Download Continental rifting as a function of lithosphere mantle strength

Tectonophysics 460 (2008) 83–93
Contents lists available at ScienceDirect
Tectonophysics
j o u r n a l h o m e p a g e : w w w. e l s e v i e r. c o m / l o c a t e / t e c t o
Continental rifting as a function of lithosphere mantle strength
Frédéric Gueydan ⁎, Christina Morency 1, Jean-Pierre Brun
Géosciences Rennes, UMR CNRS 6118, Campus de Beaulieu, Université de Rennes 1, France
a r t i c l e
i n f o
Article history:
Received 30 October 2007
Received in revised form 30 July 2008
Accepted 8 August 2008
Available online 28 August 2008
Keywords:
Continental rifts
Extensional tectonics
Lithosphere rheology
Numerical modelling
a b s t r a c t
The role of the uppermost mantle strength in the pattern of lithosphere rifting is investigated using a
thermo-mechanical finite-element code. In the lithosphere, the mantle/crust strength ratio (SM/SC) that
decreases with increasing Moho temperature TM allows two strength regimes to be defined: mantle
dominated (SM N SC) and crust dominated (SM b SC). The transition between the two regimes corresponds to
the disappearance of a high strength uppermost mantle for TM N 700 °C. 2D numerical simulations for
different values of SM/SC show how the uppermost mantle strength controls the style of continental rifting. A
high strength mantle leads to strain localisation at lithosphere scale, with two main patterns of narrow
rifting: “coupled crust–mantle” at the lowest TM values and “deep crustal décollement” for increasing TM
values, typical of some continental rifts and non-volcanic passive margins. The absence of a high strength
mantle leads to distributed deformations and wide rifting in the upper crust. These numerical results are
compared and discussed in relation with series of classical rift examples.
© 2008 Elsevier B.V. All rights reserved.
1. Introduction
The so-called “brittle–ductile” layering of the continental lithosphere is often modelled using frictional-type and viscous-type
rheological behaviours. According to this conception, most of the
lithosphere strength is located in the brittle upper crust and subMoho mantle (Brace and Kohlstedt, 1980; Carter and Tsenn, 1987;
Molnar, 1992). Such strength profiles with peaks in the upper crust
and sub-Moho mantle were found to be in good agreement with depth
location of earthquakes (Chen and Molnar, 1983; Sibson, 1983). Recent
depth re-location of the earthquakes beneath Tibet has shown that
deep earthquakes are more likely to nucleate in the lower crust (Maggi
et al., 2000) than in the mantle (Chen and Molnar, 1983). The
concentration of seismicity in the crust and the good relationship
between elastic thicknesses calculated for foreland basins and the
depth of seismicity lead Jackson (2002) to argue that most of the
overall lithosphere strength is located in the seismogenic upper crust
instead of within the uppermost mantle.
This conception of lithosphere rheological layering is however in
contradiction with the mechanics of lithosphere rifting that requires a
high strength mantle (Handy and Brun, 2004; Ziegler and Cloetingh,
2004; Burov and Watts, 2006). According to Buck (1991), continental
extension occurs according to three modes: narrow rift, wide rift and
core complex. This comes from the balance between the three types
of forces that contribute to rifting: buoyancy, thermal and strength
⁎ Corresponding author. Tel.: +33 223235193; fax: +33 223236097.
E-mail address: [email protected] (F. Gueydan).
1
Now at California Institute of Technology, Seismological Laboratory, Pasadena, CA , USA.
0040-1951/$ – see front matter © 2008 Elsevier B.V. All rights reserved.
doi:10.1016/j.tecto.2008.08.012
forces — i.e. softening the lithosphere during extension by the
thinning of brittle layers and general heating. Narrow rifts occur
when the total force change on rifting is negative, so that the ongoing
thinning is kept in the same narrow region. On the contrary, wide rifts
occur when the total force change is positive, so that ongoing thinning
tends to spread out to accommodate stretching. Finally, core
complexes form when the lower crustal flow dominates, allowed by
the low viscosity of both deep crust and mantle. This provides an
overall and simple explanation to the observed differences between
continental rifts (e.g. Baikal, Rhine) and regions of distributed
extension (e.g. Basin and Range, Aegean). This approach considers
the bulk mechanical properties of the lithosphere but the mechanical
behaviour of brittle and ductile layers can also be decisive. Lithosphere
deformation is crust or mantle dominated for thick or thin crusts,
respectively, and the coupling between the crust and mantle
decreases with increasing crustal thickness (Behn et al., 2002). The
presence of a high strength uppermost mantle exerts a direct control
on the development of mantle shear zones and subsequent lithosphere necking (Allemand and Brun, 1991; Brun and Beslier, 1996;
Frederiksen and Braun, 2001). At low strain rates, and therefore low
strength of the ductile crust, the lower crust acts as a decoupling
level – i.e. décollement – between the upper brittle crust and the high
strength uppermost mantle (Brun, 1999, 2001) providing a simple
explanation for the typical faulting pattern of passive margins (Brun
and Beslier, 1996; Nagel and Buck, 2004). The development of rift
asymmetry can be a function of the degree of strain softening in the
brittle crust (Huismans and Beaumont, 2003) but, in nature, rift
asymmetry often results from the presence of pre-existing structures
(Ziegler and Cloetingh, 2004).
84
F. Gueydan et al. / Tectonophysics 460 (2008) 83–93
The present paper aims to show that the strength of the
lithospheric mantle, and more specifically the presence of a high
strength sub-Moho mantle, exerts a strong influence on the style of
continental rifting on a lithosphere scale. We analyse lithosphere
rifting as a function of the lithosphere thermal and rheological
layering. Three patterns of deformation at lithosphere scale are
obtained without imposing any weak zone or lateral thermal gradient
to control the initial rift position (e.g, Behn et al., 2002; Huismans and
Beaumont, 2003). The study focuses in particular on the wavelength of
necking instabilities and on the deformation of the uppermost mantle
and of the ductile crust. The development of the Metamorphic Core
Complexes mode of lithosphere extension (Buck, 1991) is beyond the
scope of the paper that is dedicated to the rifting proper and the
transition between narrow and wide rifts.
An analytical approach is first used to discuss the respective
contributions of crust and mantle to lithosphere strength. Then, 2D
numerical models are presented to analyse the dependence of
continental rifting patterns on the rheological layering and more
specifically to the presence/absence of a high strength sub-Moho
mantle. Finally, the results are tentatively compared to some natural
examples of rifts.
