Mechanisms of uplift preceding rifting

Tectonophysics,

51

94 (1983) 5 1-66

Elsevier Science Publishers

MECHANISMS

JEAN-CLAUDE

B.V., Amsterdam

OF UPLIFT

- Printed

in The Netherlands

PRECEDING

RIFTING

MARESCHAL

of Geophysical Sciences, Georgia Institute of Technology, Atlanta, GA 30332 (U.S.A.)

School (Revised

version received June 24, 1982)

ABSTRACT

Mareschal,

J.-C., 1983. Mechanisms

Processes

of Continental

The feasibility anomalies

of uplift preceding

Rifting.

Tectonophysics,

of three mechanisms,

which might precede

The conductive

heating,

rifting,

following

In: P. Morgan

and B.H. Baker (Editors),

that have been proposed

to account

for the uplifts and heat flow

is examined. an increase

in the heat flux at the base of the lithosphere,

result in large scale uplifts (1000 m for 15 mW/m2 pulse of additional

rifting.

94: 51-66.

heat flow could induce

change

a more rapid

could

in heat flux) on a time scale of 10s years. A uplift but not the surface

heat flow anomaly

which is always delayed. The advection flow anomaly. about

of heat by magma

If magmas

50. IO6 years,

but it requires

volume of the lithosphere uplift and change

intrusion

are injected

into the lithosphere

could also produce

the rate of magma

injection

to be equivalent

per IO6 years. A short intense episode of magma

in surface

the uplift and heat

at a steady rate, an uplift of the order of 1000 m can be induced

heat flow but it requires

the replacement

invasion

in

to 0.3% of the total could explain a rapid

of about 30% of the total volume of

the lithosphere. The complete spheric diapir thinning reduced

material can

replacement

of the lithosphere

has been modelled

numerically.

by the rise of a diapir The model indicates

take place in a very short time (3. IO6 years) and produce

observed

in rift systems,

provided

that,

following

heating,

of lighter

and hotter

astheno-

that the rise of the asthenospheric the surface

uplift and the crustal

the lower lithosphere

viscosity

is

to - 102’ Pas.

INTRODUCTION

Intracontinental rifts are long, narrow structures where extension of the lithosphere has occurred (Burchfiel, 1980; Burke, 1980). The central rift valley, a graben between two parallel normal faults, follows the crest of broad upwarps. Because their formation is the first stage in the breakup of the continental lithosphere, rifts play a major role in the Wilson cycle of opening and closing of the ocean basins (e.g., Wilson, 1968; Dewey and Burke, 1974). If divergent motion within the lithosphere continues after the formation of the rift valley, oceanic crust will develop between two diverging plates; however, rifting may also stop before the apparition 0040-1951/83/$03.00

0 1983 Elsevier Science Publishers

B.V.

of a new ocean and the rift zone will remain rifts has now been recognized environments

(e.g.. Burke,

The best known

and

the Rhine

graben

The existence

01

extensic>nal tectonic

1980). studied

example

of a rift valley

I97 1; Fairhead,

system (Baker and Wohlenberg, include

wrthin the conttnent.

in a wide range of’ predominantly

(Kahle

and Werner.

is the East African

rift

1976: Baker, 19X1). Other examples 1980; Werner

and Kahle.

1980). the

Baikal rift (Artemjev and Artyushkov. 1971) and the Rio Grande rift (Eaton. 1979). The modern rifts, particularly the East African and Rio Grande systems, are usually associated with volcanism and broad regional uplifts. Geophysical data indicate that the main characteristics of a rift zone are a thin crust, upper mantle, and high heat flow. The mean heat flow reported 115 mW/m2 crust.

(Morgan.

