Numerical modelling of lithosphere shortening: Application to the Laramide erogenic province, western USA

385

Tectonophysics, 2210993) 385-411 Elsevier Science Publishers B.V., Amsterdam

Numerical modelling of lithosphere shortening: application to the Laramide erogenic province, western USA S.S. Egan and J.M. Urquhart Department of Geologv, Universi@ of Keele, Keele, Staffordshire, ST5 SBG, UK

(Received June 29,1992; revised version accepted December 10,1992)

ABSTRACT A two-dimensional model of lithosphere shortening is presented which quantifies crustal thickening, temperature perturbations and flexural isostatic components. The model assumes that the upper brittle layer of the crust deforms by thrusting, while the lower ductile lithosphere accommodates compressional deformation by a pure shear or “squashing” mechanism. Model results suggest that basement uplift, foreland basin development and underlying crustal structure are controlled by the amount and configuration of the compressional deformation in the upper and lower lithosphere, the perturbation of the temperature field, erosion and the flexural rigidity of the lithosphere. The model is applicable to regions of thick-skinned thrust tectonics and is applied to the Laramide erogenic province in the western USA Model simulations of structural cross-sections across the Laramide province show basement upliis and adjacent foreland basins that are comparable in magnitude with those suggested by geological data. The model has also been used to provide insights into the tectonic evolution of the Laramide province and an attempt has been made to determine the flexural rigidity of the lithosphere at the time of Laramide deformation as well as quantify both the effects of the post-shortening re-equilibration of the temperature field and thrust-uplift erosion. The amount of crustal thickening and post-shortening cooling of the geotherm predicted by the two-dimensional model of lithosphere shortening are used in strength calculations to determine the relative strength or weakness of the lithosphere. The results suggest that the lithosphere is relatively strong immediately following shortening, due to the cooling of the geotherm. Following shortening, however, gradual weakening occurs as the temperature field returns back to its unperturbed state in the presence of an enhanced crustal thickness. The results are compatible with the evolution of the Laramide province, which has experienced a change in tectonic regime to one of extension over the last 20-30 Ma.

Introduction The application of numerical modelling to the study of lithosphere shortening has provided important insights into the relationship between the compressional deformation and resulting tectonic effects. For example, Beaumont (1978, 1981) and Jordan (1981) have modelled the response of the lithosphere to thrust-sheet loading to show that foreland basin development is controlled by flexural down-warping of the lithosphere. Royden and Kamer (1984) improved upon these earlier modelling studies of compressional tectonics to include negative buoyancy effects created by an underlying subducted lithosphere slab. In this study a two-dimensional model of lithosphere shortening is presented which attempts to

integrate crustal thickening and thermal and isostatic components. The model quantifies the crustal thickening resulting from reverse movement along major basement faults. In order to maintain compatibility with major basement faults seen op deep seismic reflection data (e.g. Brewer et al., 1982; Klemperer and Hobbs, 1991), these faults detach at either mid- or lower-crustal depths (Kusznir et al., 1987). Below the fault detachment depth the model assumes the lithosphere to be ductile and compressional deformation occurs by a pure shear (“squashing”) mechanism. The model also quantifies the disturbances caused to the temperature field by lithosphere shortening. The temperature field is cooled initially as hotter material is pushed to a greater depth. This cooling drives a small amount of

