Thermal effects of thrust faulting

Earth and Planeta O' Science Letters, 56 (1981) 233-244 Elsevier Scientific Publishing Company, Amsterdam - Printed in The Netherlands

233

[31

Thermal effects of thrust faulting Jon Brewer Department of Geological Sciences, Cornell Uni~ersiO', Ithaca, N Y 14853 (U. S. A.)

Received December 4, 1979 Revised version received July 28, 1981

Calculations based on simple models of overthrust sheets in crystalline basement rocks show that significant thermal effects may result from their movements. If rates are sufficiently high (e.g. plate tectonic rates), the thrust sheets sufficiently thick (5, 10 and 15 km are modelled here), the distances moved sufficiently large, and for reasonable values of the coefficient of friction along the thrust plane overthrusting can cause metamorphic mineral zonations and heat flow anomalies observable in the field. Regions where large-scale overthrusting has occurred should be characterized by a decrease with depth of grade of metamorphic mineral assemblages and anomalously low heat flow. The theoretical effects are presented as a series of m a x i m u m temperature vs. depth and heat flow vs. time plots.

1. Introduction Simple quantitative calculations show that regions of extensive overthrusting should be characterized by anomalous heat flows and metamorphic zonations measurable in the field. Measuring and modelling these effects can provide important information about the tectonic history of an area. Such information should include age and extent of overthrusting, and thickness of overthrust sheets. Orogenic belts where extensive overthrusting of basement rock has occurred include the Alps [1], the Himalayas [2] and the Southern Appalachians

[3]. The theoretical effects of frictional heating along thrust faults have previously been considered by Reitan [4-6] and Pierce [7]. Metamorphic zonations observed in the field have also been used to quantitatively constrain models of frictional heating during thrust movements in the Austrian Alps [8], in the Transverse Ranges of California [9] and along the Olympos thrust in Greece [10]. Oxburgh and Turcotte [11] examined the associated problems of the reequilibration of a regional thermal gradient disturbed by thrust movements, and applied the results to explain some features of Alpine

metamorphism. Scholtz [12] gives a useful general review of examples of thermal effects due to faulting. The present paper generalizes these authors' results using an overthrust model that combines frictional heating along the thrust plane with the thermal effects due to relaxation of the disturbed thermal gradient. With various combinations of fault slab thickness, distance moved, rate of movement and coefficient of friction along the thrust plane, calculations of temperature profiles and surface heat flux show that, under the fairly idealized conditions modelled, thrusting effects may make significant contributions to the thermal budget of an orogenic belt. The results are presented as a series of temperature-depth plots and heat flow plots; it is hoped that these may be of direct use to field geologists assessing the metamorphic effects of overthrust faulting.

2. The thrusting model The model used is idealized and simplified (Fig. 1), and the mathematical calculations are considered in the appendix. The thrust slab is

0012-821X/81/0000-0000/$02.75 '~ 1981 Elsevier Scientific Publishing Company

234 TABLE 1

SURFACE

A

I

. . . . . .

2 3--

Variables and constants used in calculations H D

thickness of overthrust slab distance moved by slab total time of thrusting rate of slip coefficient of dynamic friction distance perpendicular to thrust plane non-dimensionalised distance perpendicular to thrust plane time since start of thrusting non-dimensionalised time since start of thrusting temperature non-dimensionalised temperature tangential stress constant regional geothermal gradient before thrusting specific heat of rock : 0.25 cal/g °C thermal diffusivity: 0.01 cm2/s thermal conductivity = 0.007 cal/g s density=2.8 gcm3 acceleration due to gravity

tl U

SURFACE

B

f X X'

.

.

.

.

.

.