2. Thermal and rheological layering
In order to calibrate the range of rheological lithosphere layering
for further 2D numerical modelling, lithosphere strength profiles are
first computed analytically for different continental geotherms. The
steady state temperature profiles (as a function of depths) T(z) are
analytically computed knowing the imposed heat flux at the base of
the lithosphere qm, the crustal thickness hC and the radiogenic crust
thickness hRC. Within the crust, the temperature T(z) reads:
z b hRC ;
T ðzÞ ¼ −
hC b z b hRC ;
r 2
qm
r
z þ
þ hRC z þ T0 ;
2kc
kc kc
T ð zÞ ¼
ð1Þ
qm
r
zþ
h 2 þ T0 ;
2kc RC
kc
where r, kc, qm and T0 are the radiogenic heat production (which
occurred over a thickness hRC), the crust conduction, the basal heat
flux and the surface temperature set to 300 °K, respectively. The values
of these parameters are given in Table 1. It is commonly assumed that
the radiogenic activity only exists in the upper part of the crust
(Turcotte and Schubert, 1982). Thus, the radiogenic thickness hRC is
assumed here to be equal to the brittle crust thickness. This
assumption requires iterative computation to obtain a suitable
strength profile, as discussed below.
Temperatures in the mantle are defined by:
z N hC ;
T ð zÞ ¼
qm
qm
r
ðz−hC Þ þ TM ; with TM ¼
hc þ
h 2 þ T0 ;
2kc RC
km
kc
ð2Þ
where km is the mantle conduction (Table 1). The thickness of the
lithosphere hL can be derived from Eq. (2) since at z = hL, the
lithosphere temperature is TL = 1200 °C:
hL ¼
km
ðTL −TM Þ þ hC
qm
ð3Þ
The lithosphere strength is computed from the temperature profile
defined above using wet quartz and dry olivine rheological paraTable 1
Parameters used to compute the 1D continental geotherm
Variable
Unit
Crust
Mantle
Density — ρc; ρm
Diffusion — kc, km
Radiogenic heat production r
kg m− 3
W m− 1 K− 1
μW m− 3
2800
2.1
1 (only brittle crust)
2.3
3.0
0.0
Table 2
Ductile rheological parameters
Mineral
Wet quartz
Dry olivine
Wet olivine
A [MPa− n s− 1]
−4
3.2 10
2.42 105
3.91 103
Q [kJ mol− 1]
n
Reference
154
540
430
2.3
3.5
3.0
Ranalli (2000)
Karato and Wu (1993)
Karato and Wu (1993)
Wet quartz and dry olivine were used for the entire 2D numerical simulation set. Wet
olivine was used to construct the deformation map in Fig. 9.
meters (Table 2) as follows. The brittle strength τB is equal to the
Mohr–Coulomb stress (Byerlee, 1978), assuming a non-cohesive
material, τB = μp, where p is the lithostatic pressure (p = ρgz, with
varying density for the crust and mantle, Table 1). The friction
coefficient is set to μ = 0.6. The ductile strength τD is derived from the
power creep law which reads:
Qr n
:
τ ;
e ¼ A exp −
RT D
ð4Þ
where ε ̇, T and τD are the strain rate (in s− 1), the temperature (in °K)
and the shear stress (in MPa), respectively. Setting the value of the
strain rate at 10− 15/s, the strength at a given depth is taken as the
lowest of the stress values calculated for brittle and ductile behaviours
at this depth. Using an initial value of the radiogenic crust thickness of
hRC = 10 km leads to a first strength profile and thus gives an estimate
of the brittle crust thickness. Then, setting hRC to the computed value
of the brittle crust thickness provides a second estimate of
temperature and strength profiles. Around four to five iterations are
required to fit the radiogenic crust thickness to the brittle crust
thickness and to thus obtain suitable strength and temperature
profiles.
In Fig. 1, the computed thicknesses of the lithosphere (solid lines)
and of the brittle mantle (dashed lines) are plotted as functions of the
Moho temperature TM with corresponding strength profiles for crustal
thicknesses hC = 30 and 50 km. The lithosphere thickness that
increases with increasing crustal thickness (Eqs. (2) and (3)),
decreases with an increasing TM. The lithosphere strength decreases
with an increasing Moho temperature TM. As an example, for
hC = 30 km, the lithosphere strength decreases from Model 1 to
Model 3, together with the decrease of the thickness of the high
strength mantle (Fig. 1). The critical Moho temperature above which
the lithosphere mantle is wholly ductile can be defined as approximately 700 °C for hC = 30 and 50 km (Fig. 1) but this value depends on
the chosen rheological parameters. For example, the use of wet olivine
instead of dry olivine leads to a much lower critical Moho temperature
of 600 °C; above which the lithosphere mantle is entirely ductile. The
above remarks show that the Moho temperature can be used as
simplified indicator of the thermal and rheological lithosphere
layering.
3. Contributions of crust and mantle to lithosphere strength
Fig. 2 shows that the mantle–crust strength ratio (SM/SC) decreases
with increasing Moho temperatures TM. At TM ~ 700 °C, SM is equal to
SC. Above and below this critical temperature; the lithosphere
strength is dominated by the strength of the crust SC and the mantle
SM, respectively. The ratio SM/SC thus defines two distinct strength
regimes: mantle dominated (SM N SC) and crust dominated (SM b SC).
The transition between the two regimes corresponds to the presence/
absence of high strength sub-Moho mantle for TM N 700 °C (Fig. 1). The
strength of the lithosphere mantle is therefore strongly controlled by
its brittle part (Molnar, 1992). Plotting SM/SC as a function of the Moho
temperature, which depends on the crustal thickness, provides
comparable values of that ratio, irrespective of the crustal thickness.
F. Gueydan et al. / Tectonophysics 460 (2008) 83–93
85
Fig. 1. 1D analytical solution giving the lithosphere thickness hL (Eq. (3)) and the high strength uppermost mantle thickness as a function of the Moho temperature TM (Eq. (2)). Four
strength profiles (Models 1 to 4) are used for a crustal thickness hC = 30 km. Two strength profiles (Models 5 and 6) are used for a crustal thickness hC = 50 km. The thermal and
rheological parameters used to construct strength profiles are given in Tables 1 and 2, respectively. Dislocation creep parameters for wet quartz and dry olivine are used for crust and
mantle, respectively. The friction coefficient is μ = 0.6.
The strength ratio SM/SC is therefore also a good indicator of the
thermal and rheological layering within the lithosphere.
4. Numerical modelling
4.1. Boundary conditions
Fig. 3 presents an example of the model set-up and the rheological
layering used for the 2D numerical simulations – i.e. Model 1 (Figs.1 and 2):
TM =356 °C and qm =20 mW m− 2 – and the mesh used for each model layer.
The same procedure was used for all models in Figs. 1 and 2. Table 3 gives
velocity, crustal thickness, basal heat flux and Moho temperature for the 6
selected models that are used for 2D simulations. The thicknesses of the
brittle and ductile layers are computed as presented in the two previous
sections. However, the thicknesses of brittle layers are slightly different
from the Mohr–Coulomb estimate, since we use Von Mises approximation
for plastic material. The initial model width is 300 km. The thickness
depends on the selected Moho temperature, which controls the lithosphere thickness (Eq. (3)). A velocity of V=1 cm/a is imposed at the right
vertical boundary of the model, while the left vertical boundary is only
allowed to move vertically. The isostatic equilibrium of the lithosphere
base is achieved by the presence of an underlying asthenospheric layer
whose viscosity is set to 1021 Pa s. A small geometrical perturbation of the
crustal brittle–ductile transition and of the Moho – i.e. a deflection with an
amplitude of 100 m – is introduced at the model centre to initiate strain
localization. The temperature profiles are the same as those used to
compute strength profiles but are however partly modified by shear
heating in the ductile layers — i.e. thermo-mechanical coupling.
