Smithson et al. 1986), and, in accordance with our model results, to the development of flat-lying
shear zones as a result of intense ductile deformation in the
lower crust (Rey 1993; Fountain et al. 1994). Fountain et al.
(1994) calculated reflection coefficients for the 30–150-m thick
eclogite facies shear zones of Caledonian age in the Bergen
Figure 2. Plots of crustal thickness (in the root area) versus time for
models with (a) a deformable and ( b) a stiff upper crust. The two plots
are extraordinarily similar, suggesting that the rate of root rebound
is not governed by the rheology of the upper crust. In both cases,
however, note the dramatic increase in the rate of rebound as the
viscosity of the mantle lithosphere decreases. Considering the realistic
time for root rebound to be between 10 and 100 Ma, the viscosity of
the mantle lithosphere is expected to be between 1022 and 1023 Pa s.
(c) Plot of root thickness with time for three cases showing the influence
of the initial thickness of mantle lithosphere on the rate of root
rebound. Note that the rate of rebound is not significantly influenced
by the thickness of the mantle lithosphere. The time axis should start
at time zero. However, in order to plot time logarithmically, the time
axis starts at 0.1 Ma.
arcs of Norway. They suggested that the ‘high calculated
reflection coefficients (0.04–0.14) of these eclogitic shear zones
indicate that they are excellent candidates for deep crustal
reflectors in portions of crust that experienced high pressure
conditions but escaped thermal reactivation’. Although the
shear zones in the Western Gneiss Complex are not themselves
eclogitic, the above example suggests that these shear zones
may still be reflective.
© 1999 RAS, GJI 139, 556–562
Ductile rebound beneath mountain belts
The intensity and style of deformation within the lower crust
are strongly governed by both the viscosity ratio between
the upper and lower crust and the viscosity of the mantle
lithosphere. In general, highly viscous (1023 Pa s) upper crust
deforms too slowly to be affected by shear in the lower crust
and acts as a rigid lid. In contrast, as in the case of a highly
viscous mantle lithosphere (1023 Pa s), a highly viscous upper
crust intensifies shearing in the lower crust by viscous drag
along its boundary. When the upper crust and mantle lithosphere are both highly viscous (1023 Pa s), deformation within
the lower crust extends to large distances (Fig. 1b), resulting
in strong shearing near the root area which diminishes nonlinearly at short distances away from it (Fig. 3a). On the other
hand, a less viscous mantle lithosphere deforms more easily so
that shear strain is lower along its boundary with the lower
crust, but decreases more smoothly towards the external parts
of the model (Fig. 3a).
In the models, cumulative shear strain in the lower crust
depends on distance from the root, and time. Shear strain at
5 km from the root margin increases rapidly until 46 Ma when
the root has rebounded half way. Thereafter, the accumulation
of shear strain slows down and the lateral gradient decreases
(Fig. 3b). In the same model, at 80 km from the root, cumulative
strain flattens out as early as after 12 Ma, when only onequarter of the root has rebounded (Fig. 3b). Since such shear
strain results from channel flow of the rebounded root material
within the lower crust, its intensity depends on the thickness
of the ductile lower crust. In the current models, the lowviscosity lower crust is relatively thick (15 km); a thinner lower
crust (5–7 km) would act as a narrow corridor for the spreading
root material and intense shearing.
While our fluid dynamical model has a non-flexible top, the
dynamic topography (h) can be calculated a posteriori by
equating the vertical stress at the top with an equivalent
lithostatic stress produced by the topography h. It implicitly
includes the isostatic contribution. Immediately after starting
the model calculation the maximum topography is reached as
a consequence of the instantaneously acting stress field. We
thus neglect the build-up stage of topography during root
growth, as it takes place on the timescale of the isostatic
relaxation time (104 yr) which is an insignificant time in
orogeny. The subsequent dynamic topography above the root
area is shown in Fig. 4 for various cases. Viscous stresses
retard the dynamic topography beneath the purely isostatic
value (which for a 22-km thick root would be 3.26 km). The
dynamic uplift (=1600 m, Fig. 4a) above the rebounding root
has a positive correlation with the viscosity of the upper crust.
A less viscous upper crust (1021 Pa s) accommodates root
rebound and lateral spreading of the lower crust by internal
deformation and is lifted less than a more viscous upper crust
(1023 Pa s), which instead accommodates root rebound by
dynamic uplift (Fig. 4b). We emphasize here that changing the
boundary condition or using other rheolgies may change the
dynamic topography formed by root rebound. Using numerical
models of lithosphere under a convergence regime, Moratta
et al. (1998) suggested that the order of amplitude of dynamic
topography is controlled by the width of the deformation
region and by the convergent velocity.
