E L S E V I E R Tectonophysics 282 (1997) 129-145
The role of rheology in extensional basin formation modelling a
M . F e r n a n d e z , , G . R a n a l l i 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
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
1. In troduct ion
Extensional (rifted) basins are formed by subsi- dence of the
Earth 's surface as a consequence of large-scale l i thospheric
stretching. This subsidence is produced by the replacement of 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 cool ing of the l i thosphere and mantle. Two end member
mechanisms have been proposed to generate extensional basins (e.g.,
Turcotte and Emer- man, 1983; Neugebauer, 1983; Keen, 1985; Morett
i and Froidevaux, 1986; Bott, 1992): active rifting in which the
ascent of the asthenosphere causes con- vective thinning, domal
uplift and li thospheric ex- tension; and passive rifting where
horizontal tectonic stresses produce l i thospheric thinning and
passive mantle upwelling. Actually, most rifts show active
0040-1951/97/$17.00 © 1997 Elsevier Science B.V. All rights
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130 M. Ferngmdez, G. Ranalli/Tectonophysics 282 (1997)
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,
occur- rence of magmatism, etc., are surface expressions of
processes that operate at crustal and mantle levels. These
processes are directly related to the deforma- tional 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 de- form in a brittle
or ductile manner depending on pressure and temperature conditions
(e.g., Goetze and Evans, 1979; Carter and Tsenn, 1987; Kohl- stedt
et al., 1995). In modelling, the mode of litho- spheric deformation
can be prescribed either implic- itly, by imposing a deformation
pattern which the lithosphere is assumed able to sustain (kinematic
models) or explicitly, by specifying equations gov- erning 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 de- tachments,
volcanism, etc. (e.g., McKenzie, 1978; Royden and Keen, 1980; Buck
et al., 1988; McKen- zie 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 pas- sive and active rifting
mechanisms and also to litho- sphere/asthenosphere interaction
(e.g., Braun and Beaumont, 1987; Lynch and Morgan, 1987; Dun- bar
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 rheol- ogy
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 under- lying substratum is treated dynamically (e.g., Keen,
1985; Buck, 1986; Keen and Boutilier, 1995). Like- wise,
rheological controls based on the depth vari- ation 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 kine- matic 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 In- ternational 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 uncer-
tainties and assumptions. Basin formation models are subdivided
into three categories from the rheologi- cal 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 rheol- ogy 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: brit- tle or frictional, governed by
the Coulomb-Navier shear failure criterion, and ductile, governed
by the power-law creep equation. The brittle/ductile transi- tion
is defined by the equality of frictional strength and ductile
strength (for a given strain rate). Al- though undoubtedly an
oversimplification of reality, strength envelopes have proven very
useful in rhe- ological modelling of lithospheric processes,
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
else- where (e.g., Ranalli, 1995, 1997a); here, we focus on their
uncertainties and their limits of applica- bility. The
uncertainties can be divided into two groups. Operational
uncertainties derive from imper- fect knowledge of composition and
structure of the lithosphere, errors in the estimated temperature
dis- tribution, scatter in experimentally determined rheo- logical
parameters, lack of constraints on pore fluid pressure, and similar
factors. Methodological uncer- tainties stem from the basic
assumptions used in the construction of strength envelopes, which
can be re- lated 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
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-exist- ing faults are often taken
to be cohesionless, with a coefficient of friction # = 0.75. The
uncertainties introduced by these approximations are low com- pared
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
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 mod- els. Although occasionally the individual
values of creep parameters differ considerably, their applica- tion
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, result- ing from the parameters adopted by Burov and Di-
ament (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 experi- mental 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 transi- tion in nature is transitional rather than
sharp, rhe- ological 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
The Coulomb-Navier frictional criterion (Byer- lee's law) is
experimentally confirmed only up to pressures corresponding to
mid-crustal depths (By- erlee, 1967; Jaeger and Cook, 1979). Its
linear ex- trapolation to lower crustal and upper mantle condi-
tions 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
depen- dence of strength as depth increases.
