Tectonophysics 320 (2000) 195–218
www.elsevier.com/locate/tecto
Dynamic link between the level of ductile crustal flow and style
of normal faulting of brittle crust
G. Bertotti a, *, Y. Podladchikov b, A. Daehler b
a Faculty of Earth Sciences, Vrije Universiteit, Amsterdam, The Netherlands
b Geologisches Institut, ETH Zentrum, Zurich, Switzerland
Accepted 18 August 1999
Abstract
In a rheologically layered crust, compositional layers have an upper, elasto-plastic part and a lower, viscous one.
When broken, the upper elastic part undergoes flexure, which is upward for the foot-wall and downward for the
hanging wall. As a consequence of bending, stresses will develop locally that can overcome the strength of the plate
and, therefore, impose the migration of active fault. In the lower, viscous part of each compositional layer, rocks can
potentially flow. Numerical modelling of the behaviour of a crust made up of two compositional layers, during and
following extension, shows that flow can take place not only in the lower crust but also, and more importantly, in
the lower part of the upper crust. The ability of crustal rocks to flow influences the style and kinematics of rifted
regions. When no flow occurs, subsidence will affect the extending areas, both hanging wall and foot-wall will subside
with respect to an absolute reference frame such as sea level, and there will be a strict proportionality between
extension and thinning. In addition, the downward movement of fault blocks will decrease the local stresses created
in the foot-wall and increase those of the hanging wall, thereby imposing a migration of the active fault towards the
hanging wall. This is the behaviour of extensional settings developed on stabilised crust and which evolved in a
passive margin. When flow does take place, middle crustal rocks will move towards the rifting zone causing isostatically
driven upward movements that will be superimposed on movements associated with crustal and lithospheric thinning.
Consequently, fault blocks will move upwards and the crust will show more extension than thinning. The upward
movements will decrease the stresses developed in the hanging walls and increase those of the foot-wall. Faults will
then migrate towards the foot-wall. Such a mode of deformation is expected in regions with thickened crust and has
its most apparent expression in core complexes. © 2000 Elsevier Science B.V. All rights reserved.
Keywords: crustal flow; fault blocks; multilayer model; numerical modelling; rifting
1. Introduction
The deformational response of the lithosphere
to applied tensional forces, which overcome its
strength, is highly variable. A wide range of large* Corresponding author. Tel.: +31-20-444-7288;
fax: +31-20-646-2457.
E-mail address: bert@geo.vu.nl (G. Bertotti)
scale phenomena, such as the striking difference in
width among different extending regions, has been
described in recent years and associated with lithosphere-scale dynamic processes (e.g. Kusznir and
Park, 1987; Buck 1991; Bassi, 1995; Govers and
Wortel, 1995; Hopper and Buck, 1996). A continuum mechanics approach has been typically
adopted in these studies.
Less attention has been devoted to tectonic
0040-1951/00/$ - see front matter © 2000 Elsevier Science B.V. All rights reserved.
PII: S0 0 4 0- 1 9 51 ( 0 0 ) 0 00 4 5 -7
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G. Bertotti et al. / Tectonophysics 320 (2000) 195–218
Fig. 1. The various possible responses of continental fault blocks to extension. (a) Absolute vertical movements; (b) patterns of fault
migration; (c) stretching versus thinning relations.
processes and phenomena occurring at a smaller
(kilometres to a few tens of kilometres) scale,
namely that of fault blocks [however, see Kusznir
et al. (1991), ter Voorde and Cloetingh (1996) and
van Balen and Podladchikov (1998)]. Such features are crucial in controlling the small-scale
evolution of the Earth’s surface and, therefore, are
of primary importance in sedimentary basin
studies. Relevant in this respect are processes
affecting not only the amount of accommodation
space created by rifting, but also the ability of an
area to rise above sea level and thereby being
eroded and providing clastic sediments to the
basin itself.
In this study, we concentrate on three groups
of phenomena: the absolute vertical movements of
fault blocks during and following rifting, the
pattern of fault propagation and, finally, relations
between amounts of extension and thinning.
Variability in these phenomena is large ( Fig. 1).
Foot-walls in core complexes experience upward
movements on the order of kilometres and contrast
with the kilometres of positive subsidence showed
by foot-wall blocks in rifted continental margins
(Fig. 1a). Patterns of fault migration are also
variable and, during stretching, the site of normal
faulting can migrate either towards the foot-wall
or towards the hanging wall (Fig. 1b). The shape
and dimension of the sedimentary basin will vary
accordingly. Finally, extension and thinning are
also related in a variable manner (Fig. 1c). In
most rifted continental margins, there is a substantial equivalence between extension and thinning.
This is not the case in core complexes where strong
extension is associated with limited crustal thinning
(e.g. Wernicke, 1985; Block and Royden, 1990).
Yield envelope profiles (e.g. Ranalli and
Murphy, 1987 and references cited therein) have
shown that a crustal compositional layer will,
under suitable conditions, have an upper part
behaving in an elasto-plastic manner overlying one
where viscous flow will be the rheological behaviour. The ability of crustal rocks to flow has been
demonstrated by various theoretical and realworld studies. Geophysical investigations, for
instance in the Basin and Range region of North
America, have demonstrated the importance of
lower crustal flow (Block and Royden, 1990; Kruse
et al., 1991; Kaufman and Royden, 1994). Viscous
flow in the lower crust is increasingly recognised
as a primary factor in controlling extensional
geometry and dynamics and its effects have been
experimentally investigated (Buck, 1991; Brun and
van den Driessche, 1994; Burov and Cloetingh,
1996; Hopper and Buck, 1996; ter Voorde et al.,
1998). One of the commonly envisaged consequences is to cause the decoupling between crust
and mantle layers (e.g. Hopper and Buck, 1996).
While these studies seem to demonstrate the relevance of lower crustal flow, there is increasing
G. Bertotti et al. / Tectonophysics 320 (2000) 195–218
geological evidence that flow of middle crustal
rocks might also be important. Geological investigations in core complexes, for instance, demonstrate that the rocks undergoing wholesale
deformation are those of the intermediate, ‘granitic’ crust often in association with widespread
magmatism (e.g. Burg et al., 1994; MacCready
et al., 1997; Vanderhaege and Teyssier, 1997).
In itself, the possibility of flow at intermediate
crustal levels is not unreasonable, given the knowledge that the upper crust is generally composed of
rocks different from and weaker than those of the
lower crust. The presence of two crustal compositional layers has not been considered in recent
numerical models dealing with continental extension (Buck, 1991; Hopper and Buck, 1996).
Because of their wavelengths, we believe that the
phenomena investigated in this paper, i.e. absolute
movements of blocks, patterns of fault migration
and relations between stretching and thinning, are
related to processes taking place within the crust
itself and, more specifically, in its upper and intermediate levels. A two-layer model is thus needed
to investigate these features.
In this paper we first analyse the real-world
variability of patterns of fault block movements,
of lateral fault migration, and extension–thinning
relationships. We then make use of numerical
modelling techniques to assess the efficiency of
middle and lower crustal flow under a wide range
of conditions and derive associated vertical movements. Our model is based on a multi-layer
approach for the crust that allows us to study the
effects of both middle and lower crustal flow. We
couple these modelling results with the flexural
behaviour of broken elastic plates to predict firstorder patterns in vertical movements at the Earth’s
surface, lateral fault propagation and extension–
thinning relationships. We eventually test these
predictions with real-world cases and conclude
that the mentioned three groups of phenomena
are not independent from each other but causally
inter-linked and associated with the potential ability of the upper crust to flow.
The overall approach we adopt in this paper is
to avoid very complex and ‘heavy’ numerical
models, which precisely because of their complexity and, therefore, of the largely unconstrained
197
feed-back processes, tend to lose their predictive
power. We rather propose a quantitative discussion
of the compositive processes and ‘assemble’ them
in the light of the geological record.
2. Variability of responses to extension
2.1. Absolute movements of fault blocks
While the relative sense of movement is implicit
in the definition of a normal fault, the sign and
magnitude of absolute vertical movements of fault
blocks, i.e. their syn-rift movements relative, for
instance, to sea level are not a priori defined. In
some cases, both fault blocks can subside below
sea level; in others, the foot-wall and, to a lesser
extent, the hanging wall will rise above sea level
and be subjected to erosion (Fig. 1a). Intermediate
situations with upward movement of the foot-wall
and substantially stable hanging wall can also be
observed.