The amplitude of dynamic uplift in our models correlates
negatively with the viscosity of the mantle lithosphere. For a
constant viscosity of the upper crust (1023 Pa s), root rebound
causes up to 1600 m of dynamic uplift when the mantle
© 1999 RAS, GJI 139, 556–562
559
Figure 3. (a) Plot showing the change in the intensity of shear strain
within the lower crust relative to the distance from the root. In the
model with a stiff upper crust (viscosity=1023 Pa s), shear strain is
more intense and covers a larger lateral distance from the root (see
also Figs 1b and c), whereas in a model where the upper crust is less
stiff (viscosity=1021 Pa s), shear strain is less intense since root
rebound is taken up by internal deformation of both the lower and
upper layers. ( b) Plots of shear strain with time at two different
locations: 5 and 80 km from the root area, for a model with a stiff
upper crust (viscosity=1023 Pa s). The area close to the root undergoes
severe shear strain, whereas the area 80 km away from the root
undergo only minor amounts of shear strain.
lithosphere is less viscous (1021 Pa s), whereas it causes only
about 500 m of dynamic uplift when the mantle lithosphere is
more viscous (1023 Pa s). The viscosity of the mantle lithosphere and upper crust govern the dynamic topography by
controlling the rebound rate of the crustal root. In the case of
a stiffer mantle lithosphere relative to the upper crust, the
mantle lithosphere controls the rate of rebound and takes
most of the buoyancy force, not allowing the buoyancy forces
to push up the topography. In the case of a stiffer upper crust
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H. A. Koyi et al.
stiff, thickening of the upper crust will modify our model
results only at very late stages.
Thermal effects play a significant role in crustal and lithospheric deformation (Marotta et al. 1998; Schott & Schmeling
1998), although it is beyond the scope of this paper to fully
incorporate solving the heat equation and include temperaturedependent rheologies. Furthermore, this paper does not address
destabilization effects caused by a cold mantle lithosphere. To
a first approximation, however, we account for the thermal
effect on the rheology by choosing low viscosities for the lower
crust and the asthenosphere.
CA LE DO N ID ES
Figure 4. Plots of dynamic topography above the root axis versus
time (a) for models with constant upper crust viscosity (1023 Pa s) but
variable mantle lithosphere viscosity, and (b) for models with constant
mantle lithosphere viscosity (1022 Pa s) but variable upper crust viscosity.
(a) shows that the dynamic topography is inversely proportional to
mantle rheology: the higher the viscosity of the mantle lithosphere,
the smaller the dynamic topography. In contrast, ( b) shows that the
dynamic uplift is directly proportional to the rheology of the upper
crust. In nature, these effects would be additional to any gravity
spreading of the mountain mass. The time axis should start at time
zero. In order to plot time logarithmically, however, the time axis
starts at 0.1 Ma.
relative to the mantle lithosphere, the faster rebound results in
a higher topography as stronger buoyancy forces are transmitted to the upper crust. In the latter case, the rebound rate
is governed by the combined system of upper and lower crust.
In all models, however, the topography diminishes rapidly to
subside above the root area during root rebound (Fig. 4).
In models with a deformable upper crust (viscosity=
1020–21 Pa s), the later stages of root rebound induce a phase of
extension and isostatic subsidence of the upper crust (Figs 1c
and 4b). This extension is caused by lateral spreading of the
root mass beneath the upper crust. In nature, stages of postorogenic extension and basin formation may indicate the
lateral spreading of a crustal root beneath a weak upper crust.
This work considers only a thickened lower crust; orogenic
crustal stacking might also involve a thickening of the upper
crust. Because the density contrast between the upper and
lower crust is relatively small and the upper crust is relatively
The fabric produced in the models corresponds to the subhorizontal foliation and stretching lineation in the Western
Gneiss Complex of southern Norway. Recently, Milnes et al.
(1997) and Milnes (1998) described in detail the structural
history along a transect through a collisional orogenic belt
(southern Norwegian Caledonides), where subsequent tectonic
processes, uplift and erosion have exposed an almost complete
cross-section through part of the orogenic root (Western
Gneiss Complex). Retro-deformation of the various structural
events enables an approximate reconstruction of the root at
its deepest level. Eclogites formed at depths of around 100 km
in the root, whereas the crustal thickness under the orogenic
foreland (the Baltic Shield) remained near 40 km. Evidence from
higher levels shows that upper crustal contraction changed to
extension soon after or at about the same time. Under these
conditions, the root became gravitationally unstable, buoyancy
forces no longer being overcome by subduction-related forces.
The root rebounded upwards against an upper crustal ‘lid’, which
in the southern Norwegian Caledonides, was the unusually
stiff and coherent Jotun nappe. Crustal root rebound raised the
presently exposed eclogites more or less isothermally, from depths
of 60 to 40 km. The surrounding felsic gneisses underwent
ductile penetrative ‘pure shear’-type deformation (subvertical
shortening, subhorizontal extension) under decreasing pressure,
mainly within the amphibolite facies. The results of kinematic
analysis suggest that the main Caledonian deformation over
a large area of the felsic gneisses was purely the result of
gravitational rebound in a process which can be described as
‘inverted gravity spreading’ of the root mass within the lower
crust.
