TECTONOPHYSICS
ELSEVIER
Tectonophysics 282 (1997) 129-145
The role of rheology in extensional basin formation modelling
M. Fernandez
a *
, , G. Ranalli b
" Institute of Earth Sciences (J. Almera), CS1C, Lluis Sold Sabarfs s/n, 08028 Barcelona, Spain
b Department of Earth Sciences and Ottawa-Carleton Geoscience Centre, Carleton University, Ottawa, K1S 5B6, Canada
Accepted 11 March 1997
Abstract
The rheology of the lithosphere determines its deformation under given initial and boundary conditions. This paper
presents a critical discussion on how rheological properties are taken into account in extensional basin modelling. Since
strength envelopes are often used in models, we review the uncertainties (in temperature and rheological parameters) and
assumptions (in type of rheology and mode of deformation) involved in their construction. Models of extensional basins
are classified into three groups: kinematic, kinematic with rheological constraints, and dynamic. Rheology enters kinematic
models only implicitly, in the assumption of an isostatic compensation mechanism. We show that there is a critical level
of necking that reconciles local isostasy with the finite strength of the lithosphere, which requires a flexural response.
Kinematic models with rheological constraints make use of strength envelopes to assess the initial lateral variations of
lithospheric strength and its evolution with time at the site of extension. Dynamic models are the only ones to explicitly
introduce rheological constitutive equations (usually in plane strain or plane stress). They usually, however, require
the presence of an initial perturbation (thickness variations, pre-existing faults, thermal inhomogeneities, rheological
inhomogeneities). The mechanical boundary conditions (kinematic and dynamic) and the thermal boundary conditions
(constant temperature or constant heat flux at the lower boundary of the lithosphere) may result in negative/positive
feedbacks leading to cessation/acceleration of extension. We conclude that, while kinematic models (with rheological
constraints if possible) are very successful in accounting for the observed characteristics of sedimentary basins, dynamic
models are necessary to gain insight into the physical processes underlying basin formation and evolution.
Keywords: deformation; isostasy; stress; strain; velocity structure
1. I n t r o d u c t i o n
Extensional (rifted) basins are formed by subsidence o f the Earth's surface as a consequence o f
large-scale lithospheric stretching. This subsidence
is produced by the replacement o f crust by denser
mantle rocks consequent upon thinning, and by the
* Corresponding author. Tel.: +34 (3) 4900 552; fax: +34 (3)
4110 012; e-mail: [email protected]
thermal cooling o f the lithosphere and mantle. Two
end m e m b e r mechanisms have been proposed to
generate extensional basins (e.g., Turcotte and Emerman, 1983; Neugebauer, 1983; Keen, 1985; Moretti
and Froidevaux, 1986; Bott, 1992): active rifting in
which the ascent of the asthenosphere causes convective thinning, d o m a l uplift and lithospheric extension; and passive rifting where horizontal tectonic
stresses produce lithospheric thinning and passive
mantle upwelling. Actually, most rifts show active
0040-1951/97/$17.00 © 1997 Elsevier Science B.V. All rights reserved.
PH S0040- 195 1 (97)002 16-3
130
M. Ferngmdez, G. Ranalli/Tectonophysics 282 (1997) 129-145
and passive signatures and the two mechanisms are
complementary (Khain, 1992; Wilson, 1993). The
resulting basin geometry, rates of subsidence/uplift
and sedimentation/erosion, depositional style, occurrence of magmatism, etc., are surface expressions of
processes that operate at crustal and mantle levels.
These processes are directly related to the deformational pattern of the lithosphere when subjected to
deviatoric tensile stresses, and consequently to its
rheological behaviour (Vilotte et al., 1993; Quinlan
et al., 1993).
Laboratory experiments show that rocks can deform in a brittle or ductile manner depending on
pressure and temperature conditions (e.g., Goetze
and Evans, 1979; Carter and Tsenn, 1987; Kohlstedt et al., 1995). In modelling, the mode of lithospheric deformation can be prescribed either implicitly, by imposing a deformation pattern which the
lithosphere is assumed able to sustain (kinematic
models) or explicitly, by specifying equations governing the rheological behaviour (dynamic models).
Kinematic models have been widely used in passive
rifts to account for a large variety of observations
such as rates of subsidence/uplift of the basement,
differential stretching, crustal and lithospheric detachments, volcanism, etc. (e.g., McKenzie, 1978;
Royden and Keen, 1980; Buck et al., 1988; McKenzie and Bickle, 1988; Weissel and Karner, 1989;
Cloetingh et al., 1993, 1994a,b, 1995a,b). Dynamic
models, on the other hand, have been applied to passive and active rifting mechanisms and also to lithosphere/asthenosphere interaction (e.g., Braun and
Beaumont, 1987; Lynch and Morgan, 1987; Dunbar and Sawyer, 1989; Sonder and England, 1989;
Bassi et al., 1993; Keen and Boutilier, 1995). The
lithosphere can be treated as a single viscous layer
with Newtonian or non-Newtonian rheology, or as a
layered medium with an elasto-visco-plastic rheology according to the predominant type of rocks at
each depth.
Some models use a mixed approach where the
mode of deformation of the lithosphere is imposed
kinematically, while the deformation of the underlying substratum is treated dynamically (e.g., Keen,
1985; Buck, 1986; Keen and Boutilier, 1995). Likewise, rheological controls based on the depth variation of brittle and ductile strength, and the effects
of gravitational buoyancy forces arising from lateral
thickness variations, have been used to externally
constrain the mode of deformation imposed in kinematic models (e.g., Kusznir and Park, 1987; Buck,
1991; Negredo et al., 1995).
In the last few years, the origin and evolution
of sedimentary basins has been the subject of a
focused research effort by a Task Force of the International Lithosphere Program (Cloetingh et al.,
1994a). As a result, the available database on natural
basins, as well as the number of models of basin
formation, have increased enormously (cf. Cloetingh
et al., 1993, 1994b, 1995a,b). The purpose of this
paper is to analyse critically the role of rheology
in extensional basin modelling, and to discuss the
consequences and limitations associated with the
different rheological assumptions. We begin with a
review of the strength envelope concept, its uncertainties and assumptions. Basin formation models are
subdivided into three categories from the rheological viewpoint, namely, kinematic models, kinematic
models with rheological constraints', and dynamic
models, which are discussed in turn. Some problems
(nature of the initial perturbation leading to basin
development, and the effects of different boundary
conditions) are treated in separate sections. Finally,
we offer some general remarks on the role of rheology in basin models and discuss the relative merits
of the different approaches.