The Bouguer

gravity

from the modern

1981) which indicates anomalies

a low velocity

rift systems ranges between

near melting

temperatures

show the superposition

length, probably associated with the low density highs, that may be related to magmatic intrusions

and density 90 and

in the lower

of lows of long wave-

mantle, and shorter in the crust (Banks

wavelength and Swain,

1978). Seismic data P-wave velocity

indicate that the crust is usually thinner and the upper mantle is lower than in the average continental regions: for example, a

crustal thickness of respectively 30 and 33 km and an upper mantle velocity of 7.6 km/s have been reported for the Kenya (Long et al., 1973) and the Rio Grande rifts (Olsen et al., 1979). Crustal thinning, thermal anomalies and uplift are clearly associated with rifting. The debates on the mechanisms of rifting are centered on whether the uplift preceded the crustal thinning and was its cause or lithospheric stretching, in response to tension, resulted in the passive rise of the asthenosphere and uplift. Vening-Meinesz (1950), recognizing that the features of the East African rift are the result of extension,

suggested

crust form by normal

faulting

uplift.

has been revised by Bott (1971, 1976) who suggests

This hypothesis

that, in response and subside

to tension,

wedges of continental

to form a rift valley between

zones of that the

first stage of rifting is the formation of a graben; the concept of wedge is applied to the elastic upper crust, with outflow in the lower crust resulting in crustal thinning. Crustal

thinning

could also be the result of plastic necking

of the crust in response

to

the tensional stresses (Artemjev and Artyushkov, 197 1). If the lithospheric extension proceeds, the lower density asthenosphere could rise passively resulting in a broad regional uplift (Atwater, 1970). Besides the stresses associated with the plate motion (Solomon et al., 1980), the stresses generated by continental collision have been suggested to cause lithospheric failure (Molnar and Tapponnier, 1975). Alternately, it has been suggested that rifting is an active mechanism. Rising hot mantle plumes (Morgan, 1972) cause thermal expansion and thinning of the lithosphere which, under the generated stresses, may fracture into (usually three) tension

53

rifts (Burke and Whiteman, 1973; Jacobs et al., 1974). Several swells may form an irregular line of domes connected by a single rift valley with arms extending on both sides. Ridge push forces are set up that pull apart the plate and, if not balanced, cause horizontal motion and opening of a new ocean basin (Dewey and Burke, 1974; Jacobs et al., 1974). Arguments have been raised in favor and against passive and active rifting and each one of the present rifts has been presented as an example supporting or excluding one or the other mechanism. The recent tectonic activity in the western United States includes the Rio Grande rift and a very broad zone of crustal extension and uplifts throughout the Basin and Range Province (Eaton, 1980). Two plumes, the Yellowstone and the Raton plume (Suppe et al., 1975), have been proposed to account for the uplifts; it is very questionable that all the uplifts and the crustal extension can be explained in terms of two local plumes, and other mechanisms relating the western United States tectonics to the plate interaction have been suggested. Domal uplifts are widespread throughout the African plate which has come to rest with respect to the mantle’s hot spots - 25 - IO6 years ago (Burke and Wilson, 1972; Gass et al., 1978). These domes include the Ethiopia and Kenya plateaux along the East African rift system as well as the Hoggar and Tibesti which are not, at present, part of a rift system. Attempts were made to relate the development of the East-African rift to plate boundary forces, but it is generally agreed that the activity of mantle hot spots explains better the overall evolution of the African plate. The mantle hot spots can cause doming by several mechanisms among which the following three will be examined: (1) Heating by conduction and thermal expansion of the lithosphere. (2) Heating by injection of hot magmas into the lithosphere. (3) Diapiric uprise of asthenospheric material into the lithosphere. These three processes are modelled: it is shown that the first two mechanisms do not account satisfactorily for the relationship between the timing, spatial extent and amplitude of the uplift and heat flow anomaly. On the other hand, diapiric uprise can occur in a geologically short time and induce the uplift and heat flow anomaly associated with rift systems. THE THERMAL CONDUCTION

MODEL

If the lithosphere is driven over a hot spot, heat will be transported by conduction into the lithosphere. The model considered for this study is two-dimensional but the analysis is similar to the one developed for the three-dimensional axially symmetric case (Mareschal, 1981). The geometry of the model is sketched on Fig. 1. A rectangular coordinate system, x horizontal distance, z vertical positive downward is used; z = 0 is the Earth’s surface, z = a is the lithosphere-asthenosphere boundary, The perturbation of the temperature field, caused by the thermal disturbance at the

/

V’T(x.r.t)

=Lnlx,r,t) K&

I

IL

k 8JCi(x,z=a

Inltiolly

:

Surface

Upllft

Fig.