3

t t'

T SURFACE g. . . . . . 3 7-/"r'~ 7"7

r-rt-7-,-r-17--1~-~

C r'~,-'r-*"r"r

T

A T/A x ('p

Fig. 1. Overthrusting model. A. Distribution of isotherms bcfore overthrusting. B. Distribution of isotherms soon after overthrusting, in absence of frictional heating. C. Distribution of metamorphic facies after overthrusting due to frictional heating and thermal relaxation. Flat portion of overthrust is modelled in this paper. assumed horizontal and is moving at a constant velocity over the g r o u n d surface along a planar slip zone. D e f o r m a t i o n is assumed to occur at a constant rate; the model is therefore a better approximation for thrust sheets driven by compressional forces, rather than those moving under the influence of the gravitational b o d y force. Frictional heating occurs along the slip zone, and the act of overthrusting causes a disturbance of the thermal gradient as illustrated in Fig. lB. Fig. IC shows the resultant distribution of thermal anomalies that would be recorded by mineral assemblages. The model assumes that the rate of heat generation per unit area q = u r , where r is the tangential stress across the slip plane (some fraction of the total weight of the overthrust sheet) and u is the rate of slip. Rock thermal properties are assumed to be constant; representative values for the granites and gneisses of the earth's crust are given in Table 1. The variables of the model are the thickness H of the thrust slab, the distance D moved by the slab, the rate of slip u, and the coefficient of friction f at the base of the slab. The values used for these variables are given in Table 2. The frictional heating problem is formulated in

K

k P g

such a way that the temperature at any depth x and time t after start of thrusting is: ~'(x,t) : f,D/[pc,(,,~t,) :

'/2]

T/g

where the non-dimen'sional temperature T varies between 0 and 1 (see the appendix), Cp is the specific heat at constant pressure, ~ the thermal diffusivity, and t j the total time of thrusting.

3. Discussion of assumptions The model is one-dimensional although in reality the temperature profiles and magnitudes of the thermal anomaly vary between the toe of the thrust and the root zone; the solution assumes that the heat flux parallel to the fault is small c o m p a r e d with the heat flux perpendicular to the fault. F r o m a geological point of view it is unlikely that, for a given overthrust, the temperature anomaly could be sufficiently accurately m a p p e d to demonstrate the difference between a one- and two-dimensional solution. Other variables such as fluid circulation m a y be important and rock exposure is unlikely to be adequate.

235

The rate of heating is proportional to the tangential stress across the fault plane; ~"=fogH. Byerlee [13] has shown from laboratory experiments on dry rock that above 2kbar pressure (about 6 km depth) an upper limit t o f i s about 0.6 regardless of rock type. I have therefore chosen this as an upper limit. Values of f of 0.4 and 0.2 are considered as possible approximations for situations where overthrusts move along planes of high pore pressures [14] or wide zones of plastic deformation [ 15,16]. No account is taken of convective transfer of heat by fluids which are difficult to model in a general way, but which may be important in some cases. The model best applies to large thrust in dry granitic or gneissic rocks typical of the deeper crust. Thrusting is assumed concentrated in a single plane. This is approximately the case in some thrusts, such as the Moine thrust system [17], the Glarus thrust [18] and the Champlain thrust [19], but in other cases the effect of a thick zone of thrusting may be important [5,20,21]. Cardwell et al. [20] assume constant heat production within a fault zone of finite width w, and demonstrate that f o r w>(xtl/2) 1/2 the effect of finite fault width greatly affects the rate of heat production away from the fault zone. In my models the minimum time of thrusting is 0.5 Myr and maximum time 30 Myr, and so finite fault widths will only be important when w > 2.5 km and 20 km respectively. Typically, widths of thrusts deforming under brittle conditions are significantly less than these figures, but ductile shear zones may be several kilometers wide and in this case the thin fault approximation probably breaks down. These solutions may also be applied to the situation where thrusting is restricted to a number of sub-parallel shear z o n e s - - t h e increments in temperature developed along the individual shear zones are additive, and the total heat generated is due to the sum of the relative displacements of the individual shear zones. In calculating surface heat flow anomalies I have assumed a crustal temperature gradient of 3 0 ° C / k m which gives a regional equilibrium heat flow of 2.1 heat flow units (HFU). The effect of heat-producing elements within and below the base

