Thermo-mechanical constraints on kinematic models of lithospheric extension

EPSL ELSEVIER

Earth and Planetary Science Letters 134 (1995) 87-98

Thermo-mechanical constraints on kinematic models of lithospheric extension A.M. Negredo a M. FernSndez a, H. Zeyen b a Institute of Earth Sciences, C.S.LC. Martl i Franqu~s sin., 08028 Barcelona, Spain b Geophysical Institute, University ofKarlsruhe, Herzstrasse 16, Bau 42, 75000 Karlsruhe 21, Germany

Received 12 January 1995; accepted 30 May 1995 after revision

Abstract

Two-dimensional kinematic modelling of extension based on the numerical solution of the heat transport equation is used to investigate the lateral evolution of lithospheric yield strength during rifting and during postrift relaxation. Two yield strength minima are shown to exist, one beneath the rift centre and the other beneath the undeformed area adjacent to the rift. These are separated by a relative maximum in the transition zone between the rift and the outer area. Initially cold (thick) lithosphere and fast extension give rise to an absolute strength minimum beneath the rift, leading to a narrow rift. On the other hand, initially hot (thin) lithosphere and slow extension lead to an absolute strength minimum beneath the rift sides, which could cause outward migration of the area of principal strain and formation of a wide rift. In contrast to some existing one-dimensional analyses, no lithospheric hardening is necessary for the formation of a wide rift and the conditions for its formation are consequently less restricted. The maximum of strength in the transition zone suggests a third mode of extension characterized by the activation of extension parallel to the rift, with undeforrned areas in between. During postrift evolution, the strength of the thinned area progressively increases until the zone adjacent to the rift becomes the weakest area, inducing a widening of the rift in subsequent rifting episodes, The minimum time required for migration of deformation in successive rifting stages is termed the critical relaxation time (CRT) and is shorter for an initially hot lithosphere and low strain rate. CRT values range from few million years to more than 130 Ma for a stretching factor of 1.65. This study highlights major differences with respect to previous one-dimensional analyses when considering lateral heat transport and a progressive crustal and lithospheric thinning from the rift flanks.

1. Introduction During the last decade much attention has been paid to the modelling of continental rift processes. These models generally fall into two categories, dynamic and kinematic. In the first category, lithospheric deformation is calculated by coupling the constitutive and thermal equations [1-7], whereas in the second category the mode o f deformation is controlled by a predefined velocity field which is Elsevier Science B.V. SSDI 0012-821X(95)00107-7

linked, as an advective term, to the heat transport equation [8-11]. Despite the fact that dynamic models are more self-consistent, the high non-linearity o f the equations renders the results very sensitive to the initial conditions. It is, therefore, very difficult to reproduce the present-day crustal structure of a given extended area. Furthermore, the uncertainties associated with rock deformation parameters, actual strain rate values and rheological stratification of the continental

88

A.M. Negredo et aL / Earth and Planetary Science Letters 134 (1995) 87-98

lithosphere lead to considerable discrepancies in the results obtained by different authors. Kinematic models are more intuitive and allow for different modes of lithospheric deformation, especially in the brittle domain (crustal detachments, faulting, block rotation, etc.). However, in this model category there is no control over the compatibility between the imposed velocity field and the actual mechanical behaviour of the rocks. Some authors have attempted to introduce rheological controls on one-dimensional kinematic models by calculating changes in the lithospheric yield strength during the synrift phase [12,13]. These authors predict that, depending on the strain rate and the initial geometry of the lithosphere, conductive cooling during extension can lead to an increase in the force needed to produce rifting (lithospheric hardening). When this hardening occurs, extensional strain migrates to adjacent undeformed areas and a wide rift is predicted. An alternative mechanism for the creation of wide rifts was proposed by Buck [14]. In Buck's approach the force required to extend the lithosphere includes yield strength and gravitational buoyancy forces due to crustal deformation. This model does not invoke yield strength changes as being responsible for wide rifts. Conversely, wide rift mode is predicted when compressional stresses caused by crustal thinning result in an increase in the force required to produce extension. Buck [14] introduces a model for lower crustal flow, which is responsible for a core-complex mode, and suggests that initial crustal thickness and thermal conditions are the dominant factors in determining the mode of extension. Owing to the one-dimensional approach employed in these studies, the force required to produce rifting at the rift axis must be compared to the initial (unperturbed) situation, and lateral thermal effects are not accounted for. In this paper we examine the consequences of introducing dynamic controls on a two-dimensional fully kinematic model of uniform lithospheric extension. We calculate lateral variations in lithospheric strength during extension and during the thermal relaxation that follows rifting. This calculation reveals that lateral thermal effects are important in determining the tectonic style of continuous or episodic extension. We show that under certain conditions thermal weakening at the rift edges can in-