2. Rheology of the lithosphere and strength
envelopes
The rheology of the lithosphere is a function of
its composition and structure, pressure, temperature,
and state of stress. The concept of strength envelope
(rheological profile), firstly developed by Goetze and
Evans (1979), is well known (cf. Ranalli, 1995). On
the basis of a generalization of experimental results,
it is assumed that the deformation regime for any
given rock can be subdivided into two domains: brittle or frictional, governed by the Coulomb-Navier
shear failure criterion, and ductile, governed by the
power-law creep equation. The brittle/ductile transition is defined by the equality of frictional strength
and ductile strength (for a given strain rate). Although undoubtedly an oversimplification of reality,
strength envelopes have proven very useful in rheological modelling of lithospheric processes, espe-
M. Ferngmdez, G. Ranalli/Tectonophysics 282 (1997) 129-145
cially in providing rheological constraints for basin
modelling (see discussion in the following sections).
Assumptions and uncertainties associated with
strength envelopes naturally affect the final model
of basin formation. Reviews of the construction and
applications of strength envelopes can be found elsewhere (e.g., Ranalli, 1995, 1997a); here, we focus
on their uncertainties and their limits of applicability. The uncertainties can be divided into two
groups. Operational uncertainties derive from imperfect knowledge of composition and structure of the
lithosphere, errors in the estimated temperature distribution, scatter in experimentally determined rheological parameters, lack of constraints on pore fluid
pressure, and similar factors. Methodological uncertainties stem from the basic assumptions used in the
construction of strength envelopes, which can be related to the rheology (i.e., the assumption of simple
brittle-over-ductile behaviour), or to the deformation
regime (i.e., uniform strain and constant strain rate),
and which are not necessarily realistic.
The main operational uncertainties (assuming that
the composition and structure of the lithosphere are
reasonably well known) derive from temperature,
rheological parameters, and pore fluid pressure. Not
much - - except direct observation - - can be done
about the last, and usually the hydrostatic assumption
(pore pressure equal to the pressure of an overlying
column of water at any depth) is adopted. Most of the
uncertainty in the geotherm derives from the scatter
of surface heat flow values (Chapman and Furlong,
1992). Uncertainties in the lower crust of 4-100°C
are the norm rather than the exception (cf. also
Lamontagne and Ranalli, 1996). This can result in
peak-to-peak variations in estimated creep strength
of about one order of magnitude, and consequent
displacements of several kilometres of the estimated
depth of the brittle/ductile transition (Fadaie and
Ranalli, 1990).
Rheological parameters in the brittle regime are
usually assumed constant for all rock types. Pre-existing faults are often taken to be cohesionless, with a
coefficient of friction # = 0.75. The uncertainties
introduced by these approximations are low compared to those generated by the lack of constraints
on the pore fluid pressure. Rheological parameters
in the ductile regime for different rock types, on the
other hand, show considerable scatter (see e.g., Kirby
131
and Kronenberg, 1987a,b; Ranalli, 1995). Table 1 is a
compilation of representative rheological parameters
for different lithospheric layers (upper crust, lower
crust, upper mantle) used in basin formation models. Although occasionally the individual values of
creep parameters differ considerably, their application in the creep equation in any given case results in
creep strengths that usually vary no more than 4-50%
at any given depth. A notable exception is the softer
upper crust, and to a lesser extent lower crust, resulting from the parameters adopted by Burov and Diament (1995) and Cloetingh and Burov (1996). The
harder lower crust in the models of Mareschal (1994)
and Lamontagne and Ranalli (1996) is a consequence
of a specific composition (mafic granulite) which may
apply only to certain areas. The parameters listed in
Table 1 can be compared to compilation of experimental results (e.g., Kirby and Kronenberg, 1987a,b;
Ranalli, 1995, 1997a).
Methodological uncertainties are potentially very
significant. They arise from basic assumptions used
in the construction of strength envelopes. Leaving
aside the consideration that the brittle/ductile transition in nature is transitional rather than sharp, rheological assumptions used in strength envelopes are
that the Coulomb-Navier frictional criterion applies
at any depth where the material is not ductile, and
that power-law creep is the only kind of behaviour
in the ductile field. Both of these are only first-order
approximations.
The Coulomb-Navier frictional criterion (Byerlee's law) is experimentally confirmed only up to
pressures corresponding to mid-crustal depths (Byerlee, 1967; Jaeger and Cook, 1979). Its linear extrapolation to lower crustal and upper mantle conditions results in unrealistically high brittle strengths.
The assumption of a linear Moho envelope (constant
friction coefficient) is often not confirmed in practice,
and there are indications that the coefficient of friction
decreases with increasing pressure (Jaeger and Cook,
1979). Furthermore, other deformation mechanisms
such as high-pressure fracture (Shimada, 1993) and
plastic yielding (Ord and Hobbs, 1989), expected to
take over from frictional failure as pressure increases
and being only weakly dependent on pressure (cf.
Ranalli, 1997b), are neglected in strength envelopes.
Their effect would be to decrease the pressure dependence of strength as depth increases.
M. Ferngmdez, G. Ranalli/Tectonophysics 282 (1997) 129-145
132
Table 1
Ductile creep parameters A (pre-exponential factor), n (stress
exponent), and E (activation energy) in power-law equation/: =
Ac~"exp(-E/RT) used in basin modelling studies for upper
crust (UC), lower crust (LC), and lithospheric upper mantle
(UM); W denotes hydrated conditions
Layer
A (MPa -n s - 1)
n
E (kJ mol- I)
Ref.