TABLE 2 Values of parameters used Thickness of slab, H = 5 , 10, 15 km Distance moved, D = 5 H , 10H, 2 0 H Rate of slip, u = 1, 5 c m / y r Coefficient of friction,f=0.2, 0.4, 0.6

of the thrust sheet are ignored. This may be an important contribution to thermal effects observed in overthrust regimes of the Alps [8]. Erosion will cause an apparent increase in the thermal gradient above the thrust plane [22]. If rates of erosion are high enough, mineral assemblages formed by burial due to overthrusting may reflect a metamorphic gradient rather than the true geothermal gradient since in this case the rocks will have relatively higher-pressure and lower-temperature mineralogies [22]. For a thick thrust sheet moving several hundreds of kilometers isostatic readjustments and resulting erosion might cause significant overprinting by the metamorphic gradient of mineral assemblages formed by frictional heating, and thus a steeper gradient. Buffering reactions might be important under certain conditions, and in granites and gneisses of the earth's crust the main reaction is probably the breakdown of quartz and muscovite (at about 800°C at mid-crustal pressures). This will release water and may initiate melting or, alternatively, release of water might result in higher pore fluid pressures and more brittle behaviour [14]. For hydrous granites and gneisses, melting may be

0

50 -

T,°C 150

I00 T

.

.

.

DEPTH.

KM

200 .

iO L

~

300 1

"

5 ......................

250

.

~:1:

.

FA T P

~'~i ....... ~

NE

~ ..................

"\\

Fig. 2. Profiles of maximum temperatures developed by overthrusting 5 km thick slab for various parameter values.

236

T.*C O

DEPTH, KM

I0'

I00

200

500

m°c

400

60O

500

FAULt PLANE

i

T z~'

,K~o , 6oo

eoo. iooo T 12oo

6~ /

,/

15,

o

700

ili

~::~

DEPTH. KM

"

'~

+:

~i

~

............; 7 )

/

\ '

.................

/

21} 20

Fig. 3. Profiles of m a x i m u m temperatures developed by overthrusting 10 km thick slab for various parameter values.

~

/

i

i'

25

Fig. 4. Profiles of m a x i m u m temperatures developed by over. thrusting 15 km thick slab for various parameter values.

:5.5 /

/

&O

i9

2.5 HEAT FLOW, HFU

I

"

i!

/ /~ / I/

'

.

.

. ~.~-~ . . . . . . . . .

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EQUILIBRIUM SURFACE HEAT FLOW

x

........

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Distance moved

. .. . ..

. ~---

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25 km 50 50

5 cm/yr 5 I

0.6 0.4 0,6

4 5 6 7 8 9

50 I00 I00 I00 I00 100

5 5 I 5 I 5

0.6 O. 2 0.4 0.4 0.6 0.6

I

I

I

I

I

I

I

I

I

[

I

2

3

4

5

6

7

8

9

I0

II

AFTER

START OF

~

- ~

~--..~ --=

"

Rote of Coefficient movement of friction

I

TIME

~ - c ~

THRUSTING,

I

12

I

I

I

13

14.

15

M.Y.

Fig. 5. Heat flow profiles arising from overthrusting 5 km thick slab. Black circles on the curves indicate end of thrusting.

237

initiated at 600-700°C at mid-crustal pressures [23]. If partial melting does occur, friction along the thrust plane would probably drop and cause a decrease in heat generation, and thus melting may be a selfqimiting process, restricted in areal extent. Even if melting did not occur, high temperatures along the fault plane might result in loss of shear strength and extensive ductile flow. In the model, this would represent an apparent drop in the coefficient of friction, and thus in the amount of shear heating. Some authors think ductile flow might occur at temperatures as low as 250-300°C (lower greenschist facies) [24].

blages developed in the field should reflect these temperatures if reactions go to completion. The results of Ahrens and Schubert [25] imply that this would be the case in the presence of hydrous minerals. Fig. 10 shows the transient temperatures developed along a particular thrust; maximum temperatures are ~reached at the cessation of thrusting and then drop sharply, so retrogressive effects should not be important. Fig. 2 shows maximum temperatures reached for a fault slab 5 km thick using the variables of Table 2. If f = 0.2 there is a negligible temperature increase due to frictional heating, and for the minimum distance moved, D--25 km, frictional heating is only important for u = 5 cm/yr and f : 0.6, when the temperature increase on the fault plane is about 50°C. For D : 100 km, u -- 5 cm/yr and f = 0.6, the temperature increase on the fault plane may be as high as 150°C. Fig. 3 shows the maximum temperatures reached for a fault slab 10 km thick. Under suita-