.t) =qo(x.t)

az T(x.z.t=O)=O o~;T(x.r’,t

ldz’

I, The lithosphere for the heat conduction model. Heat is transported by conduction from the base of (I = a) where the heat flow varies with time and distance. n = thermal expansion

the lithosphere coefficient.

base of the lithosphere,

is obtained

as a solution

of the heat equation:

(1) where K is the thermal diffusivity, with the appropriate conditions. Initially, the lithosphere is in equilibrium:

initial

and

boundary

T(x,z.t=O)=O As boundary

(2) conditions,

it is assumed

that the temperature

stays constant

at the

Earth’s surface: T(x.z=O,t)=O

(3u)

and that a heat flow or a temperature anomaly is specified at the lithosphere-asthenosphere boundary. In this study, it is assumed that the heat flow (varying

with position

and time) is specified

on the lower boundary.

k~(x.;=o.r)=q,(x,r) where k is the thermal conductivity. The uplift caused by the thermal h(x,

r)=i%(x.

z, t)dz

(3b) expansion,

h(x, t), is obtained

as: (4)

where cr is proportional to the coefficient of thermal expansion. For a purely elastic coeffilithosphere, (Y= (r,(3h + 2~)/( X + 2~), (‘(Y, is the linear thermal expansion cient and X and p are the Lame parameters), for a fluid (Y= ~CX,(Pollack, 1979). The solution of eq. 1 with the initial condition (2) and the boundary conditions (3a) and (3b) is determined by integral transform techniques (e.g., Sneddon, 1972). The analytical expressions for the Fourier transforms of the uplift and of the surface

55

heat flow, after heat is conducted identical

to the Hankel

symmetric

either during

transforms

case by Mareschal

determined

The

Fourier

in the three

(198 1). In space-time

the surface heat flow are different: for the two dimensional

a short pulse or at a steady rate, are

the amplitude

domain,

of the anomalies

than for the three dimensional

spectra

contain

all the

relevant

character

of the heat flow and uplift anomaly.

spectrum

as a function

dimensional

however,

axially

the uplift and

is slightly

larger

situation.

information

about

the general

Figure 2 shows the surface heat flow

of time after the initiation

of a constant

heat flux anomaly

across the lower boundary. It shows the variation with time of the amplitude of the surface heat flow after a sinusoidal heat flow anomaly is initiated on the lower boundary. On this figure, the time is normalized to the lithospheric time constant, a2/u, the heat flow to the amplitude of the anomaly at the lower boundary. As previously noted by Gass et al. (1978), the heat flow does not change at the surface before a time of - 0.2 c.x~,/K; the amplitude of the anomaly becomes large only after 0.5 a’/~. The anomalies corresponding to the higher wavenumbers (or shorter wavelength compared to the lithospheric thickness) are attenuated. Figure 3 shows the uplift spectrum: the uplift amplitudes as a functibn after

the initiation

normalized

to the final uplift

The spectrum change

of a constant

sinusoidal

heat flow anomaly.

that would be observed

shows that: (1) the uplift

lithospheric heat flow.

thickness)

are attenuated;

if the anomaly

starts instantly

in surface heat flow, and (2) the shorter

is

were uniform.

and is more rapid than the

wavelengths

this selection

of time

The amplitude

(in comparison

is not as pronounced

to the

as for the

Step functron response Heat conduction model IOOVA = 010 VA = 0.30

E :

VA =I00

0.60.

1 g 040s =

0.004y

000

I

0.25

Fig. 2. The anomalous at the lower boundary.

a50 Time

1.00

1.25

surface heat flow spectrum as a function of time after a sudden increase in the flow Spatially,

surface heat flow is normalized of (622/K)_

075

the flow varies as a sinusoidal

function

of given wavenumber.

The

to the change in flow at the lower boundary; the time is measured in units

VA = 300

02oj

I 000 000

025

050

075

1Oc‘

125

Time

Fig. 3. The uplift spectrum,

i.e., the amplitude

the heat flow at the lower boundary. wavenumbers.

The amplitude

were transported

Spatially,

is normalized

of the uplift of the surface

caused

by a sudden

the heat flux and uplift are sinusoidal to the maximum

functions

change

in

with given

final uplift that would be observed if heat

only vertically.