C040-1951/93/$06.00 8 1993 - Elsevier Science Publishers B.V. Ah rights reserved

386

basement subsidence. Following shortening the temperature field heats back to an unperturbed state, generating gradual uplift of the surface. The final component included in the model is flexural isostasy. Both crustal thickening and temperature perturbations constitute load forces upon the lithosphere, which have to pass through an isostatic filter in order to generate a resultant basement geometry and crustal structure. The model is applicable to regions of thickskinned thrust tectonics such as the Laramide erogenic province, western USA. Models of sections across major Laramide structures in Wyoming have been generated to both test the validity of the model and also provide insights into aspects of the evolution of the Laramide region. In particular, the effects of flexural isostasy, the post-shortening re-equilibration of the temperature field and thrust-uplift erosion are investigated. Previous studies of lithosphere rheology by Vink et al. (1984) and Glazner and Bartley (1985) suggested that areas that have undergone largescale shortening are weak and will preferentially rift. This hypothesis is tested using the model described above to quantify post-shortening crustal thickening and temperature field perturbations. These parameters are then used in strength calculations to determine the relative strength or weakness of the lithosphere. Compressional tectonics produces two opposing effects in terms of lithosphere strength; firstly, crustal thickening enhances the proportion of weak quartz-dominated (crustal) compositions relative to the stronger olivine-dominated (mantle) component, thus causing weakening (Kusznir and Park, 1987). Secondly, thrusting depresses the geothexm, which produces a strengthening of the lithosphere. This cooling is temporary, however, so that the thermally induced strengthening gradually disappears leaving the lithosphere weakened by the more permanent effects of the thickened crust (Egan, 1991). The investigation of lithosphere strength presented here is more sophisticated than that used in previous studies. Two-dimensional (cf. one-dimensional) strength profiles are generated for the shortened lithosphere. An attempt has also been

‘iS I:(iANAND .I.MI!KOCIHAH I

made to model the evolution of lithosphere strength over time in response to the re-equilibration of the temperature field. The model results are used to explain the timing of the extension experienced in the Laramide province, which has been occurring for the last 20-30 Ma. A two-dimensional

model of lithosphere

shorten-

ing

The model presented is illustrated diagrammatically in Figure 1 and quantifies the following components: (1) Crustal thickening resulting from thrusting in the brittle environment of the crust. (2) Thickening of the ductile lower crust by a regionally distributed pure shear mechanism. (3) Perturbation of the lithosphere temperature field by thrusting and pure shear at depth. Re-equilibration of the lithosphere tempera(4) ture field after shortening. (5) The flexural isostatic response of the lithosphere to the individual loads generated by shortening. A detailed description of each of these components is given in the sections below.

____-----__

__----

Fig. 1. Diagrammatic representation of a numerical model of lithosphere shortening. The model assumes that the brittle environment of the upper crust shortens by reverse movement along major basement faults, while the lower crust and mantle lithosphere accommodate compression by a pure shear mechanism. The diagram also illustrates the deformation caused to the isotherms by coupled thrusting-pure shear deformation. The deflection of the lithosphere in response to loading caused by crustal thickening and temperature perturbations is quantified using flexural isostasy.

NUMEXKXL

MODELLING

OF LITHOSPHERE

387

SHORTENING

Crustal thickening

TABLE 1 List of symbols

Thickening of the brittle crust is assumed in the model to occur by reverse movement along major basement faults. Crustal thickening caused by thrusting is quantified by using the vertical shear or “chevron” construction (e.g. Verall, 1982; Gibbs, 1983), which assumes that the unsupported part of the hanging wall following thrust movement collapses vertically downwards onto a rigid footwall. Although the chevron construction provides a very simplified representation of hanging wall deformation following fault movement and does have several weaknesses (White et al., 1986), it is accepted as being sufficiently accurate for the lithosphere-scale modelling being described here. The amount of crustal thickening due to thrusting, C77”, is given by: Crrr, = D, - Dx_s

(1)

where S is the amount of horizontal shortening (entered as a negative heave value) and D, defines the thrust geometry such that: D,=Ofor

a

Bx CO

Cr, CTP, Crr, D DX E -if l? k LX Pair PC Pi

Pm

Q (T u1-

0‘3

t T

AT

XQX,

T, To

and: D, = 2, * [ 1 - exp( -x/Z,)]

for x > x0

(2)

where Z, is the detachment depth of the thrust and x0 is the horizontal position of the outcrop of the thrust at the surface (all symbols are defined in Table 1). Below the detachment depth of the thrust the lithosphere is assumed to be ductile and shortening, along with thickening of the crust, is assumed to occur by pure shear. This deformation can be represented by a sinusoidal pure shear compression factor, &, such that: /S, = [c - sin( 7r *x/W)]

a

+ 1

(3)

where (1 + c) is the maximum compression factor such that a value of 1 represents no deformation, while a value of 0.5 defines 50% compression. W defines the width over which the pure shear is distributed. In order to avoid mass balancing problems it is assumed that the amount of shortening by thrust-