duce lateral migration of strain and widening of the rift without requiring an increase in the force necessary to drive extension. The mode of extension deduced from lateral strength variations has to be consistent with the deformational pattern assumed in the kinematic model. Therefore, yield strength considerations enable us to constrain velocity fields for kinematic modelling that are more in agreement with the thermo-mechanical behaviour of the lithosphere.

2. Model description 2.1. Thermal calculation

We consider a two-dimensional kinematic model that accounts for advective heat transport and radiogenic heat production. The defined velocity field is

Distance (km) 0 0

~ i

,

,

I

d

,

g

l

d

l

J

l

l

t

l

l

,

50 ,

75 I

,

l

,

,

l~ l

l

~

J t / /////~\\\\ t t / / / / / / _

~_

t t t t t///

. . . . . . . . . .

t .f t t l . / . / /

rtttt///

.

.

# I/1II// #/1111I~

'/'t't~~-L

~ =uJL PI~

.

.

___ __

~ =0

P

~g. 1, Geome~c evo|ution of h~f a section of extending lithosphere and representation of ~ e pure shear veloc~y field. ~ e velocity of ex~nsion is u 0 = 2.5 ~ / M a and ~ e rest of parameters are ~ven in T ~ l e 1. ~ y e r geome~y is shown from 2 to 10 Ma (eve~ 2 Ma).

A.M. Negredo et al. / Earth and Planetary Science Letters 134 (1995) 87-98

essentially the same as that proposed by Buck et al. [11] for pure shear deformation (half a lithospheric section shown in Fig. 1). Extension is assumed to be concentrated in a zone of width 2L, whereas the outer zones (I xl > L) separate with a constant velocity u 0. Within the stretching (inner) zone the horizontal component v x changes linearly from v x = 0 at the rift axis (x = 0), to vx = u 0 at x = L. The continuity condition, div v-* = 0, implies a linear variation of the vertical component of the velocity, which has the form U0

Vz =

(1)

L

where z is the depth, which is defined positive downwards. The strain rate has a constant value = u o / L in the inner zone. After the rift starts, three areas can be defined (Fig. 1): (1) the inner zone (L wide), with laterally constant thinning, (2) the transition zone (Uot k m wide), where the thickness of each layer progressively increases to its initial value, and (3) the outer unstretched zone. The thermal evolution of the extending litho-

89

sphere is determined by the two-dimensional heat transport equation OT -Ot -+

OT

-+ Vx -Ox

OT

[ 02T

02Tt

- = K [ - ~ - g x 2 + - - ]o3z2 Vz -Oz

+H

(2)

where T is temperature, t is time, K is thermal diffusivity, and H = A / p c , where A is the crustal radiogenic heat production, p is density and c is specific heat. The upper and lower boundaries of the model in Fig. 1 are maintained at constant temperatures of T ( z = 0) = 0°C and T ( z = a) = 1333°C. The initial temperature distribution is given by the steady-state solution to Eq. (2) with v x = v z = O. A constant distribution of radiogenic elements is assumed in the entire crust (see Table 1). Such a uniform distribution, instead of an exponential decrease of heat sources with depth [15], simplifies the model and does not significantly affect the results, as discussed by Buck [14]. The presence of heat sources in the mantle is assumed to be negligible. Eq. (2) is solved using an explicit two-dimensional finite difference method, with centred differences for the diffusive terms and upwind differences