4. Thermal effects of thrust faulting Figs. 2-4 show the maximum temperatures reached after the start of thrusting as a function of depth. Assuming extensive post-thrusting retrogression has not occurred, metamorphic assem-

4sp t

/

4.0~

/

z

!

,0o ,o0 ~%

/ s

5.5 ~

200

~

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04 o2

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0,

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3.0^

I ,

HEATFLOW, F ~ ~~ HFU 2,.0i~ '7 ~

\

J\ ?~. 1.5~-'!// /

i.oF

o~ o

~

,o

,~5

2o~

2~

~o

TIME, M.Y.

Fig. 6. Heat flow profiles arising from overthrusting 10 km thick slab. Black circles on the curves indicate end of thrusting.

238 ble conditions, for D = 200 km and f = 0.6, the temperature change on the fault plane may be as high as 350°C, giving an absolute temperature of 650°C. At these temperatures it is unlikely that brittle slip is occurring [26] in which case the model may be inapplicable. Fig. 4 shows maximum temperatures reached for a fault slab 15 km thick. Temperatures reached are extreme for the upper ranges of the variables, and depending on the temperature dependence of shear stress, probably indicate partial melting con-

ditions. Melting along fault planes has been observed in the field (e.g. 27-30]), and these calculations show that such partial melting can occur for reasonable values of slab thickness, distance moved and plate tectonic rates of movement. The heat flow plots (Figs. 5-8) show that while the thrust is moving, frictionally generated heat will dominate the surface heat flow for the larger values of f, and in extreme cases may result in surface heat flow double the background value. However, by the time 2t] has elapsed since the

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4.5

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EQUILIBRIUM HEAT FLOW ............................................................................

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msq~co movl(l

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75 ~50 I~0

5 ~ 5 i ~ I 5 5 ~

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2o

5cm/~r

.

.

.

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- - - - -

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o2 04 0.4 0.6 0.6

0.4

0.6

2'~ TIME.

~o

3'5

Xo

~

M.Y.

Fig. 7. Heat flow profiles arising from overthrusting 15 km thick slab. Black circles on the curves indicate end of thrusting.

~b

239

start of thrusting, this positive anomaly has essentially disappeared and the presence of overthrusting is marked by a negative anomaly due to the suppression of the regional thermal gradient by the thrust slab. It is interesting to note that even if the frictional heat flow is suppressed by the various mechanisms discussed above, the long-term negative anomaly is not affected by these and should be diagnostic of large scale overthrusting. The thrust slab is modelled as moving over an infinite half-space, and in this case the surface heat flow would approach its original value as t--* ~ . However, the effect of constant temperature at the base of the lithosphere is to restore the heat flow to its equilibrium value 200-300 Myr after start of thrusting (D.L. Turcotte, personal communication, 1979). Fig. 8 shows this long-term surface heat flow. Anomalously low heat flow in

2.5

r

l.Oj£,

o.sl ~,' oJ

A

,

2.5

2"0t ~

~~ o.5.o

t

orogenic belts may therefore indicate large-scale overthrusting within the last 200-300 Myr.