If the wavelength of the anomaly is larger than two lithospheric thickness, the uplift amplitude will be larger than 80% of the one dimensional amplitude given by aqaa2/2k, (qa is the amplitude

of the heat flux anomaly at the lower boundary, (Y,k above). An uplift of 1000 m requires a heat flow anomaly

and a have been defined

of 15 mW/m’ (if the thermal expansion ity k = 2.5 W/m/K and the lithospheric

coefficient thickness

(Y= 3. 1O-5 K- ‘, the conductiva = 100 km). This is reasonable.

well below the observed excess surface heat flow in rift zones. One difficulty is that the temperature will rise by 600 K at the base of the lithosphere, melting could occur and the heat conduction model become irrelevant. The major problem is related to the timing of the uplift: for the longer wavenumbers, 50% of the uplift will be completed

in 0.3

magnitude

than the time inferred

U2/K

or

about

8. 10’ years. This is larger by almost for the Rio Grande

uplift (Stewart,

one order of

1977) or for the

East African rift (Baker, 1981). It would also require the plate to stay at rest relative to the mantle hot spot during a very long time. The uplift could still be accounted for by the heat conduction model if heat is supplied at a high rate during a short pulse. However, the surface heat flow would not change significantly before - 3 . 10’ years, in contradiction with the observation of high heat flow in active rifts. The surface heat flux anomaly could still occur in a much shorter time if the effect of the pulse is to cause doming, tension, and rifting and to permit the advection of heat by injection of magmas, or to soften the lithosphere and induce the diapiric uprise of the asthenosphere.

THE TRANSPORT OF HEAT BY MAGMA INJECTIONS

If magmas from the asthenosphere penetrate through fractures into the lithosphere, they carry latent and specific heat; their effect can be described by the addition of heat sources in the region invaded. Figure 4 shows a sketch of the model. As above, the lithospheric thickness is a; the magmas are intruded uniformly between the depths z = a and z = b at a rate that varies both horizontally and with time. The temperature perturbation is determined by the solution of the heat equation: 1 ar --= K at

02T+$

where ,4(x, t) is the rate of heat injection per unit volume (A(x, t) = 0 for 0 < z < b and A(x, t) is a given function for b -c z < a). All the other symbols are as above. Initially, there is no temperature perturbation, The boundary conditions assume that the temperature is constant at the Earth’s surface and that no additional heat flows at the lower boundary. This latter condition could be changed and, if the conductive heat flux at the lower boundary was increased, the solution described above would be superposed to the present one. The analytical expressions for the Fourier spectra of the temperature, the surface heat flow and the uplift have been determined (Mareschal, 1982) as a function of time after a short pulse of heat advection into the lower lithosphere or after the initiation of magma injections at a constant rate. Figure 5 shows the heat flow spectrum as a function of time when the lower 60% of the lithosphere is being intruded at a constant rate; it shows the time variation of the amplitude of the surface heat flow anomaly when the horizontal variation in the heat sources intensity is a sinusoidal function. The time is measured in units of a2/~, Model

2 : Heat

source5

injected

lower Tk.z.t)

into

the

lithosphere

=O

Y Z=O

V2T

= 1 aT i?x

z=b

---------------

Initmlly Surface

:

T(x.z

Uplift

.t = 0)

:a~oT(x,r’,t)

=

9’7

b-a

0 dz’

Fig. 4. The model lithosphere for the heat advection mechanism. The heat carried by the magma is injected in the lower layer of the lithosphere (b < z c a). This is equivalent to the addition of heat sources in that layer.

5X

VA =OlO VA =03C

-VA

Fig. 5. The heat flow spectrum measured

in the lithospheric

produced

if sources

fraction

after heat is advected

conduction invaded

by magma

injection

time. The heat flow is compared

of the same intensity

of the lithosphere

=300

were uniformly

distributed

at constant

rate. The time is

to the heat flow that would be throughout

the lithosphere.

the lithospheric heat conduction time constant; the heat flux is normalized flux that would be observed if the whole lithosphere were uniformly intruded present example, the heat flux will never exceed 0.6). The essential features spectrum

are essentially

The

is 0.6.