132 M. Ferngmdez, G. Ranalli/Tectonophysics 282 (1997)
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 2.5 x 10 8 3.0 138  UC 1.3 x 10 -3 2.4 219  UC 3.4 x 10
.6 2.8 185 [5, 13] UC 1.3 × 10 -7 2.9 149  UC 1.0 × 10 .6 2.8
150  UC 1.6 × 10 -9 3.0 123  UC 1.3 × 10 -9 3.2 144 It0[ UC
5.8 × 10 -5 2.4 142  UC 2.0 × 10 4 1.9 141  UC 5.0 x 106
3.0 190 [14, 15] UC 2.5 × 10 - s 3.0 140  UCW 1.0 × 10 -2 1.8
151  UCW 2.0 × 10 -4 1.9 134  UCW 2.9 x 10 -3 1.8 150  UCW
3.3 x 10 .6 2.4 134  UCW 3.1 × 10 7 3.1 135  UCW 5.6 × 10 -5
2.4 160  LC 3.2 x 10 .3 3.0 25l  LC 1.3 x 10 3 2.4 219 
LC 3.2 x 10 3 3.3 268 [4[ LC 3.3 × 10 4 3.2 238 [5, 10] LC 8.9 × 10
4 3.2 238  LC 1.0 x 10 -3 3.0 230 ]7] LC 3.2 × 10 3 3.2 270 
LC 3.8 x 10 .2 3.1 243  LC 2.0 × 10 -4 3.4 260  LC 3.3 × 10 4
3.2 384  LC 1.4 × 10 4 4.2 445 [12, 17] LC 2.3 x 10 6 3.9 235
 LC 1.3 2.4 212 [14, 15] LC 0.13 3.1 276 [14, 15] LC 3.2 × 10
-3 3.0 250  LC 8.0 x 10 -3 3.1 243  LCW 3.0 × 10 -2 3.2 239
 LCW 3.3 × 10 -4 3.2 238  LCW 6.3 x 10 -3 2.8 271  UM 1.0
x 103 3.0 523 [1, 16] UM 7.0 × 104 3.0 510  UM 3.2 × 104 3.6 535
 UM 2.9 × 104 3.6 535 [5, 13] UM 1.0 × 103 3.0 500  UM 3.2 x
104 3.5 535  UM 1.9 x lO 3 3.0 420  UM 1.4 × 105 3.5 535 
UM 7.0 × 104 3.0 530 [111 UM 4.3 × 102 3.0 527 [121 UM 7.0 × 104
3.0 520 [14, 15] UMW 1.9 x 105 4.5 498  UMW 2.0 x 103 4.0 471
Table I (continued)
Layer A (MPa " s l) n E (ld m o l l ) Ref.
