- Email: [email protected]
Thermal regime and post-orogenic extension in collision belts
ELSWIER
Tectonophysics 238 (1994) 471-484
Thermal regime and post-erogenic Jean-Claude GEOTOP,
University of Quebec, Monhal,
extension in collision belts
Mareschal
P.O. Box 8888, sta. A, Mont&al. H3C 3P8, Canada
Received 10 May 1993; accepted 7 January 1994
Abstract In order to assess the conditions leading to post-erogenic extension, the temperature and strength of the lithosphere during continental collision are calculated. The calculations assume that heat is transported by conduction and either that the lithosphere is homogeneously thickened or that only the crust is thickened during the collision. Despite increased crustal thickness and heat production, the temperature does not increase if the rate of shortening is moderate (5 x lo-l6 s-l, leading to 100% increase in crustal thickness in 40 Myears). The temperature distribution is used to determine a rheological profile that is compared with the stress induced by compensated topography. The calculations show that, for homogeneous lithospheric thickening, the strength of the lithosphere increases and is higher than the tensile stress except in the shallow crust. The total strength of stable continental lithosphere at the end of shortening is on the order of 1013 N m-‘; it is larger by one order than the force induced by compensated topography (10” N m-l). It appears that homogeneous lithospheric thickening would not lead to post-erogenic extension unless the initial conditions are very special (with the lithosphere hotter than normal). For crustal thickening only, the strength of the lithosphere decreases slightly and is on the same order as the tensile stress. Extension does not necessarily follow from thickening of the crust only but it could take place for a relatively wide range of initial conditions (with initial surface heat-flow 60 mW mm2 or higher). Alternatively, an event such as rapid removal of the mantle lithosphere by delamination or small-scale convection would increase the tensile stress, heat rapidly the lithosphere, reduce its strength, and always trigger extension.
1. Introduction It has long been recognized that diffuse extension can develop during the late stages of evolution of collision belts. Several papers in this volume present evidence for post-erogenic extension in different collision belts. The suggestion that the topography of erogenic belts induces a tensile stress regime and could trigger extension dates back to the work of Love and Jeffreys. Love
(1911) calculated the stress induced by isostatitally compensated topography in an elastic Earth. Jeffreys (1929) used similar calculations and pro-
posed that the tensile stress regime could cause the collapse of mountain belts. More recently, several authors investigated the stress induced by compensated topography in an elastic lithosphere overlying the asthenosphere. Artemjev et al. (1972) suggested that the stress induced by mountain belts could explain some intraplahe earthquakes. Artyushkov (1973) suggested that large stress induced by compensated topography could not be sustained by the lithosphere and would lead to extension. Fleitout and Froidevavx (1982) have also investigated the stress inducqd in the lithosphere by different types of density hetero-
0040-1951/94/$07.00 0 1994 Elsevier Science B.V. All rights reserved SSDI 0040-1951(94)00074-J
J.-C Mawschal / Tectotwphysics 238 (IYY4) 471-484
472
geneities and they suggested that it could drive different types of tectonic activity. When the stress of compensated topography is no longer balanced by plate tectonic stresses, it could trigger lithospheric-scale extension if it is sufficiently large to overcome the strength of the lithosphere. The deformation induced by lithospheric thickening was investigated with thin sheet models which use vertical averages of the stress and the rheology. In the study of Bird and Piper (1980) where the vertical velocity is zero, the deformation pattern is caused by lateral extrusion of crustal material. In the model by England and McKenzie (1982), the vertical velocity does not vanish and the deformation pattern is caused by variations in crustal thickness: the stress induced by crustal thickening triggers extension and lateral movement in front of the orogen. In these calculations, the rheology of the sheet follows a power law of the form: (r)
=B&l/n-l)(&j)
where ( rij) is the vertically averaged stress, (iii) is the vertically averaged strain rate and & is the second invariant of the strain rate tensor; B and n are constants that depend on the rheology of the lithosphere. The relationship between the parameters of the thin sheet rheology and the actual rheology of the lithosphere was investigated by Sonder and England (1986). They concluded that the rheology can indeed be approximated by a single power law which is determined by the thermal state of the mantle and on the stress in the upper crust. Sander et al. (1987) examined how the temperature and rheology of the thickened lithosphere vary with time; they concluded that, depending on the initial thermal state of the lithosphere, a delay can occur between the end of compression and the beginning of extension. These authors suggested that extension in the Basin and Range followed the end of compression by 20-40 Myears because of the time necessary for heating and softening of the lithosphere. England (1983) showed that the thermal regime determines whether the lithosphere can fail in extension and rifting can occur. He suggested that cooling of lithosphere will rapidly stop extension unless it takes place at a very high
rate. Similar conclusions were reached by Kusznir and Park (1984, 19871 who calculated the total strength of the lithosphere and compared it with the tectonic forces causing extension. They concluded that extension will continue in the zone that is weakest provided that it proceeds at such a high rate that the lithosphere does not cool; at a low rate of extension, the extended lithosphere becomes stronger and the locus will migrate to a new weak zone. Murrell (1986) showed that the initial crustal thickness determines whether shortening results in uplift and tensile stress or subsidence and compressiona stress. The control of crustal thickness and thermal regime on the mode of extension was further investigated by Buck (1991) who recognized three modes of extension (core complex, wide rift, and narrow rift) and suggested that a temporal progression should normally take place from core complex to narrow rift mode. The thermal structure of the lithosphere during crustal thickening was investigated by Gaudemer et al. (1988). These authors proposed that temperature increases in mountain belts because of increased heat production in the thickened crust. They presented two-dimensional calculations of the thermal regime during compression and they showed that the temperature increases provided that thickening occurs over a wide region (500 km) and at very low rate (1 mm yr-’ which implies 500 Myears for 500 km shortening). Zhou and Sandiford (1992) compared the tensile stress induced by crustal and lithospheric thickening with the total strength of the lithosphere. They concluded that, if Moho temperature is higher than 650-700°C the orogen will experience extensional collapse; alternatively, if the Moho temperature remains low, the mountain belt will be attenuated by erosion. Ramberg (1981) had suggested that crustal thickening can be attenuated by lower-crustal flow. Bird (1991) examined the effect of rheological layering in the lithosphere and suggested that high topography and changes in crustal thickness could be attenuated by lower-crustal flow with a time constant depending on Moho temperature and on the wavelength of the topography. He concurred with the conclusions of several studies that this GOIlapse will be most dramatic in regions where the
J.-C. Mareschal/
473
Tectonophysics 238 (1994) 471-484
lithosphere has been delaminated or actively thinned (i.e. Houseman et al., 1981; England and Houseman, 1988, 1989). There are several examples of compressional belts that did not experience lithospheric-scale post-erogenic extension. A crustal root is preserved beneath the Appalachians and some parts of the Grenville Front. The persistence of these roots suggests that post-erogenic extension was confined to the upper crust and did not involve the lower crust and mantle. A crustal root also seems to have persisted for 2000 Myears under the Kapuskasing structural zone, in the Superior Province of the Canadian Shield (Percival, 1990). The rheology and thermal conditions that lead to the formation and preservation of this crustal root have been discussed by Parphenuk et al. (1994). The objective of this paper is to discuss further the conditions leading to post-erogenic extension. The thermal regime and the rheology of the lithosphere will be determined for a range of thermal parameters compatible with present knowledge of the continental lithosphere. The conditions permitting post-erogenic extension can be assessed by comparison between the stress distribution and the rheology of the lithosphere. The temperature distribution during homogeneous and non-homogeneous lithospheric thickening is determined and a rheological profile is estimated. The calculations show that, for homogeneous thickening of the lithosphere at any geologically reasonable rate, the lithosphere does not heat sufficiently and it becomes stronger. If the temperature profile of stable continental lithosphere is assumed as initial condition, the strength is larger than the stress at depth below a few km, and the total strength of the lithosphere is one order larger than the tensile force. When thickening involves only the crust but not the lithospheric mantle, the total strength of the lithosphere decreases slightly during shortening; in addition, the tensile stress is larger throughout the crust, and the compressional stress is smaller in the mantle. Extension could thus take place if the lithosphere is sufficiently hot initially. Alternatively, the lithosphere could be weakened by rapid heating following removal of the litho-
spheric mantle by convection or delamination. The latter hypothesis is preferred because, after removal of the lithospheric root, the stress becomes tensile throughout the lithosphere and the force is larger than the tensile stress for any initial conditions.
2. Stress induced by lithospheric thickening If the wavelength of the compensated topography is large as compared with lithospheric thickness, the stress induced in the lithosphere by the surface loading and density heterogeneities is easily calculated. The deviatoric stress at given depth is the difference between the vertical and the horizontal stress. The vertical stress uZzr (in the long-wavelength approximation) is the local lithostatic pressure, and the horizontal stress a,, is the confining pressure (i.e. the lithostatic pressure in standard continental lithosphere away from topography and crustal density heterogeneities): u ZL
-
uxx =
j-;hgp( 2’) dz’ - /I, adz’)
dz’
0
where z is depth (z positive downward), h is the elevation, h, is the elevation of the reference continental lithosphere, p(z’) is the density distribution and pJ.z’) is the density distribution in the reference lithosphere. The elevation difference is determined by the isostatic equilibrium condition, i.e. the deviatoric stress (a,, - a,,) vanishes at the base of the lithosphere. By convention, the origin of the coordinate system coincides with the surface of the reference lithosphere (i.e. h, = 0). Integrating the stress over the entire lithospheric thickness yields the force per unit length:
F’=jhL[uzz(z’) -a,,(~‘)]
dz’
where L is the base of the lithosphere cr - a** = 0. The force per unit length &rsion of energy density; it is equivalent difference in potential energy per unit between the thickened and the reference sphere (e.g. Ramberg, 1981).
where has dito the surface litho-
473
J.-C. Marrschal / iktonopttysics 238 (1994) 471-484
The difference in potential energy of the thickened lithosphere can be calculated if the density distribution in the reference lithosphere is known. It is shown in the Appendix that this energy difference is: AT= (y’-
1) i?‘(z) I
dz - -$
d
1
where y is the thickening factor, P(z) is the lithostatic pressure at depth z in the nonthickened lithosphere, L is the initial depth of the lithosphere-asthenosphere boundary, P, is the lithostatic pressure at the lithosphere-asthenosphere boundary, g is the acceleration of gravity, and pa is the asthenosphere density. If thickening involves the crust only, the stress difference is given by: AT=
(y2-
1) i?‘(z) I
dz-
5
aI Pl. -P, gP,
1
where y is the crustal thickening factor, M and L denote initial depth of Moho and asthenosphere,
PRINCIPAL
HORIZONTAL
P, and P, are the initial lithostatic pressure at Moho and the base of the lithosphere. The deviatoric stress distribution induced by 100% homogeneous thickening of the lithosphere is compared with the stress induced by crustal thickening only in Figs. la and lb. For both figures, the densities are 2.75, 2.95, 3.175 Mg me3 in the upper crust, lower crust, and lithospheric mantle, respectively. The density of the asthenosphere is 3.125 Mg mm3 in Fig. la and 3.15 in Fig. lb. The thicknesses before thickening are 20, 20, and 80 km for the upper crust, lower crust and lithospheric mantle, respectively. The stress is always tensile in the crust and compressional in the mantle. The lithospheric thickness and the density distribution are the key factors determining the magnitude of the stress and whether the resulting force will be tensional or compressive. Increasing the average density of the lithosphere by increasing its thickness or decreasing the crustal thickness, decreases the uplift and tensile stress in the crust and increases the compressional stress in the mantle. Homogeneous thickening could produce a resulting compressional force. If the crust is initially thin, homogeneous thickening could even bring subsidence (Murrell,
PRINCIPAL
STRESS
HORIZONTAL
STRESS
T HPa)
Lithospheric lhkkening = -3.1 10” N/m -5O-
Crustsi thbzkenmg= 5.2 10”
Crustal thickfmmg = 4 5 10”
_2501 (a)
N/m
N/m
J.
lb)
Fig. 1. Stress distribution for isostatically compensated thickened lithosphere after 100% thickening of the entire lithosphere or of the crust only. In (a), the densities are 2.75, 2.95, 3.175, and 3.125 Mg me3 in the upper crust, lower crust, Iithospheric’mantk and asthenosphere, respectively. In (b), the density of the asthenosphere is 3.15. Initial layer thicknesses are 20, 20, and 80 km. Note that the tensile stress drops in the lower crust and that the stress is compressive in lowermost crust and mantle.