Situations of the first kind, with both hanging
wall and foot-wall undergoing downward movement during extension, are typical for continental
rifts that developed during passive margin formation. Deep basins form in these settings with up
to several kilometres of sediments being accommodated by the downward movement of the hanging
wall. Foot-wall subsidence is also common, typically in the order of several hundreds of metres to
a few kilometres. Well-constrained field examples
are provided, for instance, by the Mesozoic SouthAlpine margin presently exposed in the Alps of
North Italy and Switzerland (e.g. Bernoulli et al.,
1979; Bertotti et al., 1993a) and by the Galicia
margin (Mauffret and Montadert, 1987; Boillot
et al., 1989).
The opposite configuration is characterised by
substantial foot-wall uplift and stable to slightly
moving hanging wall. Fault blocks following this
evolution are typically found in thickened crustal
segments (e.g. Dart et al., 1995; Cello et al., 1997;
Cogan et al., 1998). With the onset of extension
the hanging wall will rise and morphology will
develop, thereby activating erosion. Persisting
upward movement of the foot-wall coupled with
effective erosion can lead to the exhumation of
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G. Bertotti et al. / Tectonophysics 320 (2000) 195–218
deep-seated crustal rocks. The hanging wall will
undergo more limited displacement. Depending on
the amount of upward displacement and on local
hydrographic conditions, the hanging wall can
host syn-tectonic intramontane basins or be
slightly eroded.
2.2. Patterns of fault migration
Normal faults, both smaller and major ones,
have finite lifetimes (e.g. Buck, 1988, 1993; Forsyth,
1992). In most cases, however, the cessation of
activity along a fault does not represent the end
of extension at the scale of the entire lithospheric
plate. In this case, the site of deformation migrates,
new faults are activated and previously undeformed crustal segments undergo extension. New
normal faults can be created in the hanging wall
or on the foot-wall ( Fig. 1b). Although existing
modelling studies ( Forsyth, 1992; Buck, 1993) are
able to provide estimates of the lifetime of normal
faults, they fail to predict where the new fault
would be activated. Attempts in this direction have
been made by Hassani and Chéry (1996) and Bott
(1997). It is our goal to relate patterns of fault
migration with absolute vertical motions of fault
blocks.
Lateral migrations of single normal faults are
poorly documented in geologic literature, partly
because of the difficulty of stratigraphically resolving the timing of fault activity. Migration towards
the hanging wall has been proposed by Dart et al.
(1995) for continental rifts in western Turkey, and
propagation towards the foot-wall has been considered as likely by Bertotti et al. (1997a) for the
Bologna fault of the Northern Apennines of Italy.
In a somewhat less documented case, Spadini and
Podladchikov (1996) postulated a migration of
normal faults towards the hanging wall in the
upper mantle of the E-Sardinia passive continental margin.
( Fig. 1c). On one side, extension can be directly
proportional to thinning, which implies a volume
(or area in two dimensions) preservation. With
progressing extension the crust will thin, possibly
leading to crustal separation and to the formation
of passive continental margins. In other situations,
the amount of thinning is significantly lower than
that of extension. In these cases, material is added
into the extending zone and mass is not preserved
along the profile. It has been speculated that
magmatic underplating (e.g. Hill et al., 1995) or,
more importantly, flow of lower crustal material
could be the processes able to explain the observations. Geophysical data from the Basin and Range
Province of the western United States (Block and
Royden, 1990; Kaufman and Royden, 1994) seem
to confirm the viability of such mechanisms.
However, the field evidence from core complexes
of the same belt documents very widespread flow
of middle crustal rocks (e.g. MacCready et al.,
1997; Vanderhaege and Teyssier, 1997). This raises
the possibility that at least part of the material
flowing in the extending zone is of middle crustal
origin.
3. Rheological stratification of the lithosphere and
crustal flow
It is generally accepted that the lithosphere can
be mechanically envisaged as a multilayer formed
by a variable number of layers of different composition (Fig. 2) (e.g. Ranalli and Murphy, 1987).
2.3. Relations between magnitudes of extension and
thinning
While normal faulting is necessarily associated
with horizontal extension, the amount of crustal
thinning observed in various settings is variable
Fig. 2. The multilayer description of the lithosphere. The
different dips of faults cutting the various layers are only symbolic. Arrows close to rheological profiles indicate the layers of
potential material flow considered in the model.
G. Bertotti et al. / Tectonophysics 320 (2000) 195–218
From a rheological perspective, each compositional layer will potentially have an upper part
with elasto-plastic rheology described by Hook’s
and Byerlee’s laws, and a lower one with a viscous
behaviour described by high-temperature flow laws
(Carter and Tsenn, 1987). One can therefore think
of the lithosphere in terms of a multilayer composed by a number of elasto-plastic plates separated by viscous layers. In our model, we consider
the crust as composed of two compositional layers.
In mechanical terms, this means that the crust we
model has potentially two elasto-plastic and two
viscous sub-layers. This differs from available
numerical models ( Kusznir et al., 1991; Hopper
and Buck, 1996).
During rifting, the rigid sublayers will break
along normal faults and will flex ( Vening-Meinesz,
1950; Turcotte and Schubert, 1982; Bott, 1996;
Spadini and Podladchikov, 1996). The hanging
wall will bend downward, while the foot-wall will
flex upward. In the absence of gravity forces and
of sedimentation/erosion, the geometry of flexure
and the stress distribution in the two plates is
symmetrical. Viscous layers between rigid plates
will thin by pure shear, typically accommodated
by systems of anastomosing shear zones (e.g.
Brodie and Rutter, 1987). Thinning causes changes
in the shape and geometry of the previously flat
surfaces separating layers with different densities
such as the boundary between upper and lower
crust and between lower crust and mantle. As a
consequence, load changes occur in the lithospheric column that, in turn, will provoke isostatically
199
driven vertical movements. In the case where no
lateral crustal flow takes place, the lithosphere will
move vertically as a whole. On the contrary, if
flow is efficient, then denser layers will tend to
decouple and subside independently from other
layers. As compensation, lighter material may flow
towards the centre of the rift (Fig. 3). As a result,
material is redistributed, causing further isostatically driven vertical movements, namely subsidence at the rift flanks and possibly uplift in the
centre of the rift. By spreading out the crustal
thinning, the subsurface topography of a compensation horizon is flattened.
In the following we analyse separately the patterns of vertical movements associated with crustal
thinning both in the presence and absence of flow
and with the flexural rebound of a broken plate.
We will show that several geological features can
be adequately explained by combining the two
components of the system.
4. Modelling crustal flow and associated vertical
movements
4.1. Basic structure of the model
Our numerical model uses the thin sheet approximation widely adopted in passive rifting modelling
(McKenzie, 1978; Kusznir et al., 1991). In order
to keep calculations simple and make results more
visible, the model artificially separates processes
taking place during rifting from those occurring
during drifting.
Fig. 3. The main features of the numerical model used to describe the effects of crustal flow. (a) Situation before the onset of rifting.
(b) Extension thins the crust with pure shear geometry and produces a thermal anomaly. (c) Following the end of rifting, the heavy,
elevated parts of the system (i.e. the upper mantle and the upper lower crust) will ‘sink’ (white arrows) if viscous rocks in the ‘soft’
layers can flow (solid arrows) into the extending zone. Isostatic movements occur in response to thickness changes. Note that the
distinction between rifting and compensation is purely conceptual and only reflects the structure of the program used (see text).
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G. Bertotti et al. / Tectonophysics 320 (2000) 195–218
Before the onset of rifting, layer boundaries are
flat with the exception of a cosinusoidal perturbation of the Moho (Fig. 3). The detailed geometry
of the perturbation has a minor impact on the
basin kinematics but influences the amplitude of
subsurface topography. A steady-state geotherm is
assumed at the onset of rifting.