UMW 1.4 x 104 3.4 445  UMW 8.6 x 103 3.0 420  UMW 4.0 ×
102 4.5 498 
References.  Lynch and Morgan, 1987;  Braun and Beau-
mont, 1989b;  Dunbar and Sawyer, 1989;  Fadaie and Ranalli,
1990;  Bassi, 1991;  Buck, 1991;  Ranalli, 1991; 
Govers and Wortel, 1993;  Liu and Furlong, 1993;  Lowe and
Ranalli, 1993;  Boutilier and Keen, 1994;  Mareschal, 1994;
 Bassi, 1995;  Burov and Dia- ment, 1995;  Cloetingh
and Burov, 1996;  Negredo et al., 1995;  Lamontagne and
Ranalli, 1996. Notes. Upper crust is usually taken as quartz-rich
or granitic ex- cept in  where it is assumed to be
quartz-dioritic: lower crust varies between intermediate
(quartz-dioritic) and basic composi- tion (the parameters in 
and  apply to mafic granulites); upper mantle is ultrabasic
In t h e d u c t i l e r e g i m e , at l e a s t fo 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 tha t a t r a n s i t i o n o c c u
r s w i t h in-
c 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 low 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 e t 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 ig . 1 fo r t h e
s i m p l e c a s e
o f a c r u s t o f u n i f o r m f e l s i c c o m p o s i t i
o n a n d a l o w
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 -
t le. 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 ike ly to be m o r e c o m
p l e x than
u s u a l l y a s s u m e d in s t r e n g t h e n v e l o p e s
A s s u m p t i o n s c o n c e r n i n g d e f o r m a t i o n
s ty l e a re an
i n t e g r a l pa r t o f s t r e n g t h e n v e l o p e s . T
h e a s s u m p -
t i o n o f u n i f o r m s t r a in i m p l i e s t ha t al l l
a y e r s su f f e r
t h e s a m e e x t e n s i o n a l d e f o r m a t i o n , a n
d c o n s e q u e n t l y
s t r i c t l y l i m i t t he 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
w i t h t h e s t r e t c h i n g f a c t o r i n d e p e n d e
n t o f d e p t h . T h i s
is o f c o u r s e n o t n e c e s s a r i l y t rue. 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 he 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 i m p o r t a n t ro l e in l i t h o s p h e r i c e x t e n
s i o n ( B u c k ,
1991). S o m e i m p l i c a t i o n s fo r s t r e n g t h e n
v e l o p e s a re
s h o w n in F ig . 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 in ra te
( A L / L ) / t , w h e r e t is t i m e , is n o t t he p h y s
i c a l l y re l - e v a n t o b s e r v a b l e . T h e ac t ua l
s t r a in ra te is t he 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 the t h i ck -
M. Ferngmdez, G. Ranalli/Tectonophysics 282 (1997) 129-145
B . . . . . . . . . I . . . . . . . . . . . . . . . . .
(3"1- - ~ 3
iiiiiiiiiiiiiiiiiiiii 6 o oooc " ~ - 911 +50°C .......
................. 1250+100oc ...............
3F BF ..
BF • " -'II
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. Stan- dard
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 high- pressure
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
ness of the shear zone. The strength in this case is determined
by the variations of rheological proper- ties along the zone
separating the two lithospheric blocks, not along the vertical
The assumption of constant strain rate (upon
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.
3. Kinematic models
A common 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 shoul- ders, and
mass redistribution due to lithospheric stretching. In this section
we will focus on the rela- tionship between isostatic mechanisms
and rheology, which governs the response of the lithosphere to
A very simple one-dimensional approach to ex- plain the
subsidence observed in passive margins and sedimentary basins was
proposed by McKenzie (1978). The model assumes local isostatic
compen- sation, pure shear deformation and instantaneous
lithospheric stretching followed by thermal relax- ation.
Extensions of this model to two dimensions consider the effects of
finite duration of rifting, lat- eral heat transport, and
differential stretching (e.g., Royden and Keen, 1980; Jarvis and
McKenzie, 1980; Cochran, 1983; Buck et al., 1988; White and McKen-
zie, 1988). These models have permitted to bet- ter constrain the
observed basin subsidence, crustal
k L+ A L ~t I( L :,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)
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 strati- graphic
onlaps (White and McKenzie, 1988) and prominent and permanent rift
shoulders (Zeyen et al., 1996).
Local isostasy assumes that the lithosphere is un- able to
support vertical shear stresses. Therefore, any vertical force is
compensated by lithosphere buoy- ancy. From a rheological
viewpoint, this assump- tion 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-consis- tent
rheological model of the lithosphere.