J.-C. Mareschal/ Tectonophysics 238 (1994) 471-484
1986). If the density contrast between lithosphere and asthenosphere is small or if the lithosphere is initially thick, the resulting force is tensional, but remains small (i.e. < 1012 N m-l>. For crustal thickening only, the resulting force will always be tensile and on the order of 1012 N m-l. The trends outlined above and the order of magnitude of the stress are not modified for a more refined density distribution in the lithosphere, although the absolute value of the energy difference are slightly different. It is necessary to compare the stress distribution with the strength of the lithosphere to determine whether extension will take place over uniformly thickened lithosphere. If the wavelength of the topography and of the heterogeneities is not much larger than lithospheric thickness, the stress is smaller than for the long-wavelength approximation. The stress distribution can be calculated by assuming that the density differences are concentrated on horizontal boundaries (e.g. Fleitout and Froidevaux, 1982; Mareschal and Kuang, 1986). The estimates obtained in the long-wavelength approximation provide an upper limit on the stress which is adequate for the objectives of this paper.
3. Thermal evolution and strength of thickened lithosphere Geophysical observations and laboratory experiments have led to a better understanding of the rheology of the continental lithosphere (e.g. Kirby, 1983; Kirby and Kronenberg, 1987; Ranalli, 1987). The lithosphere is rheologically stratified and its mechanical behaviour depends on the composition and thermal regime. Experimental investigations of deformation properties of many rocks have yielded rheological laws that have been tested in a variety of tectonic settings. At low temperature and pressure and high strain rate, the brittle behaviour of rocks, described as frictional sliding, is governed by Byerlee’s law (Byerlee, 1978):
where a, is the shear stress required for sliding, (Y
475
is the coefficient of friction (approximately 0.85 for lithostatic pressure below 200 MPa and 0.6 above 200 MPa), a,, is the normal stress, and p, is the pore fluid pressure. For extension, the deviatoric stress 6a necessary to trigger movement along the fault is related to the lithostatic pressure, p, and the pore fluid pressure as follows: 24P-P,) &=
J1+;;“+1
For compression, the deviatoric stress is given by: 24P-P,> 6a=
di-s-1
Assuming that the pore fluid pressure is hydrostatic and that the ratio of pore fluid to lithostatic pressure is constant, the deviatoric stress required to trigger frictional sliding increases with pressure and depth at a rate of about 15 MPa km- ’ for extension and 60 MPa km- ’ for compression. Such estimation of the deviatoric stress necessary for failure is based on several’ simplifying assumptions: the vertical stress is a principal stress whose magnitude is the lithostatic pressure, the fluid pressure is the weight of a column of water extending to the surface, the orientation of the fault is that given by frictional theory, there is no cohesion on the fault, and the coefficient of friction is given by Byerlee’s law. Extrapolating Byerlee’s law to depths greater than a few km implies faults that are strong. The validity of such extrapolation has caused considerable debate (see for instance Lachenbruch and Sass, 1992; Zoback and Healy, 1992). Several authors have suggested that the strength of the fault is reduced by local high fluid pressure (Scholz, 1989; Byerlee, 1990). Alternatively, other authors have speculated that Byerlee’s law breaks down at depth (Carter and Tsenn, 1987) but have not suggested an alternative. It is recognized that this is an outstanding problem but, in the present state of knowledge, there is no alternative to Byerlee’s law to estimate fault strength at depth. In the intermediate stress regime, which is often assumed to hold for stress smaller than 0.01 shear modulus, steady-state creep is the domi-
.1.-C: Mareschal / Tectonophgsics
476
238 (19941 471-484
nant deformation mechanism. Laboratory data are fit by a relationship of the type (Weertman, 1978): i =Aun
exp( -H/RT)
2 is the strain rate, u is the stress, A is a material constant, n is a constant between 3 and 5, H is the activation enthalpy for creep, R is the gas constant (R = 8.3 J mol- ’ K-l), and T is ther-
modynamic temperature. This non-linear relationship can be used to determine the stress necessary to maintain a given strain rate: g=
i i A 1
1/II
! i
J
exp( H/nRT
)
The relationships above can be used to determine the minimum stress necessary to maintain a given strain rate provided that the composition and the temperature profile of the lithosphere are known. For rocks of granitic composition, which are common in the upper crust, the parameters of the creep law have been determined by Carter et al. (1982). The parameters in the stress rate of strain relation are: log A = -3.7 MPa-” s-l, n = 1.9, and H = 141 kJ mol-‘. Wilks and Carter (1990) have studied the rheology of rocks of lower-crustal origin and determined the parameters of the relationship of stress and rate of strain. For the Pikwitonei granulites, these parameters are: n = 4.2, A = 1.4 x lo4 MPa-” s-‘, and H = 445 kJ mol- ‘. From a study of deformation creep in dunite, which may have a rheology similar to that of the lithospheric mantle, Post (1977) obtained the following parameters for the stress-strain rate relationship: n = 3, A = 4.3 X lo2 MPa-” s-l, and H = 527 kJ mol- ‘. Experimental data for the flow of olivine have been published by many workers (see Kirby and Kronenberg, 1987, for a review) and yield effective viscosity estimates similar to those of dunite at mantle conditions: n = 3.5, A = 3 x lo4 MPa-” s-l, and H = 533 kJ mol-‘. The parameters of dunite are often used for the mantle rheology because they yield an effective viscosity in the range of 1021-1020 Pa s at the base of the lithosphere. Fig. 2 compares the variation in strength for granite, the Pik-
15lxl
Fig. 2. Strength of granite (solid line), granulite blotted ii&, and dunite (dash-dotted line) for temperatur&x%ween 500 and 1WC (i.e. stress required to maintain a strain rate of 2x10-‘6 s-1).
witonei granulites, and dry dun&e, in the 500 to 1000°C temperature range and at a strain rate of 2 x lo-l6 s-‘. The strength is here defined as the stress required to maintain the strain-rate of 2 X lo-l6 s- ‘. The strength of the lithosphere at any depth is thus the minimum between the stress for brittle deformation given by Byerlee’s law and the stress required to maintain a given strain rate. It depends on composition, pressure and temperature. Because the stress-strain relationship depends strongly on temperature, the stress required to trigger extension depends on the assumed temperature profile. The temperature distribution in the lithosphere depends on surface heat flow, on the distribution of heat sources in the crust, and on thermal conductivity of the crust. Except for surface heat flow, none of these parameters is directly measured in the field and there is a wide range of thermal models compatible with continental heat flow data. Recently, Pinet et al. (1991) have compiled all available data on heat generation in continental rocks to interpret heat flow data from eastern Canada. They concluded that heat generation in the crust is the largest contribution to surface heat flow in stable continental regions and that the mantle heat flow is low (12 mW m-*1. This estimate is lower than tradition-
J.-C. Mareschal/ TEMPERATURE
TENSILE STRENGTH
T (‘C) 600
o”
Time
Strength(MPa) low
15w
0
100
= 0 MVrs
-60
-60
P
ii-‘*
-ml
:\
102
Amalachians
10’
F 1.2 lOI
-160
-150
N/m
Total strecqth
Strain rate 2 1O-‘8 -MO t
Tectonophysics 238 (1994) 471-484
-MO
se’
t
Fig. 3. Temperature and rheological profile for the Appalachians. The temperature profile follows that of Pinet et al. (1991). The strength is calculated assuming a rheology of granite for the upper crust, granulite for the lower crust, and dunite in the mantle. The strength is the lowest between the frictional stress and the stress to maintain a strain rate of 2x lo-‘6 s-1.