similar

to the heat flow spectrum

discussed

to the (in the of this

above, but the

Magma InjectIon model step function response G=06 100

1

080 i

VA = 010 VA = 030

VA =

““”

3.00

I

000

0’25

Fig. 6. The uphft spectrum The uplift amplitude in the lithosphere.

ois

&O Time

700

after magmas

is compared The fraction

155

are transported

at constant

to the uplift corresponding of the tithosphere

invaded

rate. The time is measured

to uniform is 0.6.

distribution

as above.

of the heat sources

59

time lag between

the initiation

of the thermal

event and the change in surface flux is

shorter. Figure

6 shows the spectrum

heat source distribution. whole

lithosphere

temperature

for the uplift

It is normalized

was intruded.

is [&(a

uplift,

the same assumptions

Because

the deeper

sources

more than the shallow sources, the uplift amplitude

0.6 (0.72) when the lower 60% of the lithosphere uplift

under

- b)(2n2 + 2ab - b2)]/6k.

the model

of heat advection

on the

to the uplift that would be observed

is intruded.

With respect

at steady

affect

if the

the average

may be larger than The amplitude

of the

to the time needed

for the

rate is not very different

from the

conduction model. If 60% of the lithosphere is invaded, an uplift of 1000 m requires a rate of heat production of 0.2. 1O-6 W/m3 (with the same assumptions as above for the thermal constants). If the molten magma transport 4. lo5 J/kg as latent heat and 2 . lo5 J/kg as specific heat (700 J K- ’ kg-‘, for 300 K temperature difference), the rate of magma injection needed is lo- I6 SC’: this is equivalent to 0.3% of the total volume of the lithosphere in lo6 years. It is questionable that this is at all possible. Furthermore, it has been mentioned above that, with a constant rate of magma injection,

the uplift

time. The uplift amount

is proportional

to the average change

of heat that has been transported

conducted within,

will take place in a time not shorter

and heats

the lithosphere

the temperature

change

than the heat conduction

in temperature

into the lithosphere.

from below as is advected

and the uplift

amplitude

or to the net

If as much heat is and heats it from

are the same;

only

the

spatial dependence of the uplift could show some difference. The situation is different for the surface heat flow: it changes more rapidly when heat is advected into

the lithosphere

than

when

it is conducted

from

surface. The uplift and the surface heat flow anomaly short intense episode of magma invasion. However,

the lower boundary

to the

could therefore result from a a 1000 m uplift requires the

average temperature of the lithosphere to rise by about 300 K: with the parameter values retained above, the amount of magma needed represents 30% of the total volume (or 50% of the volume of the invaded lower part) of the lithosphere. Subsidence of the uplifted region would follow the ending of the magma intrusion event unless advection continues at a rate that balances the heat loss at the surface. It is questionable that the required amount of magma could be injected into the lower lithosphere without either some form of lithospheric stretching which would allow

the passive

spheric mantle

uprise

of asthenospheric

by active diapirism

materials

or replacement

of the litho-

of the asthenosphere.

THE DIAPIRIC UPRISE MODEL

An alternate mechanism of uplift is the diapiric uprise of the asthenosphere into the lithosphere (Ramberg, 1968; 1972; 1977; Artyushkov, 1971; or, for a modified version, Bird, 1979). This process requires a density inversion between the litho-

and the asthenosphere (Press. 1970: Anderson and Hart. 1976). If there is such an inversion. the system 15 gravitationally unstable and the tighter asthen+ sphere

sphere will rise into the lithosphere.

This does not happen

in most situations

because

the stresses involved are small and the lower lithosphere, with an effective viscosity of - 10” Pa s (e.g.. Walcott, 1973). can withstand them for (geologically) long times. In order for the lower lithosphere in a shorter magnitude.

time, it is necessarv In the temperature

thermally

activated

an equation

to flow and for the diapiric

to reduce range

rate process;

its viscosity

considered,

steady

uprise to occur

by at least three orders state

flow of rocks

of is a

the stress, T. and the rate of strain. i. are related by

of the type (Carter.