Extension is assumed to occur with a pure shear
geometry and the particular kinematics of faulting
are ignored ( Fig. 3). Stretching and thinning are
controlled by the cosinusoidal lateral variations of
the strain rate, namely with the relation
ė(x)=
ln( b
max
)
C
A BD
1+cos
p
x
2t
L
rift
where x is the initial distance from the extension
centre of the rift (other symbols are explained in
Table 1). The shape of the basin obtained remains
constant through rifting, while its dimensions
increase and in its final geometry it roughly corresponds to ‘real-world’ basins (e.g. Kusznir and
Park, 1987). Since deformation is assumed to have
a pure shear geometry, vertical velocities are a
linear function of depth. During active extension,
a basin forms that is filled by sediments. At the
same time, a subsurface topography is created on
surfaces separating layers with differing densities
(Fig. 3). Vertical movements recorded during this
stage are associated with the local isostatic compensation of the entire lithospheric column on top
of the asthenosphere. Subsidence is calculated bal-
Table 1
Symbols used in the text
L
t
rift
h ,r
sed sed
h ,r
uc uc
h ,r
ucb ucb
h ,r
lc lc
h ,r
lcb lcb
h ,r
m m
r
ast
b
b
max
A
R
half width of the extending zone
rift duration
thickness and density of sediments
thickness and density of upper crust
thickness and density of mobile upper crust
thickness and density of lower crust
thickness and density of mobile lower crust
thickness and density of lithospheric mantle
density of asthenosphere
thinning factor
stretching factor at the rift centre
activation energy
gas constant
ancing the ‘current’ load at the moment of observation with the initial load of a lithostatic column
prior to rifting (McKenzie, 1978).
An implicit finite difference scheme with fixed
temperatures at top and bottom is used to calculate
temperatures within the model and their control
on rheological behaviour. Thermal calculations are
based on one-dimensional heat equations with
diffusion, advection and heat production that take
place in a two-dimensional space. Lateral heat
conduction and sediment blanketing effects are not
taken into account.
Following the cessation of rifting, viscous flow
is allowed in the rheologically weak parts of the
system (e.g. Bird, 1991). The weak parts of the
lithosphere where flow takes place are localised on
yield strength profiles and are typically located at
the hottest, bottom, part of each compositional
layer (Fig. 2). In our model we envisage three
horizons where flow can potentially take place: in
the upper crust, in the lower crust and in the
asthenosphere. The motor of flow lies in the lateral
pressure gradients generated by rifting. Deeper,
denser rocks risen under the rift axis during extension create subsurface topographic highs of denser
material that will tend to subside. If rheologically
possible, lighter rocks will flow towards the rift
axis, thereby redistributing material and causing a
flattening of the compensation level ( Fig. 3). To
describe crustal flow, the model adopts the
approach proposed by Buck (1991). The
rearrangement of crustal material produces new
isostatic vertical movements, which are expected
to take place at an early post-rift stage. The postrift waning of the thermal anomaly is not considered in these calculations.
4.2. Post-rift isostasy, pressure gradients and
vertical movements
4.2.1. Situation at the end of rifting
Syn-rift thinning causes (a) isostatic movements
and (b) lateral pressure gradients in the various
lithospheric layers. In conjunction with lithospheric stretching, surfaces bounding layers with
different densities acquire a morphology and lateral pressure gradients are imposed within each
layer which tend to displace rocks towards the
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G. Bertotti et al. / Tectonophysics 320 (2000) 195–218
Table 2
Lateral pressure gradients
Layer
Density
(g/cm3)
Initial thickness
(km)
1.
2.
3.
4.
5.
6.
7.
2.2
2.7
2.6
2.8
2.75
3.3
3.2
0
40
0
20
0
60
0
sediments
initial upper crust
flowing upper crust
initial lower crust
mobile lower crust
mantle lithosphere
asthenosphere
flow takes place, this pattern is predicted to continue throughout the post-rift stage.
Substituting Eq. (1) into Eq. (2) for i=2 and
i=4, the expressions for the hydrostatic pressure
anomalies at the base of the lower and upper crust
are obtained:
={−[(r −r )(r −r )h ]
uc
sed ast
ucb uc
+[(r −r ) (r −r )h ]
ucb
sed m
ast m
−[(r −r ) (r −r )h ]}
ucb
sed ast
lc lc
g
1
×
1−
r −r
b
ast
sed
DP
={−[(r −r ) (r −r )h ]
lc,ini
uc
sed ast
lcb uc
+[(r −r ) (r −r )h ]
lcb
sed m
ast m
−[(r −r ) (r −r )h ]}
lc
sed ast
lcb lc
1
1
1− .
×
r −r
b
ast
sed
Results for a specific example are shown in Fig. 4.
DP
uc,ini
A B
zone of thinning. The hydrostatic pressure anomalies at the base of a given layer i at the end of
rifting are calculated by comparing the initial load
of the overlying column with that subsequent to
thinning:
DP =P −[P −g(Z −Z )r ],
i
i
0i
0i
i i+1
where g is the gravity acceleration,
i
P =g ∑ h r
i
k k
1
and
(1)
i
P =g ∑ h r
0i
0k 0k
1
i
i
Z =∑ h Z =∑ h .
i
k
0i
0k
1
1
Symbols are explained in Tables 1 and 2. In our
modelling, average densities of each layer remain
constant during thinning, which is expected for
pure shear deformation if density changes associated with long-term cooling are neglected. The
thickness of the asthenospheric layer h is calcua
lated by setting Z =Z .
7
07
Subsidence h is calculated by setting DP to
sed
7
zero. The subsidence of the basin floor at the end
of rifting is given by:
A
r −r
r −r
lc h
uc h + ast
S =h = ast
uc
lc
ini
sed
r −r
r −r
ast
sed
ast
sed
r −r
1
ast h
− m
1− .
(2)
m
r −r
b
ast
sed
In accordance with general knowledge, Eq. (2)
predicts generalised subsidence except in the case
of a very thin crust when uplift is predicted. If no
BA B
A B
4.2.2. Isostasy and pressure gradients during
compensation
Once crustal rocks begin to flow (see below),
then (a) the weight of the lithospheric column is
modified, thereby causing isostatic vertical movements, and (b) the lateral pressure gradient along
a given layer is gradually eliminated. Such changes
in pressure gradients need to be tracked because
they control the flow of crustal rocks.
Isostatic vertical movement of the basin floor is
modified to the following expression:
A
BA B
1
r −r
r −r
lcb h
ucb h + ast
S=S − ast
1− ,
ini
ucb
lcb
r −r
r −r
b
ast
sed
ast
sed
where S is the subsidence achieved at the end of
ini
rifting as defined in Eq. (1). Eq. (1) includes the
thickness and density of ‘mobile’ crustal layers, i.e.
of the layers that can flow. Positive terms causing
subsidence are associated with thinning of the
upper and lower crust. Negative terms, i.e. those
causing uplift, are related to mantle thinning and
to the flow in the upper and lower crust. This is
explained by the notion that the mobile layers will
be formed by rocks warmer than those immediately
above them and possibly even partly molten. The
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G. Bertotti et al. / Tectonophysics 320 (2000) 195–218
Fig. 4. Hydrostatic pressure anomalies developed at the bottom of the lower crust and of the upper crust in different extensional
modes. All models have the same stretching factor b=2 and duration of rifting (3 Myr) (see Table 1 for other parameters).
following relations are thus expected:
<r and r <r .
ucb
uc
lcb
lc
The equation v(z) is comprehensive of all terms.
In reality, relations describing subsidence and lateral pressure gradients in the case of efficient upper
or lower crustal flow are simpler. This is due to
the idea that, in the case of complete compensation, phenomena taking place beneath the compensation horizons become irrelevant to the upper
crustal features we are investigating.
The thickness of the mobile lower crustal layer
h after complete compensation is calculated by
lcb
setting DP to zero. Consequently, subsidence in
5
the case of efficient lower crustal compensation is
described by the following equation:
r
A
r −r
r −r
r −r
ucb − lc
lcb h
uc h − lcb
S= lcb
uc
lc
r −r
r −r
r −r
lcb
sed
lcb
sed
lcb
sed
1
× 1− .
b
B
A B
It is apparent from the equation immediately above
that the only term ‘resisting’ uplift is the one controlled by the thickness of the stretched upper crust.