ally assumed for heat flow from the mantle beneath stable continental provinces (20 mW m-*1. Fig. 3 shows the geotherm calculated by Pinet et al. (1991) for the Appalachians and the resulting strength of the lithosphere at 2 x lo-l6 s-r strain rate. The temperature profile is calculated for the average surface heat flow in the Appalachians, 55 mW m-*; crustal heat sources are distributed between a layer of young granites 8 km thick with 2.5 ~.LWme3 heat generation, a 10 km layer of tonalitic composition with heat generation 1.1 PW rnp3, and 30 km of granulitic lower crust with 0.4 PW rnm3. The thermal conductivity was assumed to be 2.0 W m- ’ K- ‘. The lower crust appears brittle up to 35 km; the strength decreases in the lowermost part of the crust which is ductile. The mantle below Moho is stronger but its strength decreases below 55 km. Integrating the stress envelope yields the total tensile strength of the lithosphere, 1.2 X 1013 N m-l, which is higher by one order than the difference in potential energy density between the Appalachians and the surrounding region. It can be noted that,
471
throughout most of the crust, the strength is larger than the tensile stress. The strength of the lithosphere depends on the temperature profile. Because the thickened crust produces more heat, the equilibrium heat flow will be higher, resulting in higher equilibrium temperature throughout the crust and mantle. On the other hand, the temperature profile of instantly thickened lithosphere is simply stretched. Before new equilibrium conditions are established, the thickened lithosphere will be stronger. The effect of stretching the temperature profile competes with increased crustal heat production. The temperature in thickened crust and lithosphere was calculated to better assess the net effect of thickening on the strength of the lithosphere. The following simplified assumptions were made to calculate the temperature profile: (1) before thickening, the lithosphere is in equilibrium; (2a) thickening is homogeneous throughout the lithosphere or (2b) the crust is thickened but the mantle is not affected; (3) heat is transported by conduction; and (4) the temperature is constant at the base of the lithosphere (1350°C isotherm). The temperature is determined by the solution of the heat equation: aT
aT
a*T
H
--$+L’z=K---g+PC
where t is time, z is depth, v is the vertical velocity, K is the thermal diffusivity, p is density, H is heat generation, and C is the specific heat. The initial equilibrium temperature is given as: T(z)
= To -t /,
where To is surface temperature, q,, is surface heat flow, and K is thermal conductivity. In the finite difference scheme used to solve the heat equation, grid points are attached to the material and the advection term disappears. The calculations were done for two different values of surface heat flow and initial conditions. The standard model assumes that surface heat flow is 52 mW m-* and that the crustal heat sources are distributed between three layers: an
478
.I.-C. Mareschai / Tectonophysics 238 (19941 471-484
enriched 8 km thick layer with 2.5 PW rnm3, a 10 km tonalitic layer with 1.1 PW rnw3, and the lower crust with 0.4 @W mS3; the heat flow from the mantle is 12 mW me2. This model is similar to that proposed by Pinet et al. (1991) for eastern Canada. A model with 60 mW rnp2 surface heat flow and the same distribution of heat sources leads to mantle heat flow of 20 mW mm2 and higher crustal temperatures. The thermal conductivity was assumed to be 2.0 W m -’ K- *. Higher
TEMPERATURE
TENSILE STRENQTH s1rangttlwP&t)
T PC)
values of the thermal conductivity would lead to lower temperatures and increase lithospheric strength. Fig. 4a shows the initial geotherm and the stress envelope for the standard model. The strength of the lithosphere for 2 X lo-l6 s- ’ strain rate increases all the way down to 60 km. The integrated strength is 2.7 x lo*” N m-‘. Fig. 4b shows the geotherm and the stress envelope after 40 Myears, when the lithosphere has been
TEMPERATURE T (‘C)
TENSILE STRENGTH s!renQthmm)
2.7 1013 N/m -150 -
-150 -
Total alreftgth
~0 = 30 mW.m“
Strain rat* 2 to-** -200 -
-2oo-
i’
strain rcste2 fo-‘” s-1 Ia)
TEMPERATURE T VW
04
TENSILESTRENGTH streneth wPa>
Fig. 4. Temperature and rheokqical profile for stable continental lithosphere with surface heat flow of 50 mW rnT2: (a) before thickening, (b) at&r 100% hom&meous thickening in 40 Myears, and (c) after 100% thickening of the crust c&y in 4t.biyears.
J.-C. Mareschal / Tectonophysics 238 (1994) 471-484
homogeneously thickened by 100%. Fig. 4c shows the geotherm and the stress envelope after 100% thickening of the crust only in 40 Myears. Homogeneous thickening increases the strength of the lithosphere to 6.2 x 1013 N m-‘: this is greater than the potential energy by more than one order. For crustal thickening, the strength remains constant (2.7 X 1013 N m-l> and is about one order above the potential energy. At any depth
TENSILE
TEMPERATURE
below the shallowest 5-10 km, the strength of the crust is higher than the tensile stress. In the mantle, where the strength decreases, the stress is compressional. It appears that with these initial conditions, extension would never follow lithospheric or crustal thickening. The calculations were carried out with different shortening rates. They showed that the lithospheric strength decreases only when shortening rates are smaller by
two
TENSILE
TEMPERATURE
STRENGTH
0
15m 7
Id
100
-54 ,-
P t f
STRENGTH
Strength IMPa)
T (‘C)
Strength (MPa)
T t*C)
479
-1M I-
10’
5
-1m -
B
-160
-150 -
-
/
1.0 1013 N/m Total strength
-lY O
1.0 1013 N/m
Total strength
q. = 60 mW.m?
stra,n rat* 2
-2COL
-2wJ
lo-'6
nomogenaous
s-1
1
Strain rate 2 lo-l6
se’
thickenmg
(a)
-20 O-
TENSILE
TEMPERATURE
(b)
STRENGTH
Strength (MPa)
T (‘0
3.1 10"
N/m Total streqth
-160
t
L
Strain rate 2 1O“8 se’
Crustal thickening -MO
(d
Fig. 5. Temperature and rheological profiles for continental lithosphere with 60 mW m-* surface heat flow: (a) initiril profiles, (b) after 100% homogeneous thickening in 40 Myears, and Cc) after 100% thickening of the crust in 40 Myears.
480
J.-c’. Mareschal/ Tectonophysics238 (1994) 471-484
one order of magnitude (i.e. doubling crustal thickness would take 400 Myears) and if no erosion occurs. The initial temperature distribution is critical in determining the strength of the lithosphere. Fig. 5a shows the temperature distribution and stress envelope with the initial condition corresponding to a hotter lithosphere (the surface heat flow is 60 mW me2, the crust has the same thermal structure as in the standard model and heat flow from the mantle correspondingly increased to 20 mW mP2). This change in initial conditions leads to a weaker lithosphere with a total strength of 1.0 x 1013 N m- ‘. Fig. 5b shows the temperature and the strength of the lithosphere after homogeneous thickening by 100% in 40 Myears. Fig. 5c shows the temperature and strength after 100% thickening of the crust only in 40 Myears. For such initial conditions, homogeneous lithospheric thickening does not increase the strength of the lithosphere and crustal thickening only has reduced the strength of the lithosphere to 3 X 101* N m-l. For this example, the tensile stress is greater than the strength in most of the crust and it could produce extension. The initial temperature required for crustal thickening to bring about extension is high but not extreme. It thus appears that, for an appropriate initial temperature distribution, crustal thickening only could indeed bring the conditions for extension. The stress available in homogeneously thickened lithosphere varies with depth: the tensile stress is highest in the upper crust, it decreases in the lower crust, and it becomes compressional in the mantle. The distribution of stress and strength of the lithosphere limits extension to the topmost crust, and hampers lithospheric-scale extension. The effect of erosion has not been included in these calculations; erosion steepens the temperature gradient in the shallow crust but has little effect in the lower crust. In addition, if very high rates of erosion are assumed, the rate of thickening required to double crustal thickness would be even larger, and would lead to a colder lower crust and mantle. The effect of shear heating has been debated
(e.g. Molnar et al., 1983; Molnar and England, 1990 and references therein). An upper limit on the heat produced by friction can be obtained by assuming that the work done by the tectonic forces is entirely converted into heat:
dQ -
where F is the total force on a lithospheric column and i is the strain rate. If the force is 2 x 1Or3 N m-l, and the strain rate is 5 X 10-l” SK’, friction could produce as much as 10 mW mw2. This is a large value, but still smaller than the increased heat production in the crust, which is not sufficient to heat rapidly the lithosphere. Indeed, this additional heat distributed uniformly in the lithosphere converts in a rate of heating of 0.5 x lo-‘*“C s-r (i.e. about 15°C Myear-‘). Shear heating may cause large effects locally but it is not sufficient to heat the lithosphere. The intrusion of a significant volume of magma into the lithosphere is unlikely in a compressional context. The volume of magma necessary to heat the lithosphere can also be estimated. The heat transported by the magma can be estimated at about 60 kJ kg-’ (assuming that the latent heat is 40 kJ kg-’ and the specific heat 700 J kg-’ “C-I). A volume of magma corresponding to 1% of the volume of the lithosphere would raise the average lithospheric temperature by only 1°C. In order to heat the lithosphere and lower its strength, a volume of magma representing a significant volume of the lithosphere is required. This seems difficult in a compressional context and replacing the lithospheric mantle by asthenosphere is a more feasible alternative.
4. Efkct of removal of the litbospherk masttIe Removal of. the lithospheric mantle by delamination (Bird, 1979) or by convection (Houseman and England, 1986; England and Houseman, 1986) modifies the distribution of stress and the temperature in the lithosphere. The stress distribution after 100% thickening of the lithosphere and complete removal of the lithospheric mantle is shown in Fig. 6 for the same two density
J.-C. Mareschal/ Tectonophysics 238 (1994) 471-484
PRINCIPAL
HORIZONTAL
STRESS
T (Mpa)
Energy dift = 6.5 10”
N/m
Energy Utt = 7.6 10”
N/m
-2OOL Fig. 6. Stress distribution in thickened crust after removal of lithospheric mantle after 100% thickening. The densities are 2.75, 2.95 in the upper and lower crust. The density of the asthenosphere is 3.15 or 3.125 Mg me3.
distributions as in Fig. 1. The stress is much larger than after lithospheric or crustal thickening and it is tensile all the way down to the initial lithosphere-asthenosphere boundary. The total stress (difference in potential energy density) is on the order of 1013 N m-‘. Fig. 7 shows the temperature profile and the strength of the lithosphere that was thickened by 100% and delaminated at 40 Myears. The temTENSILE
TEMPERATURE
perature profiles are calculated just after the delamination (Fig. 7a) and 10 Myears after delamination (Fig. 7b). The total strength of the lithosphere drops very rapidly to 1012 N m-l, and is one order less than the energy available. Also, the stress is tensile throughout the lithosphere, including the now weaker lower crust and mantle. Removal of the lithospheric mantle would always bring about the conditions permitting extension to start. If extension begins, the thermal effect of extension will be the opposite of that of compression. For rapid extension, the steepening of the geotherm dominates over the effect of reduced crustal heat production and the strength of the lithosphere decreases. The tensile stress is reduced by crustal thinning but is maintained by a hot and buoyant mantle. Extension would thus proceed in conditions similar to those of the present Basin and Range (Lachenbruch and Sass, 1978) unless it is opposed by plate boundary forces.
5. Conclusion Uniform thickening of the lithosphere collision produces a tensile stress regime thickened crust, and compressional stress mantle. Depending on initial lithospheric TEMPERATURE
STRENGTH
TENSILE
T (‘Cl)
Strength (MPa)
T (‘0
481
“/ -50
i
-150 -
1.2 1013 N/m Total strenpth
-150 -
-150
~0 = 50 mW.6’
L
Strain rate 2 lO+
-2W
102
too
Time = 40 Myra
-60
STRENGTH
Strength WPa) 0
o”W
-200
10’
F I
1.910'2
Nlrn Total strength
Strain rate 2 lo-‘”
6’ (4
during in the in the thick-
6’
Fig. 7. Temperature and rheological profiles after 100% thickening in 40 Myears and removal of the lithospheric mantle.
(b)
187
J.-C. Mureschal / Tectonophvsics 238 (1994) 471-484
ness and density distribution, the resulting force can be tensional or compressional. It will be on the order of lo’* N m-‘. If shortening and crustal thickening occur at a reasonable rate (3 to 5 X lo-l6 s-l), the thickened crust and lithosphere remain relatively cold. The strength of the lithosphere remains larger than the tensile stress, except in the very shallow crust. In the mantle, where the strength drops, the stress is compressive. The integrated strength is at least one order of magnitude larger than the potential energy difference. It seems implausible that, at the release of compressive tectonic forces, lithosphericscale extension could start. Erosion will progressively reduce the topography and the stress difference, before increased crustal heat production warms and weakens the lithosphere. If thickening involves the crust only, the resulting force will always be tensional and larger than for homogeneous lithospheric thickening (i.e. 5 X lo’* N m-l). The strength of the lithosphere does not increase for crustal thickening, and depending on the initial conditions, it may be less than the tensile force. It appears that the lithosphere is too strong for extension to take place if the heat flow is 50 mW me2 or less, but that extension could occur for heat flows greater than 60 mW m-*. Alternatively, the removal of the lithospheric mantle produces uplift and increases the stress which will be tensional throughout the lithosphere. Also, heating of the crust reduces its strength. If compressional tectonic forces subside, the tensile stress available throughout most of the lithosphere is on the order or larger than the strength of the lithosphere. Extension can proceed until the stress diminishes or until it is counteracted by plate boundary forces.