If, on the other hand, it is assumed that the litho- sphere
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,
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). How- ever, this empirical relationship is much more debat-
able 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 dur- ing lithospheric deformation. For a thermally
young lithosphere, Te is dominated by quartz-feldspar rhe- ology,
while for older lithospheres it is dominated by olivine rheology
(Kusznir and Karner, 1985). Pure- shear flexural models have been
used to account for the basement subsidence and stratigraphy at
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
From the rheological viewpoint, several problems arise when
modelling the lithosphere as a linear elastic plate. First, in a
bent elastic plate, the calcu- lated stresses can be considerably
higher than those deduced from lithospheric strength envelopes;
sec- ond, 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 compo- nent. Several attempts have been made to
reconcile the flexural behaviour of the lithosphere with its ac-
tual 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 re-
sult is that the effective elastic thickness depends on rock
rheology and curvature for a given structure, composition, and
Whatever mechanism of isostasy is assumed, lo- cal 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 en- tire lithosphere to explain
the uplift of the Colorado Plateau adjacent to the Basin and Range
by local isostasy. Simple-shear deformation produces a lat- eral
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 quan- titative analysis). Depending on the depth, dip,
and number of detachments, different styles of deforma- tion 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 lev- els 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 kine- matics of
lithosphere extension is the level of neck-
M. Ferngmdez, G. Ranalli/Tectonophysics 282 (1997) 129-145
(a) "'- -t--." (i) . . . . . ~ . . . . . .
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;/3 is the
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 re- sponses
(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
indepen- dent 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
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
4. Mechanical controls on kinematic models: 'back-door
Kinematic models are very powerful in account- ing for the main
features of extensional sedimentary basins and their evolution
through time. This capa- bility 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 com- peting effects arise during finite
continental exten- sion: weakening produced by lithospheric
thinning and strengthening produced by thermal relaxation
136 M. Fern?mdez, G. Ranalli/Tectonophysics 282 (1997)
(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 correspond- ing to an
undeformed lithosphere on the basis of some rheological model.
These one-dimensional ap- proaches do not provide the actual
deformation of the lithosphere, but they introduce rheological
controls on the mode of deformation. We call them 'back- door
rheological models'. One example is the anal- ysis 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 geomet- ric meaning.
Assuming a thin sheet viscous lithosphere, Eng- land (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 ex- ceeds 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 ex- tension. 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 rang- ing from 3.25 to 6, the duration of
rifting must be less than 10-20 Ma.
The thin sheet approach assumes that the litho- sphere 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 me- chanical behaviour of the lithosphere
that tends to overestimate lithospheric strengthening, since nei-
ther the role of crustal rocks (both in the brittle and in the
ductile fields), nor the changes in ther- mal gradient are
considered (Sawyer, 1985). Kusznir and Park (1987) considered a
layered rheology for the lithosphere and analyzed its response to
an ap- plied tectonic tensile force by assuming conservation
of the total horizontal force and uniform horizontal strain with
depth. The model predicts high stretch- ing factors and localized
extension for fast strain rates, while wide basins with low
stretching fac- tors result for slow strain rates. Fast strain
rates are only possible in initially hot lithosphere; cold litho-
sphere 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
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 as- sociated 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)
dif- fer from those of Kusznir and Park (1987). Narrow rifts
develop for initially cold lithosphere (heat flow
M. Ferngmdez, G. Ranalli/Tectonophysics 282 (1997) 129-145
part of the basin becomes stronger than the adja- cent
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 defor- mation (narrow/wide rifts) and strain rate,
initial geotherm, and crust/mantle thickness ratio. However, a
complete account of lithospheric deformation re- quires the use of
two- or three-dimensional dynamic models. By definition, a dynamic
model involves constitutive equations which relate dynamic quanti-
ties (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, tem- perature, pressure, and stress
conditions (elastic, vis- cous, plastic, viscoelastic, etc.).
Accordingly, dy- namic 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 cross-
sections 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 deforma- tion
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 ef- fects of
mantle convection on topography, as well as of the role of active
versus passive rifting mecha- nisms. The results are highly
sensitive to the adopted viscosity, but show that in general mantle
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 incor- poration of more realistic
theologies in plane-strain models (see e.g., Braun and Beaumont,
1987; Dun- bar 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 mod- els have clarified the relations
between the exten- sional 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 hetero- geneities is discussed
separately in Section 6.