UC
UC
UC
UC
UC
UC
UC
UC
UC
UC
UC
UCW
UCW
UCW
UCW
UCW
UCW
LC
LC
LC
LC
LC
LC
LC
LC
LC
LC
LC
LC
LC
LC
LC
LC
LCW
LCW
LCW
UM
UM
UM
UM
UM
UM
UM
UM
UM
UM
UM
UMW
UMW
2.5 x
1.3 x
3.4 x
1.3 ×
1.0 ×
1.6 ×
1.3 ×
5.8 ×
2.0 ×
5.0 x
2.5 ×
1.0 ×
2.0 ×
2.9 x
3.3 x
3.1 ×
5.6 ×
3.2 x
1.3 x
3.2 x
3.3 ×
8.9 ×
1.0 x
3.2 ×
3.8 x
2.0 ×
3.3 ×
1.4 ×
2.3 x
1.3
0.13
3.2 ×
8.0 x
3.0 ×
3.3 ×
6.3 x
1.0 x
7.0 ×
3.2 ×
2.9 ×
1.0 ×
3.2 x
1.9 x
1.4 ×
7.0 ×
4.3 ×
7.0 ×
1.9 x
2.0 x
3.0
2.4
2.8
2.9
2.8
3.0
3.2
2.4
1.9
3.0
3.0
1.8
1.9
1.8
2.4
3.1
2.4
3.0
2.4
3.3
3.2
3.2
3.0
3.2
3.1
3.4
3.2
4.2
3.9
2.4
3.1
3.0
3.1
3.2
3.2
2.8
3.0
3.0
3.6
3.6
3.0
3.5
3.0
3.5
3.0
3.0
3.0
4.5
4.0
138
219
185
149
150
123
144
142
141
190
140
151
134
150
134
135
160
25l
219
268
238
238
230
270
243
260
384
445
235
212
276
250
243
239
238
271
523
510
535
535
500
535
420
535
530
527
520
498
471
[1]
[4]
[5, 13]
[6]
[7]
[9]
It0[
[11]
[12]
[14, 15]
[16]
[2]
[3]
[5]
[6]
[8]
[13]
[1]
[3]
[4[
[5, 10]
[6]
]7]
[7]
[8]
[9]
[11]
[12, 17]
[13]
[14, 15]
[14, 15]
[16]
[17]
[2]
[5]
[17]
[1, 16]
[3]
[4]
[5, 13]
[6]
[7]
[9]
[10]
[111
[121
[14, 15]
[2]
[4]
10 8
10 -3
10.6
10 -7
10 .6
10-9
10-9
10 -5
10 4
106
10- s
10-2
10-4
10-3
10.6
10 7
10 -5
10.3
10 3
10 3
10 4
10 4
10-3
10 3
10 .2
10 -4
10 4
10 4
10 6
10-3
10 -3
10 -2
10-4
10 -3
103
104
104
104
103
104
lO3
105
104
102
104
105
103
Table I (continued)
Layer
A (MPa " s l)
n
E (ld m o l l )
Ref.
UMW
UMW
UMW
1.4 x 104
8.6 x 103
4.0 × 102
3.4
3.0
4.5
445
420
498
[5]
[8]
[12]
References. [1] Lynch and Morgan, 1987; [2] Braun and Beaumont, 1989b; [3] Dunbar and Sawyer, 1989; [4] Fadaie and
Ranalli, 1990; [5] Bassi, 1991; [6] Buck, 1991; [7] Ranalli,
1991; [8] Govers and Wortel, 1993; [9] Liu and Furlong, 1993;
[10] Lowe and Ranalli, 1993; [11] Boutilier and Keen, 1994;
[12] Mareschal, 1994; [13] Bassi, 1995; [14] Burov and Diament, 1995; [15] Cloetingh and Burov, 1996; [16] Negredo et al.,
1995; [17] Lamontagne and Ranalli, 1996.
Notes. Upper crust is usually taken as quartz-rich or granitic except in [4] where it is assumed to be quartz-dioritic: lower crust
varies between intermediate (quartz-dioritic) and basic composition (the parameters in [12] and [17] apply to mafic granulites);
upper mantle is ultrabasic (olivine-rich).
In t h e d u c t i l e r e g i m e , at l e a s t f o r p e r i d o t i t i c r o c k s ,
t h e r e is e v i d e n c e t h a t a t r a n s i t i o n o c c u r s w i t h inc r e a s i n g t e m p e r a t u r e b e t w e e n shear zone ductility,
w h e r e f l o w is c o n c e n t r a t e d a l o n g d i s c r e t e s h e a r
z o n e s , a n d bulk ductility, w h e r e f l o w is p e r v a s i v e
( D r u r y e t al., 1991; V i s s e r s et al., 1991). T h e c o m b i n e d e f f e c t s o f t h e s e t h e o l o g i c a l c o m p l i c a t i o n s are
d e p i c t e d q u a l i t a t i v e l y in F i g . 1 f o r t h e s i m p l e c a s e
of a crust of uniform felsic composition and a low
g e o t h e r m a l g r a d i e n t r e s u l t i n g in a b r i t t l e u p p e r m a n tle. C r i t i c a l t e m p e r a t u r e s a r e a l s o s h o w n . A l t h o u g h
it c a n n o t y e t b e q u a n t i f i e d , t h e r h e o l o g i c a l l a y e r i n g
o f t h e l i t h o s p h e r e is l i k e l y to b e m o r e c o m p l e x t h a n
usually assumed in strength envelopes.
Assumptions concerning deformation style are an
integral part of strength envelopes. The assumpt i o n o f u n i f o r m s t r a i n i m p l i e s t h a t all l a y e r s s u f f e r
the same extensional deformation, and consequently
s t r i c t l y l i m i t t h e a p p l i c a t i o n to p u r e s h e a r e x t e n s i o n
with the stretching factor independent of depth. This
is o f c o u r s e n o t n e c e s s a r i l y true. D e f o r m a t i o n in t h e
l o w e r d u c t i l e p a r t o f t h e c r u s t is v e r y h e t e r o g e n e o u s
( R u t t e r a n d B r o d i e , 1992), a n d s i m p l e s h e a r p l a y s
an important role in lithospheric extension (Buck,
1991). S o m e i m p l i c a t i o n s f o r s t r e n g t h e n v e l o p e s a r e
s h o w n in F i g . 2. T h e a p p a r e n t e x t e n s i o n a l s t r a i n r a t e
( A L / L ) / t , w h e r e t is t i m e , is n o t t h e p h y s i c a l l y rele v a n t o b s e r v a b l e . T h e a c t u a l s t r a i n r a t e is t h e s h e a r
vJd, w h e r e v~ is t h e r e l a t i v e v e l o c i t y a n d d t h e t h i c k -
M. Ferngmdez, G. Ranalli/Tectonophysics
(3"1-- ~ 3
B
M
L1
L2
.........
I .................
which strength envelopes are built) has implications
for the extensional velocity that will be considered
when discussing the effects of boundary conditions.
The above considerations are not meant to deny
the usefulness of strength envelopes as a first-order
tool to constrain models of basin formation, but
rather as a plea not to overlook their limitations and
to take into consideration more realistic rheologies
and deformation styles.
3F
BF ..
300±50oc .......... ... -II
D D
BF
•" -'II
iiiiiiiiiiiiiiiiiiiii
6 o
oooc
3. Kinematic models
3~
L3 "
~
-
911+50°C .......
D
L4
................. 1250+100oc ...............
D
Z
Fig. 1. Type rheological profiles (left), critical temperatures
(where known), and variation of rheology with depth (right)
for a uniform felsic crust and low geothermal gradient. Standard strength envelope is shown by the full line; changes
due to high-pressure failure and to shear ductility by dashed
lines. Critical depths B: crustal brittle/ductile transition; Ll:
mantle brittle/ductile transition; F1F2, ML2: ranges of highpressure failure (qualitative) in crust and upper mantle; L3:
mantle shear ductility/bulk ductility transition; M: Moho; L4:
lithosphere/asthenosphere boundary. Variations of rheology with
depth (left column: corresponding to standard strength envelope;
right column: modified strength envelope): BF: brittle frictional;
D: ductile (power-law); HP: high-pressure failure; DS: shear
zone ductility.
ness of the shear zone. The strength in this case is
determined by the variations of rheological properties along the zone separating the two lithospheric
blocks, not along the vertical direction.