Table 1 Thermal and geometric parameters

Symbol

Meaning

Value

Tc

crustal thickness

40 km

Tuc

upper crust thickness

20 km

Pc

crustal density

2800 kg m 3

Pm

mantle density

3330 kg m 3

~c

thermal diffusivity

21.8 km 2 Ma l

thermal expansion coefficient

3.28 x 10.5 K 1

k

thermal conductivity

3.1 W m -1 K -1

Ta

bottom boundary temperature

1333 °C

L

half width of the inner zone

50 km

A

crustal heat production

0.64 taW m 3

90

A.M. Negredo et al. / Earth and Planetary Science Letters 134 (1995) 87-98

for the advective terms. As boundary conditions we imposed O T / O x = O at x = 0 and 0 2 T / O x 2 = 0 at the right boundary. A vertical grid interval of 0.25 km and a horizontal interval of 1 km were defined for the calculations.

Yield 0

0

20o i

i

stress 400 i ,

(MPa) 600 L ,

800 i

looo i

O.C 20

L.C

\

2.2. Yield stress calculation e~

Yield stress envelopes are calculated for every column of the model in order to obtain the lateral lithospheric strength variation during rifting evolution. This permits us to infer the style of rifting and to check whether the deformational pattem imposed by the predefined velocity field is consistent with the thermo-mechanical behaviour of the lithosphere. The maximum deviatoric stress that can be elastically supported by the lithosphere, called the yield stress, is given by the lesser of the brittle and ductile stresses [16,17]. Brittle stress depends on lithostatic pressure or depth [18] as (3)

crb = Bz

where B is taken to be 16 MPa km -1 [19] for extension. Ductile yield stress, O'd, depends on the rock type and temperature, and is related to strain rate through a power law [20] of the form

L.M

Fig. 2. Yield stress (solid line) as a function of depth for a 90 km thick lithosphere. The thickness of the crust is 40 kin. The applied strain rate is 1.6X 10-is s -1.

ing on the rock type. We consider a stratified lithosphere (Fig. 2) consisting of a quartz upper crust, a diabase/diorite lower crust, and an olivine mantle. The parameters assumed are in Table 2 and correspond to averaged values from Lynch and Morgan [19]. We have assumed the empirical relation P V * = 293z J m o l e - 1 k m - 1

1

o-d =

60-

exp

3RT

(4)

~being the strain rate, R the universal gas constant, T absolute temperature, P pressure, V * the activation volume, and %, n and Q* parameters depend-

where z is depth in kilometres [19]. Fig. 2 shows the yield stress envelope calculated for a 90 km thick lithosphere with a crustal thickness of 40 km. Such lithosphere results in a surface heat flow of 71 m W m -2 when the thermal parameters

Table 2 Rheological parameters

Layer

~0 (MPa" s l)

n

Q* (kJ mol -l)

upper crust

2.5 x 10.8

3

140

lower crust

3.2 x 10-3

3

250

103

3

523

lithospheric mantle

(5)

A.M. Negredo et al. /Earth and Planetary Science Letters 134 (1995) 87-98

listed in Table 1 are considered. The extensional strain rate applied is 1.6 × 10 -15 s -1. This profile illustrates the strong dependence of stress on depth and the need to use a dense grid for numerical calculations. The total lithospheric strength, which is given by the depth integral of the yield stress profile, is the horizontal force required to produce extension of the lithosphere at the given strain rate. The uncertainties associated with the experimental determination of rheological parameters, as well as the chosen rock type for each lithospheric layer, can introduce major changes in calculating the total lithospheric strength [13,14]. However, such changes have little influence on our results because this study is not focused on absolute values of lithospheric strength but on its relative changes when varying geometric and kinematic parameters. As shown in Fig. 2, total lithospheric strength is mainly determined by the uppermost part of the lithospheric mantle. Therefore, a decrease in crustal thickness without changing total lithospheric thickness would produce an increase in lithospheric strength. By contrast, subcrustal lithospheric thinning and the subsequent temperature increase would lead to a reduction in strength because the brittle-ductile transition moves to shallower depths. Different effects must be considered in evaluating strength changes associated with lithospheric extension. One effect is the weakening of the lithosphere due to heating. On the other hand, the replacement of weak crustal material by stronger mantle related to crustal thinning produces lithospheric strengthening. Furthermore, heat dissipation during extension increases the depth of the brittle-ductile transition at each layer, thus increasing lithospheric yield strength. Therefore, the evolution of lithospheric strength during extension is controlled by the competition of both effects: lithospheric heating due to the passive upwelling of the asthenophere, and the sum of diffusive heat loss and crustal thinning. Whereas weakening due to heating is the dominant effect at high strain rates, strengthening caused by diffusive heat loss becomes dominant at low strain rates. The strain rate required to produce lithospheric strengthening and as a result rifting inhibition depends on the initial state of the lithosphere [13,14].