In the case of efficient flow in the upper crust,
the thickness of the mobile upper crustal layer
h after complete compensation is calculated by
ucb
setting DP to zero and subsidence becomes:
3
r −r
1
ucb h
S= − uc
1− .
uc
r −r
b
ucb
sed
As a consequence of the complete decoupling
underneath the base of the upper crust, uplift is
predicted.
Following the same procedure described in
Section 4.2.1, we also calculate the hydrostatic
pressure anomalies at the base of the lower and
upper crust:
A
BA B
DP =DP
+g
uc
uc,ini
[(r −r ) (r −r )h ]
ucb
sed ast
ucb ucb
+[(r −r ) (r −r )h ]
ucb
sed ast
lcb lcb
r −r
ast
sed
A B
DP =DP
+g
lc
lc,ini
[(r −r ) (r −r )h ]
ucb
sed ast
lcb ucb
+[(r −r ) (r −r )h ]
lcb
sed ast
lcb lcb
r −r
ast
sed
A B
1−
1−
1
b
1
b
.
.
Results for specific examples are shown in Fig. 4.
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G. Bertotti et al. / Tectonophysics 320 (2000) 195–218
4.3. Post-rift crustal flow
4.3.1. Rheology
A lithostatic modification of Byerlee’s law with
a friction coefficient of 0.75 is adopted for the
extensional deformation of brittle part of the layers
(Ranalli, 1987):
Ds
=
brittle
W−1
W
rgz,
where
W=[(1+m2)1/2−m]−2.
z is the depth. Other symbols are explained in
Table 1.
A power law creep is used for the ‘ductile’
domain ( Tsenn and Carter, 1987):
AB A B
ė 1/n
A
.
Ds
=
exp
ductile
A
nRT
Lithospheric temperatures at the onset of drifting
are obtained from thermal modelling. Rheological
parameters are taken from Carter and Tsenn
(1987) and Ranalli (1987). Combining the two
curves, the characteristic function of the yield
strength envelopes is obtained ( Fig. 2).
4.3.2. Viscosity and efficiency of crustal flow
Crustal flow can occur only if the hotter, i.e.
the lower parts, of each compositional layer have
a viscous behaviour. This depends on the crustal
thermal structure and on its composition.
Following Buck (1991), flow at a reference level
z (x), corresponding to the potential compensaref
tion horizon, i.e. the base of the upper or the lower
crust, will be restricted to a channel above the
reference level. The parameter z (x) is a
ref
Lagrangian coordinate associated with the layer
boundary. Vertical viscosity variations in the channel are controlled by the characteristic length-scale
of viscosity changes h :
0
RT2
zref .
h =
0
∂T
E
∂z
h represents a measure of the channel width and
0
of the volume of material that can be mobilised
during flow. As demonstrated by the previous equations, h is a non-linear function of material parame0
ters, temperature at the compensation horizon and,
very importantly, of the geothermal gradient.
This is even truer for the viscosity at a given
depth. The viscosity g as function of depth z in
the channel above the reference level is:
A
B
z −z
ref
.
h
0
The reference level viscosity g of a given layer
0
with non-Newtonian rheology is assumed to be
described by
g=g exp
0
A
B
E
g =A−1 exp
.
0
RT
zref
The ability of a crustal layer to flow can be
approximately described by the effective flow
diffusivity k , which is a measure for the effective
f
flow taking place in a viscous layer in the crust
(Buck, 1991). k is a function of the crustal viscosf
ity structure and of the density contrast across a
crustal surface separating layers with different
densities:
gDr1h3
0.
g
0
The characteristic density contrast Dr1 is:
k=
f
(r −r ) (r −r )
uc
sed a
uc
r −r
a
sed
for upper crustal flow and
Dr1=
(r −r ) (r −r )
uc
sed a
lcb
r −r
a
sed
for lower crust flow. From the above, it becomes
clear how the effective flow diffusivity k is a
f
complex function dependent not only on temperatures but also on thermal gradients. In fact, k
f
values can vary by several orders of magnitude in
the different rift settings and kinematics.
Once k is calculated and the ability of the layer
f
to flow ascertained, the thickness changes of the
flowing layer h can be described by an equation
f
Dr1=
204
G. Bertotti et al. / Tectonophysics 320 (2000) 195–218
analogous to the heat equation (cf. Buck, 1991).
∂h
A
B
∂ h3 ∂DP
f=
0
f .
∂t
∂x g ∂x
0
Substituting the expression for DP as a function
f
of the layers thickness [e.g. Eq. (2)] yields:
A B
∂h
∂
f +Q(x),
f=
k
f ∂x
∂t
∂x
∂h
where Q(x) are time-independent source-like
terms. Thus, k is an appropriate measure for the
f
ability of the crust to flow. The solution of the
crustal flow equation is obtained with a finite
difference method.
Finally, a further factor needs to be taken into
account, which is the competition between thermal
diffusion and viscous flow diffusion. In order to
be efficient, flow has to be faster than cooling, i.e.
the effective flow diffusivity k needs to be larger
f
than the thermal diffusivity k obtained from the
t
previously presented heat equation. To track these
variations we define for each layer a normalised
effective diffusivity:
nk =k /k .
f
f t
Effective flow will take place when nk >1. If
f
nk <1, cooling will prevail and no flow will occur.
f
4.3.3. Upper versus lower crustal flow
The calculations presented above are performed
for both the upper and lower compositional layers
which form the crust of our model, thereby producing two sets of normalised diffusivity values nk
fuc
and nk for the upper and lower crust respectively.
flc
In an nk versus nk space, four fields will be
fuc
flc
defined with different flow regimes and, consequently, different modes of compensation and patterns of vertical movements (Fig. 5). The various
fields of the diagram are contiguous and, therefore,
all intermediate situations can be theoretically
envisaged. In field (I ), both nk and nk are
fuc
flc
smaller than unity and neither the upper nor the
lower crust will be able to flow; as a consequence
no crustal compensation will occur. In fields (II )
and (III ), normalised flow diffusivity values are
such that flow can take place in the upper and/or
lower crust. In field ( II ), where k <nk , flow
fuc
flc
Fig. 5. An nk
versus nk
diagram with the
fupper crust
flower crust
different fields of crustal flow. Lines separating the different
fields are symbolic, since transition from one area to the other
is continuous.
will mainly take place in the lower crust and the
crustal column following extension will have
acquired a higher proportion of lower crustal
rocks. In field (III ), on the contrary, k >nk
fuc
flc
and flow will mainly take place in the upper crust
and the post-extensional lithospheric column will
have a higher percentage of light upper crustal
material. In field (IV ), diffusivity values both for
the upper and lower crust are so high that both
layers are expected to flow efficiently.
4.4. Modelling results and predicted vertical
movements
4.4.1. Flow patterns during extension: thinning and
vertical movements
In Fig. 6 we present the results of a large
number of numerical experiments performed under
a wide range of initial crustal thicknesses, crustal
compositions, stretching factors, rheologies and
strain rates, intended to show the overall variability
of predicted flow patterns. On the whole, points
form two major clusters. The first one is mainly
located in the no-flow domain (field I ) and has
some outliers in field (II ) where flow in the lower
crust is predicted. The second cluster is in a zone
where both crustal levels are expected to flow but
that of the upper crust should dominate. Only
G. Bertotti et al. / Tectonophysics 320 (2000) 195–218
205
Fig. 6. Flow patterns of a large range of crustal settings following extension. Variations in rheologies, thicknesses of crustal layers,
stretching factors and strain rates are considered (see Fig. 7 for the disaggregate presentation).
some points of this second cluster fall in the
no-flow field. The most apparent feature of the
diagram is that crustal flow is likely to occur in
several settings and that, where this is the case,
flow in the upper crust is at least as important as
flow in the lower crust.
The different responses of the system for settings
representative of the fields of Fig. 6 are shown in
Figs. 7 and 8. The case of contemporaneous flow
in the upper and lower crust is not mentioned
because its upper crustal features coincide with
those of field III (upper crustal flow). While Fig. 7
shows the overall lithospheric geometries resulting
from rifting and subsequent phenomena, details of
the basin floor, the top of the lower crust and of
the mantle are shown in Fig. 8. All examples
have the same initial geometry and amount of
extension ( b=2). A thick initial crust has been
chosen in all cases to underline the predicted
effects. Different compositions of upper and lower
crustal layers, as well as of the mantle, have been
imposed in order to prevent or allow viscous flow
(details are given in the figure caption).