Apart from the initial perturbation, most plane- strain 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
defor- mation. The opposite, however (i.e., that low strain rates
induce wide rifts), is not always true. The oc- currence 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 af-
fecting the lithospheric mantle, e.g., asthenospheric upwelling
(Lynch and Morgan, 1990; Christensen, 1992; Chery et al.,
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)
ing large isostatic anomalies. Then, if the lithosphere retains
a finite elastic rigidity, the consequent iso- static adjustment
can result in different basin mor- phologies. 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 con- sequently initial geotherm and structure,
also play a major role in the resulting mode of deformation.
Therefore, initial heterogeneities causing lateral vari- ations 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 ver- tical gradients
of horizontal velocity are small com- pared 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, per- mit 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
us- ing 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 assump- tions for its application:
theological parameters are depth-independent, deformation is
anelastic, topog- raphy is locally supported, and heat conduction
is vertical. However, gravitationally induced stresses related to
variations in crustal and lithospheric thick- ness can be taken
into account. Moreover, plane- stress models are not restricted to
a single layer and it is possible to define two layers in order to
the effects of detachments between crust and mantle (Bird,
Plane-stress models have been widely used to simulate different
tectonic settings such as conti- nental collision (e.g., England
and McKenzie, 1982, 1983; England and Houseman, 1985; Vilotte et
al., 1986), extensional basins (e.g., Houseman and Eng- land, 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 mi- grates 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-dimen- sional 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 (lat- eral
heterogeneities) in order to concentrate defor- mation in a finite
area. This is a necessary con- dition in plane-strain approaches
which usually as- sume boundary conditions such as depth-indepen-
dent strain rate or velocity, or a constant extensional force. In
contrast, plane-stress approaches can con- centrate deformation
without initial perturbations by applying specific boundary
conditions such as in- denters, fixed/slipping boundaries, and the
like. Both types of approach, as well as pure or simple shear
kinematic models, can incorporate initial perturba- tions in order
to modify the mode of deformation. Initial perturbations may be
grouped in four cate- gories: thickness variations, pre-existing
faults, ther- mal 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 weaken- ing due to both
the replacement of stronger mantle material by softer crustal
rocks, and the tempera- ture increase produced by radiogenic heat
sources. Therefore, thermally relaxed orogens and areas with
relatively high crustal thickness but without promi- nent
lithospheric mantle roots are favourable struc- tures 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 lay- ers separated by a weak layer (Zuber and
Parmentier, 1986; Zuber et al., 1986); an elastic layer with a
plas- tic weak zone overlying an inviscid layer (Lin and
Parmentier, 1990). These models show that, in most cases, an
initial perturbation grows during exten- sion. The rate of growth
depends on the wavelength of the initial perturbation, and the
resulting charac- teristic 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 de- tachments are by definition surfaces of
discontinuity, and therefore cannot be incorporated in continuum
mechanics models. To avoid this problem in nu- merical 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
plastic shear bands (e.g., Dunbar and Sawyer, 1989; Makel and
Walters, 1993). Their position and orien- tation 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 tran- sition and consequent fault growth (Willacy
et al., 1996).
6.3. Thermal inhomogeneities
Temperature is one of the most important param- eters in
determining the total lithospheric strength: the higher the
temperature the weaker the litho- sphere. Thus, initial lateral
variations in temperature concentrate the deformation around the
warmer ar- eas, which under extension will enhance the ther- mal
anomaly. Thermal inhomogeneities applied to plane-strain models
result in narrow rifts which are characterized by a very fast
evolution and a large de- parture from local isostatic equilibrium
(e.g., Chery et al., 1990; Lynch and Morgan, 1990). Plane-stress
approaches are also capable to simulate thermal per- turbations 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 sta- ble
mineral phases. Granite intrusions at mid-crustal levels result in
localized weaknesses which, when combined with an offset crustal
thickening, can pro- duce a simple-shear mode of extension (Harry
and Sawyer, 1992). Lateral variations in rheology ap- plied to
plane stress models can simulate cratonic and basin environments,
corresponding to hard and weak areas, respectively, which may
affect the ini- tiation and propagation of shear zones (Tommasi
140 M. Ferng~ndez, G. Ranalli/Tectonophysics 282 (1997)
al., 1995). Lateral variations in pore fluid pressure may
enhance these heterogeneities. If the forma- tion 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, rheologi- cal 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 dis-
cuss the differences between constant heat flux and constant
temperature conditions at the lower bound- ary 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 con- stant 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 bound- ary 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 exten- sion velocity.