The assumption of constant strain rate (upon
k
A c o m m o n characteristic of kinematic models of
lithospheric extension is that deformation is imposed
by prescribing a velocity field which is linked, as an
advective term, to the heat transport equation, and no
constitutive equations are incorporated. Only vertical
forces are considered, related to loading/unloading
associated with infilling of basins, erosion of shoulders, and mass redistribution due to lithospheric
stretching. In this section we will focus on the relationship between isostatic mechanisms and rheology,
which governs the response of the lithosphere to
vertical forces.
A very simple one-dimensional approach to explain the subsidence observed in passive margins
and sedimentary basins was proposed by McKenzie
(1978). The model assumes local isostatic compensation, pure shear deformation and instantaneous
lithospheric stretching followed by thermal relaxation. Extensions of this model to two dimensions
consider the effects of finite duration of rifting, lateral heat transport, and differential stretching (e.g.,
Royden and Keen, 1980; Jarvis and McKenzie, 1980;
Cochran, 1983; Buck et al., 1988; White and McKenzie, 1988). These models have permitted to better constrain the observed basin subsidence, crustal
L+ A L
L
I(
. . . . . . .
.----
133
282 (1997) 129-145
~t
:,1
--,--.--
. . . . . . . . . . . . . . . . . . . . . . . . . . . .
"
" .
"
"
~ . . . .
"
~
°
°
°
°
°
.
Fig. 2. Extension of lithosphere in simple shear. Increase in width AL is accomplished by relative motion across the shear zone. See text
for details.
134
M. Ferngmdez, G. Ranalli/Tectonophysics 282 (1997) 129-145
structure, and surface heat flow. They show that flank
uplift is primarily produced by thermal effects and
therefore it progresses during the syn-rift phase but
tends to vanish during the post-rift phase (Buck et
al., 1988). Changes in the crust-mantle ratio caused
by differential stretching can explain post-rift stratigraphic onlaps (White and McKenzie, 1988) and
prominent and permanent rift shoulders (Zeyen et
al., 1996).
Local isostasy assumes that the lithosphere is unable to support vertical shear stresses. Therefore, any
vertical force is compensated by lithosphere buoyancy. From a rheological viewpoint, this assumption implies that the lithosphere behaves as a solid
with zero threshold shear stress under any vertical
load, while at the same time possessing high lateral
strength to prevent deformation caused by horizontal
stress gradients (since the lithostatic pressure at a
given depth above the compensation level varies in
different columns). Thus, local isostasy appears at
first sight difficult to reconcile with any self-consistent rheological model of the lithosphere.
If, on the other hand, it is assumed that the lithosphere retains a finite strength when loaded, then
it responds to vertical loads by flexure, resulting in
regional isostatic compensation. The simplest model
is that of a thin elastic plate. The elastic behaviour
of the lithosphere has been successfully proven for
the oceanic lithosphere, where combined gravity and
bathymetry analyses have shown that topographic
features with a wavelength less than 100 km are
compensated by flexural isostasy (McKenzie and
Bowin, 1976).
Flexural studies indicate that the effective elastic
thickness (ire) of the oceanic lithosphere is correlated
with the 450-600°C isotherm and therefore to its
age (Watts, 1978; McNutt and Menard, 1982). However, this empirical relationship is much more debatable for continental lithosphere, since the effective
elastic thickness depends on the crustal thickness,
the lithospheric thickness through the temperature
structure, and the interaction of these factors during lithospheric deformation. For a thermally young
lithosphere, Te is dominated by quartz-feldspar rheology, while for older lithospheres it is dominated by
olivine rheology (Kusznir and Karner, 1985). Pureshear flexural models have been used to account
for the basement subsidence and stratigraphy at pas-
sive margins and sedimentary basins (e.g., Watts and
Ryan, 1976; Beaumont et al., 1982; Watts et al.,
1982). Decreasing Te results in deeper and narrower
basins; at the limit Te = 0 is equivalent to local
isostasy.
From the rheological viewpoint, several problems
arise when modelling the lithosphere as a linear
elastic plate. First, in a bent elastic plate, the calculated stresses can be considerably higher than those
deduced from lithospheric strength envelopes; second, the effective elastic thickness depends not only
on age, but also on plate curvature and load; and
third, the initial elastic response of the lithosphere
to loading is followed by a delayed viscous component. Several attempts have been made to reconcile
the flexural behaviour of the lithosphere with its actual rheology, constraining the flexural stresses by
the strength envelopes (e.g., Bodine et al., 1981;
McAdoo et al., 1985; McNutt et al., 1988; Burov
and Diament, 1992; Ranalli, 1994). The main result is that the effective elastic thickness depends on
rock rheology and curvature for a given structure,
composition, and thermal regime.
Whatever mechanism of isostasy is assumed, local or regional, pure-shear models do not account
for the asymmetry and/or high uplift of the flanks
observed in many basins. An alternative kinematic
model of basin formation was proposed by Wernicke
(1985), who assumed a detachment across the entire lithosphere to explain the uplift of the Colorado
Plateau adjacent to the Basin and Range by local
isostasy. Simple-shear deformation produces a lateral offset between mantle and crustal thinning and
asymmetry in the resulting basin (see e.g., Buck et
al., 1988, and Kusznir and Egan, 1989, tbr a quantitative analysis). Depending on the depth, dip, and
number of detachments, different styles of deformation can be reproduced, such as simple shear (Buck
et al., 1988), combined simple shear and pure shear
(Kusznir et al., 1987), and cantilever (Kusznir and
Ziegler, 1992). Including detachments and faults in
kinematic models implies that some lithospheric levels can act as decoupling horizons. However, faults
and detachments merely play a role of slip surfaces
and no considerations on the stress necessary to
produce this slip are taken into account.
An important concept in the study of the kinematics of lithosphere extension is the level of neck-
135
M. Ferngmdez, G. Ranalli/Tectonophysics 282 (1997) 129-145
¢,
,,
(a)
"'- -t--."