V

W WX zd

Thickness of lithosphere Thermal expansion Compression/“squashing” factor Original crustal thickness Total crustal thickening Crustal thickening due to pure shear Crustal thickening due to thrusting Flexural rigidity Fault geometry Young’s Modulus Strain rate Acceleration due to gravity Thermal conductivity Load function Density of air Density of crust Density of infill Density of mantle Surface heat flow Specific heat Yield stress Time Temperature Temperature perturbation Effective elastic thickness Temperature at base of lithosphere Poisson’s ratio Width of pure shear/ “squashing” Flexural uplift/subsidence Fault detachment depth

125km 3.28x 1O-5 K-’

35 km

-

70X lo9 Pa 10-U s-1 9.81 m*s-’ 25 W.m-‘.sK-’ 0 2800 kg*rne3 3300 kg.rnm3 1 kJ.kg-‘.sK-’

1333°C 0.25

Values assigned to symbols imply they have been assumed to be constants.

ing, S, balances the deformation depth. Hence: 5=kw’@,-

by pure shear at

1 dx=_/W;*sin(rr*x/W)

dx

(4)

0

where W’ is the pre-shortening width of the pure shear region (i.e. W- S). Provided W * S, then integration of eq. (4) gives: rr

s

c=2’w-s

(5)

388

S.S. EGAN

It is now possible to calculate the amount of thickening of the lower crust, CTP,, from: CTp,=(C,-Z&(1-1/&) where C, is original crustal thickness. Total crustal thickening, CT,, generated shortening event is given by: CT’ = C77” + CTP,

(6) by a

AND

J.M.

lJKOUHAK

I

sphere temperature field by a coupled faultingpure shear process in the context of extensional tectonics. Their methodology is equally applicable lithosphere-scale shortening whereby the temperature field, T, above the thrust detachment horizon (i.e. z < Z,) is given by: T = T,, (hangingwall)

(7)

It follows from eq. (6) that

the amount of crustal thickening due to pure shear is dependent upon the detachment depth of the overlying thrusts. Geological evidence and modelling work suggests that these major basement faults detach at either mid- or lower-crustal levels (Kusznir et al., 1987). The model assumes, therefore, that the crust will be thickened by both thrusting and pure shear for intra-crustally detaching thrusts, but crustal thickening will take place by thrusting alone for a basal thrust detachment depth. The methodology presented for the modelling of pure shear deformation has been taken from Kusznir and Egan (1989). Temperature perturbations

T = TrffCTTx (footwall)

while below the thrust detachment T= ~zd+(Z~+CTTx-zd).&,

(9) horizon: (IO)

where z’ is the depth beneath basement. After shortening, the model calculates the gradual re-equilibration of the temperature field, which is predicted by the following two-dimensional differential equation for heat conduction: d$;.(Z+Z) where t is time, k is thermal conductivity, u is specific heat, and p is density. The above equation is solved using the finite difference method under the assumption of the following boundary conditions: T,=, = 0°C

The model sentation of Each vertical is assigned geotherm, T,,

includes a two-dimensional reprethe lithosphere temperature field, section of this two-dimensional grid a pre-deformationai steady-state such that:

T, = ” . TO a

where z is depth, a is lithosphere thickness and TO is the temperature at the base of the lithosphere. The model calculates the perturbation caused to the lithosphere temperature field by both thrusting and underlying pure shear. Reverse movement along a major basement thrust causes the emplacement of hangingwall material onto the footwall. Cool footwall material is, therefore, displaced to a greater depth and the geotherm is cooled. Similarly, the geotherm will be cooled by the thickening of the lower lithosphere due to pure shear. Kusznir and Egan (1989) presented a methodology for modelling the perturbation of the litho-