91

3. Model results 3.1. Mechanical evolution during extension

The total lithospheric strength is calculated by using the strain rate deduced from the previously defined velocity field, and the temperature distribution given by the numerical solution to Eq. (2). In the outer/unstretched zone we consider the same strain rate as in the inner zone in order to calculate the lithospheric strength and to evaluate the location of the weakest areas. As long as the strength minimum is located in the inner zone, deformation will concentrate in this area and the kinematic model can be applied. If, however, the strength reaches its minimum value in the adjacent zones, strain must migrate to these weaker areas. In this case the deformational pattern given by the kinematic model--with deformation centred in the inner zone--becomes invalid. Therefore, the calculation of strength evolution during extension permits us to check the validity of the imposed velocity field as well as to constrain the conditions for wide or narrow rift modes of extension. High strain rate model

In the first case considered, a piece of lithosphere 100 km wide (L = 50 km) is extended with a constant velocity u 0 = 2.5 k m / M a , which is equivalent to a strain rate ~ of 1.6× 10 -15 S-1. Strength evolution in time is shown in Fig. 3 for two different values of initial lithospheric thickness. In both cases we can observe a decrease in yield strength in the rift centre of about 45% after 9 Ma of rifting. Although the crust has been thinned by a factor of 1.65 the effect of lithospheric heating is dominant due to the high strain rate. This changes as we approach the limit of the inner extension zone at L = 50 km. There, the lateral heat exchange with the outer area leads to a reduced heating and an increased influence of crustal thinning. This is the reason why we find a relative maximum of total yield strength in this area. A relative minimum which migrates outwards with time coincides with the limit of the transition zone at every time step (x = L + u 0 t). At this point, the crust maintains its initial thickness, but the lateral heat transfer from the inner zone heats up the litho-

A.M. Negredo et al. / Earth and Planetary Science Letters 134 (1995) 87-98

92 Synrift,

u o _- 2.5 km/Ma

10

I

I

I

I

I

~Z 9 E~ 8-

7 Ma

J

6-

9M

#

~

/

a = 80 km

~

5 0

2~5

510

7J5

100

1.~5

Distance (krn) 16

I

I

I

I

I

Intermediate strain rate model

15,Ma

Although this model has the same geometry and initial conditions as the previous one, it is character-

14Z o

13-

3Ma

~12-

the transition area (x = 75 km), however, temperature increases by 60°C. A comparison between the plots in Fig. 3 shows that for a thicker initial lithosphere, although the strength reduction at the rift centre is somewhat larger than for a thinner lithosphere, the relative minimum at the outer limit of the transition area is less well developed. The reason for this observation is that lateral heat diffusion is more effective for an initially thin lithosphere. In both cases shown in Fig. 3 the weakest area is situated in the inner zone. Therefore, extension remains localized in this area, as imposed in the kinematic model, and a narrow rift is created.

j

11

110

5 Ma J

I

I

, 25

,0

I

I

I

, 100

, 125

E

o

lO0-

g

.---- 9 >-

a = 90 km

8-

~

90-

7 0

2'5

;o

~'5

1~o

1~5

Distance (km) Fig. 3. Lateral variation of total lithospheric strength at different times after the beginning of rifting, with a velocity u 0 = 2.5

70-

g~ 7'5 (km)

Distance

and a halfwidth of the inner zone L = 50 km. This is equivalent to an applied strain rate of 1.6 × 10 -15 s -1. Two initial km/Ma

lithospheric thickness values have been considered, 80 k m and 90 km. The crustal thickness is assumed to be Tc = 40 km. Strain remains localized in the inner zone because strength is minimum there.