5. Conclusions The simple model of overthrusting, where frictional heating is generated along a slip zone deforming at constant strain rates (plate tectonic rates) indicates that sizeable thermal anomalies are produced. For the models considered here, temperatures may rise as high as 300°C above those due to the normal geothermal gradient, and should result in prograde metamorphic reaction zonations near the fault. Inversions of metamorphic zonations should occur below the fault, and such effects have been described from western Newfoundland [31], the Himalayas [2,32], in the Transverse Ranges of California [9], along the Olympos thrust [10] and in the Prealps [33]. Another prediction of the model is that heat flow anomalies should occur at the surface. During thrusting of sufficiently large faults, positive anomalies perhaps twice the background value could be generated. After the end of thrusting, heat flow anomalies will be negative for the next 200-300 Myr. These results, of course, assume no extra contributions to the thermal budget such as magmatic activity. Orogenic belts whose metamorphic assemblages have been explained in terms of thermal relaxations of overthrust sheets include the Eastern Alps [8, 34].

j~ B

~ o, i

2'51

I should like to thank J. Ahern, D. Chinn, and G. Long for their help. D. Turcotte provided much advice and funds for this work. This research was funded by NSF grant EAR 76-84257. Cornell Contribution to Geological Sciences No. 666.

i

2.oJ

J

1,5 i

i

I

0.5-

o2 o

Acknowledgements

r

i i

C

F

120 /,50 I~) 21'0 240 270 ~)0 TIME ,M.¥.

Fig. 8. Generalized heat flow profiles arising form overthrusting up to 300 Ma after the start of movements: (A) 5 km thick slab; (B) 10 km thick slab; (C) 15 km thick slab. Shaded areas in lower two figures represent ranges of heat flows for the different parameters.

240

Appendix--Thermal calculations

Frictional heating The thrust slab is assumed horizontal, moving at a constant rate along the planar slip zone (Fig. 1). Slip is assumed to occur under brittle conditions, and heating is confined to the plane of slip. Rock properties assumed constant are given in Table 1. The equation for one-dimensional conduction of heat is: 2 - 0r/0/]

pc,,[,,o2r/Ox

= -- Q ( x , t )

(A-l)

where Q(x,t) is the rate of heat generation by shearing forces per unit volume. Along the plane of slip, the rate of heat generation per unit area is:

Q( xo,t ) = 0 ;

t~<0

= 8(Xo)~'u;

t>0

where 8(Xo) is the Dirac delta function. The resulting displacement is:

D= ut I where t I is the total time of thrusting. The initial conditions are:

T=Q(xo,t)=O ; t<~O Let:

A = x / { 2 [ x ( t - t o ) ] 1/2} A o = x o / { 2 [ x ( t - t o ) ] I/2} Az, = (2H-x)/{2[,(tF=[exp(-AZ)]/[tt(t

to)] 1/2} -

to) '/2]

F 2 . = [exp( - A2 ) - e x p ( - A~.q)]/[ t l < t - t0) 1/2] then the solution to (A-l) is [35]:

T(x,t)=[l/2oc,,(~,,)l/~lfo'F_([exp--(A--Ao)2lQ(xo,to)/(t--to)'/~ } d x 0 d t 0 Following McKenzie and Brune [36] and substituting Q = ur and u = T(.X',I) :

D/t~

(A-2)

into (A-2):

('/[20Cp(77~)I/2]} fotgOdto; t~tll

/

(A-3)

The ground surface is constrained to be at 0°C. This is achieved by adding a fault plane image to (A-3)

[35]: (A-n) I/2

tl F

241 For ease of computation, the equations are non-dimensionalised:

f =[pcp(~rxt,)'/2/(D,)]T(x,t); t'=t/t,; t"=to/t,; x'=x/H;

X=H/(2xt,) 1/2

(A-5)

Integration by parts then gives (after McKenzie and Brune [36]):

x'2xa/2t ') --exp[- (2 - x') 2X2/2t'] } -- (rr/2)'/2lx'lX erfc[lx'lX/(2t') '/2] + (~r/2)'/2

T = (t')'/2 ( e x p ( -

T = (t')t/2{ e x p ( -

xa~2/Zt ') -

[2 -

x']X erfc[I 2 -- x'lX/(2t') '/2] (A-6)

,'>1

(A-7)

e x p [ - (2 -- x') 2X2/2t'] }

-(t'--1)'/2{exp[--x'2~z/2(t ' -

1)]-exp[-(Z-x')2~2/2(t

--(¢r/2)l/2]x'l$ {erfc[]x'l~/(2t') l/2] --erfc[] x'l.~/(2 + (~r/2)'/212 --

0~
'-

1)]}

{ t ' - - I }),/2] }

x'lX { erfc[I 2 -- x'lX/(2t' )'/2]

--erfc[12--x'l~/(2{t'--1;)'/2]

}

The general form of this temperature profile without the image is shown in fig. la of McKenzie and Brune [36]. Equation (A-6) is solved and redimensionalised for values of the variables of Table 2.