T,=, = TO= 1333°C

(11) As yet no account is taken within the model of convectional heat transfer or the radiogenic heat contribution from the crust, although the importance of this latter process is illustrated by the work of Glazner and Bartley (1985). Flexural isostasy

Lithosphere shortening generates a suite of vertical loads, which may vary both laterally and with time. The following loads are considered within the model: (1) Positive (downward) loading due to crustal thickening caused by thrusting. This load, L,,, is given by: L CT*,=CJ-TxY%*g

(12)

where pc is the density of the crust and g is acceleration due to gravity.

NUMERICAL

MODELLING

OF LITHOSPHERE

389

SHORTENING

(2) Negative (buoyancy) load caused by thickening of the lower crust by pure shear. This load, LmX, is given by: L CTP,

action of all applied Schubert, 1982): d*

d*w,

dx*

dx*

-D=c~p,*(P,-P,)~g

(13)

where pm is the density of mantle substratum. (3) Positive load caused by the cooling of the lithosphere temperature field by thrusting and pure shear. This load, LTHx,, is time-dependent in that it decreases after shortening in response to the re-equilibration of the temperature field. It is given by: a

L =Hx,, =

I0 cz. AT.p’.g

dz

(14)

where (Y is the coefficient of thermal expansion, AT is the temperature perturbation at a particular depth defined in comparison to an equivalent depth at the edge boundary condition (see eqs. 8 and 11) and p’ is density, which is dependent upon temperature and, hence, depth. (4) Positive load due to infilling surface depressions with water and/or sediment. This load, L,=,, is also time dependent due, for example, to the gradual infill of a basin over time in response to increased basement subsidence. It is given by: =z;pi*g LIZ.,

(15)

where Z, is the depth of the depression to be infilled and pi is the density of the infilling material (2500 kg * mm3 is assumed for sediment, while 1000 kg * me3 is assumed for water). (5) Negative load due to erosion of topography. This load, LER,, is given by:

(P*-PA

*g*wx=L

and

(17)

where D is flexural rigidity, which defines the flexural strength (resistance to bending) of the lithosphere and is given by the following equation: 0

D=

- 1,

12( 1 - L?)

where E is Young’s modulus, u is Poisson’s ratio and T, is the effective elastic thickness of the lithosphere. The flexural deflection, w,, of the lithosphere in response to each of the loads described above can be quantified by substituting the relevant load definition (eqs. 12-16) and density contrast (p2 - p1> into eq. (17): Crustal thickening due to thrusting: d2

d*w,

dx*

dx*

-D-

+ (Pm-Pair)

‘g’wx=cnx’Pc’g (19)

Crustal thickening due to pure shear: d*

d*w,

-D-

dx* +(Pm

dx*

-Pair)

*gewx

(20)

=CW(P,-P&g

Thermal perturbations: d*

d*w,

dx*

dx*

-D-

+(Pm-Poir)‘g*Wx

a

=

L ERx=ER,*P,,‘g

+

loads (e.g. Turcotte

I cz*AT.p’.g 0

(16)

dz

(21)

Basin fill: where ER, defines the amount of material to be eroded and PER is its density. The deflection of the lithosphere in response to each of these tectonically generated loads is determined by flexural isostasy (Walcott, 1970; Beaumont, 1978, 1981; Watts et al., 1982; Egan, 1992). The flexural isostatic response of the lithosphere, w,, caused by loading can be modelled by assuming that the lithosphere behaves as a thin elastic plate, which is in equilibrium under the

d*

d2w,

dx*

dx*

-D-

f(P,-Pi)‘g’w,=I,‘Pi’g

(22)

Erosion: d*

d2wX

dx*

dx*

-D-

+(pt?t

-PER)

‘g’w,=ER;PEReg (23)

The resulting, flexurally compensated, basement elevation is obtained by superimposing the

390

S 5 EGAN

calculated flexural deflections, wX, from eqs. (19)~(23) onto the crustal thickening due to th~sting (CT7;). A more detailed explanation of the flexural isostatic response of the lithosphere to tectonic loading, along with a methodology for solving eqs. (19)-(231, can be found in Egan (1992).