10-

2030-

E 40-

sphere, resulting in an overall decrease in yield strength. Fig. 4 shows the surface heat flow, isotherm distribution and the kinematic evolution of an initially 90 km thick lithosphere, after 10 Ma of extension. The remaining parameters used in the calculations are summarized in Table 1. The temperature at the crust-mantle boundary, which was originally 700°C in this model, decreases little (20°C) at the centre of the rift but much more (90°C) at the limit of the inner zone (x = 50 km). At the outer limit of

A= Q- 5 0 -

708090-

r

i

Distance

(km)

Fig. 4. Thermal and kinematic evolution of the right half of a lithospheric section, after 10 Ma of extension with a velocity u 0 = 2,5 k m / M a . The halfwidth of the inner zone is L = 50 km.

(Top) Surface heat flow. (Bottom) Temperature distribution superimposed on the geometry of the lithospheric layers.

A.M. Negredo et aL/Earth and Planetary Science Letters 134 (1995) 87-98 Synrift,

u o = 1 km/Ma I

9

I

I

93

to the initial lithospheric thickness) controls the deformational pattern of rifting. High initial geotherms favour the creation of wide rifts, whereas narrow rifts preferentially develop in areas with a cold and thick lithosphere.

I

Us x

111 V

a = 80 km

6

50 75 Distance (krn)

o

I

I

I

100

125

I

1Ma ~13O

L o w strain rate model In a third model we have reduced the extension velocity to u 0 = 0.5 k m / M a (~ = 3.2 × 10 -a6 s - l ) . Fig. 6 shows the evolution of lithospheric yield strength with time. Even for the cooler initial model with a lithospheric thickness of 90 kin, conductive cooling during extension is so important that the zones adjacent to the zone of extension have become weaker than the centre of the rift. This model therefore predicts the creation of a wide rift for both values of initial lithospheric thickness.

3 Ma

Synrift,

uo = 0.5 knYMa

.¢: 125 Ma

°t

"o

7 Ma.._.~/

I

T-

I0

8.0 V

I

I

I

I

;•E7. 5-

9

~

E~

a = 90 km

x

I

15

5'0

7'5

1~0

125

~" 7.0-

Distance (km)

Fig. 5. The same as in Fig. 3 with u0 = 1 km/Ma (~ = 6.3 × 10 -16 s-1 ). Initial lithospheric thickness is demonstrated to be a critical parameter in determining the location of the weakest areas.

-~ 6.5-

a = 80 km 6.0

215

ized by having a slightly lower value of the extension velocity (u 0 = 1 k m / M a , ~ = 6.4 × 1 0 - 1 6 S - I ) . For a lithospheric thickness a = 80 km conductive cooling during extension makes the inner zone more resistant than the outer boundary of the transition zone (Fig. 5, top). Therefore, extension should be partially transferred to this weaker area. Outwards migration of strain then produces a wide rift, which is characterized by a small amount of stretching distributed over a broad region. By contrast, the centre of the rift becomes weaker than the adjacent zones when an initially thicker and cooler lithosphere ( a = 90 km) is considered (Fig. 5, bottom). Extension concentrates in the inner zone and a narrow rift is created. It can be inferred that, for intermediate velocities of extension, the initial thermal state of the lithosphere (related in the present model

13.0

I

50 7J$ Distance (kin) I

100

125

I

• E12.5" ~ 12.0 ~ 11.5~ 11.0" a = 90 km

10.5

15

i

5o

7'~

100

125

Distance (km)

Fig. 6. The same as Fig. 4 with u0 = 0.5 km/Ma (~ = 3.2× 10 - 1 6 s-1). In both models the minimum in strength is reached at the sides of the zone of rifting.