4.2. Brittle rheology: Von Mises approximation
The brittle layers are modeled by a Von Mises associated elasto-viscoplasticity. Before yielding, the material is described by a classical linear
elasticity law — i.e. a Poisson ratio equal to 0.25 and a Young modulus
equal to 5.1010 Pa and 1.5 1011 Pa for the crust and mantle, respectively
(Turcotte and Schubert, 1982). Yielding occurs when the equivalent Von
Mises shear stress τv is greater than the yield stress σ y (εp), which is a
function of the equivalent plastic strain εp history. The equivalent Von
Mises shear stress and the equivalent plastic strain are defined by:
Fig. 2. Ratio of mantle strength SM to crustal strength SC as a function of Moho
temperature TM for a crustal thickness of 30 km (solid line) and 50 km (dashed line) for
Models 1 to 6 (Fig. 1, Table 3). The sinuous grey line indicates the position of TM = 700 °C
that separates lithospheres with and without a high strength mantle (Fig. 1). Dislocation
creep parameters for wet quartz and dry olivine are used for crust and mantle,
respectively (Table 2). The friction coefficient is μ = 0.6.
τv ¼
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
rffiffiffiffiffiffiffiffiffiffiffiffiffiffi
3
2 p p
τ ij τij ; and ep ¼
D D ;
2
3 ij ij
ð5Þ
where ―
D p stands for the plastic strain tensor. The yield stress σ y is a
three-linear function of the plastic strain εp (Fig. 3; inset). The material
86
F. Gueydan et al. / Tectonophysics 460 (2008) 83–93
Fig. 3. Set-up of numerical modelling showing the initial model geometry and boundary conditions (left) and the initial strength profile (right). Brittle layers behave according to a
Von Mises criterion corresponding to a pressure-independent elasto-viscoplastic material. Ductile layers behave as non-Newtonian fluids sensitive to temperature and strain rate
(See parameters in Table 2). The inset shows yield stress as a function of the plastic strain in brittle layers.
remains elastic until its plastic stress reaches σ y0 . It then undergoes a
hardening until the plastic strain ε p1 = 0.02 is reached for the peak
stress σ y1. Then the yield stress decreases towards a residual state with
increasing plastic strain (until the plastic strain εp2 = 0.12), defining the
softening, during which localised plastic shear zones fully develop. For
larger values of plastic strain, the material can reach an infinite strain
with no increase in strength. In the present paper, fracturing will thus
be modelled by regions where the plastic strain εp is larger than
εp2 = 0.12. Modifications in the values of εp1 and εp2 will delay or speed
up the development of faults. The viscosity of the plastic material ηp,
which has been introduced to avoid catastrophic fault propagation,
defines a time-scale for the change of plastic deformation:
τv −σ ðe Þ
:
ep ¼
;
ηp
y
p
ð6Þ
where ε ̇ is the plastic strain rate. Increasing η will thus decrease the
plastic strain rate and therefore increase the time necessary to change
the plastic strain. A value of 3.1020 Pa s for the plastic viscosity was
found sufficient to stabilise the numerical development of the faults
and has therefore been selected in the following computations. Note
that this plastic viscosity was set to the same value in all of the
simulations presented. Changing this value will not change the fracture
pattern, but will solely modify the timing of its development (Schueller
et al., 2005). The Von Mises plastic criterion used in this study, with the
above selected values of hardening, softening and plastic viscosity, has
been validated to model modes of faulting (Schueller et al., 2005).
The thicknesses of the Von Mises-type layers are computed so that
the strength is identical to a classical Mohr–Coulomb prediction. This
leads to greater depths of brittle–ductile transitions in the crust and in
the mantle. This assumption permits keeping the same value of the
strength ratio SM/SC for the 2D modeling and the analytical calculation
presented above. The value of σ y0 is thus defined by the integral of the
Mohr–Coulomb strength for each brittle layer. The value of σ y1 is set to
1.10 times σ y0 (10% hardening) and σ y2 is equal to 0.70 times σ y1 (30%
softening).
The Von Mises criterion imposes that faults trend at 45° to the
principal compression axis, since it is a pressure-independent failure
criterion. Mohr–Coulomb criterion has been previously used, at a
crustal scale, to more accurately model the fault displacement as a
function of brittle softening, with a particular emphasis on the
reduction of the cohesion or of the friction coefficient (Lavier et al.,
1999; Lavier et al., 2000; Huismans and Beaumont, 2003; Huismans
et al., 2005). Our purpose differs from that of the above previous
studies as it aims primarily to capture the role of mantle strength on
p
the deformation patterns at lithosphere scale. The Von Mises criterion
yields fault patterns at lithosphere scale that are rather similar to
those produce by pressure-sensitive criteria (Huismans et al., 2005).
The applicability of the Mohr–Coulomb criterion to model mantle
deformation is moreover still a matter of debate (Jackson, 2002). As
proposed by Bassi (1995) under the term of “power law breakdown
stress” it is probably more accurate to limit the mantle strength. This is
what is implicitly done by the Von Mises criterion.
4.3. Ductile rheology: dislocation creep
The ductile layers are modeled by an incompressible non-Newtonian fluid such that the Kirchhoff stress tensor ―
τ is given by
τ
P
P
: D I
P −pP
P;
¼ 2ηðT; e ÞP
ð7Þ
p
where p, η(T, ε̇) and ―
D are the pressure, the secant viscosity and the
rate of deformation tensor, respectively. The material incompressibility constrains the trace of D at zero. Note that the tensors are
―
underlined twice. Eq. (7) is the multi-dimensional generalization of
the creep law (Eq. (4)). In Eq. (4), the equivalent shear stress and strain
rate are derived from the stress and strain rate tensors:
rffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1
τ ij τij
τ¼
2
:
and e ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2Dij Dij :
ð8Þ
Thus, the secant viscosity is simply η(T,ε ̇) = τ/ε ̇. The sensitivity of
viscosity to strain rate and temperature could therefore be defined
using the 1D creep law (Eq. (4)).
Table 3
Velocity, crustal thickness, basal heat flux and Moho temperature for the 6 models used
for the 2D numerical simulations
Model
1
2
3
4
5
6
Velocity
Crustal thickness
Basal heat flux
Moho temperature
V [cm/a]
hc [km]
qm [mW/m2]
TM [°C]
0.1–1
0.1–1
0.1–1
1
1
1
30
30
30
30
50
50
20
30
50
40
17
20
356
482
753
550
482
550
F. Gueydan et al. / Tectonophysics 460 (2008) 83–93
4.4. Governing equations and numerical scheme
Mechanical equilibrium and heat conduction are solved by
numerical means using the thermo-mechanical finite-element code
SARPP (Gueydan et al., 2004). The layered structure is discretised into
60 × 40 Lagrangian elements with 9 nodes. Shear heating is accounted
for in the heat conduction (source term τε̇), inducing a thermomechanical coupling. Heat advection is disregarded in this study.