The model combines the crustal thickening, thermal and flexural isostatic components described above to allow the forward modefling of lithosphere shortening. Deformation is controlled by the following definable parameters: Number, spacing, shape and angle of dip of thrusts. The amount of shortening aIong each thrust Time since sho~ening Distribution of pure shear (“squashing”) in the crust and mantle lithosphere

a>

AND .I M IJROIJHARI

- The elastic thickness/flexural rigidity of the lithosphere - Type and amount of infill for surface depressions - Amount of erosion Output from the model is generated in the form of a two-dimensional profile of basement geometry and underlying crustal structure. For example, Figure 2 shows a simple model simulation of lithosphere shortening along a single thrust with underlying regionally distributed pure shear. The arrangement of deformation assumed in the model is shown in Figure 2a with 20 km of reverse movement modelled along a thrust which detaches within the crust at a depth of 20 km. The pure shear is distributed sinusoidally over a width of 100 km below. The flexural rigidity of the lithosphere is defined by an effective elastic thickness of 10 km. The resultant model profile (Fig. 2b) shows a maximum topography of approximately 8 km generated by reverse fault move-

2 -7

b)

0

50

50

200

Distance

250

400

(km)

Fig. 2. (a) Profile showing some of the input parameters required for the modetling of lithosphere shorteniqg. In thii example a single thrust has been assumed which datacbes witbin the crust at a tip& of 26 km. Below the thrust cotnpressi~nal deformation is assumed to be accommodated by a regionally distri&ted pure shear. The Bexural rigidity of the tithospbere is defined by a oons%nt effective elastic thickness of 10 km. (b) Resubant model profile using input parameters from a. Tbe model shows up to 10 km of topography wbiih has resulted mainly from 20 km of reverse movement along the ma&r fault. The fiexurai isostatic adjustments in response to tbe compressionaUy induced loading has caused the development of a foreland basin and a broad downward depression of the Moho. The pure shear deformation has also thickened the lower crust.

NUMERICAL MODELLING OF LITHOSPHERE SHORTENING

ment. Surface uplift is also enhanced by thickening of the lower crust by pure shear. The loading of the lithosphere in response to thrust-sheet emplacement has caused the lithosphere to flex downwards and generate the adjacent foreland basin, which has a maximum depth of approximately 5 km, as well as the broad depression in the Moho profile. Application of model to the Laramide erogenic province, western USA The model presented is applicable to regions of thick-skinned thrust tectonics and has been tested against geological data from the Laramide province within the Rocky Mountain region of the western USA (Fig. 3). The structural style of the region is one of thick-skinned thrust tectonics

--Laramide Sevier ~~~--

391

where Precambrian basement has been uplifted due to shortening along large basement faults (Berg, 1%2; Allmendinger et al., 1982; Brewer et al., 1982). These thrusts have orientations varying from N-S to E-W and are well developed in the state of Wyoming, although the Laramide province extends from Montana southwards to New Mexico. To the west of the Laramide region is a contrasting area of thin-skinned thrusting, known as the Sevier thrust-belt (Armstrong, 1968; Royse et al., 1975; Dixon, 1982). The Laramide orogeny occurred between the Late Cretaceous and mid- to Late Eocene (Gries, 1983; Steidtmann and Middleton, 1991) and was both preceded and overlapped in time by the thin-skinned Sevier thrust event to the west (Fig. 4). Both of these major erogenic periods are thought to have been driven by compressive

thrusts thrusts

Fig. 3. The Laramide province forms part of the Rocky Mountain region in the western USA (inset). The structural style of the region is one of thick-skinned thrust tectonics where Precambrian basement has been uplifted due to crustal shortening along large basement faults. To the west of the Laramide province is a contrasting area of thin-skinned thrusting knmvn as the Sevier thrust-belt. In the northwest of Wyoming is an area of Tertiary extrusive volcanics forming part of the Snake River Plateau. Model profiles have been generated for sections A-A’, B-B’ and C-C’.