Consequently, the extensional strain rate k(t) = (1 /L ) (dL /d t )
is a decreasing function
of time. On the other hand, constant-strain rate boundary
conditions (see e.g., Jarvis and McKen- zie, 1980) require that the
width varies with time as L = Loexp(~ot), where ~o is the strain
rate. Con- sequently, the extension velocity v = (dL/dt) is an
increasing function of time.
Kinematic boundary conditions cannot, by defini- tion, lead to
an instability, unless they are coupled with the assumption of a
pre-existing lateral strength inhomogeneity of the type discussed
in the pre- vious section. Also, if constant-velocity conditions
apply, rheological constraints imposed by strength envelopes are
themselves a function of time (be- cause of the constant strain
rate assumption used in the estimation of envelopes, as discussed
previous- ly). Therefore, relevant strength envelopes at a given
stage of basin formation should take into account not only varying
lithospheric structure and tempera- ture distribution, but also
varying strain rate. If, on the other hand, constant-strain rate
conditions ap- ply, 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 uni- vocally
related to dynamic boundary conditions, where tectonic force (or
stress) is prescribed on the boundaries of the extending
lithosphere. A condi- tion of constant tectonic force (equivalent
to constant tectonic stress at infinity, that is, away from the ex-
tending 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 struc- ture 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
At the site of necking (either imposed a priori or resulting
from initial conditions), the reduction in lithospheric
cross-sectional area results in geo- metric 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 stretch- ing, and
thermal relaxation depends on a variety of factors (structure and
temperature of the lithosphere before extension, applied tectonic
force and its time- dependence, 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 trans- port 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 as- sumed that there are no heat sources
such as small- scale 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-
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 defini- tion 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 peri- dotite Tm, including hydration
effects (for instance, 0.85 Tm; Pollack and Chapman, 1977). The
tem- perature in the asthenosphere is considered to have a
negligible gradient. This condition is particularly useful when the
mechanical coupling between litho- sphere 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
Mode of Deformation 'a posteriori'
Basin Formation Models
f Kinematic ""
No controls on actual rock-rheology Thermal and subsidence
, ~ of given basins
constraints ~ , , ~ J of total strength ~ R h e ° l ° g y
Partial controls on actual f ~
Self-consistent with actual rock-rheology ,~ Fundamental
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)
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
hydrocar- bon deposits. Furthermore, the fact that an imposed
deformation field is compatible with observation im- plies that the
mechanical properties of the lithosphere must be such as to allow
that deformation field. From the predictive viewpoint, therefore,
the present situ- ation 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 rhe- ology' models
cannot account, except in an ad hoc way, for physical processes
such as the localiza- tion 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
con- stitutive equations and the uncertainties on the actual
structure, composition and rheology of the litho- sphere 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 litho- spheric deformation.
In a sense, kinematic models (with or without rhe- ological
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 evo- lution 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.
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 sup- port from NSERC (Natural
Sciences and Engineer- ing Research Council of Canada). M.E
acknowl- edges support from the European Union 'Integrated Basin
Studies' project (Nr. JOU2-CT92-0110). Fruit- ful suggestions and
comments from E. Burov, S. Cloetingh, and G. Spadini have been
incorporated during the review process.
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