5. Three patterns of continental rifting
5.1. Total strain patterns as a function of mantle strength
The strength profiles, Moho temperature and strength ratio for the
three Models 1, 2 and 3 are defined in Figs. 1 and 2. The total strain for
these three models, are plotted in Fig. 4, after a horizontal
displacement of both 30 and 60 km, with an applied velocity of
1 cm/a. The two first models are typical of a mantle dominated
strength regime, while the third one is marked by the absence of a
high strength mantle and corresponds to a crust dominated strength
regime (Figs. 1 and 2; Table 3). The Moho temperature TM increases
and thus the strength ratio SM/SC decreases from Model 1 to Model 3.
For low TM, the brittle mantle is affected by distributed faulting
that gives numerous necks with a wavelength dictated by the depth of
the brittle–ductile transition in the mantle (Model 1; Fig. 4). This
wavelength is indeed defined by an upward propagation along a 45°
dipping mantle shear zone. A reflection occurs at the free surface
leading to a 45° downward dipping propagation of the shear zone.
This is responsible for a strain concentration and the nucleation
of new faults in the brittle mantle. Thus, the distance between
the two regions of intense faulting within the brittle mantle is simply
2(hC + hBM), where hBM is the brittle mantle thickness. For Model 1,
hC = 30 km and hBM = 40 km (Fig. 1), which leads to a mantle necking
wavelength of approximately 140 km. This estimate is very consistent
with the results after 30 km of horizontal displacement (Fig. 4). The
distance between the two regions of intense strain is almost the same
in both the brittle crust and the uppermost mantle — i.e. the crust and
mantle are strongly coupled. In this paper, the term coupling means
that two layers undergo rather similar amounts of strain. For larger
87
horizontal displacement, rift spacing increases due to large strain and
fault motion. The presence of two major lithosphere scale normal fault
zones in the central part of the model induces a strong Moho
deflection at model centre. Rift spacing is controlled by the
wavelength of mantle necking and is thus of the order of 2(hC + hBM).
For larger TM, the deformation is more localized on the whole
lithosphere scale, leading to a more pronounced necking (Model 2;
Fig. 4). After 30 km of horizontal displacement, the brittle mantle is
still affected by distributed faulting. Here, the wavelength of mantle
necking is of the order of 100 km. The analysis for the wavelength of
mantle necking remains valid and gives a very consistent estimate of 2
(hC + hBM) = 96 km — i.e. hBM = 18 km for Model 2; Fig. 1. With increasing
horizontal displacement, a single zone of mantle necking localizes at
model centre. This strain localization on a lithospheric scale is favored
by a strong layer-parallel shearing – i.e. décollement – at the ductile
crust base. This décollement zone tends also to distribute strain that is
concentrated in a narrow mantle zone into a large upper crustal
domain. Consistently, minor faults in the mantle are still accumulating
strain at the tip of the décollement zone where the intensity of deep
crustal shearing strongly decreases. Lower crust décollement was not
observed in Model 1 as the Moho temperature was low; therefore the
strength of the deep crust was high. Incipient layer-parallel shearing
in the deep crust leading to lithosphere scale necking is therefore
strongly controlled by the Moho temperature and the mantle/crust
strength ratio SM/SC. Regions of intense strain in the upper crust are
located aside the mantle neck above two deep crustal décollements
with converging senses of shear (see red arrows; Fig. 4). As a
consequence, the upper crust deforms through two sets of parallel
faults dipping towards the rift axis. They can be seen as two branches
of a large rift issued from a central mantle neck. The wavelength of
mantle necking 2(hC + hBM) thus defines the initial rift width.
In the absence of a high strength sub-Moho mantle, deformation is
more distributed and the rift spacing is fully controlled by the brittle
crust thickness (Model 3; Fig. 4). The above analysis for rift spacing
and rift width is not relevant since the mantle lithosphere cannot
localize strain. The brittle crust is the only layer that induces plastic
strain localization and thus controls rift spacing.
From the above results, three basic patterns of continental rifting
can be defined (Fig. 4; right): “coupled crust–mantle” for high mantle
Fig. 4. Role of the initial Moho temperature TM. Patterns of total strain in Models 1 to 3 for an initial crustal thickness of 30 km, after 30 km and 60 km of boundary extensional
displacement, with V = 1 cm/a, and line drawings of corresponding lithosphere scale structures. See Figs. 1 and 2 and Tables 1, 2 and 3 for model parameters. (For interpretation of the
references to colour in this figure legend, the reader is referred to the web version of this article.)
88
F. Gueydan et al. / Tectonophysics 460 (2008) 83–93
subsidence. Fig. 5 that displays the topographic profiles of Models 1, 2
and 3, after 60 km of extension, shows that rift topography increases
with decreasing Moho temperature TM and thus with increasing
mantle strength. When crust and mantle are coupled, rift flanks are
well marked with a maximum uplift of 1.2 km while the tectonic
subsidence is low, around 500–700 m. When deep crustal décollement occurs, the tectonic subsidence reaches a large value at rift
centre, around 2 km, close to the prediction of the pure shear model of
extension (McKenzie, 1978). In that case, rift flanks are less
pronounced. Finally, the topography of wide rift is low, with regularly
spaced highs and lows. These results are consistent with previous
numerical models (e.g. Braun and Beaumont, 1989) and show the
control exerted by the high strength mantle on rift topography and
subsidence.
6. The effects of variations in stretching rate
Fig. 5. Rift topography in Models 1 to 3 after 60 km of boundary extensional
displacement, with V = 1 cm/a.
strength, “deep crustal décollement” when the strength of the deep
crust is low enough to decouple the crust from the mantle and, finally,
“wide rift” when the lithosphere mantle is wholly ductile and low
strength. The “coupled crust–mantle” and “deep crustal décollement”
both belong to the “narrow rift mode” of Buck (1991).
5.2. Rift topography as a function of mantle strength
Since our modelling approach accounts for elasticity, the topography of the free surface can be extracted from the numerical results.