Council (Canada) through an operating grant to the author is gratefully acknowledged.
Appendix-deviatoric stress induced by non-homogeneous lithospheric thickening Let p(r) be the density distribution in the lithosphere before thickening, where z is positive downward and z = 0 is the Earth’s surface before thickening, z = M is Moho, and z = L is the base of the lithosphere. The lithostatic pressure is P, at Moho and PL at the base of the lithosphere. The asthenosphere density is pa. The crustal thickening Factor is y and the lithospheric mantle thickening factor is 6. After isostatic adjustment, the Earth’s surface is z = - h, Moho is at depth z = - h + yM, and the base of the lithosphere is at depth z = - h + yM + 6(L - Ml The lithostatic pressure is yP, at Moho and yP, +6(P, - P,) at the base of the lithosphere. Isostatic condition requires: P,+gp,[-h+yM+6(L-M)-L]=yPh4++(PI_-PPM)
therefore, the uplift is given by: h=(&l)(L-$)+(y-S)(M-2)
The energy difference is given as: AT=/
-h+yM+S(L-M)P1(z)dZ --;-
h+YM+S(L-M$&)dz
where P,(z) is the lithostatic pressure in the thickened lithosphere and the P,(z) is the lithostatic pressure before thickening. tt gives: AT=/
-h+yMdzl’hgp,(z’)dz i;_-~h++~~+bll~‘dz[yPu+~~~iI~g~,(zf)dz~] -hM dzcgPo(z’)
dz’
-/:dz[P,+~~gp,(l’)dz’] -~~‘L-~‘+y~-hdz(PI+lLigp~dz’) where p0 and p1 denote the density distribution before and after thickening. Integrating the equation yields:
Acknowledltements
The author is thankful to Francis Lucazeau for a very thorough and thoughtful review. Helpful comments by Olga I. Parphenuk and Catherine Meriaux are greatly appreciated. The support of the Natural Sciences and Engineering Research
AT = yz&MPO(z) dz + yGP,(L
- M)
+62/ML[PO(z)-P41]dz-~~P0(z)dz-PPh((L-M) -jML[P&)-Py]dz-PL[S(L-M)+yM-h-L] -~[S(L-M)+yM-h-L]Z
J.-C. Mareschal / Tectonophysics 238 (1994) 471-484
It gives: AT=(y2-l)/o~P0(~)dz+(SZ-l)/--[Pa(z)-Phl]dz +(yS-l)&(L-M)-[(S-l)P,_+(y-6)&]
If thickening is uniform (y = 6), the stress difference gives: loLp,(z)dz-$
1
a If the crust only is thickened and the lithospheric mantle is not affected (6 = l), the stress gives: AT=(y*-1)
h”P(z)dz-$ [
1 tA-PM, 1 gP,
The above formulas can be used to demonstrate how some parameters affect the total stress. In particular, it is easy to see that lower asthenosphere density will decrease the total stress. It is clear also that, if the lithospheric mantle is denser than the asthenosphere, crustal thickening only results in larger isostatic uplift and stress than homogeneous thickening.
References Artemjev, M.E., Bune, V.I., Dubrovski, V.I. and Kambarov, N.S., 1972. Seismicity and isostasy. Phys. Earth Planet. Inter., 6: 2.56-262. Artyushkov, E.V., 1973. The stresses in the lithosphere induced by crustal thickness inhomogeneities. J. Geophys. Res., 78: 7675-7708. Bird, P., 1979. Continental delamination and the Colorado Plateau. J. Geophys. Res., 84: 7561-7571. Bird, P., 1991. Lateral extrusion of lower crust from under high topography, in the isostatic limit. J. Geophys. Res., 96: 10,275-10,286. Bird, P. and Piper, K., 1980. Plane-stress finite element models of tectonic flow in southern California. Phys. Earth Planet. Inter., 21: 158-175. Brace, W.F. and Kohlstedt, D.L., 1980. Limits on lithospheric stress imposed by laboratory experiments. J. Geophys. Res., 85: 6248-6252. Buck, W.R., 1991. Modes of continental lithospheric extension. J. Geophys. Res., 96: 20,161-20,178. Byerlee, J.D., 1978. Friction of rocks. Pure Appl. Geophys., 116: 615-626. Byerlee, J.D., 1990. Friction, normal pressure, and fault normal compression. Geophys. Res. Lett., 17: 2109-2112. Carter, N.L. and Tsenn, M.C., 1987. Flow properties of continental lithosphere. Tectonophysics, 136: 27-63. Carter, N.L., Anderson, D.A., Hansen, F.D. and Kranz, R.L., 1982. Creep and creep rupture of granitic rocks. Am. Geophys. Union, Geophys. Monogr., 24: 61-82.
483
England, P.C., 1983. Constraints on extension of continental lithosphere. J. Geophys. Res., 88: 1145-1152. England, PC. and Houseman, G.A., 1986. Finite #train calculations of continental deformation, II. Comparison with the India-Asia collision. J. Geophys. Res., 91: 3664-3676. England, P.C. and Houseman, G.A., 1988. The mechanics of the Tibetan Plateau. Philos. Trans. R. Sot. London, Ser. A, 326: 301-319. England, P.C. and Houseman, G.A., 1989. Extension during convergence with application to the Tibetan Plateau. J. Geophys. Res., 94: 17,561-17,579. England, P.C. and McKenzie, D.P., 1982. A thin vrscous sheet model for continental deformation. Geophys. J.R. Astron. Sot., 70: 295-321. Fleitout, L. and Froidevaux, C., 1982. Tectonics and topography for a lithosphere containing density heterogeneities. Tectonics, 1: 21-56. Gaudemer, Y., Jaupart, C. and Tapponnier, P., 1988. Thermal control on post-erogenic extension in collision belts. Earth Planet. Sci. Lett., 89: 48-62. Houseman, G.A. and England, P.C., 1986. Finite strain calculations of continental deformation, I. Method and general results for convergent zones. J. Geophys. Res., 91: 36513663. Houseman, G.A., McKenzie, D.P. and Molnar, P., 1981. Convective instability of a thickened boundary layer and its relevance for the thermal evolution of continental convergence belts. J. Geophys. Res., 86: 6115-6132. Jeffreys, H., 1929. The Earth. Cambridge University Press, Cambridge, 2nd ed., 346 pp. Kirby, S.H., 1983. Rheology of the lithosphere. Rev. Geophys. Space Phys., 21: 1458-1487. Kirby, S.H. and Kronenberg, A.K., 1987. Rheology of the lithosphere: selected topics. Rev. Geophys., 25: 1219-1244. Kusznir, N.G. and Park, R.G., 1984. Intraplate lithosphere deformation and the strength of the lithosphere. Geophys. J.R. Astron. Sot., 70: 513-538. Kusznir, N.G. and Park, R.G., 1987. The extensional strength of the continental lithosphere: its dependence on geothermal gradient, and crustal composition and thickness. In: M.P. Coward, J.F. Dewey and P.L. Hancock (Editors), Continental Extensional Tectonics. Geol. Sot. Spec. Publ., 28: 35-52. Lachenbruch, A.H. and Sass, J.H., 1978. Models of an extending lithosphere and heat flow in the Basin and Range Province. Geol. Sot. Am. Mem., 152: 209-250. Lachenbruch, A.H. and Sass, J.H., 1992. Heat flow from Cajun Pass, fault strength, and tectonic implications. J. Geophys. Res., 97: 4995-5015. Love, A.E.H., 1911. Some Problems of Geodynamics. Cambridge University Press, Cambridge, Dover reprint, 180 pp. Mareschal, J.C. and Kuang, J., 1986. Intraplate stresses and seismicity: the role of topography and density heterogeneities. Tectonophysics, 132: 153-162. Molnar, P. and England, P., 1990. Temperatures, heat flux, and frictional stress near major thrust faults. J. Geophys. Res., 95: 4833-4856.
484
J.-C. Mareschal/
Tectonophysics 238 (19941 471-484
Molnar, P., Chen, W.-P. and Padovani, E., 1983. Calculated temperatures in overthrust terrains and possible combination of heat sources responsible for the tertiary granites in the Himalaya. J. Geophys. Res., 88: 6415-6429. Murrell, S.A.F., 1986. Mechanics of tectogenesis in plate collision zones. In: M.P. Coward and AC. Ries (Editors). Collision Tectonics. Geol. Sot. Spec. Publ., 19: 95-111. Parphenuk, O.I., Dechoux, V. and Mareschal, J.C., 1994. A finite element model of evolution for the Kapuskasing structural zone. Can. J. Earth Sci., in press. Percival, J.A., 1990. A field guide through the Kapuskasing uplift, a cross section through the Archean Superior Province. In: M.H. Salisbury and D.M. Fountain (Editors), Exposed Cross-Sections of the Continental Crust. Nato ASI Ser., 317: 227-283. Pinet, C., Jaupart, C., Mareschal, J.C., GariCpy, C., Bienfait, G. and Lapointe, R., 1991. Heat flow and structure of the lithosphere in the eastern Canadian Shield. J. Geophys. Res., 96: 19,941-19, 963. Post, R.L., 1977. High temperature creep of Mt Burnet dunite. Tectonophysics, 42: 75-110. Ramberg, H., 1981. Gravity, Deformation, and the Earth’s Crust. 2nd ed. Academic Press, New York.
Ranalli, G., 1987. Rheology of the Earth. Allen and Unwin, Boston, Mass., 366 pp. Scholz, C.H., 1989. Mechanics of faulting. Annu. Rev. Earth Planet. Sci., 17: 319-328. Sonder, L.J. and England, P.C., 1986. Vertical averages of rheology of the continental lithosphere: relation to thin sheet parameters. Earth Planet. Sci. Lett., 77: 81-90. Sonder, L.J., England, P.C., Wernicke, B.P. and Christiansen, R.L., 1987. A physical model for Cenozoic extension of western North America. In: M.P. Coward, J.F. Dewey and P.L. Hancock (Editors), Continental Extensional Tectonics. Geol. Sot. Spec. Publ., 28: 187-201. Weertman, J., 1978. Creep laws for the mantle of the Earth. Philos. Trans. R. Sot. London, Ser., A 288: 9-26. Wilks, K.R. and Carter, N.L., 1990. Rheology of some continental lower crustal rocks. Tectonophysics, 182: 57-77. Zhou, S. and Sandiford, M., 1992. On the stability of isostatitally compensated mountain belts. J. Geophys. Res., 97: 14,207-14, 221. Zoback, M.D. and HeaIy, J.H., 1992. In situ stress measurements to 3.5 km depth in the Cajun Pass scientific research borehole: implication for the mechanics of crustal faulting, J. Geophys. Res., 97: 5039-5057.