(i) . . . . . ~
......
ho
hc
Pc
hm/[3
(c)
hm
Pm
ha
Fig. 3. (a) Upward, and (b) downward flexure of necked lithosphere. (c) Equilibrium level of necking, resulting in no flexure and
therefore local isostasy (mass defects, denoted by minus signs, compensate mass excesses, denoted by plus sign). Thicknesses (h) and
densities p of crust, mantle, and sediments denoted by subscripts c, m, and o, respectively;/3is the stretching factor.
ing, defined as the level which, in the absence of
buoyancy forces, would not move vertically during
extension (Braun and Beaumont, 1989a; Weissel and
Karner, 1989; Kooi et al., 1992). Because of the
changes in mass distribution related to extension,
different necking levels result in different flexural responses (see Fig. 3). Deep necking levels produce
regionally supported high basin shoulders, while
shallow necking levels produce downwarped basin
flanks. Note, however, that if the depth of necking
is such that no lithospheric loading or unloading
results, no flexural isostatic deflection will occur,
and the basin will be in local isostatic equilibrium
(Fig. 3c). This 'neutral' level of necking is independent of the stretching factor, and is about 10 km deep
for a lithosphere initially 100 km thick including a
33 km crust, if the basin is filled with sediments
(the actual value depends on initial configuration and
adopted densities). Therefore, local isostasy can fit
the evidence in some sedimentary basins, without
contradicting the fact that the lithosphere has finite
strength.
Kinematic necking models account for a variety
of basin morphologies (e.g., Kooi et al., 1992; van
der Beek et al., 1995; Spadini et al., 1995). Although
in principle the necking level should coincide with
the level of maximum lithospheric strength, a review
of Mediterranean and intracratonic basins (Cloetingh
et al., 1995a) shows depths varying from 4 to 35 km
(see also next section). This is, in part, a consequence
of large lateral variations in lithospheric strength, but
it also reflects that the relationship between strength
envelopes and kinematic level of necking is more
complicated than previously thought.
4. Mechanical controls on kinematic models:
'back-door rheology'
Kinematic models are very powerful in accounting for the main features of extensional sedimentary
basins and their evolution through time. This capability is due to the high variety of deformation modes
that can be imposed by predefining the velocity field.
However, in kinematic models there is no control
over the compatibility between the imposed mode of
deformation and the actual mechanical behaviour of
rocks. Lithospheric rheology predicts that two competing effects arise during finite continental extension: weakening produced by lithospheric thinning
and strengthening produced by thermal relaxation
136
M. Fern?mdez, G. Ranalli/Tectonophysics 282 (1997) 129-145
(see e.g., England, 1983). According to the interplay
of these effects, the locus of extension may migrate
and the predefined velocity field will no longer be
valid. A simple procedure to evaluate the progress
of extension is to compare the total strength of a
stretched lithospheric column with that corresponding to an undeformed lithosphere on the basis of
some rheological model. These one-dimensional approaches do not provide the actual deformation of the
lithosphere, but they introduce rheological controls
on the mode of deformation. We call them 'backdoor rheological models'. One example is the analysis of the correlation of necking level, mentioned
in Section 3, with strength envelopes (Cloetingh et
al., 1995a). The necking level usually corresponds
to a strong layer in the lithosphere (upper-middle
crust or uppermost mantle, according to geothermal
gradient). When two well-defined strong layers are
present, however, the necking level loses its geometric meaning.
Assuming a thin sheet viscous lithosphere, England (1983) showed that the force required to deform
the lithosphere at a given strain rate is inversely
proportional to the geothermal gradient and depends
exponentially on the Moho temperature. In the early
stages of rifting, this force decreases until strain exceeds a value which depends on the P6clet number,
the rheological parameters, and the initial crustal
thickness. Once this critical value is reached, the
strength increases very rapidly and limits further extension. The effect of lithospheric strengthening is
higher at low strain rates. As an example, England
(1983) concludes that if the transition to oceanic
lithosphere is produced by a stretching factor fl ranging from 3.25 to 6, the duration of rifting must be
less than 10-20 Ma.
The thin sheet approach assumes that the lithosphere consists of a single viscous layer with olivine
rheology, and that the thermal gradient within this
layer is constant. This is a simplification of the mechanical behaviour of the lithosphere that tends to
overestimate lithospheric strengthening, since neither the role of crustal rocks (both in the brittle
and in the ductile fields), nor the changes in thermal gradient are considered (Sawyer, 1985). Kusznir
and Park (1987) considered a layered rheology for
the lithosphere and analyzed its response to an applied tectonic tensile force by assuming conservation
of the total horizontal force and uniform horizontal
strain with depth. The model predicts high stretching factors and localized extension for fast strain
rates, while wide basins with low stretching factors result for slow strain rates. Fast strain rates are
only possible in initially hot lithosphere; cold lithosphere requires an unrealistic high force to begin
extension. Intermediate geotherms (heat flow ~ 6 0 70 mW m -2) result in pronounced zones of low
stress and low ductile strength at the base of the
middle and lower crust, which can act as detachment
surfaces.
A similar one-dimensional approach, using
strength envelopes in conjunction with a constant
strain rate and gravitational buoyancy forces, was
proposed by Buck (1991). In this model, changes in
total lithospheric strength during extension are associated not only with changes in crustal thickness
and temperature distribution, but also with lateral
pressure differences which may drive flow in the
lower crust. The results obtained by Buck (1991) differ from those of Kusznir and Park (1987). Narrow
rifts develop for initially cold lithosphere (heat flow
<75 mW m-2), almost independently of the applied
strain rate. Under these conditions, only very low
strain rates lead to wide rifts. Hot lithosphere and
high strain rates result in wide rifts, while low strain
rates result in a core complex mode of deformation.
Lithospheric strength envelopes have been used
also to constrain the pre-tectonic conditions under
which the lithosphere deforms in extension (Morgan and Fernhndez, 1992; Cloetingh et al., 1995a)
and in post-orogenic tectonic inversion (Lowe and
Ranalli, 1993; Mareschal, 1994). Consideration of
lateral heat transport and estimation of lateral variations in lithospheric strength in a two-dimensional
kinematic model led Negredo et al. (1995) to establish some conditions under which the predefined
velocity field is compatible with rock rheology. Similarly to Buck (1991), these authors propose that high
strain rates in cold areas produce a narrow basin,
the crustal/mantle thickness ratio being a determinant factor. Lateral heat flow towards the flanks may
result in a mode of deformation characterized by
extensional structures parallel to the basin, with undeformed areas in between. The evolution of the total
lithospheric strength during the post-rift phase indicates that, after a critical relaxation time, the central
M. Ferngmdez, G. Ranalli/Tectonophysics 282 (1997) 129-145
part of the basin becomes stronger than the adjacent undeformed areas and hence any new extension
event will shift the locus of deformation.
5. Dynamic models
The use of 'back-door rheology' puts important
constraints on models of lithospheric extension, and
yields some relations between the mode of deformation (narrow/wide rifts) and strain rate, initial
geotherm, and crust/mantle thickness ratio. However,
a complete account of lithospheric deformation requires the use of two- or three-dimensional dynamic
models. By definition, a dynamic model involves
constitutive equations which relate dynamic quantities (stress) to kinematic quantities (strain or strain
rate) through material parameters (Ranalli, 1995).