392

S.S. EC;AN

stresses originating from the plate boundary some 1200 km to the west where the Farallon plate was undergoing eastward subduction beneath the North American plate (Dickinson and Snyder, 1978). It has also been suggested (Gries, 1983) that Arctic ocean spreading caused the uplift of some of the E-W-trending Laramide structures. Section A-A’ in Figure 5a (see Fig. 3 for location) shows major Laramide structures from the SW to NE of Wyoming. The section has been constructed from data collated from both field work carried out in Wyoming and published material available on the Laramide province @harry et al., 1986; Blackstone, 1990; Paylor and Lang, 1990; Steidtman, 1990). The thrust geometries and associated amounts of shortening have been taken from section A-A’ and input into the two-dimensional lithosphere shortening model (described above). The resulting model (Fig. 5b) shows shortening along a sequence of 7 thrusts and one back-thrust. The thrusts were set-up with a pre-compressional dip

TIMING OF TECTONC EVENTS a r%% I”t==-

j

L Cfetaceou

8

1

Jurassic

Fig. 4. The Laramide orogeny occurred from the Late Cretaceous to mid- to Late Eocene and was both preceded and overlapped in time by the thin-skinned Sevier thrust event to the west, Since about 20 Ma there has been a switch in tectonic regime in the Laramide provinceto one of extension.

AND

J M

IJKQUHAH

I

of 45” and have a planar geometry over most of their profile, abruptly detaching either within the crust at a depth of approximately 15 km or at the base of the crust. There has not been much reverse movement along each of the thrusts in the section-usually only a few kilometres. The exceptions are the Wind River and Owl Creek thrust faults exhibiting approximately 15 and 9 km of shortening, respectively. The loading of the lithosphere resulting from the crustal thickening generated by the shortening along these thrusts has produced large flexural depressions up to 7 km deep. The magnitude of this subsidence has been increased due to the effects of sediment loading. Within the models shortening by thrusting has been balanced by pure shear compressional deformation in the mantle lithosphere, which has been regionally distributed as defined by the dashed line in the model profile. The pure shear has been widely dispersed so that the deformational effects that it generates are relatively low at any point across the model. Although this is probably a simplification, there is no information available in order to define the shortening in the lower lithosphere more accurately. Subsidence attributable to loading from the Sevier thrust belt is seen at the southwest edge of both the geological section and models. The details of the Sevier thrusting have not been modelled accurately because our studies are, as yet, confined to the Laramide region. It was, however, necessary to incorporate the flexural loading effects of the Sevier thrusting into the modelling in order to asses their influence upon the adjacent Laramide province. An approximate simulation of the western thin-skinned thrust belt has been achieved by thickening the crust by 50% in a position to coincide with the main Sevier structures (Royse et al., 1975). Figures 6 and 7 show two other sections and associated models across major Laramide structures to the north and south of Wyoming, respectively. The modelled profiles are comparable to those shown in the structural sections which suggests that the model described above is a reasonably accurate representation of thick-skinned contractional tectonics. For example, section A-A’ (Fig. 5a) shows a maximum uneroded to-

A

0

Southwest

50 100

1 km

15km

150

200

DISTANCE (KM)

250

12 km

300

1 km

350

400

Precambrian

Poloeozoic

Cenozoic +

450

Mesozoic

Northeast

500

-40

P -

.3 -20 -30

P

-10

.x .=

Ii

Fig. 5. (a) Cross-section A-A’, constructed from a variety of geological and geophysical data, showing Laramide structures from the southwest to the northeast of Wyoming. (b) Model profile across the Laramide province constructed from parameters taken from cross-section A-A’. The model represents crustal shortening along a sequence of seven thrusts and one back-thrust balanced by regionally distributed pure shear deformation in the mantle lithosphere (dashed line). Surface depressions are assumed to be sediment-filled to sea level and the flexural rigidity of the lithosphere is defined by an elastic thickness of 5 km.