Tectonophysics 238 (1994) 471-484
Thermal regime and post-erogenic Jean-Claude GEOTOP,
University of Quebec, Monhal,
extension in collision belts
Mareschal
P.O. Box 8888, sta. A, Mont&al. H3C 3P8, Canada
Received 10 May 1993; accepted 7 January 1994
Abstract In order to assess the conditions leading to post-erogenic extension, the temperature and strength of the lithosphere during continental collision are calculated. The calculations assume that heat is transported by conduction and either that the lithosphere is homogeneously thickened or that only the crust is thickened during the collision. Despite increased crustal thickness and heat production, the temperature does not increase if the rate of shortening is moderate (5 x lo-l6 s-l, leading to 100% increase in crustal thickness in 40 Myears). The temperature distribution is used to determine a rheological profile that is compared with the stress induced by compensated topography. The calculations show that, for homogeneous lithospheric thickening, the strength of the lithosphere increases and is higher than the tensile stress except in the shallow crust. The total strength of stable continental lithosphere at the end of shortening is on the order of 1013 N m-‘; it is larger by one order than the force induced by compensated topography (10” N m-l). It appears that homogeneous lithospheric thickening would not lead to post-erogenic extension unless the initial conditions are very special (with the lithosphere hotter than normal). For crustal thickening only, the strength of the lithosphere decreases slightly and is on the same order as the tensile stress. Extension does not necessarily follow from thickening of the crust only but it could take place for a relatively wide range of initial conditions (with initial surface heat-flow 60 mW mm2 or higher). Alternatively, an event such as rapid removal of the mantle lithosphere by delamination or small-scale convection would increase the tensile stress, heat rapidly the lithosphere, reduce its strength, and always trigger extension.
1. Introduction It has long been recognized that diffuse extension can develop during the late stages of evolution of collision belts. Several papers in this volume present evidence for post-erogenic extension in different collision belts. The suggestion that the topography of erogenic belts induces a tensile stress regime and could trigger extension dates back to the work of Love and Jeffreys. Love
(1911) calculated the stress induced by isostatitally compensated topography in an elastic Earth. Jeffreys (1929) used similar calculations and pro-
posed that the tensile stress regime could cause the collapse of mountain belts. More recently, several authors investigated the stress induced by compensated topography in an elastic lithosphere overlying the asthenosphere. Artemjev et al. (1972) suggested that the stress induced by mountain belts could explain some intraplahe earthquakes. Artyushkov (1973) suggested that large stress induced by compensated topography could not be sustained by the lithosphere and would lead to extension. Fleitout and Froidevavx (1982) have also investigated the stress inducqd in the lithosphere by different types of density hetero-
0040-1951/94/$07.00 0 1994 Elsevier Science B.V. All rights reserved SSDI 0040-1951(94)00074-J
J.-C Mawschal / Tectotwphysics 238 (IYY4) 471-484
472
geneities and they suggested that it could drive different types of tectonic activity. When the stress of compensated topography is no longer balanced by plate tectonic stresses, it could trigger lithospheric-scale extension if it is sufficiently large to overcome the strength of the lithosphere. The deformation induced by lithospheric thickening was investigated with thin sheet models which use vertical averages of the stress and the rheology. In the study of Bird and Piper (1980) where the vertical velocity is zero, the deformation pattern is caused by lateral extrusion of crustal material. In the model by England and McKenzie (1982), the vertical velocity does not vanish and the deformation pattern is caused by variations in crustal thickness: the stress induced by crustal thickening triggers extension and lateral movement in front of the orogen. In these calculations, the rheology of the sheet follows a power law of the form: (r)
=B&l/n-l)(&j)
where ( rij) is the vertically averaged stress, (iii) is the vertically averaged strain rate and & is the second invariant of the strain rate tensor; B and n are constants that depend on the rheology of the lithosphere. The relationship between the parameters of the thin sheet rheology and the actual rheology of the lithosphere was investigated by Sonder and England (1986). They concluded that the rheology can indeed be approximated by a single power law which is determined by the thermal state of the mantle and on the stress in the upper crust. Sander et al. (1987) examined how the temperature and rheology of the thickened lithosphere vary with time; they concluded that, depending on the initial thermal state of the lithosphere, a delay can occur between the end of compression and the beginning of extension. These authors suggested that extension in the Basin and Range followed the end of compression by 20-40 Myears because of the time necessary for heating and softening of the lithosphere. England (1983) showed that the thermal regime determines whether the lithosphere can fail in extension and rifting can occur. He suggested that cooling of lithosphere will rapidly stop extension unless it takes place at a very high
rate. Similar conclusions were reached by Kusznir and Park (1984, 19871 who calculated the total strength of the lithosphere and compared it with the tectonic forces causing extension. They concluded that extension will continue in the zone that is weakest provided that it proceeds at such a high rate that the lithosphere does not cool; at a low rate of extension, the extended lithosphere becomes stronger and the locus will migrate to a new weak zone. Murrell (1986) showed that the initial crustal thickness determines whether shortening results in uplift and tensile stress or subsidence and compressiona stress. The control of crustal thickness and thermal regime on the mode of extension was further investigated by Buck (1991) who recognized three modes of extension (core complex, wide rift, and narrow rift) and suggested that a temporal progression should normally take place from core complex to narrow rift mode. The thermal structure of the lithosphere during crustal thickening was investigated by Gaudemer et al. (1988). These authors proposed that temperature increases in mountain belts because of increased heat production in the thickened crust. They presented two-dimensional calculations of the thermal regime during compression and they showed that the temperature increases provided that thickening occurs over a wide region (500 km) and at very low rate (1 mm yr-’ which implies 500 Myears for 500 km shortening). Zhou and Sandiford (1992) compared the tensile stress induced by crustal and lithospheric thickening with the total strength of the lithosphere. They concluded that, if Moho temperature is higher than 650-700°C the orogen will experience extensional collapse; alternatively, if the Moho temperature remains low, the mountain belt will be attenuated by erosion. Ramberg (1981) had suggested that crustal thickening can be attenuated by lower-crustal flow. Bird (1991) examined the effect of rheological layering in the lithosphere and suggested that high topography and changes in crustal thickness could be attenuated by lower-crustal flow with a time constant depending on Moho temperature and on the wavelength of the topography. He concurred with the conclusions of several studies that this GOIlapse will be most dramatic in regions where the
J.-C. Mareschal/
473
Tectonophysics 238 (1994) 471-484
lithosphere has been delaminated or actively thinned (i.e. Houseman et al., 1981; England and Houseman, 1988, 1989). There are several examples of compressional belts that did not experience lithospheric-scale post-erogenic extension. A crustal root is preserved beneath the Appalachians and some parts of the Grenville Front. The persistence of these roots suggests that post-erogenic extension was confined to the upper crust and did not involve the lower crust and mantle. A crustal root also seems to have persisted for 2000 Myears under the Kapuskasing structural zone, in the Superior Province of the Canadian Shield (Percival, 1990). The rheology and thermal conditions that lead to the formation and preservation of this crustal root have been discussed by Parphenuk et al. (1994). The objective of this paper is to discuss further the conditions leading to post-erogenic extension. The thermal regime and the rheology of the lithosphere will be determined for a range of thermal parameters compatible with present knowledge of the continental lithosphere. The conditions permitting post-erogenic extension can be assessed by comparison between the stress distribution and the rheology of the lithosphere. The temperature distribution during homogeneous and non-homogeneous lithospheric thickening is determined and a rheological profile is estimated. The calculations show that, for homogeneous thickening of the lithosphere at any geologically reasonable rate, the lithosphere does not heat sufficiently and it becomes stronger. If the temperature profile of stable continental lithosphere is assumed as initial condition, the strength is larger than the stress at depth below a few km, and the total strength of the lithosphere is one order larger than the tensile force. When thickening involves only the crust but not the lithospheric mantle, the total strength of the lithosphere decreases slightly during shortening; in addition, the tensile stress is larger throughout the crust, and the compressional stress is smaller in the mantle. Extension could thus take place if the lithosphere is sufficiently hot initially. Alternatively, the lithosphere could be weakened by rapid heating following removal of the litho-
spheric mantle by convection or delamination. The latter hypothesis is preferred because, after removal of the lithospheric root, the stress becomes tensile throughout the lithosphere and the force is larger than the tensile stress for any initial conditions.
2. Stress induced by lithospheric thickening If the wavelength of the compensated topography is large as compared with lithospheric thickness, the stress induced in the lithosphere by the surface loading and density heterogeneities is easily calculated. The deviatoric stress at given depth is the difference between the vertical and the horizontal stress. The vertical stress uZzr (in the long-wavelength approximation) is the local lithostatic pressure, and the horizontal stress a,, is the confining pressure (i.e. the lithostatic pressure in standard continental lithosphere away from topography and crustal density heterogeneities): u ZL
-
uxx =
j-;hgp( 2’) dz’ - /I, adz’)
dz’
0
where z is depth (z positive downward), h is the elevation, h, is the elevation of the reference continental lithosphere, p(z’) is the density distribution and pJ.z’) is the density distribution in the reference lithosphere. The elevation difference is determined by the isostatic equilibrium condition, i.e. the deviatoric stress (a,, - a,,) vanishes at the base of the lithosphere. By convention, the origin of the coordinate system coincides with the surface of the reference lithosphere (i.e. h, = 0). Integrating the stress over the entire lithospheric thickness yields the force per unit length:
F’=jhL[uzz(z’) -a,,(~‘)]
dz’
where L is the base of the lithosphere cr - a** = 0. The force per unit length &rsion of energy density; it is equivalent difference in potential energy per unit between the thickened and the reference sphere (e.g. Ramberg, 1981).
where has dito the surface litho-
473
J.-C. Marrschal / iktonopttysics 238 (1994) 471-484
The difference in potential energy of the thickened lithosphere can be calculated if the density distribution in the reference lithosphere is known. It is shown in the Appendix that this energy difference is: AT= (y’-
1) i?‘(z) I
dz - -$
d
1
where y is the thickening factor, P(z) is the lithostatic pressure at depth z in the nonthickened lithosphere, L is the initial depth of the lithosphere-asthenosphere boundary, P, is the lithostatic pressure at the lithosphere-asthenosphere boundary, g is the acceleration of gravity, and pa is the asthenosphere density. If thickening involves the crust only, the stress difference is given by: AT=
(y2-
1) i?‘(z) I
dz-
5
aI Pl. -P, gP,
1
where y is the crustal thickening factor, M and L denote initial depth of Moho and asthenosphere,
PRINCIPAL
HORIZONTAL
P, and P, are the initial lithostatic pressure at Moho and the base of the lithosphere. The deviatoric stress distribution induced by 100% homogeneous thickening of the lithosphere is compared with the stress induced by crustal thickening only in Figs. la and lb. For both figures, the densities are 2.75, 2.95, 3.175 Mg me3 in the upper crust, lower crust, and lithospheric mantle, respectively. The density of the asthenosphere is 3.125 Mg mm3 in Fig. la and 3.15 in Fig. lb. The thicknesses before thickening are 20, 20, and 80 km for the upper crust, lower crust and lithospheric mantle, respectively. The stress is always tensile in the crust and compressional in the mantle. The lithospheric thickness and the density distribution are the key factors determining the magnitude of the stress and whether the resulting force will be tensional or compressive. Increasing the average density of the lithosphere by increasing its thickness or decreasing the crustal thickness, decreases the uplift and tensile stress in the crust and increases the compressional stress in the mantle. Homogeneous thickening could produce a resulting compressional force. If the crust is initially thin, homogeneous thickening could even bring subsidence (Murrell,
PRINCIPAL
STRESS
HORIZONTAL
STRESS
T HPa)
Lithospheric lhkkening = -3.1 10” N/m -5O-
Crustsi thbzkenmg= 5.2 10”
Crustal thickfmmg = 4 5 10”
_2501 (a)
N/m
N/m
J.
lb)
Fig. 1. Stress distribution for isostatically compensated thickened lithosphere after 100% thickening of the entire lithosphere or of the crust only. In (a), the densities are 2.75, 2.95, 3.175, and 3.125 Mg me3 in the upper crust, lower crust, Iithospheric’mantk and asthenosphere, respectively. In (b), the density of the asthenosphere is 3.15. Initial layer thicknesses are 20, 20, and 80 km. Note that the tensile stress drops in the lower crust and that the stress is compressive in lowermost crust and mantle.