Geometries and vertical movements taking
place in a no-flow situation are shown in Fig. 7a
and can be used as a comparison for the other,
more complex cases. When no flow takes place,
subsidence and thinning patterns are similar to
McKenzie-type models. Thinning is directly proportional to extension and the thickness of the
different layers does not change after the end of
rifting. Subsidence of the basement of the sediment-filled basin is in the order of several kilometres (Fig. 8a).
A substantially different pattern is expected
when the composition of the crustal layers allows
Fig. 7. Lithospheric configuration after stretching and compensation under different flow modes. The three cases are representative
of the fields of Figs. 5 and 6. All models have the same initial thicknesses of upper and lower crust (40 km and 20 km respectively)
and stretching factor b=2 (see Table 1 for other parameters values used). Crustal compositions are as follows: (a) VC=dry granite,
LC=mafic granulite; (b) VC=dry granite, LC=felsic granulite; (c) VC=wet quartzite, LC=mafic granulite.
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G. Bertotti et al. / Tectonophysics 320 (2000) 195–218
Fig. 8. Detailed geometry of the basin floor, the top of the lower crust and the Moho for the three numerical examples of Fig. 7.
efficient viscous flow of the lower crust (Fig. 7b).
In this case, the upper mantle is decoupled from
the crust and subsides. The resulting space is filled
with lower crustal material producing a crust
thicker than that obtained in the absence of flow.
The upper crust, on the contrary, does not flow
and remains thin following rifting. Increased lower
crustal thickness clearly decreases basin floor subsidence but does not change its sign (Fig. 8a). The
decoupling effect caused by lower crustal flow is
evident from Fig. 8c. As a result of flow, the top
of the mantle has dramatically dropped with
respect to the position it had in the absence of
crustal flow.
The most interesting features, however, are
obtained when flow is allowed in the upper crust.
As a result of efficient flow, and of complete
decoupling from underlying material, the thickness
of the lower crust can be larger than the initial
one ( Fig. 7c). The consequence is that the basement will not subside and might even undergo
uplift ( Fig. 8a). Not surprisingly, the top of the
mantle ( Fig. 8c) has a geometry similar to that
obtained by flow in the lower crust. In both cases,
decoupling allows the mantle to subside and keep
a nearly flat morphology.
4.4.2. Factors controlling flow modes and vertical
movements
A number of numerical experiments have been
performed under widely differing conditions in
order to explore the variability and sensitivity of
flow patterns (Fig. 9). Parameters are given in the
caption of Fig. 9.
The composition of the crust exerts a primary
control on the flow effectiveness of the various
layers. Points representative of different crustal
compositions plot in two clusters ( Fig. 9a) similar
to those visible in the general diagram ( Fig. 6).
The group of points centred in the no-flow field
(field I ) is formed by crusts made up of ‘hard’
lithologies, namely dry quartzite, dry granite and
gneiss for the upper crust and mafic granulite for
the lower crust. Points in the upper crustal flow
field (field III and immediate surroundings) have
upper crusts made up of wet quartzite and granite
and lower crusts of dry diabase and mafic granulite
The effect of replacing dry lithologies with wet
ones is obviously to soften the rocks (see Kohlstedt
et al., 1995). The changes obtained are substantial
( Fig. 9b) and points previously situated in the
no-flow field (I ) are generally displaced towards
the upper crustal flow field (III ). The activation
of upper crustal flow will obviously influence the
pattern of vertical movements.
The initial thicknesses of the crust and of its
two single compositional layers also impose significant control on the flow mode ( Fig. 9a and c),
but they are normally unable to provoke major
shifts from one field to another. A nearly twofold
increase in overall thickness brings only some
points originally in the no-flow field to field II,
which is characterised by lower crustal flow.
However, absolute and relative thicknesses of the
upper crust are very important in controlling the
amplitude of vertical movements (see Section 4.2).
The amount of stretching experienced by an
extending domain does not play a substantial role
G. Bertotti et al. / Tectonophysics 320 (2000) 195–218
207
Fig. 9. Sensitivity analysis of patterns of crustal flow. (a) Influence of rheologies. All points have d=2 and ė=10−15 s−1. For each
composition, eight points are shown; these correspond to different crustal thicknesses and different proportions of upper versus lower
crust and are arranged in one group of two (on the left-hand side) and two groups of three (centre and right-hand side). Each group
has constant total crustal thickness but variable proportions of upper and lower crust. Values for the group of two are 10–20 km
and 20–10 km for a total thickness of 30 km. The central group of three has 15–30 km, 25–20 km and 40–5 km for a total of 45 km.
The third has 60 km thick crusts with the following values: 20–40 km, 30–30 km and 40–15 km. Composition symbols are as in
Fig. 6. (b) Influence of wet versus dry rheologies. All experiments have the same lower crust composed of mafic granulites. Different
upper crustal lithologies are marked by different symbols. All points have d=2 and ė=10−15 s−1. (c) Influence of the stretching
factors. Fields marked by the dashed lines group points with the same initial configuration given by the small numbers (thickness of
the upper and lower crust respectively). Within each field, five points are shown which correspond to increasing d from left to right.
Values are 1.2, 1.4, 1.6, 2.0 and 2.5. (e) Influence of strain rate. Fields marked by dashed lines group points with the same initial
configuration given by the small numbers (thickness of the upper and lower crust respectively). Within each field, three points are
shown corresponding to strain rate values of 10−14, 10−15 and 10−16 s−1 from left to right.
in controlling the mode of extension (Fig. 9c)
unless the crust is initially very thick. The general
effect of increasing stretching factors is to shift the
representative points towards fields of more efficient flow. These effects, however, become really
important only when high values of d>2 are
reached. In the case of very thick initial crusts,
points initially in the no-flow field can even enter
the field of lower crustal flow. The amount of
stretching does have an important influence on the
magnitude of vertical movements (Section 4.2).
Symmetrically, crustal segments, which begin their
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G. Bertotti et al. / Tectonophysics 320 (2000) 195–218
extensional deformation with upward movements,
will persist in the same pattern.
Changes in strain rate are only relatively important (Fig. 9d). In most cases, namely for not
particularly thick crusts, a substantial increase in
strain rate causes only minor shifts of the representative points towards regions of more efficient flow.
These effects become more pronounced for very
thick crusts and very fast rifting stages. The reason
for these changes is the increased thermal anomaly
that is developed during fast rifts, which, in turn,
favours flow in viscous rheologies.
controlling the amplitude of vertical movements
and, therefore, of the associated geological phenomena. These results are particularly important
because they indicate that the mode of extension
will tend to remain the same despite increasing
stretching. In geological terms, this suggests that
no major changes in uplift/subsidence and faulting
pattern and stretching–thinning relations should
take place with increasing extension.
4.4.3. Influence of melting
Although not included in our calculation, melting is likely to play a significant role in the
phenomena that we have discussed. During extension, deeper-seated rocks will typically move
upward and might cross the Clapeyron (solidus)
curve, thereby generating melt (e.g. Podladchikov
et al., 1994). The formation of magma will not
only decrease the load of the crustal column but
also greatly facilitate lateral flow of material.
Consequently, the previously mentioned vertical
movements will increase in amplitude.