b)

a)

b)

20

E

-40

I & -20

W8St

0

go

B

M

Fig. 6. (a) Cross-section

!W

B-B’,

150

DISIAti%

(KM)

300

350

400

Mesozoic

450

+

and (b) associated model profile across Laramide structures in northern Wyoming.

200

Precambrian

Poloeozoic

Cenozoic

East

8’

NUMERICAL. MODELLING OF LITHOSPHERE SHORTENING

t

KU. am.w.1

395

396

S.S.EGANANDJ

pography of about 10 km in the vicinity of the Wind River Range, while relative subsidence in the adjacent Green River basin is about. 5 km. These values correspond in the associated model (Fig. 5b) to 4 km for the uplift and 6 km for the basin. The mis-match between models and geological data can partly be explained by the fact that the geological sections represent the present-

a)

M.UKOlJHAKl

day structures that have had about 50 Ma tn evolve since the Laramide shortening event. During this time interval the re-equilibration of the temperature field and thrust-sheet erosion have had important effects. A major discrepancy, however, between the models and structural sections is the large amount of pre-erosion thrust-related topography apparent in the latter. The reason for

A-SW

A’- NE 2km

d)

0

It.0

xx)

DISTAN% (KM)

JM

roe

430

500

Fig. 8. Models showing basement geometry and crustal structure for section A-A’ from the southwest to the northeast of Wyoming. Model (a) has assumed a low flexural rigidity defined by an elastic thickness of 2 km and shows unrealistically low amounts of topography and shallow, narrow foreland basins. Models (c) and (d) generate unreahaticahy high topography and foreland basins that are too wide. The most realisticmodel, when compared to the structural section in Fig. 5a, has been generated with a low flexural rigidity defined by an elastic thickness of 5 km.

397

NUMERICAL MODELLING OF LITHOSPHERE SHORTENING

this difference is mainly because the structural sections have been generated using geometric se~on-b~~c~g techniques, which wiIl tend to exaggerate surface topography and produce an unrealistic underlying crustal structure (e.g. note flat Moho). The models, on the other hand, have been generated by considering both the geometry of thrust movement and associated flexural isostatic adj~~ents and, consequently, show less surface topography, but with an accommodation of crustal thickening below the surface (e.g. note depression of Moho). It is suggested, therefore, that the models provide a more accurate repre~ntation of pre-erosion surface to~~aphy and underlying crustal structure compared to the structural sections. It was clear from generating the models described above that the magnitudes of “thrusttopography” and associated foreland basins are very sensitive to the value of flexural rigidity assumed for the lithosphere. Model results are used in the next section to investigate the effect of flexural rigidity upon the formation of the Laramide structures, while the subsequent section describes modelling of their evolution to the present day by simulating the effects arising from

the post-shortening re-equilibration of the temperature field and erosion. The effect of feral fonnation

rigiditydurirrgLura~~

de-

In order to establish an approximate value for the flexural rigidity of the Laramide lithosphere, several models were generated for section A-A’ (Fig. 5a), each with a different flexural rigidity (Fig. 8). The models were then examined to assess which gave the most sensible basement geometry-crustal structure combination. The Moxa Arch to the west of the section was an errant feature used to gauge the accuracy of the models. This structure has previously been interpreted as being generated partly by thrusting (Wach, 1977; Stockton and Hawkins, 1985). Modelling suggests, however, that the Moxa Arch has been generated by the flexing of the lithosphere. As illustrated in the schematic model profiles in Figure 9, the loading of the lithosphere caused by both Sevier and Laramide orogenies would have caused substantial downw~d flexing and the generation of large foreland basins. Flexural bulges would have also been generated in front of the foreland

a)

bl Foreland

0

d

km

0 [ 10

Fig. 9. (3 Schematic model representing Sevier and Laramide compressional tectonics in the west and east, reqectivciy.
events.