There are several constitutive equations that describe
rheological behaviour as a function of material, temperature, pressure, and stress conditions (elastic, viscous, plastic, viscoelastic, etc.). Accordingly, dynamic models of lithospheric extension cover a wide
range of lithospheric rheologies. For simplicity, and
because most of the models are two-dimensional,
we classify them into plane-strain and plane-stress
models.
5.1. Plane-strain models
The hypothesis of plane strain assumes that flow
is everywhere parallel to a plane containing any two
axes and independent of the third axis. Consequently,
one principal strain component is zero. Plane-strain
models are usually applied to lithospheric crosssections of elongated geological structures such
as basins and rifts, orogenic belts, and subduction
zones. Some early analyses of lithospheric extension
adopted this approach, and assumed that the mantle
behaves as a viscous fluid while the crustal deformation is imposed kinematically (see e.g., Mareschal,
1983; Neugebauer, 1983; Keen, 1985, 1987; Buck,
1986). These studies incorporated progressively the
effects of pressure, temperature, and strain rate on
mantle viscosity, and allowed discussion of the effects of mantle convection on topography, as well as
of the role of active versus passive rifting mechanisms. The results are highly sensitive to the adopted
viscosity, but show that in general mantle convection
137
induces uplift of the rift flanks (e.g., Buck, 1986). A
dynamic component of elevation is generated due to
mantle flow, which has to be added to the isostatic
component (Keen, 1987).
Improvements in experimental rock mechanics
and in computing facilities allowed for the incorporation of more realistic theologies in plane-strain
models (see e.g., Braun and Beaumont, 1987; Dunbar and Sawyer, 1989; Lynch and Morgan, 1990;
Bassi, 1991). In this second generation of models,
the lithosphere is assumed to consist of three layers
which correspond to the upper crust, lower crust and
lithospheric mantle. Each of these layers behaves
as an elastic/viscous/plastic medium according to
chosen rheological equations (non-linear viscosity is
adopted for ductile flow). The results of these models have clarified the relations between the extensional deformation of the lithosphere, its rheology,
and boundary conditions. The initiation of extension
depends usually on the presence of a perturbation
(strength heterogeneity). The nature of these heterogeneities is discussed separately in Section 6.
Apart from the initial perturbation, most planestrain dynamic models focus on the relative effects
of extension rate and theology. In principle, high
strain rates produce narrow rifts, since the thermally
induced lithospheric weakening concentrates deformation. The opposite, however (i.e., that low strain
rates induce wide rifts), is not always true. The occurrence of wide rifts depends largely on the adopted
theology. In particular, wide rifts are produced at
low strain rates only when combined with a soft and
viscous lithosphere.
Conversely, if the adopted rheology is plastic,
deformation cannot migrate due to the reduction
in strength contrasts within the lithosphere and to
the mechanical instability associated with plasticity,
which tends to concentrate deformation (Bassi et al.,
1993; Bassi, 1995). Localization of deformation in
the lithosphere can be produced by incorporating a
power-law breakdown in the yield stress envelopes
(Bassi, 1991), or by deep-seated weaknesses affecting the lithospheric mantle, e.g., asthenospheric
upwelling (Lynch and Morgan, 1990; Christensen,
1992; Chery et al., 1992).
Another common result of plane-strain models is
that, in the absence of restoring forces, the Earth's
surface subsides due to lithospheric necking, produc-
138
M. Fernandez, G. Ranalli / Tectonophysics 282 (1997) 129-145
ing large isostatic anomalies. Then, if the lithosphere
retains a finite elastic rigidity, the consequent isostatic adjustment can result in different basin morphologies. In particular, when differential stretching
occurs with larger deformation at deep levels, the
isostatic adjustment leads to an upward elastically
supported rebound and rift shoulders are formed
(Lynch and Morgan, 1990; Chery et al., 1990, 1992;
Bassi, 1991). These results agree qualitatively with
the previously discussed kinematic necking.
In general, results of plane-strain modelling show
that strain rate is not the only factor determining
the style of extension, but that rheology, and consequently initial geotherm and structure, also play
a major role in the resulting mode of deformation.
Therefore, initial heterogeneities causing lateral variations in the mechanical properties of the lithosphere
exert a strong influence on the deformation pattern.
These aspects will be treated in more detail in the
following section.
5.2. Plane-stress models
The hypothesis of plane stress assumes that vertical gradients of horizontal velocity are small compared with horizontal gradients, and that deviatoric
stresses above and beneath the lithosphere vanish.
This assumption, and the integration with depth of
the differential equations for stress equilibrium, permit to treat the lithosphere as a thin sheet or plate
(e.g., Bird and Piper, 1980; Vilotte et al., 1982;
England and McKenzie, 1982, 1983). In this way,
lithospheric deformation is studied in map view using a quasi-three-dimensional model. In order to
have a vertically averaged rheology, lithospheric
strength envelopes are approximated by a single
viscous (England and McKenzie, 1982, 1983) or
visco-plastic (Bird, 1989) layer, which accounts for
ductile flow and frictional sliding on fault surfaces.
The plane-stress approach requires several assumptions for its application: theological parameters are
depth-independent, deformation is anelastic, topography is locally supported, and heat conduction is
vertical. However, gravitationally induced stresses
related to variations in crustal and lithospheric thickness can be taken into account. Moreover, planestress models are not restricted to a single layer and
it is possible to define two layers in order to simulate
the effects of detachments between crust and mantle
(Bird, 1989).
Plane-stress models have been widely used to
simulate different tectonic settings such as continental collision (e.g., England and McKenzie, 1982,
1983; England and Houseman, 1985; Vilotte et al.,
1986), extensional basins (e.g., Houseman and England, 1986; Sonder and England, 1989; Bassi and
Sabadini, 1994), and strike-slip regimes (e.g., Bird
and Piper, 1980; England et al., 1985; Sonder et al.,
1986). Of particular interest are the results obtained
by Sonder and England (1989), which show that for
low strain rates the locus of maximum strain rate migrates during extension from regions of high strain
to regions of low strain.
Clearly, a vertically averaged rheology implies
a simplification of the actual mechanical behaviour
of the lithosphere. However, as shown by Sonder
and England (1986), a single power-law rheology
is sufficient to describe the major features related
to lithospheric deformation. The main advantage of
the plane-stress approach lies in the ability to model
those geological structures that show a three-dimensional geometry (arcuate orogens, finite structures,
transpression, etc.). As a trade-off, details of the
vertical variations of deformation are lost.