J.-C. Mareschal/ Tectonophysics 238 (1994) 471-484
1986). If the density contrast between lithosphere and asthenosphere is small or if the lithosphere is initially thick, the resulting force is tensional, but remains small (i.e. < 1012 N m-l>. For crustal thickening only, the resulting force will always be tensile and on the order of 1012 N m-l. The trends outlined above and the order of magnitude of the stress are not modified for a more refined density distribution in the lithosphere, although the absolute value of the energy difference are slightly different. It is necessary to compare the stress distribution with the strength of the lithosphere to determine whether extension will take place over uniformly thickened lithosphere. If the wavelength of the topography and of the heterogeneities is not much larger than lithospheric thickness, the stress is smaller than for the long-wavelength approximation. The stress distribution can be calculated by assuming that the density differences are concentrated on horizontal boundaries (e.g. Fleitout and Froidevaux, 1982; Mareschal and Kuang, 1986). The estimates obtained in the long-wavelength approximation provide an upper limit on the stress which is adequate for the objectives of this paper.
3. Thermal evolution and strength of thickened lithosphere Geophysical observations and laboratory experiments have led to a better understanding of the rheology of the continental lithosphere (e.g. Kirby, 1983; Kirby and Kronenberg, 1987; Ranalli, 1987). The lithosphere is rheologically stratified and its mechanical behaviour depends on the composition and thermal regime. Experimental investigations of deformation properties of many rocks have yielded rheological laws that have been tested in a variety of tectonic settings. At low temperature and pressure and high strain rate, the brittle behaviour of rocks, described as frictional sliding, is governed by Byerlee’s law (Byerlee, 1978):
where a, is the shear stress required for sliding, (Y
475
is the coefficient of friction (approximately 0.85 for lithostatic pressure below 200 MPa and 0.6 above 200 MPa), a,, is the normal stress, and p, is the pore fluid pressure. For extension, the deviatoric stress 6a necessary to trigger movement along the fault is related to the lithostatic pressure, p, and the pore fluid pressure as follows: 24P-P,) &=
J1+;;“+1
For compression, the deviatoric stress is given by: 24P-P,> 6a=
di-s-1
Assuming that the pore fluid pressure is hydrostatic and that the ratio of pore fluid to lithostatic pressure is constant, the deviatoric stress required to trigger frictional sliding increases with pressure and depth at a rate of about 15 MPa km- ’ for extension and 60 MPa km- ’ for compression. Such estimation of the deviatoric stress necessary for failure is based on several’ simplifying assumptions: the vertical stress is a principal stress whose magnitude is the lithostatic pressure, the fluid pressure is the weight of a column of water extending to the surface, the orientation of the fault is that given by frictional theory, there is no cohesion on the fault, and the coefficient of friction is given by Byerlee’s law. Extrapolating Byerlee’s law to depths greater than a few km implies faults that are strong. The validity of such extrapolation has caused considerable debate (see for instance Lachenbruch and Sass, 1992; Zoback and Healy, 1992). Several authors have suggested that the strength of the fault is reduced by local high fluid pressure (Scholz, 1989; Byerlee, 1990). Alternatively, other authors have speculated that Byerlee’s law breaks down at depth (Carter and Tsenn, 1987) but have not suggested an alternative. It is recognized that this is an outstanding problem but, in the present state of knowledge, there is no alternative to Byerlee’s law to estimate fault strength at depth. In the intermediate stress regime, which is often assumed to hold for stress smaller than 0.01 shear modulus, steady-state creep is the domi-
.1.-C: Mareschal / Tectonophgsics
476
238 (19941 471-484
nant deformation mechanism. Laboratory data are fit by a relationship of the type (Weertman, 1978): i =Aun
exp( -H/RT)
2 is the strain rate, u is the stress, A is a material constant, n is a constant between 3 and 5, H is the activation enthalpy for creep, R is the gas constant (R = 8.3 J mol- ’ K-l), and T is ther-
modynamic temperature. This non-linear relationship can be used to determine the stress necessary to maintain a given strain rate: g=
i i A 1
1/II
! i
J
exp( H/nRT
)
The relationships above can be used to determine the minimum stress necessary to maintain a given strain rate provided that the composition and the temperature profile of the lithosphere are known. For rocks of granitic composition, which are common in the upper crust, the parameters of the creep law have been determined by Carter et al. (1982). The parameters in the stress rate of strain relation are: log A = -3.7 MPa-” s-l, n = 1.9, and H = 141 kJ mol-‘. Wilks and Carter (1990) have studied the rheology of rocks of lower-crustal origin and determined the parameters of the relationship of stress and rate of strain. For the Pikwitonei granulites, these parameters are: n = 4.2, A = 1.4 x lo4 MPa-” s-‘, and H = 445 kJ mol- ‘. From a study of deformation creep in dunite, which may have a rheology similar to that of the lithospheric mantle, Post (1977) obtained the following parameters for the stress-strain rate relationship: n = 3, A = 4.3 X lo2 MPa-” s-l, and H = 527 kJ mol- ‘. Experimental data for the flow of olivine have been published by many workers (see Kirby and Kronenberg, 1987, for a review) and yield effective viscosity estimates similar to those of dunite at mantle conditions: n = 3.5, A = 3 x lo4 MPa-” s-l, and H = 533 kJ mol-‘. The parameters of dunite are often used for the mantle rheology because they yield an effective viscosity in the range of 1021-1020 Pa s at the base of the lithosphere. Fig. 2 compares the variation in strength for granite, the Pik-
15lxl
Fig. 2. Strength of granite (solid line), granulite blotted ii&, and dunite (dash-dotted line) for temperatur&x%ween 500 and 1WC (i.e. stress required to maintain a strain rate of 2x10-‘6 s-1).
witonei granulites, and dry dun&e, in the 500 to 1000°C temperature range and at a strain rate of 2 x lo-l6 s-‘. The strength is here defined as the stress required to maintain the strain-rate of 2 X lo-l6 s- ‘. The strength of the lithosphere at any depth is thus the minimum between the stress for brittle deformation given by Byerlee’s law and the stress required to maintain a given strain rate. It depends on composition, pressure and temperature. Because the stress-strain relationship depends strongly on temperature, the stress required to trigger extension depends on the assumed temperature profile. The temperature distribution in the lithosphere depends on surface heat flow, on the distribution of heat sources in the crust, and on thermal conductivity of the crust. Except for surface heat flow, none of these parameters is directly measured in the field and there is a wide range of thermal models compatible with continental heat flow data. Recently, Pinet et al. (1991) have compiled all available data on heat generation in continental rocks to interpret heat flow data from eastern Canada. They concluded that heat generation in the crust is the largest contribution to surface heat flow in stable continental regions and that the mantle heat flow is low (12 mW m-*1. This estimate is lower than tradition-
J.-C. Mareschal/ TEMPERATURE
TENSILE STRENGTH
T (‘C) 600
o”
Time
Strength(MPa) low
15w
0
100
= 0 MVrs
-60
-60
P
ii-‘*
-ml
:\
102
Amalachians
10’
F 1.2 lOI
-160
-150
N/m
Total strecqth
Strain rate 2 1O-‘8 -MO t
Tectonophysics 238 (1994) 471-484
-MO
se’
t
Fig. 3. Temperature and rheological profile for the Appalachians. The temperature profile follows that of Pinet et al. (1991). The strength is calculated assuming a rheology of granite for the upper crust, granulite for the lower crust, and dunite in the mantle. The strength is the lowest between the frictional stress and the stress to maintain a strain rate of 2x lo-‘6 s-1.
ally assumed for heat flow from the mantle beneath stable continental provinces (20 mW m-*1. Fig. 3 shows the geotherm calculated by Pinet et al. (1991) for the Appalachians and the resulting strength of the lithosphere at 2 x lo-l6 s-r strain rate. The temperature profile is calculated for the average surface heat flow in the Appalachians, 55 mW m-*; crustal heat sources are distributed between a layer of young granites 8 km thick with 2.5 ~.LWme3 heat generation, a 10 km layer of tonalitic composition with heat generation 1.1 PW rnp3, and 30 km of granulitic lower crust with 0.4 PW rnm3. The thermal conductivity was assumed to be 2.0 W m- ’ K- ‘. The lower crust appears brittle up to 35 km; the strength decreases in the lowermost part of the crust which is ductile. The mantle below Moho is stronger but its strength decreases below 55 km. Integrating the stress envelope yields the total tensile strength of the lithosphere, 1.2 X 1013 N m-l, which is higher by one order than the difference in potential energy density between the Appalachians and the surrounding region. It can be noted that,
471
throughout most of the crust, the strength is larger than the tensile stress. The strength of the lithosphere depends on the temperature profile. Because the thickened crust produces more heat, the equilibrium heat flow will be higher, resulting in higher equilibrium temperature throughout the crust and mantle. On the other hand, the temperature profile of instantly thickened lithosphere is simply stretched. Before new equilibrium conditions are established, the thickened lithosphere will be stronger. The effect of stretching the temperature profile competes with increased crustal heat production. The temperature in thickened crust and lithosphere was calculated to better assess the net effect of thickening on the strength of the lithosphere. The following simplified assumptions were made to calculate the temperature profile: (1) before thickening, the lithosphere is in equilibrium; (2a) thickening is homogeneous throughout the lithosphere or (2b) the crust is thickened but the mantle is not affected; (3) heat is transported by conduction; and (4) the temperature is constant at the base of the lithosphere (1350°C isotherm). The temperature is determined by the solution of the heat equation: aT
aT
a*T
H
--$+L’z=K---g+PC
where t is time, z is depth, v is the vertical velocity, K is the thermal diffusivity, p is density, H is heat generation, and C is the specific heat. The initial equilibrium temperature is given as: T(z)
= To -t /,
where To is surface temperature, q,, is surface heat flow, and K is thermal conductivity. In the finite difference scheme used to solve the heat equation, grid points are attached to the material and the advection term disappears. The calculations were done for two different values of surface heat flow and initial conditions. The standard model assumes that surface heat flow is 52 mW m-* and that the crustal heat sources are distributed between three layers: an
478
.I.-C. Mareschai / Tectonophysics 238 (19941 471-484
enriched 8 km thick layer with 2.5 PW rnm3, a 10 km tonalitic layer with 1.1 PW rnw3, and the lower crust with 0.4 @W mS3; the heat flow from the mantle is 12 mW me2. This model is similar to that proposed by Pinet et al. (1991) for eastern Canada. A model with 60 mW rnp2 surface heat flow and the same distribution of heat sources leads to mantle heat flow of 20 mW mm2 and higher crustal temperatures. The thermal conductivity was assumed to be 2.0 W m -’ K- *. Higher
TEMPERATURE
TENSILE STRENQTH s1rangttlwP&t)
T PC)
values of the thermal conductivity would lead to lower temperatures and increase lithospheric strength. Fig. 4a shows the initial geotherm and the stress envelope for the standard model. The strength of the lithosphere for 2 X lo-l6 s- ’ strain rate increases all the way down to 60 km. The integrated strength is 2.7 x lo*” N m-‘. Fig. 4b shows the geotherm and the stress envelope after 40 Myears, when the lithosphere has been
TEMPERATURE T (‘C)
TENSILE STRENGTH s!renQthmm)
2.7 1013 N/m -150 -
-150 -
Total alreftgth
~0 = 30 mW.m“
Strain rat* 2 to-** -200 -
-2oo-
i’
strain rcste2 fo-‘” s-1 Ia)
TEMPERATURE T VW
04
TENSILESTRENGTH streneth wPa>
Fig. 4. Temperature and rheokqical profile for stable continental lithosphere with surface heat flow of 50 mW rnT2: (a) before thickening, (b) at&r 100% hom&meous thickening in 40 Myears, and (c) after 100% thickening of the crust c&y in 4t.biyears.