A.M. Negredo et al. / Earth and Planetary Science Letters 134 (1995) 87-98

94

= 10

-15 S-t

140 120 100 ~

8060411-

~o

;o

~'o

io

Tc (km) = 10 .is s.1 140

~

120 ~

IO0-

E ~

. 8060Wide

Rift

40

2'0

3'0

used in the calculation of o"0 (Eq. 4) to determine the yield strength for rifting reactivation. The results show a progressive strengthening of the central part of the rift due to lithospheric cooling, whereas the sides of the rift are weakened because of the heat received from the stretched area (Fig. 8). Thus, the inner zone can become stronger than the adjacent areas some time after the cessation of rifting. We call the time required for this strengthening to occur the critical relaxation time (CRT). If the reactivation time of extension in a rifted area is shorter than the critical time, extensional strain will be concentrated in the predeformed area. If, however, the reactivation time exceeds the CRT, renewed extension will activate extensional structures at the margins of the basin. The critical relaxation time is calculated by com-

,~ ;0

Postrift u o = 0 km/Ma

T c (km)

Fig. 7. Representation of the conditions for a wide or narrow rift

depending on the initial thickness of the lithosphere (a) and crust (Tc). Two different strain rate values have been considered, ~ = 1 0 -15 s -1 and ~ = 1 0 -16 s - 1 .

15

13 z 12e~ ~-. 11 ~

}9: x

The initial conditions for the creation of wide or narrow rifts are mapped out in Fig. 7 for two different values of strain rate. It is inferred that the development of a wide rift from a thin continental crust requires an initially thin lithosphere and, therefore, a high regional surface heat flow.

I

10

-

8-"

I

I

I

I

30

26 22 18

7~ ~~.

6-

a =80

1 0 i a ~

km

5-

2'5

;0

75'

' I00

' 125

I

I

Distance (km)

3.2. Mechanical evolution during postextensional

18

thermal relaxation

17"

I

I

16 -

Thermal relaxation after rifting modifies the strength distribution of the lithosphere and can consequently cause the migration of the locus of deformation when extension is reactivated. Fig. 8 shows the mechanical evolution of the lithosphere during the thermal relaxation which follows a rifting event of 10 Ma in duration. The velocity of extension during the rifting phase is set to be u o = 2.5 k m / M a , which is equivalent to a strain rate value of ~ = 1.6 × 10 -aS s -a for a halfwidth of the inner zone L = 50 km. Thermal evolution during the postrift phase is given by the solution to Eq. (2) with v x = vz = 0. The same strain rate (~ = 1.6 × 10 -15 s -1) is

7EI5-

~

14-

~ll

I1) -~10"

"

"~

9-

>"

8-

a = 90 k m 215

510

7t5

100

129

Distance (km)

Fig. 8. Strength evolution along the thermal relaxation that follows a rifting process of 10 M a duration with a velocity u 0 = 2.5 k m / M a . Other parameters as in Fig. 3.

A.M. Negredo et al. / Earth and Planetary Science Letters 134 (1995) 87-98

paring the lithospheric yield strength at the centre of the rift and at the outer boundary of the transition zone, where its minimum is located (Fig. 8). Fig. 9 shows the time evolution of the lithospheric yield strength at these two locations (x = 0 km and x = 75 kin) for initial lithospheric thicknesses of 80 and 90 km. The CRT is then given by the intersection of the two curves, being about 2.3 Ma (after the end of rifting) for a lithosphere with an initial thickness of 80 kin, and about 8.8 Ma for 90 kin. Fig. lO(top) shows the dependence of CRT on the pre-extensional lithospheric structure. The final stretching factor and duration of the synrift phase are the same for all cases. The lower the ratio crustal/lithospheric thickness, the higher the efficiency of the weakening during extension; the CRT is then expected to be higher. Fig. lO(top) also states that the CRT is very sensitive to the prerift crustal thickness, especially for an initially cold (thick) lithosphere. CRT values exceeding 100 Ma are only obtained for very low crustal/lithospheric thickness ratios. Fig. lO(bottom) shows the CRT as a function of

95

=1;65, t ~ . 1 0 M a ,

140

120

-

100

-

I

I

80(9

604020-

/,o

7'0

Tc = 40 km,

~

i

t

90 loo a (km)

I

,

,

,

I

,

,

,

,

I

,

,

,

.

,io

' 120

t®xt = 10 Ma 2

90

I

3

i

I

I

4 I

5

i II

711-

60~v

km

50 -

0 30km

20-

8.0

I

,

"7, Z

E

10 7.5

Q

-15.50

-15.25

-15.00

k

-14.75

m

-1,~30

-14.25

log [ ~(sl)]

7.0-

,~x 6.s-

~

~

o

c~

Fig. 10. Critical time of relaxation as a function of (top) pre-extensional lithospheric thickness for different values of initial crustal thickness and (bottom) strain rate and final stretching factor for different initial lithospheric thicknesses.