6. The problem of the initial perturbation
Dynamic models need initial perturbations (lateral heterogeneities) in order to concentrate deformation in a finite area. This is a necessary condition in plane-strain approaches which usually assume boundary conditions such as depth-independent strain rate or velocity, or a constant extensional
force. In contrast, plane-stress approaches can concentrate deformation without initial perturbations by
applying specific boundary conditions such as indenters, fixed/slipping boundaries, and the like. Both
types of approach, as well as pure or simple shear
kinematic models, can incorporate initial perturbations in order to modify the mode of deformation.
Initial perturbations may be grouped in four categories: thickness variations, pre-existing faults, thermal anomalies, and rheological inhomogeneities. All
of them result in a lateral strength variation.
M. Ferngmdez, G. Ranalli/Tectonophysics 282 (1997) 129-145
6.1. Thickness variations
Crustal thickening produces lithospheric weakening due to both the replacement of stronger mantle
material by softer crustal rocks, and the temperature increase produced by radiogenic heat sources.
Therefore, thermally relaxed orogens and areas with
relatively high crustal thickness but without prominent lithospheric mantle roots are favourable structures to concentrate deformation (see e.g., Lynch
and Morgan, 1990; Harry and Sawyer, 1992; Bassi
et al., 1993). Several plane-strain dynamic models,
based on perturbation theory, address the problem of
the evolution and stability of the initial perturbation
during extension. Different rheologies are used: for
example, a strong plastic layer overlying a viscous
layer (Fletcher and Hallet, 1983); two strong layers separated by a weak layer (Zuber and Parmentier,
1986; Zuber et al., 1986); an elastic layer with a plastic weak zone overlying an inviscid layer (Lin and
Parmentier, 1990). These models show that, in most
cases, an initial perturbation grows during extension. The rate of growth depends on the wavelength
of the initial perturbation, and the resulting characteristic wavelength depends on the layer thickness.
Two strong layers give two predominant wavelengths
under both extension and compression (Froidevaux,
1986; Ricard and Froidevaux, 1986; Burov et al.,
1993). However, Bassi and Bonnin (1988) found that
a layered lithosphere behaves stably unless it is more
dense than the asthenosphere. Similar results were
obtained by Govers and Wortel (1993, 1995), who
used a two-dimensional layered model and found
that initial boudinage is amplified only for very high
strain rates.
6.2. Pre-existing faults
Deep faults can also concentrate deformation
since they are assumed to behave as slip surfaces
with very low resistance to motion. Faults and detachments are by definition surfaces of discontinuity,
and therefore cannot be incorporated in continuum
mechanics models. To avoid this problem in numerical algorithms, faults are commonly treated as
narrow channels with very low viscosity (e.g., Braun
and Beaumont, 1989b; Boutilier and Keen, 1994), as
slippery nodes (Melosh and Williams, 1989) or as
139
plastic shear bands (e.g., Dunbar and Sawyer, 1989;
Makel and Walters, 1993). Their position and orientation are usually pre-determined. The incorporation
of faults strongly modifies the resulting pattern of
deformation because of the associated mechanical
and thermal effects. Kinematic models show that
heat advection related to the relative displacement
between the hanging- and foot-wall can produce a
downward displacement of the brittle-ductile transition and consequent fault growth (Willacy et al.,
1996).
6.3. Thermal inhomogeneities
Temperature is one of the most important parameters in determining the total lithospheric strength:
the higher the temperature the weaker the lithosphere. Thus, initial lateral variations in temperature
concentrate the deformation around the warmer areas, which under extension will enhance the thermal anomaly. Thermal inhomogeneities applied to
plane-strain models result in narrow rifts which are
characterized by a very fast evolution and a large departure from local isostatic equilibrium (e.g., Chery
et al., 1990; Lynch and Morgan, 1990). Plane-stress
approaches are also capable to simulate thermal perturbations by varying the initial surface heat flow
distribution, which induces changes in the average
lithospheric viscosity (Vilotte et al., 1986; Bassi and
Sabadini, 1994).
6.4. Rheological inhomogeneities
Lateral variations in rock properties related to
changes in composition, grain size, and pore fluid
pressure lead to rheological inhomogeneities and
consequent strength variations. Lithological changes
are particularly common in the crust where pressure
and temperature conditions allow for different stable mineral phases. Granite intrusions at mid-crustal
levels result in localized weaknesses which, when
combined with an offset crustal thickening, can produce a simple-shear mode of extension (Harry and
Sawyer, 1992). Lateral variations in rheology applied to plane stress models can simulate cratonic
and basin environments, corresponding to hard and
weak areas, respectively, which may affect the initiation and propagation of shear zones (Tommasi et
140
M. Ferng~ndez, G. Ranalli/Tectonophysics 282 (1997) 129-145
al., 1995). Lateral variations in pore fluid pressure
may enhance these heterogeneities. If the formation of a shear zone is accompanied by dynamic
recrystallization with consequent reduction in grain
size (cf. Ranalli, 1995 for details), and subsequently
the small grain size is frozen into the rock due to
a decrease in temperature, a new heating episode
will reactivate the shear zone. Therefore, rheological heterogeneities may sometimes be inherited from
previous tectonothermal events.
7. Boundary conditions
For discussion purposes, we consider separately
mechanical and thermal boundary conditions. With
respect to the former, we focus essentially on passive
rifting (in active rifting, the drag of the asthenosphere
on the lithosphere is prescribed, either kinematically
or dynamically). With respect to the latter, we discuss the differences between constant heat flux and
constant temperature conditions at the lower boundary of the lithosphere (the condition of zero heat flux
in the horizontal direction is commonly imposed on
the side boundaries of the model).
7.1. Mechanical boundary conditions
When conditions are imposed on the vertical sides
of the extending lithosphere (passive rifting), they
can be either kinematic (constant strain rate or constant velocity) or dynamic (constant tectonic force).
In both cases, these conditions are usually coupled
with the assumption that the deformation (implicitly
assumed to be pure shear) is homogeneous, that is,
different layers at a given site undergo the same
amount of extension. Where this is not the case, i.e.,
where the stretching factor is a function of depth, the
model is usually one-dimensional and the question
of how differential stretching is compensated in the
horizontal direction is left unanswered.
Constant-velocity and constant-strain rate boundary conditions were discussed by England (1983).
Constant-velocity boundary conditions imply that
the across-strike width of the extending basin at time
t since the beginning of extension is L = Lo + rot,
where L,, is the initial width andvo the extension velocity. Consequently, the extensional strain
rate k(t) = ( 1 / L ) ( d L / d t ) is a decreasing function
of time. On the other hand, constant-strain rate
boundary conditions (see e.g., Jarvis and McKenzie, 1980) require that the width varies with time as
L = Loexp(~ot), where ~o is the strain rate. Consequently, the extension velocity v = (dL/dt) is an
increasing function of time.