J.-C. Mareschal / Tectonophysics 238 (1994) 471-484
homogeneously thickened by 100%. Fig. 4c shows the geotherm and the stress envelope after 100% thickening of the crust only in 40 Myears. Homogeneous thickening increases the strength of the lithosphere to 6.2 x 1013 N m-‘: this is greater than the potential energy by more than one order. For crustal thickening, the strength remains constant (2.7 X 1013 N m-l> and is about one order above the potential energy. At any depth
TENSILE
TEMPERATURE
below the shallowest 5-10 km, the strength of the crust is higher than the tensile stress. In the mantle, where the strength decreases, the stress is compressional. It appears that with these initial conditions, extension would never follow lithospheric or crustal thickening. The calculations were carried out with different shortening rates. They showed that the lithospheric strength decreases only when shortening rates are smaller by
two
TENSILE
TEMPERATURE
STRENGTH
0
15m 7
Id
100
-54 ,-
P t f
STRENGTH
Strength IMPa)
T (‘C)
Strength (MPa)
T t*C)
479
-1M I-
10’
5
-1m -
B
-160
-150 -
-
/
1.0 1013 N/m Total strength
-lY O
1.0 1013 N/m
Total strength
q. = 60 mW.m?
stra,n rat* 2
-2COL
-2wJ
lo-'6
nomogenaous
s-1
1
Strain rate 2 lo-l6
se’
thickenmg
(a)
-20 O-
TENSILE
TEMPERATURE
(b)
STRENGTH
Strength (MPa)
T (‘0
3.1 10"
N/m Total streqth
-160
t
L
Strain rate 2 1O“8 se’
Crustal thickening -MO
(d
Fig. 5. Temperature and rheological profiles for continental lithosphere with 60 mW m-* surface heat flow: (a) initiril profiles, (b) after 100% homogeneous thickening in 40 Myears, and Cc) after 100% thickening of the crust in 40 Myears.
480
J.-c’. Mareschal/ Tectonophysics238 (1994) 471-484
one order of magnitude (i.e. doubling crustal thickness would take 400 Myears) and if no erosion occurs. The initial temperature distribution is critical in determining the strength of the lithosphere. Fig. 5a shows the temperature distribution and stress envelope with the initial condition corresponding to a hotter lithosphere (the surface heat flow is 60 mW me2, the crust has the same thermal structure as in the standard model and heat flow from the mantle correspondingly increased to 20 mW mP2). This change in initial conditions leads to a weaker lithosphere with a total strength of 1.0 x 1013 N m- ‘. Fig. 5b shows the temperature and the strength of the lithosphere after homogeneous thickening by 100% in 40 Myears. Fig. 5c shows the temperature and strength after 100% thickening of the crust only in 40 Myears. For such initial conditions, homogeneous lithospheric thickening does not increase the strength of the lithosphere and crustal thickening only has reduced the strength of the lithosphere to 3 X 101* N m-l. For this example, the tensile stress is greater than the strength in most of the crust and it could produce extension. The initial temperature required for crustal thickening to bring about extension is high but not extreme. It thus appears that, for an appropriate initial temperature distribution, crustal thickening only could indeed bring the conditions for extension. The stress available in homogeneously thickened lithosphere varies with depth: the tensile stress is highest in the upper crust, it decreases in the lower crust, and it becomes compressional in the mantle. The distribution of stress and strength of the lithosphere limits extension to the topmost crust, and hampers lithospheric-scale extension. The effect of erosion has not been included in these calculations; erosion steepens the temperature gradient in the shallow crust but has little effect in the lower crust. In addition, if very high rates of erosion are assumed, the rate of thickening required to double crustal thickness would be even larger, and would lead to a colder lower crust and mantle. The effect of shear heating has been debated
(e.g. Molnar et al., 1983; Molnar and England, 1990 and references therein). An upper limit on the heat produced by friction can be obtained by assuming that the work done by the tectonic forces is entirely converted into heat:
dQ -
where F is the total force on a lithospheric column and i is the strain rate. If the force is 2 x 1Or3 N m-l, and the strain rate is 5 X 10-l” SK’, friction could produce as much as 10 mW mw2. This is a large value, but still smaller than the increased heat production in the crust, which is not sufficient to heat rapidly the lithosphere. Indeed, this additional heat distributed uniformly in the lithosphere converts in a rate of heating of 0.5 x lo-‘*“C s-r (i.e. about 15°C Myear-‘). Shear heating may cause large effects locally but it is not sufficient to heat the lithosphere. The intrusion of a significant volume of magma into the lithosphere is unlikely in a compressional context. The volume of magma necessary to heat the lithosphere can also be estimated. The heat transported by the magma can be estimated at about 60 kJ kg-’ (assuming that the latent heat is 40 kJ kg-’ and the specific heat 700 J kg-’ “C-I). A volume of magma corresponding to 1% of the volume of the lithosphere would raise the average lithospheric temperature by only 1°C. In order to heat the lithosphere and lower its strength, a volume of magma representing a significant volume of the lithosphere is required. This seems difficult in a compressional context and replacing the lithospheric mantle by asthenosphere is a more feasible alternative.
4. Efkct of removal of the litbospherk masttIe Removal of. the lithospheric mantle by delamination (Bird, 1979) or by convection (Houseman and England, 1986; England and Houseman, 1986) modifies the distribution of stress and the temperature in the lithosphere. The stress distribution after 100% thickening of the lithosphere and complete removal of the lithospheric mantle is shown in Fig. 6 for the same two density
J.-C. Mareschal/ Tectonophysics 238 (1994) 471-484
PRINCIPAL
HORIZONTAL
STRESS
T (Mpa)
Energy dift = 6.5 10”
N/m
Energy Utt = 7.6 10”
N/m
-2OOL Fig. 6. Stress distribution in thickened crust after removal of lithospheric mantle after 100% thickening. The densities are 2.75, 2.95 in the upper and lower crust. The density of the asthenosphere is 3.15 or 3.125 Mg me3.
distributions as in Fig. 1. The stress is much larger than after lithospheric or crustal thickening and it is tensile all the way down to the initial lithosphere-asthenosphere boundary. The total stress (difference in potential energy density) is on the order of 1013 N m-‘. Fig. 7 shows the temperature profile and the strength of the lithosphere that was thickened by 100% and delaminated at 40 Myears. The temTENSILE
TEMPERATURE
perature profiles are calculated just after the delamination (Fig. 7a) and 10 Myears after delamination (Fig. 7b). The total strength of the lithosphere drops very rapidly to 1012 N m-l, and is one order less than the energy available. Also, the stress is tensile throughout the lithosphere, including the now weaker lower crust and mantle. Removal of the lithospheric mantle would always bring about the conditions permitting extension to start. If extension begins, the thermal effect of extension will be the opposite of that of compression. For rapid extension, the steepening of the geotherm dominates over the effect of reduced crustal heat production and the strength of the lithosphere decreases. The tensile stress is reduced by crustal thinning but is maintained by a hot and buoyant mantle. Extension would thus proceed in conditions similar to those of the present Basin and Range (Lachenbruch and Sass, 1978) unless it is opposed by plate boundary forces.
5. Conclusion Uniform thickening of the lithosphere collision produces a tensile stress regime thickened crust, and compressional stress mantle. Depending on initial lithospheric TEMPERATURE
STRENGTH
TENSILE
T (‘Cl)
Strength (MPa)
T (‘0
481
“/ -50
i
-150 -
1.2 1013 N/m Total strenpth
-150 -
-150
~0 = 50 mW.6’
L
Strain rate 2 lO+
-2W
102
too
Time = 40 Myra
-60
STRENGTH
Strength WPa) 0
o”W
-200
10’
F I
1.910'2
Nlrn Total strength
Strain rate 2 lo-‘”
6’ (4
during in the in the thick-
6’
Fig. 7. Temperature and rheological profiles after 100% thickening in 40 Myears and removal of the lithospheric mantle.
(b)
187
J.-C. Mureschal / Tectonophvsics 238 (1994) 471-484
ness and density distribution, the resulting force can be tensional or compressional. It will be on the order of lo’* N m-‘. If shortening and crustal thickening occur at a reasonable rate (3 to 5 X lo-l6 s-l), the thickened crust and lithosphere remain relatively cold. The strength of the lithosphere remains larger than the tensile stress, except in the very shallow crust. In the mantle, where the strength drops, the stress is compressive. The integrated strength is at least one order of magnitude larger than the potential energy difference. It seems implausible that, at the release of compressive tectonic forces, lithosphericscale extension could start. Erosion will progressively reduce the topography and the stress difference, before increased crustal heat production warms and weakens the lithosphere. If thickening involves the crust only, the resulting force will always be tensional and larger than for homogeneous lithospheric thickening (i.e. 5 X lo’* N m-l). The strength of the lithosphere does not increase for crustal thickening, and depending on the initial conditions, it may be less than the tensile force. It appears that the lithosphere is too strong for extension to take place if the heat flow is 50 mW me2 or less, but that extension could occur for heat flows greater than 60 mW m-*. Alternatively, the removal of the lithospheric mantle produces uplift and increases the stress which will be tensional throughout the lithosphere. Also, heating of the crust reduces its strength. If compressional tectonic forces subside, the tensile stress available throughout most of the lithosphere is on the order or larger than the strength of the lithosphere. Extension can proceed until the stress diminishes or until it is counteracted by plate boundary forces.