1976):

i = A exp{-Q/RT)r”

(8)

where n ranges between

2 and 4, A is a constant,

R is the gas constant. The effective viscosity

of the lower

Q is the creep activation

lithosphere

will thus

drop

energy and if there

is a

substantial increase in temperature. Bridwell (1977) suggests that, 50 km beneath the Rio Grande rift, the effective viscosity is less than 1O’e Pa s. In these conditions, a gravitationally Analytical

Model

3

unstable layer could not be maintained over a long time. studies (Ramberg. 1968, 1976; Artyushkov. 1971: and others)

D~op!r~c uprise

of the

lower

Nave-Stokes

osthenosphere

show

Into the

ilthosphere

equotlon

:pg

=,LV~G-VP-PC~ vii=0

P : density e

viscosity

u

velocity

tleld

P : pressure g : accelerotlon

Fig. 7. The diapiric

gmwty

uprise model. The system consists

and the asthenosphere; lithosphere.

of

the main characteristic

of 3 main layers:

the crust, the lithospheric

of the model is the density

inversion

mantle

at the base of the

61

that a small sinusoidal gravitational

perturbation

instability

depending

(see Fig. 7) increases

on the wavelength

is given by a relationship

of gravity,

between

two fluids in a state of

exponentially

of the perturbation.

(Ramberg,

where g is the acceleration the unstable

at the interface

with

time

The characteristic

at a rate

growth time, r,

1968):

Ap is the density

layer, p, and pz are the viscosities

contrast,

a is the thickness

and X is the perturbation

of

wavelength.

f is a function which depends on the boundary conditions. The wavelength, X, which maximizes f will be the most amplified. Depending on the boundary conditions and viscosity contrast, the optimal wavelength is 4- 10 times the first layer thickness; the corresponding value off is 0.1 to 0.2. For a viscosity of 10” Pa s, the characteristic time (the time it takes for the amplitude of the interface perturbation to be multiplied by e) is of the order of lo6 years (a = 100 km, Ap = 0.2. lo3 kg/m’). The analytical approximations mentioned above give a good idea of the relationships between the dimension of the system, the viscosity and the characteristic time for the growth of a gravitational instability. It cannot be used to predict the evolution

of the system when the viscosity

when the amplitude are needed.

of the interface

depends

perturbation

strongly

becomes

The temperature regime of the model is determined its boundary and initial conditions. The mechanical

evolution

and an equation condition :

larger; numerical

by the equation

and

methods

by the heat equation

of the system is determined

of state. The equation

on the temperature

(7) with of motion

of state is given by the incompressibility

O.s=()

(10)

where U is the velocity field. In order to keep the numerics of a Newtonian (e.g., Malvern,

tractable,

fluid. The equation

the constitutive

of motion

equation

assumed

is then the Navier-Stokes

is that

equation

1969):

du P-df=pV2ii+pg-VPt0

-

(111

where p is the density,

g is the acceleration

the viscosity

to have a temperature

assumed

of gravity and P is the pressure dependence

field; p is

of the form:

p = p. exp{UT) In the Navier-Stokes equation, the second order terms of the form EU been neglected. Because the viscosity is high, the viscous forces are many magnitude larger than the inertial forces which can be neglected. The conditions require the velocity and the stress to be continuous across each

(12) - VT have orders of boundary interface.

TABLE

I

The Parameters -___

of the numerical

model ~~~~_~

Layer thickness

(km)

Densit>

(g,/cm’)

Heat production

([LW/m’ (Pa S)

Viscosit\i Thermal

diffusivity

.~_____ 40

)

(m2/s)

conductivity

60 13

3.5

0.6 ,013

-I K-1 (W m ) Heat flow from below 160 km: 10 mW/m*

Thermal

60

2.9

0.12

(I

SIO?

s I(,~’

exp(2000/7)

exp( 2000/ 7‘ )

10Kh

10-h

IO fi

2.5

2.5

2,s ____.._

The finite element

method

(e.g., Huebner,

1975; Strang

._.

and Fix. 1973) has been

used to solve the system consisting of the Navier-Stokes equation. the incompressibility condition and the heat equation. The numerical method used in this study is identical to the one described by Mareschal and West (1980). The main parameters of the very simplified model of the lithosphere and asthenosphere considered in this study are summarized in Table I. The mode1 consists of three layers: a 40 km thick crust (with density 2.9 g/cm’), a 60 km thick layer of lithospheric mantle (density 3.5 g/cm3) over the lighter asthenosphere (3.3 g/cm3). Initially, the Earth surface and all the interfaces are flat with the exception of a small 500 m perturbation of the lithosphere-asthenosphere boundary. In order to use the finite element region of space and boundary

method,

conditions

the problem

are imposed

is restricted

on arbitrarily

to a limited

chosen boundary.