Kinematic boundary conditions cannot, by definition, lead to an instability, unless they are coupled
with the assumption of a pre-existing lateral strength
inhomogeneity of the type discussed in the previous section. Also, if constant-velocity conditions
apply, rheological constraints imposed by strength
envelopes are themselves a function of time (because of the constant strain rate assumption used in
the estimation of envelopes, as discussed previously). Therefore, relevant strength envelopes at a given
stage of basin formation should take into account
not only varying lithospheric structure and temperature distribution, but also varying strain rate. If, on
the other hand, constant-strain rate conditions apply, they must do so only for a limited period of
time, as they imply exponentially increasing opening
velocity.
Neither of the above kinematic conditions is univocally related to dynamic boundary conditions,
where tectonic force (or stress) is prescribed on the
boundaries of the extending lithosphere. A condition of constant tectonic force (equivalent to constant
tectonic stress at infinity, that is, away from the extending zone, where the lithospheric thickness does
not change) leads to a two-dimensional stress (and
therefore strain rate) distribution depending on the
spatial and temporal variations of lithospheric structure and temperature (see e.g., Bassi, 1995). Even
in the one-dimensional case, stress is concentrated
in those parts of the lithosphere which are most
resistant to deformation (Kusznir, 1982).
At the site of necking (either imposed a priori
or resulting from initial conditions), the reduction
in lithospheric cross-sectional area results in geometric stress amplification, independently of and in
addition to any dynamic stress amplification due to
yielding of the softer layers. Consequently, under
constant tectonic force, the deviatoric tensile stress
at the site of necking increases with time. This may
lead to an instability (accelerating strain rate), if not
counteracted by structural and/or thermal hardening
processes. The interplay between stress concentra-
M. Fern~ndez, G. Ranalli/Tectonophysics 282 (1997) 129-145
tion, changes in lithospheric strength due to stretching, and thermal relaxation depends on a variety of
factors (structure and temperature of the lithosphere
before extension, applied tectonic force and its timedependence, magnitude of strength inhomogeneity).
Only a fully coupled dynamic analysis can identify
criteria for lithospheric instability.
7.2. Thermal boundary conditions
The boundary conditions to solve the heat transport equation (apart from fixed temperature at the
surface and no lateral heat flow through the side
boundaries) are either a fixed heat flow or a fixed
temperature at the base of the lithosphere. Which
conditions apply depends on the coupling between
the lithosphere and the asthenosphere. If it is assumed that there are no heat sources such as smallscale convective cells in the asthenosphere, the heat
flow trough the base of the lithosphere should be
constant during extension. However, this requires
that the temperature at the base of the lithosphere
decreases with time as extension progresses. In con-
14l
trast, a constant basal temperature implies that the
heat flow increases with time which, in turn, requires
heat sources within the asthenosphere. A constant
temperature boundary condition matches the definition of a cooling lithospheric plate given by Parsons
and Sclater (1977) and is, in fact, the most widely
used in basin modelling. The temperature at the base
of the lithosphere is taken to be the solidus of peridotite Tm, including hydration effects (for instance,
0.85 Tm; Pollack and Chapman, 1977). The temperature in the asthenosphere is considered to have
a negligible gradient. This condition is particularly
useful when the mechanical coupling between lithosphere and asthenosphere is modelled (e.g., Buck,
1986; Keen and Boutilier, 1995).
8. Concluding remarks
Our critical review of the role of rheology in
the modelling of lithospheric extension (basins and
rifted margins), summarized in the diagram shown in
Fig. 4, allows two important general statements to be
made. The first is that kinematic and 'back-door rhe-
Basin Formation Models
f
Kinematic
""
No controls on actual rock-rheology
Thermal and subsidence evolution
,~
of given basins
Mode of Deformation
'a posteriori'
constraints ~ , , ~
J
Partial controls on actual
rock-rheology
of total strength
~ R h~e ° l ° g y
f
j
Dynamic
Self-consistent with actual rock-rheology
,~
Fundamental processes
j
Fig. 4. Diagram showing the linking between the mode of deformation and the role of rheology in basin formation models. Consistency
of models increases at the expense of versatility.
142
M. Fernandez, G. Ranalli/Tectonophysics 282 (1997) 129-145
ology' models are very successful in reproducing the
subsidence~uplift and thermal histories of extensional
basins. Given that these models are subject only to
first-order rheological constraints, this success may
appear surprising. Methodologically, it is due to the
possibility of adjusting parameters freely, through
the kinematically imposed deformation field. This is
not to detract from their importance. The accurate
prediction of sedimentary patterns and temperatures
is not only interesting per se, but has also economic
applications, for example in the estimation of the
degree of thermal maturation of potential hydrocarbon deposits. Furthermore, the fact that an imposed
deformation field is compatible with observation implies that the mechanical properties of the lithosphere
must be such as to allow that deformation field. From
the predictive viewpoint, therefore, the present situation in rheological modelling of sedimentary basins
seems to be one of 'simplest is best', in the sense
that kinematic conditions together with simplified
rheological constraints produce excellent agreement
with observation.
On the other hand, kinematic and 'back-door rheology' models cannot account, except in an ad hoc
way, for physical processes such as the localization of extension, the weakening or strengthening of
the lithosphere during extension (leading to whole
lithospheric failure or to cessation of stretching),
and for the interplay between tectonic forces and
time- and space-dependent rheological properties.
Although dynamic models explain consistently the
mode of deformation, the high non-linearity of constitutive equations and the uncertainties on the actual
structure, composition and rheology of the lithosphere make the results very sensitive to the initial
and boundary conditions. Consequently, a second
general statement is that progress in the knowledge
of the rheological properties of the lithosphere and
further refinement of dynamic models are necessary
conditions for new insights into the physics of lithospheric deformation.
In a sense, kinematic models (with or without rheological constraints, and 'thermomechanical' in the
sense that they yield velocity and temperature fields)
and dynamic models have complementary roles. The
former successfully simulate the formation and evolution of given basins. The latter give insight into
the fundamental processes governing basin dynam-
ics. Despite remarkable advances in both types of
modelling, a lot of work remains to be done.
Acknowledgements
This paper was presented, in a preliminary form,
at the Sixth Workshop on 'Origin of Sedimentary
Basins' held at Sitges, Spain, in September 1995.
The authors thank all the colleagues who, through
discussion and criticism, have contributed to the
evolution of their ideas. G.R. acknowledges support from NSERC (Natural Sciences and Engineering Research Council of Canada). M.E acknowledges support from the European Union 'Integrated
Basin Studies' project (Nr. JOU2-CT92-0110). Fruitful suggestions and comments from E. Burov, S.
Cloetingh, and G. Spadini have been incorporated
during the review process.
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