As we did not take into account sedimentation and erosion, our
estimates of topography are maximum for reliefs and minimum for
Fig. 6 presents the total strain in Models 1, 2 and 3 for a velocity
of 1 cm/a and 1 mm/a, after a horizontal displacement of 40 km. At
1 cm/a, the results are identical to those seen in Fig. 4, but are shown at
an earlier stage of extension (40 km instead of 60 km). A decrease in
the applied velocity by one order of magnitude (1 mm/a) gives a more
localized deformation at lithosphere scale. More specifically, at low
TM, a decrease in the applied velocity drastically changes the pattern of
continental rifting (Model 1; Fig. 6). For similar thermal conditions,
V = 1 cm/a and 1 mm/a give patterns of “coupled crust–mantle” and
“deep crustal décollement”, respectively. A decrease in the applied
velocity, and therefore of strain rate, decreases the ductile crust
strength and thus enhances the decoupling between the crust and
mantle (Brun, 2001). The presence of a very high strain zone in the
deep crust highlights this feature. For higher Moho temperatures, no
significant change of continental rifting pattern is observed (Models 2
and 3; Fig. 6). The deformation in brittle layers is however more
localized at lower velocities. This feature reflects brittle–ductile
coupling, as recently discussed in Schueller et al. (2005). In a
brittle–ductile material, ductile layers exert a viscous resistance to
fault motion, which limits the maximum displacement rate along any
fault connected to the ductile interface. Therefore the viscosity of
Fig. 6. Role of the applied boundary velocity. Patterns of total strain after 40 km of boundary extensional displacement for V = 1 cm/a (left) and V = 1 mm/a (right) for Models 1 to 3. See
Figs. 1 and 2 and Tables 1, 2 and 3 for model parameters.
F. Gueydan et al. / Tectonophysics 460 (2008) 83–93
89
Fig. 7. Role of the crustal thickness. Patterns of total strain after 45 km of boundary extensional displacement for hC = 30 km (left) and hC = 50 km (right) for Moho temperatures
TM = 482 °C (up) and TM = 550 °C (down), and with V = 1 cm/a. See Figs. 1 and 2 and Tables 1, 2 and 3 for model parameters.
ductile layers controls the fault displacement rate. Low/high viscosity
induces high/low fault displacement rate, respectively. An increase of
the viscosity therefore makes new fault nucleation necessary in order
to accommodate the applied velocity. Low viscosities favour a
localized mode of fracturing, while high viscosities favour a
distributed mode of fracturing. Following this analysis, a decrease in
the applied velocity decreases the overall strain rate and the ductile
strength (Eq. (3)), leading to a more localized fracturing, as shown for
Models 2 and 3. These results exemplify the role of the deep crust
strength in the patterns of continental rifting.
The effect of crustal thickness (Fig. 7) is fully represented by the
strength ratio SM/SC. At a constant Moho temperature TM, the increase
in crustal thickness increases the strength ratio SM/SC, and leads to a
transition from the “coupled crust–mantle” to the “deep crustal
décollement” patterns, as illustrated by Models 2 and 5 (Figs. 7 and 8).
On the contrary, the effect of the boundary velocity is not well
represented by the strength ratio SM/SC. A decrease in the overall
strain rate, used to compute the strength profiles, decreases the
ductile strength in both the crust and mantle and therefore the SM/SC
value remains almost unchanged.
7. The effects of crustal thickness
9. Deformation maps of continental rifting patterns
The role of crustal thickness is documented in Fig. 7, which
presents the total strain patterns for four models after a horizontal
displacement of 45 km at a velocity V = 1 cm/a. The crustal thickness
for Models 2 and 4 is 30 km and 50 km for Models 5 and 6 whereas the
Moho temperature for Models 2 and 5 is 482 °C and 550 °C for Models
4 and 6 (Table 3).
For TM = 482 °C, the increase in the crustal thickness leads to a
switch from “crustal décollement” to “coupled crust–mantle”, marked
by distributed faulting in the brittle mantle. This change corresponds
to an increase in lithosphere strength and more specifically in mantle
strength (Fig. 1). In Model 5, the mantle strength is significantly larger
than in Model 2. This again highlights the crucial role of the
uppermost mantle strength in the pattern of continental rifting. No
significant change is observed for TM = 550 °C.
In order to compare our modelling results with natural examples
of rifts, the domains representing the three patterns of continental
rifting – i.e. “coupled crust–mantle”, “deep crustal décollement” and
“wide rift” – are mapped as a function of the whole crust and brittle
8. Transitions between the three patterns of continental rifting
The plot of the set of models computed in the SM/SC − TM diagram
according to the stretching patterns observed shows that three
domains can be identified according to the SM/SC value (Fig. 8).
“Coupled crust–mantle” occurs when SM/SC N 10 corresponding to the
presence of a very high strength mantle that imposes its pattern of
strain localization at lithosphere scale. “Deep crustal décollement”
occurs when 1 b SM/SC b 10, with mantle stretching, localized into a
single neck zone, transmitted to the crust through two layer-parallel
shear zones located in the deep crust. Finally, “wide rifting” occurs
when SM b SC, corresponding to the absence of a high strength “brittle”
mantle.
Fig. 8. Patterns of continental rifting as a function of the crust–mantle strength ratio SM/SC
and Moho temperature TM, for hC = 30 km (squares) and hC = 50 km (dots). The patterns
“coupled crust–mantle” and “deep crustal décollement” both belong to the “narrow rift”
mode of Buck (1991).
90
F. Gueydan et al. / Tectonophysics 460 (2008) 83–93
Fig. 9. Patterns of continental rifting as a function of brittle crust and whole crust thicknesses for dry olivine at V = 1 cm/a (top) and 1 mm/a (middle) and for wet olivine at V = 1 cm/a
(bottom). The patterns boundaries are plotted using the strength ratio value SM/SC (See Fig. 8). Curves of initial Moho temperatures TM = 400, 600 and 800 °C are calculated with Eq. (2).
crust thicknesses (Fig. 9). The boundaries between the three
patterns are first defined analytically by the strength ratio SM/SC that
corresponds to the inception of a deep crustal décollement (SM/SC ~ 10)
and to the disappearance of a high strength mantle (SM/SC ~ 1; Fig. 8).
Numerical simulations are then carried out to validate the pattern
boundaries that correspond to progressive transitions rather than to
sharp boundaries. Contours of Moho temperatures are also reported
on deformation maps, based on Eq. (2) (Fig. 9). For a boundary
velocity of 1 cm/a, the transition between the “coupled crust–mantle”
and “deep crustal décollement” patterns occurs at TM ~ 450 °C and at
higher TM for larger crustal thicknesses. The transition between
“deep crustal décollement” and “wide rift” occurs at TM ~ 700 °C
regardless of the crustal thickness, as it is controlled by the absence of
a high strength mantle. These transitions between the continental
rifting patterns also depend on the rheological parameters and
boundary velocities chosen to compute the models. A decrease of the
boundary velocity by an order of magnitude decreases the ductile
crust strength and thus enhances the decoupling between the crust
and mantle. Consequently, the boundary of the “deep crustal
décollement” pattern shifts towards lower TM values (Fig. 9; top).
The same effect occurs if wet olivine parameters are used instead of
those for dry olivine (Table 2 and Fig. 9; bottom). In contrast, using
Plagioclase instead of wet quartz increases the crustal strength and
thus shifts the boundary between the rifting patterns towards higher
TM values.