It has long been known that the rupture of an
elastic plate causes vertical movements of the two
fault blocks and namely an upward bending of the
foot-wall and subsidence of the hanging-wall
( Vening-Meinesz, 1950; Turcotte and Schubert,
1982). Analytical solutions worked out for purely
elastic plates show that, in the absence of other
applied forces, the curvature and displacements
experienced by the two blocks are the same and
are controlled by the rigidity (or effective elastic
thickness) of the plate. Typically, several kilometres-thick elastic plates will show maximum vertical
movements of several hundred metres close to the
fault, decreasing away from it. The introduction
of gravity makes the system more asymmetric,
with hanging wall subsidence larger than foot-wall
uplift ( Fig. 10) ( King et al., 1988; Stein et al.,
1988; Armijo et al., 1996; Bott, 1996). This pattern
is further enhanced by the deposition of sediments
in the depression formed on the hanging wall and
by the erosion of the relief developed by the footwall. Classical elastic models have been recently
improved by considering elasto-plastic rheologies
(Hassani and Chéry, 1996; Bott, 1997). Basins
4.5. Main results of the crustal flow model
The equations presented in Section 4.2 and the
modelling results demonstrate the variability of
the response of different crustal segments to the
applied extension and their main controlling
factors ( Figs. 7 and 8). Crusts with ‘hard’ lithologies will not flow and will subside during extension.
Crusts characterised by ‘softer’ rocks, especially if
these are wet, will tend to have efficient upper
crustal flow. In this case, compensation will balance thinning-related subsidence and can even
result in basement uplift. Situations characterised
by dominant lower crustal flow are less common
and limited to systems where the lower crust is
composed of very soft rocks. In such a setting,
subsidence of the basin floor will be quite limited.
Variations in other parameters, such as the
initial thickness of crustal layers, the stretching
factor and the stretching rate, are generally unable
to provoke substantial shifts from one field to
another. They are, however, very important in
5. Broken plate component
Fig. 10. Flexure and deformation pattern associated with faulting of an elasto-plastic plate [from Bott (1997)]. The different
fields indicate degrees of fracturing.
G. Bertotti et al. / Tectonophysics 320 (2000) 195–218
obtained by incorporating brittle failure are deeper
and narrower than those developed on elastic
plates of comparable thicknesses. More importantly, the progressive deformation causes a weakening of the plate and, therefore, a narrowing of
the graben.
During unloading-related flexure, new local
stresses are created in the areas of maximum
curvature. Stresses will be compressive in the
internal parts and tensional in the external parts
of the flexed plates. Although the distribution of
stresses in an elastic plate is fairly symmetrical,
this is not true for the deformation pattern because
of the different strengths of rocks under tension
and under compression and because of their
strength increase with depth (Hassani and Chéry,
1996; Bott, 1997) (Fig. 10). In the hanging wall,
the upper part of the plate is subjected to tension
and will deform. The lower parts, on the contrary,
will undergo little strain because of (a) the decrease
of stress intensity due to the addition of far-field
tension to local compression, and (b) the higher
compressional strength of rocks at depth. A
different picture is expected for the foot-wall,
where compressional stresses are sufficient to strain
the upper part of the plate. Rocks in the lower
part will also fail because of their lower strength
209
when submitted to tension. Numerical models
therefore predict that, in the absence of other
processes, fractures cutting the entire plate should
form on the foot-wall rather than on the hanging
wall (Hassani and Chéry, 1996; Bott, 1997).
6. Tectonics of normal faulting: from predictions to
real world
Superimposing the two groups of processes
analysed in the preceding sections, namely (a) the
vertical movements caused by syn- and post-rift
load changes affecting the lithospheric column
(inclusive of those caused by crustal flow), and
(b) the fault-related flexure of a non-zero-strength
plate, predictions can be made on how the crust
and fault blocks will respond to extension
( Fig. 11).
In the initial stages of rifting, when extension is
still limited (<10–15%), isostatic movements associated with changes in lithospheric loads will be
small and the behaviour of the system will be
controlled by that of the broken plate. With
increasing extension, load changes in the lithospheric column will become progressively more important and significant vertical movements will be
Fig. 11. Conceptual cartoon showing the effects of combining isostasy-driven movements and flexure of a broken plate.
210
G. Bertotti et al. / Tectonophysics 320 (2000) 195–218
imposed to the system. During this stage, two
different modes of deformation are expected,
depending on the ability of the upper and, less
importantly, of the lower crust to flow. The parameter analysis we have performed has allowed for a
definition of the crustal characteristics that hamper
or enhance crustal flow. Predictions can also be
derived on the possibility of an extending system
to move from one mode of deformation to another
and can be tested against real-world cases. Indeed,
it turns out that the subsidence pattern, fault
migration and extension–thinning relations are not
randomly associated, but are related to the mode
of flow in the upper crust.
6.1. The initial situation: broken-plate dominated
settings
6.1.1. Predictions
When extension is small, faults and fault blocks
are expected to behave in accordance with the
broken-plate model. In these cases, the foot-wall
of the fault will be uplifted possibly by several
hundred metres, with magnitudes being basically
controlled by the rigidity of the broken plate. The
hanging wall will show gentle uplift or subsidence
generally subside. If the basin is sediment-filled,
subsidence can be of the order of several hundreds
metres to a few kilometres (e.g. King et al., 1988;
Stein et al., 1988; Bott, 1997). According to numerical experiments (Hassani and Chéry, 1996; Bott,
1997), fault migration is expected to occur towards
the foot-wall.
6.1.2. Real-world occurrences
Most narrow rifts typically have extension
<10–15% and, therefore, are the settings where
features predicted for the initial stages of stretching
are most likely to be observed. In narrow rifts, the
foot-walls typically show upward movements
whereas the hanging walls undergo variable displacements. The Rhine graben (Meier and
Eisbacher, 1991) and the external parts of the
Apennine of Italy (Bertotti et al., 1997a) provide
two fine examples of broken-plate dominated settings. The two cases show significant differences,
mainly in the pattern of hanging wall vertical
Fig. 12. The Bologna fault as an example of broken-plate dominated setting. Activation of the Bologna fault caused the uplift
to the present-day elevation of marine sediments on the hanging
wall and a ca. 2 km upward movement of foot-wall rocks.
Modified after Bertotti et al. (1997a).
movements. We interpret these variations as associated with differing initial conditions.
The Rhine graben is one of the best-known rift
systems of the world. In its northern parts, which,
differently from the southern segments, are not
affected by deep-seated thermal disturbances, footwall uplift was estimated at a few hundred metres
whereas the hanging wall has subsided and hosts
a ca. 2 km thick sedimentary basin (Meier and
Eisbacher, 1991).
Faults in the Apennines show a somewhat
different picture, and are characterised by larger
upward displacements of the foot-walls, which can
be in the order of a few kilometres, and quite
stable hanging walls. This is the case of the
Bologna fault (Bertotti et al., 1997a), where
upward movements of the foot-wall of the fault
are in the order of 2 km and have clear morphological expression with linear gorges being eroded in
the block despite the soft nature of the constituent
rocks (Fig. 12). The hanging wall of the Bologna
fault was also uplifted during extension by several
hundred metres, as demonstrated by the exposure
of pre-rift Pliocene shales that were deposited ca
300–500 m below sea level. Similar features are
common in most of the normal faults developed
in the northern Apennines (e.g. Calamita and Pizzi,
1994; Cello et al., 1997), where intramontane
basins are typically developed on the hanging
walls. The two considered rifts affect two very
different crusts: the Rhine graben a normally thick,
stabilised Variscan crust, whereas the Apennine
rift formed on crust thickened by very young
contractional episodes (e.g. Carmignani et al.,
G. Bertotti et al. / Tectonophysics 320 (2000) 195–218
1995). We thus conclude that the initial configuration of the crust exerted a control on rifting even
for small amounts of stretching.
Patterns of fault migration are more difficult to
decipher. However, for the Bologna fault a progressive incorporation of foot-wall segments has
been proposed (Bertotti et al., 1997a).
In continental rifts of this kind, the amount of
extension compares well with the amount of overall
thinning (Brun et al., 1991), suggesting surface
preservation along the section and that no crustal
material flowed in or out of the system.
6.2. Settings with high extension: the no-flow mode
6.2.1. Predictions
The results of the numerical models presented
in the previous sections provide indications on the
features characteristic for no-flow settings.
In the absence of crustal flow, extension will
cause subsidence ( Fig. 11a) which essentially
results from the replacement of light crustal material by denser mantle rocks and has been theoretically quantified in a number of progressively more
advanced models beginning from McKenzie (1978)
onwards. The magnitude of downward movements
associated with crustal thinning is in the order of
some kilometres in the case of a water-loaded
basin and of several kilometres in the case that
sediments fill the newly created accommodation
space. Thinning-related vertical movements are
thus typically larger than those associated with
flexural unloading. As a result, it is predicted that
not only the hanging wall but also the foot-wall
will subside.