The region considered is 500 km wide and 160 km deep. On the lateral boundaries, periodic conditions have been imposed although other conditions would be more realistic impact

for modelling

the rift. In a different

of the lower boundary

condition

study (Mareschal

had been reduced

below the rising diapir layer. Because of computer not done, and the results are therefore influenced boundary conditions.

and West, 1980) the

by adding

a dense layer

memory and time limits, this was by both the lateral and the lower

Figure 8a shows the state of the system and the velocity distribution 11.2 . lo6 years. The interface perturbation has grown and smaller oscillations

after seem

to develop, possibly as a result of wavelength selection (but this development may also be affected by the lateral boundary conditions). Figure 8b shows the state of the model and the velocity distribution after 13 . lo6 years. The asthenosphere diapir has raised almost to the crust mantle boundary and the lithospheric mantle sinks. The relief on the Earth’s surface is - 1200 m. The width of the uplifted region is 150 km. Crustal thinning seems to develop. The computer programs were not run further than this stage because cal errors were accumulating and it was felt that additional computations provide

better than an extrapolation

of the models.

the numeriwould not

63

b Fig. 8a. The state of the system and the velocity km. The maximum

velocity

is 0.09 m/year.

field after

The surface

11.2.IO6 years. The asthenosphere

b. The state of the system and the velocity field after 13. IO6 years. The asthenosphere 65 km coming

close to the crust. The maximum

rose by 10

uplift is 300 m.

velocity is 0.5 m/years.

The surface

diapir has risen to uplift is 1200 m.

The numerical model presented is a relatively crude model and it does not intend to make a detailed prediction of the evolution of the rift zone. The choice of some of the parameters (listed in Table I) may be debatable: for instance, the lithosphere asthenosphere density contrast is unreasonably high; the crustal layer is assumed of uniform density and viscous rheology, but with much higher viscosity than the mantle; the absence of flow on the lateral boundaries affects the convection pattern

64

and

restricts

predictions

the development on the evolution

on the thickness would include The purpose asthenosphere

and faulting

during

of the present is a feasible

which

pattern

a more realistic

is that the numerical

of crustal

In order

mndelling

mechanism

accurate

is desirable

for the crust and allow lateral

model \;as to determine

whether diapiric

of uplift before rifting. that it 1s feasible.

lithosphere

to make

and the surface heat flow. as well as

of the crust. further

rheology

model indicates

the lower

thinning.

of the topography

is heated

and

uprise of the

The author‘s

opinion

After an initiation

period,

a small

boundary between the lithosphere and the asthenosphere and the uplift occur within 2. lOh to 10’ years depending

that

flow.

perturbation

of the

grows, the diapiric uprise on the effective viscosity of

the lower lithosphere. This time is in agreement with some of the reported uplift rates of more than 1000 m during the past 10’ years in the Rio Cirande and East African

rifts (Stewart.

1977).

CONCLUSIONS

Heating of the lithosphere, heat carried by the injection

either through conduction or through advection of the of magmas, is not adequate to account for the uplift

and heat flow in rifted regions. It could, however. play an important part in the rifting process because heating and softening of the lower lithosphere is needed for flow to take place in a geologically If, following

a heating

short time.

event, the effective viscosity

of the lower lithosphere

drops

to lo’“-102’ Pa s, the diapiric uprise of a low density layer from the asthenosphere could take place in the geologically short time of 2. 10” to 10’ years, resulting in the uplift rates observed near rift systems. Although the present model indicates

that diapiric

uprise is a feasible mechanism

of rift initiation, it is too crude a model to demonstrate that the process actually occurs and to determine the conditions for rifting to continue. Further models, that would include tions,

the exact rheology

are needed

geophysical

to make

of the crust and more adequate

predictions

that

can be tested

model

based

boundary

against

condi-

geological

and

observations.

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