6.0-

"~ 5.5._ >-

a = 80 km

5.11

the total amount of stretching achieved after a rifting episode for different initial lithospheric thicknesses. A Forty kilometre thick crust is assumed in each case. The duration of rifting is constrained to occur for 10 Ma and so different values of stretching correspond to different assumed deformational strain rates, which are plotted along the bottom axis. At high strain rates (high/3), weakening at the centre of the rift caused by lithospheric heating becomes more relevant and the CRT increases.

10

Time (Ma) 12

,

i

i

i

I

I

i

I

,

I

i

,

i

,

"7

"10 f13

//

8-

a =.90 km

7

10

1~5

'

'

2 0'

. . . .

25

Time (Ma) Fig. 9. Comparison of the strength evolution during thermal relaxation at the centre of the rift ( x = 0 kin) arid at the site of m i n i m u m strength ( x = 75 km). The time where both curves intersect is defined as the critical time of relaxation (CRT).

4. D i s c u s s i o n

We have shown with a simple two-dimensional kinematic model that lateral variation in lithospheric yield strength through time may play a significant

96

A.M. Negredo et aL / Earth and Planetary Science Letters 134 (1995) 87-98

role in the mode of lithospheric deformation for continuous or episodic rifting. Lateral heat transport, which can only be taken into account with two-dimensional models, is shown to strongly affect the distribution of lithospheric strength in the areas adjacent to the stretched zone. Thermal weakening at the rift sides is partly related to the discontinuity of the vertical component of the velocity at x = L (Fig. 1). We have tested the influence of this effect by introducing a gradual reduction in the vertical velocity over a narrow area adjacent to the inner zone. We have used for these tests the same conditions as for the low strain rate model with an initially thin lithosphere and have obtained the same qualitative results (a wide rift) even for an area of vertical velocity reduction 10 km wide. In the present model there is no coupling between the thermal equation and the constitutive equations relating stress and strain or strain rate, which would modify the velocity field at each time step. This uncoupling is a limitation inherent in kinematic modelling. Softening of the rift flanks would cause lateral migration of extension and a widening of the extending region. This widening would reduce the amount of heating by lateral heat transfer due to the reduction in local thinning and extension-driven heating. Therefore, the lateral heat flow is possibly overestimated in our model. However, a maximum strain at the rift flanks is also obtained by dynamic modelling [7] under certain initial conditions. The general features of this model are: (1) the creation of a weak area in the centre of the rift due to lithospheric heating, (2) a relatively resistant zone located near the boundary of the inner area, and (3) a zone with relatively low strength at the outer boundary of the transition zone. When heat conduction during extension is important (i.e., at low strain rates and/or for small values of initial lithospheric thickness) the sides of the rift can become weaker than the centre. In this case, strain is expected to migrate laterally, creating a wide rift, and the assumed simple kinematic model, which imposes deformation concentrated in the inner zone, would no longer be valid from the rheological point of view. Therefore, the calculation of lithospheric strength evolution during rifting provides a method to validate the deformational pattern prescribed in a kinematic model.