10. Discussion: comparison with natural examples of rifts
The thicknesses of the whole crust and of the brittle crust – i.e.
taken here as an equivalent of the seismogenic layer – for several
well documented examples of continental rifts are given in Table 4,
as well as the method used to obtain these thicknesses. These
examples are classically referred as continental rifts (Rhine Graben,
Baikal Rift, Main Ethiopian Rift and Rio Grande Rift), passive
margins and regularly spaced rifts (Basin and Range, Aegean and
the Tibet-type plateau extension). Fig. 10 presents the position of
F. Gueydan et al. / Tectonophysics 460 (2008) 83–93
91
Table 4
Crustal thickness and brittle crust thickness for different natural examples of rifts
Location
Crustal thickness
Brittle crust thickness
hC [km]
hRC [km]
Methods
Rhine–Limagne–Bresse
30 km
10–15 km
Baikal
40 km
20 km
East African Rift
40–45 km
30–35 km
Rio Grande
45–50 km
15–20 km
Evvia–Corinthe
40 km
7–8 km
Basin and Range
Tibet
50 km
60 km
10 km poorly constrained
10–12 km poorly constrained
TM N 700 °C (partial melting in the middle crust)
Reflection seismic for Rhine (Brun et al., 1992). Refraction seismic for
Limagne–Bresse (Zeyen et al., 1997)
Seismic profiles (ten Brink and Taylor, 2002), gravity inversion (Tibéri et al., 2003)
and earthquake depth distribution (Déverchère et al., 2001)
Receiver function (Dugda et al., 2005); gravimetry (Mahatsente et al., 1999;
Petit and Ebinger, 2000)
Local tomography (West et al., 2004; Wilson et al., 2005) and reflection seismic
(Klemperer, 1987)
Gravimetric study (Tiberi et al., 2000, 2001) and local tomography study
(Latorre et al., 2004; Rigo et al., 1996)
Seismic profiles (Stewart, 1978)
Indepth-Reflection seismic, receiver (Haines et al., 2003) and discussion
in (Armijo et al., 1986).
Partial melting in the middle crust (Mechie et al., 2004; Unsworth et al., 2005)
The methods used to estimate these thicknesses are also given.
these natural rift examples on a synthetic map of continental rifting
patterns.
The crustal structure of the Baikal rift has been investigated using
seismic profiles (ten Brink and Taylor, 2002), gravity inversion (Tibéri
et al., 2003) and earthquake depth distribution (Déverchère et al.,
2001). It yields consistent estimates of the crustal thickness at
approximately 40 km and of the brittle crust thickness at 20 km.
The Baikal rift likely belongs to the “coupled crust–mantle” pattern.
The same holds for the Main Ethiopian rift (Dugda et al., 2005;
Mahatsente et al., 1999; Petit and Ebinger, 2000) and the Rio Grande
rift (Klemperer, 1987; West et al., 2004; Wilson et al., 2005). Note that
inherited structures could induce an asymmetric structure within the
forming rift, as also invoked for the Rhine Graben (Brun et al., 1992),
the Baikal Rift (Déverchère et al., 2001) and the East African Rift
(Tommasi and Vauchez, 2001). The deep structure of the Rhine graben
has been documented by two deep seismic lines (DEKORP-ECORS) in
the northern and in the southern part of the graben (Brun et al., 1992).
The rooting of master normal faults in the lower reflective crust at
~ 15 km provides an estimate of the brittle crust thickness. The crustal
thickness was estimated to be approximately 30 km (Table 4). Below
the graben, gently dipping reflectors cross-cut the Moho with a
normal sense of offset, indicating the existence of a narrow mantle
shear zone. The Rhine graben falls within the “deep crustal
décollement” type of continental rifting. The Limagne–Bresse rift
Fig. 10. Location of some famous examples of rifts on a synthetic map of continental
rifting patterns (see natural rifts data in Table 4).
system in France is marked by two asymmetric branches separated by
~150 km (Michon and Merle, 2003). The crustal thickness is similar to
that of the Rhine graben, although the brittle crust seems to be much
smaller (~10 km). This smaller brittle crust, compared to the Rhine
graben, is consistent with a thinner thermal lithosphere of approximately 80 km (Sobolev et al., 1997) instead of 100 km below the Rhine
graben (Achauer and Masson, 2002). Like the Rhine Graben, the
Limagne and Bresse rift systems fall within the “deep crustal
décollement”. This continental rifting pattern induces efficient lithosphere necking leading to the formation of non-volcanic passive
margins for increasing amount of stretching. As most non-volcanic
passive margins lack off deep crustal partial melting, their Moho
temperature is lower than 700 °C. We thus propose to range them in
the “deep crustal décollement” (Fig. 10). This pattern has been
exemplified by analogue experiments (Brun and Beslier, 1996) and
numerical models (Nagel and Buck, 2004). That also well explains the
typical faulting pattern of modern passive margins (Nagel and Buck,
2004), as well as those exhumed in the Alps (Whitmarsh et al., 2001).
As already pointed out, it must be recalled here that the “coupled
crust–mantle” and the “deep crustal décollement” patterns of lithosphere extension both belong to the “narrow rift mode ” of Buck
(1991). In volcanic passive margins, at variance with the mechanics of
extension discussed here, the uppermost mantle is initially disrupted
by the intrusion of magma bodies that anticipate and/or strongly
control lithosphere necking (Callot et al., 2001).
Finally, the typical examples of regularly spaced rifts (Aegean rift
systems, Basin and Range and Tibet plateau-like extension) fall in the
“wide rift”. The crustal thickness of the Aegean rifts prior to extension
(e.g. Corinth and Evia) were estimated by reference to continental
Greece using gravity inversion (Tiberi et al., 2000, 2001). The brittle–
ductile transition within the crust is well marked by the presence of
microseismic clusters at depths of 7–8 km (Rigo et al., 1996) and by
local tomographic images (Latorre et al., 2004). Crustal thicknesses
prior to extension in the Basin and Range and in the Tibet plateau were
estimated using seismic profiles (Stewart, 1978), reflection seismic and
receiver functions (Indepth program, Haines et al., 2003). For the Basin
and Range, estimates were made taking into account the timing of rift
development and the corresponding amount of stretching and crustal
thinning. Brittle crust thicknesses are poorly constrained in these two
rift systems. However, evidence of partial melting in the middle crust
(Mechie et al., 2004; Unsworth et al., 2005) indicates that Moho
temperature TM is significantly higher than 700 °C (Table 4). The three
examples of regularly spaced rifts quoted above have in common a flat
lying Moho over large horizontal distances (Allmendinger et al., 1987;
Tirel et al., 2004, Braitenberg et al., 2000). Consistently, in our models,
the absence of the Moho offset is only obtained when the mantle is
wholly ductile and low strength and the deep crust strength is low
92
F. Gueydan et al. / Tectonophysics 460 (2008) 83–93
enough to permit rapid ductile flow, allowing the Moho to remain
relatively flat during continuing extension.
11. Conclusion
This study provides some mechanical hints on the consequences of
mantle and deep crustal strengths on the pattern of continental
rifting.