Thermal relaxation calculations These are modified from Oxburgh and Turcotte [11] who considered the case of instantaneously emplaced thrust sheets in which just after thrusting the thermal gradient has a "saw-tooth" form (Fig. A-1A). This saw-tooth causes an inverted thermal gradient which very soon decays (in a time on the order of 0.1 t~ ) to a thermal gradient about half its initial value. This then relaxes to its initial value over millions of years. Fig. 6 of Oxburgh and Turcotte [11] shows the relaxation of the thermal gradient after the end of thrusting. I have assumed in this paper that thermal relaxation of the thrust occurs as soon as movement starts. As the overthrust moves over the ground surface, the one-dimensional heat-conduction equation is: oc

[Ka2r/ax 2 -

a t / a t ] -- o

(A-S)

With the surface temperature kept at 0°C, the problem may be posed as the sum of two Heaviside functions, one at a depth H and one at a depth - H , which are superimposed on a linear regional geothermal gradient (Fig. A-1B). The solution to this problem is modified from Carslaw and Jaeger [37]:

T(x,t)

= Tb( ½[ - - e r f ( [ 2 H -

x]/[2(xt)'/2])+ erf(x/[2(xt)'/2])]--[(x/H)-

1]}

(A-9)

where T b is the temperature at a depth H, before overthrusting. To obtain the final temperature profiles due to frictional heating and thermal relaxation, the solution obtained from (A-8) is added to that obtained after redimensionalising (A-6). Fig. A-2 shows the transient temperature profiles for a typical combination of the variables, and Figs. 2-4 show the maximum temperatures reached as a function of depth for various values of the variables.

242

Temperature

Depth

"~-

Thrustplane A.

IOO

\

\

200

m,°c 300 400 500

600700800900

\ \

\

Image\ \ \

\

\

THRUST

-H

B.

PLANE

DEPTH,

\

KM

\

- %I

% }

,5i: zol

\'\,

i

L

\

•~•

[

psL '

,IL

30

Fig. A-I. A. "Saw-tooth" temperature profile developed immediately after start of overthrusting. B. Image of temperature profile used to solve thermal relaxation problem. T b = i n i t i a l temperature at base of thrust sheet.

Fig. A-2. Transient temperature profiles developed by combination of thermal relaxation and frictional heating. Initial "saw-tooth" profilc relaxes to original constant thermal gradient (t ~ ~). Frictional heating causes the intermediate cuspate profiles.

Heat flow calculations

The surface heat flow arising from frictional heating is obtained from (A-6):

[dTFRIC/dXlx=H-=(--'rD/(pCpKll))erfc[H/(2(Kt)I/2)];

t~t 1

= (--.rD/(pcpxt,))(erfc[H/(2(xtt)'/2)]-erfc[H/(2(x(t-t,)}'/2)]}; avRic = - k [dTFR~C/dx ]

t>t,

(A-10)

The contribution from the relaxation of the thermal gradient is obtained from (A-8):

dTRELAx/dX=-AT/Ax{H/('trrt)l/e[exp(H2/4xt)]-1} QRELAX = -- k [dTRELAx / d x ]

(A-11)

Total heat flow is then the sum of equations (A-10) and (A-11). Surface heat flow variation is shown in Figs. 5-8. The regions of the thrust plane mathematically best described by this frictional heating model are those which experience relative movements for the total time

243

of thrusting. The thermal relaxation model is most applicable in the region of actual overthrusting, however, these models are adequate approximations of the Peclet number P ( = uH/~)> 1 [11] implying that solid state convective heat transport dominates conductive flow away from the thrust. For the values of the variables considered here, P varies from 1.6 to 23.8.

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