Council (Canada) through an operating grant to the author is gratefully acknowledged.
Appendix-deviatoric stress induced by non-homogeneous lithospheric thickening Let p(r) be the density distribution in the lithosphere before thickening, where z is positive downward and z = 0 is the Earth’s surface before thickening, z = M is Moho, and z = L is the base of the lithosphere. The lithostatic pressure is P, at Moho and PL at the base of the lithosphere. The asthenosphere density is pa. The crustal thickening Factor is y and the lithospheric mantle thickening factor is 6. After isostatic adjustment, the Earth’s surface is z = - h, Moho is at depth z = - h + yM, and the base of the lithosphere is at depth z = - h + yM + 6(L - Ml The lithostatic pressure is yP, at Moho and yP, +6(P, - P,) at the base of the lithosphere. Isostatic condition requires: P,+gp,[-h+yM+6(L-M)-L]=yPh4++(PI_-PPM)
therefore, the uplift is given by: h=(&l)(L-$)+(y-S)(M-2)
The energy difference is given as: AT=/
-h+yM+S(L-M)P1(z)dZ --;-
h+YM+S(L-M$&)dz
where P,(z) is the lithostatic pressure in the thickened lithosphere and the P,(z) is the lithostatic pressure before thickening. tt gives: AT=/
-h+yMdzl’hgp,(z’)dz i;_-~h++~~+bll~‘dz[yPu+~~~iI~g~,(zf)dz~] -hM dzcgPo(z’)
dz’
-/:dz[P,+~~gp,(l’)dz’] -~~‘L-~‘+y~-hdz(PI+lLigp~dz’) where p0 and p1 denote the density distribution before and after thickening. Integrating the equation yields:
Acknowledltements
The author is thankful to Francis Lucazeau for a very thorough and thoughtful review. Helpful comments by Olga I. Parphenuk and Catherine Meriaux are greatly appreciated. The support of the Natural Sciences and Engineering Research
AT = yz&MPO(z) dz + yGP,(L
- M)
+62/ML[PO(z)-P41]dz-~~P0(z)dz-PPh((L-M) -jML[P&)-Py]dz-PL[S(L-M)+yM-h-L] -~[S(L-M)+yM-h-L]Z
J.-C. Mareschal / Tectonophysics 238 (1994) 471-484
It gives: AT=(y2-l)/o~P0(~)dz+(SZ-l)/--[Pa(z)-Phl]dz +(yS-l)&(L-M)-[(S-l)P,_+(y-6)&]
If thickening is uniform (y = 6), the stress difference gives: loLp,(z)dz-$
1
a If the crust only is thickened and the lithospheric mantle is not affected (6 = l), the stress gives: AT=(y*-1)
h”P(z)dz-$ [
1 tA-PM, 1 gP,
The above formulas can be used to demonstrate how some parameters affect the total stress. In particular, it is easy to see that lower asthenosphere density will decrease the total stress. It is clear also that, if the lithospheric mantle is denser than the asthenosphere, crustal thickening only results in larger isostatic uplift and stress than homogeneous thickening.
References Artemjev, M.E., Bune, V.I., Dubrovski, V.I. and Kambarov, N.S., 1972. Seismicity and isostasy. Phys. Earth Planet. Inter., 6: 2.56-262. Artyushkov, E.V., 1973. The stresses in the lithosphere induced by crustal thickness inhomogeneities. J. Geophys. Res., 78: 7675-7708. Bird, P., 1979. Continental delamination and the Colorado Plateau. J. Geophys. Res., 84: 7561-7571. Bird, P., 1991. Lateral extrusion of lower crust from under high topography, in the isostatic limit. J. Geophys. Res., 96: 10,275-10,286. Bird, P. and Piper, K., 1980. Plane-stress finite element models of tectonic flow in southern California. Phys. Earth Planet. Inter., 21: 158-175. Brace, W.F. and Kohlstedt, D.L., 1980. Limits on lithospheric stress imposed by laboratory experiments. J. Geophys. Res., 85: 6248-6252. Buck, W.R., 1991. Modes of continental lithospheric extension. J. Geophys. Res., 96: 20,161-20,178. Byerlee, J.D., 1978. Friction of rocks. Pure Appl. Geophys., 116: 615-626. Byerlee, J.D., 1990. Friction, normal pressure, and fault normal compression. Geophys. Res. Lett., 17: 2109-2112. Carter, N.L. and Tsenn, M.C., 1987. Flow properties of continental lithosphere. Tectonophysics, 136: 27-63. Carter, N.L., Anderson, D.A., Hansen, F.D. and Kranz, R.L., 1982. Creep and creep rupture of granitic rocks. Am. Geophys. Union, Geophys. Monogr., 24: 61-82.
483
England, P.C., 1983. Constraints on extension of continental lithosphere. J. Geophys. Res., 88: 1145-1152. England, PC. and Houseman, G.A., 1986. Finite #train calculations of continental deformation, II. Comparison with the India-Asia collision. J. Geophys. Res., 91: 3664-3676. England, P.C. and Houseman, G.A., 1988. The mechanics of the Tibetan Plateau. Philos. Trans. R. Sot. London, Ser. A, 326: 301-319. England, P.C. and Houseman, G.A., 1989. Extension during convergence with application to the Tibetan Plateau. J. Geophys. Res., 94: 17,561-17,579. England, P.C. and McKenzie, D.P., 1982. A thin vrscous sheet model for continental deformation. Geophys. J.R. Astron. Sot., 70: 295-321. Fleitout, L. and Froidevaux, C., 1982. Tectonics and topography for a lithosphere containing density heterogeneities. Tectonics, 1: 21-56. Gaudemer, Y., Jaupart, C. and Tapponnier, P., 1988. Thermal control on post-erogenic extension in collision belts. Earth Planet. Sci. Lett., 89: 48-62. Houseman, G.A. and England, P.C., 1986. Finite strain calculations of continental deformation, I. Method and general results for convergent zones. J. Geophys. Res., 91: 36513663. Houseman, G.A., McKenzie, D.P. and Molnar, P., 1981. Convective instability of a thickened boundary layer and its relevance for the thermal evolution of continental convergence belts. J. Geophys. Res., 86: 6115-6132. Jeffreys, H., 1929. The Earth. Cambridge University Press, Cambridge, 2nd ed., 346 pp. Kirby, S.H., 1983. Rheology of the lithosphere. Rev. Geophys. Space Phys., 21: 1458-1487. Kirby, S.H. and Kronenberg, A.K., 1987. Rheology of the lithosphere: selected topics. Rev. Geophys., 25: 1219-1244. Kusznir, N.G. and Park, R.G., 1984. Intraplate lithosphere deformation and the strength of the lithosphere. Geophys. J.R. Astron. Sot., 70: 513-538. Kusznir, N.G. and Park, R.G., 1987. The extensional strength of the continental lithosphere: its dependence on geothermal gradient, and crustal composition and thickness. In: M.P. Coward, J.F. Dewey and P.L. Hancock (Editors), Continental Extensional Tectonics. Geol. Sot. Spec. Publ., 28: 35-52. Lachenbruch, A.H. and Sass, J.H., 1978. Models of an extending lithosphere and heat flow in the Basin and Range Province. Geol. Sot. Am. Mem., 152: 209-250. Lachenbruch, A.H. and Sass, J.H., 1992. Heat flow from Cajun Pass, fault strength, and tectonic implications. J. Geophys. Res., 97: 4995-5015. Love, A.E.H., 1911. Some Problems of Geodynamics. Cambridge University Press, Cambridge, Dover reprint, 180 pp. Mareschal, J.C. and Kuang, J., 1986. Intraplate stresses and seismicity: the role of topography and density heterogeneities. Tectonophysics, 132: 153-162. Molnar, P. and England, P., 1990. Temperatures, heat flux, and frictional stress near major thrust faults. J. Geophys. Res., 95: 4833-4856.
484
J.-C. Mareschal/
Tectonophysics 238 (19941 471-484
Molnar, P., Chen, W.-P. and Padovani, E., 1983. Calculated temperatures in overthrust terrains and possible combination of heat sources responsible for the tertiary granites in the Himalaya. J. Geophys. Res., 88: 6415-6429. Murrell, S.A.F., 1986. Mechanics of tectogenesis in plate collision zones. In: M.P. Coward and AC. Ries (Editors). Collision Tectonics. Geol. Sot. Spec. Publ., 19: 95-111. Parphenuk, O.I., Dechoux, V. and Mareschal, J.C., 1994. A finite element model of evolution for the Kapuskasing structural zone. Can. J. Earth Sci., in press. Percival, J.A., 1990. A field guide through the Kapuskasing uplift, a cross section through the Archean Superior Province. In: M.H. Salisbury and D.M. Fountain (Editors), Exposed Cross-Sections of the Continental Crust. Nato ASI Ser., 317: 227-283. Pinet, C., Jaupart, C., Mareschal, J.C., GariCpy, C., Bienfait, G. and Lapointe, R., 1991. Heat flow and structure of the lithosphere in the eastern Canadian Shield. J. Geophys. Res., 96: 19,941-19, 963. Post, R.L., 1977. High temperature creep of Mt Burnet dunite. Tectonophysics, 42: 75-110. Ramberg, H., 1981. Gravity, Deformation, and the Earth’s Crust. 2nd ed. Academic Press, New York.
Ranalli, G., 1987. Rheology of the Earth. Allen and Unwin, Boston, Mass., 366 pp. Scholz, C.H., 1989. Mechanics of faulting. Annu. Rev. Earth Planet. Sci., 17: 319-328. Sonder, L.J. and England, P.C., 1986. Vertical averages of rheology of the continental lithosphere: relation to thin sheet parameters. Earth Planet. Sci. Lett., 77: 81-90. Sonder, L.J., England, P.C., Wernicke, B.P. and Christiansen, R.L., 1987. A physical model for Cenozoic extension of western North America. In: M.P. Coward, J.F. Dewey and P.L. Hancock (Editors), Continental Extensional Tectonics. Geol. Sot. Spec. Publ., 28: 187-201. Weertman, J., 1978. Creep laws for the mantle of the Earth. Philos. Trans. R. Sot. London, Ser., A 288: 9-26. Wilks, K.R. and Carter, N.L., 1990. Rheology of some continental lower crustal rocks. Tectonophysics, 182: 57-77. Zhou, S. and Sandiford, M., 1992. On the stability of isostatitally compensated mountain belts. J. Geophys. Res., 97: 14,207-14, 221. Zoback, M.D. and HeaIy, J.H., 1992. In situ stress measurements to 3.5 km depth in the Cajun Pass scientific research borehole: implication for the mechanics of crustal faulting, J. Geophys. Res., 97: 5039-5057.