The stress distribution in the flexed broken
plate, and therefore the fault migration pattern, is
also influenced by the overall subsidence pattern.
Since a downward component will be imposed by
isostasy on the system, it is expected that the footwall will decrease its curvature while the opposite
should happen for the hanging wall (Fig. 11a).
Consequently, stresses should decrease in the footwall and increase in the hanging wall. It is, therefore, expected that the new fault will develop on
the hanging wall of the previous structure.
The absence of crustal flow will impose a strict
proportionality between extension and thinning,
as well as on the amount of crustal thinning that
211
can be achieved. With persisting extension at the
boundaries of the system the crust will thin, eventually resulting in crustal break-up and in the formation of a passive continental margin.
Features typical for no-flow extension are predicted to occur in crusts (a) not thicker than
‘normal’ and, (b) composed of ‘strong’ rocks, such
as dry granites, dry quartzites and gneisses and a
lower crust made up of mafic granulites. These
characteristics are typical for relatively stable continental crusts, i.e. for crusts that have not suffered
major tectonics in the few tens of millions of years
preceding the onset of extension. These crusts will
lie at, or close to, sea level prior to the onset of
rifting. A no-flow behaviour is favoured by low
strain rates in the extending zone.
6.2.2. Real-world occurrences
Features predicted for the no-flow mode, i.e.
generalised syn-rift subsidence, fault migration
towards the foot-wall and the correlation between
extension and thinning, are most typically observed
at passive continental margins. Independent evidence seems to confirm the absence of crustal flow
in these settings. As an example, we will describe
the South-Alpine transect of the Mesozoic passive
margin of Adria (Bernoulli et al., 1979; Bertotti
et al., 1993a) which has been inverted in Alpine
times and is largely exposed. Features presented
here are, however, ubiquitous in most passive
continental margin such as, for example, the
Galicia margin of the Iberian plate (e.g. Mauffret
and Montadert, 1987; Boillot et al., 1989).
In Middle Triassic times, i.e. shortly before the
onset of rifting, shallow water sediments, mainly
carbonates, were deposited over the future margin
(Brack and Rieber, 1993), suggesting that the
South-Alpine crust had recovered from Hercynian
thickening and that it was not thicker than normal
(e.g. Schumacher et al., 1997). Rifting began in
the Norian and ended in the Middle Jurassic (e.g.
Bertotti et al., 1993a). Throughout this entire time
span the fault blocks underwent absolute downward movement, as demonstrated by the marine
sediments present practically along the entire
margin (e.g Bernoulli et al., 1979; Winterer and
Bosellini, 1981). Up to several kilometres thick
marine successions were deposited on the hanging
walls of normal faults, as for instance in the M.
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G. Bertotti et al. / Tectonophysics 320 (2000) 195–218
Fig. 13. An extensional basin in the Mesozoic South-Alpine
passive continental margin [ from Bertotti et al. (1993b)]. Note
the presence of marine sediments on both the hanging wall and,
more significantly, on the foot-wall.
Generoso basin ( Fig. 13) (Bernoulli, 1964;
Bertotti, 1991). Foot-walls remained always in
marine conditions and were often, but not always,
morphologically elevated relative to the surroundings. In this case, successions deposited on footwalls are often condensed with frequent erosional
surfaces, gaps, etc. (e.g. Kälin and Trümpy, 1977).
During drifting, water depths increased and no
evidence of upward movements is known
(Bernoulli, 1964; Winterer and Bosellini, 1981).
South-Alpine extension was clearly associated
with substantial thinning. Preliminary subsidence
calculations (Bertotti, 1991) have shown that the
amount of extension experienced by large parts of
the margin was comparable to their amount of
subsidence. Indeed, the fact itself that extension
led to continental break-up is evidence of effective
thinning.
The absence of crustal flow during rifted margin
formation is independently confirmed by the analysis of portions of the middle to lower crust of the
South-Alpine passive continental margin exposed
in the Southern Alps. A section across the upper
15 km of the margin inclusive of one of the most
important normal faults of the system, the
Lugano–Val Grande normal fault, outcrops in the
Lake Como region (Bertotti, 1991; Bertotti et al.,
1993b). The fault can be followed down to palaeo-
depths of 12–13 km, where it is formed by a few
hundred metres thick band of fault rocks separating basically undeformed blocks ( Fig. 13). The
data from the Lugano–Val Grande normal fault
demonstrates that deformation was localised along
a well-defined, gently dipping shear zone incompatible with the idea of distributed lateral flow of
crustal rocks. The lower crust of the same Adriatic
margin is also exposed and forms the well-known
Ivrea zone. According to generally accepted reconstructions (Handy and Zingg, 1991; Quick et al.,
1992; Rutter et al., 1993), extension in Late
Triassic to Jurassic times, during passive continental margin formation, was accommodated by one
major fault, the Pogallo normal fault (Handy,
1988). In both cases mentioned, the extension was
accommodated by shear zones that were discrete
at the crustal scale, thereby excluding wholesale
crustal flow.
6.3. Settings with high extension: the flow mode
6.3.1. Predictions
In settings with efficient crustal flow, the overall
subsidence associated with thinning will be partly
compensated by upward movements caused by
lateral inflow of crustal rocks. By superimposing
flexural unloading to this pattern (Fig. 11b), a
significant upward movement of the foot-wall is
predicted which will create morphological relief.
Effective erosion can enhance this process and lead
to very high magnitudes of upward displacements.
The hanging wall will undergo only limited vertical
movements, which are the net result of the downward component caused by flexural unloading and
the upward component due to isostasy. Whatever
the absolute magnitude, the hanging wall will
typically form a region of depressed morphology
with respect to the foot-wall and can form intramontane ‘sinks’ hosting continental and lacustrine
sediments.
The overall upward movement imposed by isostasy will affect the curvature and, therefore, the
distribution of stresses in the flexed elastic plate
( Fig. 11b). The curvature of the hanging wall will
decrease, whereas that of the foot-wall will
increase. As a consequence, fault propagation
towards the foot-wall, i.e. away from the subsiding
zone, is predicted.
G. Bertotti et al. / Tectonophysics 320 (2000) 195–218
Because of the flow of material into the extending zone, thinning will be less, possibly much less,
than that simply required by stretching. If crustal
flow is so efficient to prevent any significant localised thinning, then extension should be unable to
cause crustal separation. This, obviously, only as
long as crustal material is able to flow into the
extending domain.
Our numerical investigations suggest that configurations facilitating crustal flow are characterised by thick crusts composed of soft rocks. These
would typically be sediments and wet quartzites
and granites for the upper crust. High proportions
of upper crust are also of great importance in
favouring flow. Such conditions are verified in
crustal segments during and immediately following
contraction and thickening, as, for instance, occurring during continental collision. Under these circumstances, the top of the crust will be elevated
above sea level. Efficient crustal flow is further
favoured by high strain rates, which will be available, for instance, in the case of strongly localised
extension.
6.3.2. Real-world occurrences
Some recently studied structures provide fine
examples supporting the predictions made. This is
the case of the Yadong–Gulu rift of southern
Tibet, which developed on strongly thickened continental crust (Cogan et al., 1998). Sections across
the rift show that the foot-wall of the normal fault
has undergone upward movement of several kilometres. This is in contrast with the hanging wall,
which hosts merely a few hundred metres of sediments and, therefore, has remained practically
stable during extension. According to the authors,
and in accordance with our predictions, thinning
was compensated by flow of crustal material into
the rift zone. The wavelength of the deformation
suggests flow of middle- rather than lower-crustal
material (Cogan et al., 1998).
Core complexes, such as those of the western
USA, show in an even more extreme way the
further evolution of settings with effective flow.
The most significant features of core complexes
relevant to our study are beautifully displayed in
two localities that have been the object of thorough
investigations during the last decade: the
Montagne Noire of France (e.g. Brun and van den
213
Driessche, 1994), the Ruby Mountains and the
Sushwap core complexes of western North
America [MacCready et al. (1997) and
Vanderhaege and Teyssier (1997) respectively].