1. The presence of a high strength uppermost mantle is essential to
promote lithosphere necking. On the contrary, homogeneous
lithosphere stretching is observed if the lithosphere mantle is
entirely ductile and low strength.
2. The Moho temperature TM, the applied velocity, and thus the
strength of the deep crust control the amount of crust–mantle
coupling. For low TM, crust and mantle are strongly coupled,
leading to the formation of normal sense shear zones on a
lithosphere scale. For higher TM, the deep crust acts as a
décollement between the brittle crust and the uppermost mantle.
3. Rift spacing in the upper brittle crust is a direct function of the
mantle strength. Rift spacing is controlled by the high strength
mantle thickness and decreases with decreasing mantle strength. If
the mantle is wholly ductile and low strength, wide rifting occurs in
the upper crust with small rift spacing.
4. Three patterns of continental rifting are defined: “coupled crust–
mantle” for high mantle strength, “deep crustal décollement” when
the strength of the deep crust is low enough to decouple the crust
from the mantle and, finally, “wide rift” when the lithosphere
mantle is wholly ductile and low strength. The “coupled crust–
mantle” and “deep crustal décollement” both belong to the
“narrow rift mode” of Buck (1991).
These results, gathered with previous numerical and analogue
models, demonstrate that lithosphere necking and thus continental
break-up requires a high strength brittle mantle (Brun and Beslier,
1996; Brun, 1999; Nagel and Buck, 2004; Burov and Watts, 2006).
However, some geophysical evidences question this mechanical
prerequisite (e.g. Jackson, 2002). A high strength ductile localizing
mantle, as recently proposed by Precigout et al. (2007), could be a true
ductile alternative to the brittle mantle and thus a way to reconcile
these opposite models of lithosphere strength — i.e strong vs weak
mantle.
Acknowledgments
C. Morency wishes to thank the CNRS-INSU for a Post Doc
fellowship. This work was also partly funded by an Institut
Universitaire de France grant to J-P. Brun. Thanks are due to R. Buck,
J. Chery and an anonymous reviewer for very constructive comments.
References
Achauer, U., Masson, F., 2002. Seismic tomography of continental rifts revisited: from
relative to absolute heterogeneities. Tectonophysics 358 (1–4), 17–37.
Allemand, P., Brun, J.-P., 1991. Width of continental rifts and rheological layering of the
lithosphere. Tectonophysics 188 (1–2), 63–69.
Allmendinger, R.W., et al., 1987. Deep seismic reflection characteristics of the continental
crust. Geology 15, 304–310.
Armijo, R., Tapponnier, P., Mercier, J.P., Han, T., 1986. Quaternary extension in southern
Tibet. Journal of Geophysical Research 91, 13,803–13,872.
Bassi, G., 1995. Relative importance of strain rate and rheology for the mode of
continental extension. Geophysical Journal International 122 (1), 195–210.
Behn, M.D., Lin, J., Zuber, M.T., 2002. A continuum mechanics model for normal
faulting using a strain-rate softening rheology: implications for thermal and
rheological controls on continental and oceanic rifting. Earth and Planetary
Science Letters 202 (3–4), 725–740.
Brace, W.F., Kohlstedt, D.L., 1980. Limits on lithospheric stress imposed by laboratory
experiments. Journal of Geophysical Research 85 (B11), 6248–6252.
Braitenberg, C., Zadro, M., Fang, J., Wang, Y., Hsu, H.T., 2000. The gravity and isostatic
Moho undulations in Qinghai–Tibet plateau. Journal of Geodynamics 30 (5),
489–505.
Braun, J., Beaumont, C., 1989. A physical explanation of the relation between flank
uplifts and the breakup unconformity at rifted continental margins. Geology 17,
760–764.
Brun, J.P., 1999. Narrow rifts versus wide rifts: inferences for mechanics of rifting from
laboratory experiments. Philosophical Transactions of the Royal Society of London
357, 695–712.
Brun, J.P., 2001. Deformation of the continental lithosphere: insights form brittle–
ductile models. In: de Meer, S., de Bresser, J.H.P., Pennock, G.M. (Eds.), Deformation
Mechanisms, Rheology and Tectonics: Current Status and Future Perspectives.
Special Publications. Geological Society, London, pp. 355–370.
Brun, J.P., Beslier, M.O., 1996. Mantle exhumation at passive margins. Erath Planet. Sci.
Lett. 142 (1–2), 161–174.
Brun, J.P., Gutscher, M.-A., teams, 1992. Deep crustal structure of the Rhine Graben from
seismic reflection data: a summary. Tectonophysics 208 (1–3), 139–147.
Buck, W.R., 1991. Modes of continental lithosphere extension. Journal of Geophysical
Research 96 (B12), 20,161–20,178.
Burov, E., Watts, A.B., 2006. The long-term strength of continental lithosphere: “jelly
sandwich” or “crème brûlée”? GSA Today 16 (1). doi:10.1130/1052-5173(2006)016.
Byerlee, J.D., 1978. Friction of rocks. Pure and Applied Geophysics 116, 615–626.
Callot, J.P., Grigné, C., Geoffroy, L., Brun, J.P., 2001. Development of volcanic passive
margins: two-dimensional laboratory models. Tectonics 20 (1), 148–159.
Carter, N.L., Tsenn, M.C., 1987. Flow properties of continental lithosphere. Tectonophysics
136, 27–63.
Chen, P., Molnar, P., 1983. The depth distribution of intracontinental and intraplate
earthquake and its implications for the thermal and mechanical properties of the
lithosphere. Journal of Geophysical Research 88, 4183–4214.
Déverchère, J., et al., 2001. Depth distribution of earthquakes in the Baikal rift system
and its implications for the rheology of the lithosphere. Geophysical Journal
International 146, 714–730.
Dugda, M.T., et al., 2005. Crustal structure in Ethiopia and Kenya from receiver function
analysis: Implications for rift development in eastern Africa. Journal of Geophysical
Research 110, B01303. doi:10.1029/2004JB003065.
Frederiksen, S., Braun, J., 2001. Numerical modelling of strain localisation during
extension of the continental lithosphere. Earth and Planetary Science Letters 188
(1–2), 241–251.
Gueydan, F., Leroy, Y.M., Jolivet, L., 2004. Mechanics of low-angle extensional
shearzones at the brittle–ductile transition. Journal of Geophysical Research 109,
B12407. doi:10.1029/2003JB002806.
Haines, S.S., et al., 2003. INDEPTH III seismic data: from surface observations to deep
crustal processes in Tibet. Tectonics 22 (1), 1–1–1-18.
Handy, M.R., Brun, J.-P., 2004. Seismicity, structure and strength of the continental
lithosphere. Earth and Planetary Science Letters 223 (3–4), 427–441.
Huismans, R.S., Beaumont, C., 2003. Symmetric and asymmetric lithospheric extension:
relative effects of frictional-plastic and viscous strain softening. Journal of
Geophysical Research 108 (B10), ETG 13–1-ETG 13–22.