U R A LS
The present-day root observed below the Urals (Thouvenot
et al. 1995; Ryzhiy et al. 1992; Juhlin et al. 1996) is likely to
have formed during the Palaeozoic, when the East European
Craton collided with Asian island-arc terranes and formed the
2500-km long near-linear Uralian orogenic belt (Hamilton
1970; Zonenshain et al. 1990). The collision was followed by
some extension. Only minor extension appears to have taken
place in the Southern Urals (Brown et al. 1998), while in the
Middle Urals the amount of extension appears to have been
greater (Juhlin et al. 1998). Post-collisional extension lasted
for about 50 Myr and preceded renewed subduction below the
eastern boundary of the continent and subsequent deformation
of the accreted island-arcs.
Reflection seismic experiments over the Middle Urals (Juhlin
et al. 1998) reveal a bivergent structural geometry in the upper
© 1999 RAS, GJI 139, 556–562
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561
Figure 5. Combined migrated line across the Middle Urals (Juhlin et al. 1998) showing the rebounded root and the internal reflectors above
and on either side of the root, which is now only 6 km thick. Note the subhorizontal reflectors above the root within the lower crust and also
the gently westward-dipping (towards the root) reflectors on the eastern shoulder of the root within the lower crust. These reflectors could
be the result of shearing during lateral spreading of the root mass within the lower crust as the root rebounded. Kilometre ( km) scale refers to
distance from the Main Uralian Thrust Fault (MUTF) (positive values to the east and negative values to the west). CUZ: Central Uralian Zone;
EUZ: East Uralian Zone; MUFZ: Main Uralain Fault Zone; NF: Normal Fault; PSZ: Prianitchnikova Shear Zone; SMF: Serov-Mauk Fault;
TMZ: Tagil-Magnitogorsk Zone; TUTZ: Trans-Uralian Thrust Zone; TZ: Thrust Zone.
crust (Fig. 5). A zone of increased seismic reflectivity is
observed in the middle crust (23–32 km) along the central
80 km of the profile ( km −10 to 70, Fig. 5). On the eastern
shoulder of the root, at about km 55, lower crustal reflectivity
becomes prominent at depths of 36–44 km (Fig. 5). This
reflectivity has been interpreted by Juhlin et al. (1998) to be
different in origin from the middle crustal reflectivity further
west. The lower crust below the central portion of the section
lacks strong reflectivity down to the Moho depth at about
53 km (Juhlin et al. 1996). Most of the dipping upper crustal
reflections can be correlated to geological features such as
thrust zones or normal faults. Although the lower crustal
reflectivity to the east could be attributed to compression
during the westward subduction at the end of the Palaeozoic
or extension during the opening of the West Siberian Basin,
the middle and lower crustal reflectivity could be due to
root rebound.
If the observed middle and lower crustal reflectivity in the
Middle Urals is a result of extension and shearing during root
© 1999 RAS, GJI 139, 556–562
rebound, their spatial and temporal formation is constrained
by the following criteria.
(1) Roots reached depths of 25–35 km along an 80-km long
strip centred below the Tagil Oceanic and Volcanic-Arc
Complex.
(2) The brittle upper crust must have extended by normal
faulting.
(3) The reflectivity must have developed after arc accretion,
but before the onset of westward subduction: a time window
of approximately 50 Ma.
The observation of normal faults (some with apparently large
throws) on geological and geophysical data in the Middle Urals
(Juhlin et al. 1998) is consistent with brittle deformation in the
upper crust and ductile deformation in the middle and lower crust.
CON CLU SION S
Our models suggest intense ductile deformation of the lower
crust during root rebound as a mechanism for the formation
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H. A. Koyi et al.
of subhorizontal structures which could give the lower and
middle crust its reflective character on seismic images. It should
be noted that, in nature, root rebound takes place by ductile
flow in the lower crust and surface erosion. Therefore our
models only represent an end member, giving the maximum
possible deformation in the lower crust and the maximum
rebound times compared to cases with erosion.
Furthermore, our models show that the strength of the
mantle lithosphere dominates the timescale of crustal rebound.
The rate of root rebound in the models decreases with increasing
viscosity of the mantle lithosphere. Cases of weak mantle
lithosphere with fast crustal root rebound may be associated
with orogenies that experienced delamination or break-off of
strong mantle lithospheres (Schott & Schmeling 1998), or in
which the mantle lithosphere has been weakened by the release
of fluids during the collision stage. The dynamic topography
due to root rebound is directly proportional to the viscosity
of the mantle lithosphere.
AC KN O WL ED GM E NTS
We thank Drs Sadoon Morad and Alasdair Skelton for
reviewing this manuscript. Special thanks to Dr Bertram Schott
for help with transferring the data and computer manipulation.
HAK and CJ are supported by the Swedish Natural Sciences
Research Council (NFR).
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