Whereas the Montagne Noire core complex is of
Variscan (Late Paleozoic) age, the others are
Cenozoic. In the localities mentioned, extension
affected crustal segments that had been considerably thickened in previous orogenies ( Variscan for
the Montagne Noire and Mesozoic in West
America). In both cases it has been generally
difficult to draw a clear-cut temporal separation
between the end of contraction and the onset of
extension. There is, however, a general agreement
that not much time has elapsed between the two.
This is, in fact, a very general observation (e.g.
Coney and Harms, 1984) and has led to the widely
misused concept of ‘orogenic collapse’.
The absence of significant crustal thinning in
core complex areas has been a long known paradox
and necessarily requires compensation that can be
achieved by lateral flow of crustal material and/or
by magmatism ( Kruger and Johnson, 1994; Hill
et al., 1995). An important role is played both in
the Montagne Noire and in the western North
America core complexes by syn-extensional intrusives that were emplaced, moved upward and
deformed during extension. The efficiency of
crustal flow is geologically demonstrated by wholesale deformation of middle and lower crustal rocks.
Metamorphic rocks in core complexes show evidence of generalised flow directed towards the
extending zone. In the Ruby Mountains core complex, the large-scale folding and stretching lineation pattern demonstrate material transport
towards the core complex itself (Fig. 14).
Fig. 14. Crustal model for the Ruby Mountains core complexes.
Note that observed structures accommodate flow of middle
crustal rocks into the rift zone [modified from MacCready
et al. (1997)].
214
G. Bertotti et al. / Tectonophysics 320 (2000) 195–218
No clear pattern of fault migration has been
documented for the large normal faults associated
with core complexes.
6.4. Transitions between no-flow and flow modes
6.4.1. Predictions
The no-flow and flow modes are end-members
of a continuous range of intermediate situations.
It is of great geological importance to ascertain if
transitions from one mode to another are expected
during proceeding extension. Our numerical results
seem to discard such a possibility. Results in Fig. 9
show that the representative points do not generally change field as a consequence of increase of
stretching factor. In the few cases where this
happens, transitions are expected from no-flow to
flow fields. The only effect of increasing stretching
is the amplification of vertical movements without,
however, changing the overall pattern.
6.4.2. Real-world occurrences: the death of core
complexes
Lithospheric segments that start their extensional evolution in the no-flow mode typically
remain in the same field throughout their lifetime.
This is the case of rifts affecting well-stabilised
crusts and, most typically, of rifted continental
margins such as the Mesozoic South-Alpine
margin (Bernoulli et al., 1979; Winterer and
Bosellini, 1981) and the Galicia margin (Boillot
et al., 1989). No significant uplift has been demonstrated for these cases. Furthermore, thinning was
so efficient that it led to continental break-up and
to the formation of passive margins. These observations are compatible with several recent modelling studies that strongly suggest that no major
thermal anomaly is produced during stretching
(Bertotti et al., 1997b). We then conclude that
changes to flow-mode patterns can occur only if
boundary conditions are modified and, for
instance, an external heat source heats the crust
and softens the granitic crust.
Things seem to be somewhat different for settings beginning their evolution in the flow mode.
It is indeed a very widespread observation that
core complexes are replaced by very different
extensional structures during persisting stretching.
The most relevant modifications concern the style
of faulting and the subsidence pattern. The lowangle detachments so typical for core complex
extension are gradually deactivated and extension
is accommodated by steep, more planar normal
faults that cut older features. Furthermore, subsidence starts affecting the hanging walls of these
steep faults leading to the formation of grabens,
which are recognised in most areas. This is the
situation in the Ruby Mountains core complex
(MacCready et al., 1997), the Okanogan and
Kettle core complexes of British Columbia
(Suydam and Gaylord, 1997) and several others.
With persisting extension, both hanging wall and
foot-wall subside and the crust begins to thin. A
marine basin is typically created in this stage.
Despite obvious complications, this is what happened in the North Tyrrhenian area between North
Corsica and Tuscany. Here, extension caused the
formation of core complexes from Oligocene to
Early Miocene times which were then replaced,
during persisting stretching, by the formation of
horst-and-grabens structures, by overall subsidence and the eventual formation of the North
Tyrrhenian Sea (e.g. Jolivet et al., 1990;
Carmignani et al., 1995) (Fig. 15). These features
are all diagnostic for a ‘no-flow’ mode of extension.
The shift from one style of extension to another
implies some significant changes within the system
preventing further development of the core complex. We propose that the most likely cause for
this apparent change in deformation pattern is the
exhaustion of upper crustal material which can
flow into the extending area and which has to be
taken from increasingly distant domains. This
hypothesis is compatible with the widely observed
cessation of magmatic activity following the
change of mode.
7. Concluding remarks
In this paper we have shown that different
lithospheric segments can follow quite different
behaviours in terms of flow in the middle crust
and, therefore, of fault block movements, patterns
of fault migration and stretching–thinning relations. The crustal configuration before the onset
G. Bertotti et al. / Tectonophysics 320 (2000) 195–218
215
Fig. 15. Section across the western part of the Tyrrhenian rift [redrawn from Jolivet et al. (1990) and Carmignani et al. (1995)]
displaying the transition from a flow mode, during which the Corsica core complex developed, to a no-flow mode, during which the
Tyrrhenian basin formed. Note how the detachment associated with core complex formation is cut by steeper normal faults, which
determines the subsidence and descent below sea level of fault blocks. The position of the upper profile is indicated by the box in
the lower section.
of rifting, i.e. the geological history in the few tens
of millions of years prior to the onset of extension,
is crucial in controlling the lithospheric functioning
mode. Stabilised crustal segments, which typically
form low morphological relief at or close to sea
level, will generally follow the no-flow mode once
subjected to stretching. The extending area will
undergo positive subsidence allowing for the formation of accommodation space and the deposition of thick, typically marine, sedimentary
successions. Faults will be typically steep to listric
and will propagate towards the hanging wall, i.e.
towards the basin. Extension will continue with
the same general pattern until tensional forces are
removed or when break-up occurs. Significant
variations on this evolutionary picture can be
imposed by ‘external’ processes, such as interactions with a hot spot (e.g. Skogseid et al., 1992).
At the scale of the future margin, major shifts in
the site of extension are expected in the case of
slow rifts, i.e. when the extending lithosphere
becomes stronger than the non-extended one
( England, 1983; Bassi, 1995; Bertotti et al., 1997b).
Thick crusts, and particularly those with a
thickened upper part, will have a different response
to extension and will behave following the flow
mode. Settings where such conditions are verified
are orogenic wedges where convergence creates
very large thickness of soft material, such as sediments and low-grade to weathered metamorphic
rocks. If stretching begins during the last stages of
contraction, or shortly enough after its cessation,
216
G. Bertotti et al. / Tectonophysics 320 (2000) 195–218
extension will follow the flow mode and most of
the area will undergo upward movement. The footwall, in particular, will experience strong displacements and be subject to more or less intense
erosion, depending on the local conditions.
Limited movement is expected for the hanging
wall where intramontane basins will typically
develop. When fault propagation occurs, this will
be towards the foot-wall. In general, extension in
the flow mode does not represent a stable configuration. This is essentially due to the fact that the
system will function in this mode only as long as
new ‘granitic’ material is brought into the crustal
column undergoing extension. With persisting
extension, the ‘delivery’ of more and more granitic
material becomes increasingly difficult because of
the longer lateral distance it has to travel. Once
the ‘reservoir’ of granitic material is exhausted,
extension will shift to the no-flow mode. The most
apparent change will be a transition from upward
movements to subsidence. This can eventually lead
to crustal separation.
Acknowledgements
Discussions with V. Picotti (Bologna) have
been, as usual, mostly inspiring. F. Calamita and
A. Pizzi (Chieti) are thanked for sharing their vast
knowledge on normal faults in the Apennines.
Jean-Pierre Burg (Zurich) is thanked for his help
during most of the work. R. Buck and an anonymous reviewer are warmly thanked for their criticisms. Obviously, they do not necessarily share the
ideas presented in this paper. This is publication
991005 of the Netherlands Research School on
Sedimentary Geology (NSG).
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