Wide rift mode is shown to preferentially develop in areas with a high initial geotherm and at low strain rates. By contrast, rapid extension of cold areas produces a narrow rift. A number of authors [12,13] have attributed lateral migration of extension to hardening during extension. In contrast, in the present study the different modes of extension are predicted by evaluating lateral changes in strength. In fact, hardening during rifting does not occur in any of the models presented here where the wide rift mode is predicted, and could only be expected at extremely low strain rates. Therefore, the conditions for the creation of a wide rift are less restrictive than those predicted by previous one-dimensional models that invoke lithospheric hardening. In the model developed by Buck [14] an increase in lithospheric strength is not required to produce a wide rift. Buck [14] evaluates compressional stresses caused by the positive density anomaly related to crustal thinning. When these bouyancy forces dominate yield strength changes and extensional thermal stresses, a net increase in the force required to extend the lithosphere is produced and the wide rift mode is predicted. The development of a strong area between the centre of the rift and the outer part of the transition zone, which is especially well developed for initially hot geotherms and low strain rates (Fig. 5(top) and Fig. 6(top)), suggests a third mode of deformation. In this case, extension would be characterized by the activation of extensional structures parallel to the rift with undeformed areas in between. Many instances of this mode of deformation are discussed by Vink et al. [21]. These authors conclude that rifting near a continent-ocean boundary preferentially develops within the continent, resulting in the formation of thin continental slivers, such as Baja California and Lomonosov Ridge, and continental fragments such as the Rockall Plateau and the Seychelles. This mode of deformation could also have operated in some continental margins [22]. The latter authors find, from the present-day lithospheric structure, a lateral strength variation similar to that deduced from our model. The tectonic style produced by successive periods of rifting depends on the reactivation time of extension. If this time exceeds the critical relaxation time (CRT), renewed rifting will develop at the sides of the old rift, and ancient extensional structures will

A.M. Negredo et al. / Earth and Planetary Science Letters 134 (1995) 87-98

not be reactivated. Many sedimentary basins provide geological evidence for multiphase rift formation. The structural evolution of the Viking Graben (North Sea) is related to two rifting events occurring in Late Permian-Early Triassic and Middle Jurassic times [23]. In the Eastern Iberian Margin, Salas and Casas [24] identified, from sequence stratigraphy and backstripping analyses, two successive extensional stages during the Mesozoic (Late Permian-Hettangian and Kimmeridgian-middle Albian). Likewise, the tectonic evolution of the southwestern border of the Valencia Trough (northeastern Spain) is characterized by three Mesozoic rifting events, a Paleogene compression, and a Neogene extension [25]. These examples reveal that the reactivation time may range from few million years to more than 100 Ma, which is in agreement with our results. A case history where migration of deformation is well documented is the Canning Basin, northwestern Australia [26]. Braun [27] attributes the shifting through time of tectonic activity to a lithospheric strengthening during thermal relaxation. The CRT for this basin must be less than 45 Ma, which is modelled by Braun [27] to be the time of reactivation. Taking into account the prerift configuration assumed by Braun [27] (crustal and lithospheric thicknesses of 40 and 100 km respectively, and a final stretching factor lower than 2), our work predicts a CRT value of about 20 Ma (Fig. 10, bottom), which is in agreement with the timing of the shift in strain in the Canning Basin. The CRT in some cratonic areas (cold lithosphere and relatively thin crust) is likely to be very long (Fig. 10, top). This result is in good agreement with the reported Paleozoic rifting reactivation (during the Devonian-Carboniferous) of some Proterozoic aulacogens in the East European Platform [28].

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ized in areas of minimum strength. Wide rift mode is more likely to develop from an initially hot (thin) lithosphere and at low strain rates. (b) Conditions for the creation of a wide rift are not as strict as in previous one-dimensional models based on yield strength changes, because no lithospherc hardening is required to produce strain migration and widening of the rift. (c) The presence of a strength maximum in the transition zone suggests a third mode of deformation characterized by the activation of extensional structures parallel to the rift, leaving undeformed areas in between. (d) The critical relaxation time (CRT), or the time needed for the rift centre to become stronger than the areas adjacent to the rift, is shown to be very sensitive to the prerift configuration and to the strain rate. Episodic rifting of a cold lithosphere is more likely to concentrate strain in previously deformed areas, whereas a progressive shifting of extension is produced for an initially hot lithosphere. The CRT is not expected to exceed 100 Ma for common values of the crustal/lithospheric thickness ratio.

Acknowledgements We would like to thank two anonymous reviewers for their helpful comments and suggestions for improving the manuscript. This research was partly funded by the Integrated Basin Studies European Union Project (JOU2-CT92-0110) and the German Academic Exchange Service and the Spanish Ministry of Education and Science (DGICYT, HA-34112-91). [UC]

References 5. Conclusions The main conclusions from this work are as follows: (a) Lateral strength variations calculated from a two-dimensional kinematic model of rifting permit us to check the validity of the deformational pattern prescribed by the velocity field. Wide and narrow rift modes are predicted by assuming that strain is local-

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