Huismans, R.S., Buiter, S.J.H., Beaumont, C., 2005. Effect of plastic-viscous layering and
strain softening on mode selection during lithospheric extension. Journal of
Geophysical Research 110 (B2), 1–17. doi:10.1029/2004JB003114.
Jackson, J., 2002. Strength of the continental lithosphere: time to abandon the jelly
sandwich? GSA Today 1–9 (September).
Karato, S.-i., Wu, P., 1993. Rheology of the upper mantle: a synthesis. Science 260,
771–778.
Klemperer, S.L., 1987. A relation between continental heat flow and the seismic
reflectivity of the lower crust. Journal of Geophysics 61, 1–11.
Latorre, D., et al., 2004. A new seismic tomography of Aigion area (Gulf of Corinth, Greece)
from the 1991 data set. Geophysical Journal International 159 (3), 1013–1031.
Lavier, L.L., Buck, W.R., Poliakov, A.N.B., 1999. Self-consistent rolling-hinge model for the
evolution of large-offset low-angle normal faults. Geology 27 (12), 1127–1130.
Lavier, L.L., Buck, W.R., Poliakov, A.N.B., 2000. Factors controlling normal fault offset in
an ideal brittle layer. Journal of Geophysical Research 105 (B10), 23,431–23,442.
Maggi, A., Jackson, J.A., Priestley, K., Baker, C., 2000. A reassessment of focal depth
distributions in southern Iran, the Tien Shan and northern India: do earthquakes
really occur in the continental mantle? Geophysical Journal International 143,
629–661.
Mahatsente, R., Jentzsch, G., Jahr, T., 1999. Crustal structure of the Main Ethiopian Rift
from gravity data: 3-dimensional modeling. Tectonophysics 313 (4), 363–382.
McKenzie, D., 1978. Some remarks on the development of sedimentary basins. Earth
and Planetary Science Letters 40 (1), 25–32.
Mechie, J., et al., 2004. Precise temperature estimation in the Tibetan crust from seismic
detection of the a–b quartz transition. Geology 32 (7), 601–604. doi:10.1130/G20367.1.
Michon, L., Merle, O., 2003. Mode of lithospheric extension: conceptual models from
analogue modeling. Tectonics 22 (4), 1028. doi:10.1029/2002TC001435.
Molnar, P., 1992. Brace–Goetze strength profiles, the partitioning of strike–slip and
thrust faulting at zones of oblique convergence, and the stress-heat flow paradox of
the San Andreas fault. In: Evans, B., Wong, T.-F. (Eds.), Fault Mechanics and
Transport Properties of Rocks. Academic Press, San Diego, California, pp. 461–473.
Nagel, T.J., Buck, W.R., 2004. Symmetric alternative to asymmetric rifting models.
Geology 32 (11), 937–940.
Petit, C., Ebinger, C., 2000. Flexure and mechanical behavior of cratonic lithosphere:
gravity models of the East African and Baikal rifts. Journal of Geophysical Research
105 (B8), 19,151–19,162.
Precigout, J., Gueydan, F., Gapais, D., Garrido, C.J., Essaifi, A., 2007. Strain localisation in
the subcontinental mantle — a ductile alternative to the brittle mantle.
Tectonophysics 445 (3–4), 318–336.
Ranalli, G., 2000. Rheology of the crust and its role in tectonic reactivation. Journal of
Geodynamics 30, 3–15.
F. Gueydan et al. / Tectonophysics 460 (2008) 83–93
Rigo, A., et al., 1996. A microseismicity study in the western part of the Gulf of Corinth
(Greece): implications for large-scale normal faulting mechanisms. Geophysical
Journal International 126, 663–688.
Schueller, S., Gueydan, F., Davy, P., 2005. Brittle–ductile coupling: role of ductile
viscosity on brittle fracturing. Geophysical Research Letters 32 (L10308).
doi:10.1029/2004GL022272.
Sibson, R.H., 1983. Continental fault structure and the shallow earthquake source.
Journal of the Geological Society (London) 140, 741–767.
Sobolev, S.V., et al., 1997. Upper mantle temperatures and lithosphere–asthenosphere
system beneath the French Massif Central constrained by seismic, gravity,
petrologic and thermal observations. Tectonophysics 275 (1–3), 143–164.
Stewart, J.H., 1978. Basin-range structure in the western North America: a review. In:
Smith, R.B., Eaton, G.P. (Eds.), Cenozoic Tectonics and Regional Geophysics of the
Western Cordillera. The Geological Society of America, pp. 1–31.
ten Brink, U.S., Taylor, M.H., 2002. Crustal structure of central Lake Baikal: insights
into intracontinental rifting. Journal of Geophysical Research 107 (B7), 2132.
doi:10.1029/2001JB000300.
Tibéri, C., et al., 2003. Deep structure of the Baikal rift zone revealed by joint inversion of
gravity and seismology. Journal of Geophysical Research 108 (B3). doi:10.1029/
2002JB001880.
Tiberi, C., Diament, M., Lyon-Caen, H., King, T., 2000. Moho topography beneath the
Corinth Rift area (Greece) from inversion of gravity data. Geophysical Journal
International 145, 1–18.
Tiberi, C., et al., 2001. Crustal and Upper Mantle Structure Beneath the Corinth Rift
(Greece) from a Teleseismic Tomography Study.
93
Tirel, C., Gueydan, F., Tiberi, C., Brun, J.-P., 2004. Aegean crustal thickness inferred from
gravity inversion. Geodynamical implications. Earth and Planetary Science Letters
228 (3–4), 267–280.
Tommasi, A., Vauchez, A., 2001. Continental rifting parallel to ancient collisional belts:
an effect of the mechanical anisotropy of the lithospheric mantle. Earth and
Planetary Science Letters 185 (1–2), 199–210.
Turcotte, D.L., Schubert, G., 1982. Geodynamics. Applications of Continuum Physics to
Geological Problems. Wiley. 450 pp.
Unsworth, M.J., et al., 2005. Crustal rheology of the Himalaya and Southern Tibet
inferred from magnetotelluric data. Nature 438 (7064), 78–81.
West, M., et al., 2004. Crust and upper mantle shear wave structure of the southwest
United States: Implications for rifting and support for high elevation. Journal of
Geophysical Research 109, B03309. doi:10.1029/2003JB002575.
Whitmarsh, R.B., Manatschal, G., Minshull, T.A., 2001. Evolution of magma-poor
continental margins from rifting to seafloor spreading. Nature 413, 150–154.
Wilson, D., et al., 2005. Lithospheric structure of the Rio Grande rift. Nature 433,
851–855.
Zeyen, H., et al., 1997. Refraction-seismic investigations of the northern Massif Central
(France). Tectonophysics 275 (1–3), 99–117.
Ziegler, P.A., Cloetingh, S., 2004. Dynamic processes controlling evolution of rifted
basins. Earth-Science Reviews 64 (1–2), 1–50.