398

S S. tGAN

basins. It is suggested that the Moxa Arch has resulted from the constructive interference of the flexural bulges caused by the Sevier and Laramide Wind River loads. In the models of section A-A’ in Figure 8, the existence of the Moxa Arch profile is very sensitive to the flexural rigidity assumed for the lithosphere. The model in Figure 8a has assumed a low flexural rigidity defined by an effective elastic thickness CT’,)of 2 km and shows no Moxa Arch because the small flexing wavelength of the lithosphere localises the loading effects from the Sevier and Laramide shortening events. The predicted thrust-sheet topography is also unrealistically low and foreland basins are too narrow in this model. Similarly, assuming a high flexural rigidity as defined by a T, of 20 km (Fig. 8d), shows no Moxa Arch. At high flexural-rigidity values the lithosphere flexes over too large a wavelength to generate localised features such as the Moxa Arch. The large resistance to bending of the lithosphere at high flexural-rigidity values also generates thrust-sheet topography that is too high and unrealistically wide foreland basins. In

AND J.M. UHWJHAK’I

fact, a relatively low T, value of about 5 km is required in order to generate the Moxa Arch as well as produce realistic amounts of uplift and foreland basin depths. The effects of the post-shortening re-equilibration of the lithosphere temperature field and thrust-sheet erosion upon the evolution of the Laramide region

The Laramide shortening event ended in the mid- to Late Eocene. The re-equilibration of the temperature field and thrust-sheet erosion have had important tectonic effects during the 50 Ma since the termination of shortening. For example, the model in Figure 10 illustrates the effects of the former process and shows 20 km of shortening along a sequence of three thrusts with regionally distributed pure shear deforming the lower crust and mantle lithosphere. The dotted profile represents basement and crustal structure immediately following shortening (time = 0 Ma), while the solid line profile defines basement and crustal structure 100 Ma after shortening. Up to 1 km of uplift has been generated in response to the

Thermal Uplift

-60 0 1.5~ vertical Emgperakm

50

100

150

DISTANCE

200

250

300

(KM)

Fig. 10. Model illustrating the thermally generated uplift caused by the re-equilibration of the lithosphere temperature field following shortening. The dotted profile represents basement geometry and crustal structure imrwdiately following 20 km of shortening along three basement thrusts with regionally distributed pure shear in the mantle lithosphere. The solid line profile represents the thermal uplift that has occurred 100 Ma following shortening.

NUMERKXL

MODJiiLLlNG

OF LITHOSPHERE

399

SHORTENING

,A. No Erosion 2okm

km

Mkm

2okm

0

-60 0

100

So

150

200

300

250

B. Erosion

II---

-

Erosion

I

---c____

I

--me-_..___m.._---

,_---

a--

I

C. Erosion + Sediment Loading

[Elastic TtWness -60

:

1

t

I

I

I

0

50

100

150

203

250

= 7 km 1 1 MO

DISTANCE

(KM)

Fig. 11. Model profiles illustrating the flexural isostatic response of the lithosphere to large-scale thrust-sheet erosion. Model (AI is included for reference and shows pre-erosion basement geometry and underlying crustal structure generated by 20 km of crustal sho~ening along major thrusts with ~der~~ regionally distributed pure shear in the mantle lith~phere. Model (B) takes the process of erosion to the extreme by assuming that all topography above sea level is eroded. Flexural isostatic uplift occurs as shown by the difference between the dotted and solid line profiles. Model (C) includes the effects of sediment loading to sea level, which suppresses some of the erosionally induced uplift and results in the preservation of the foreland basin.

-40

lkm

15km 2km

DtSTANCE

(KM)

12 km

1

km

1 km

3km

NE -

A'

Fig. 12. Model profile for section A-A’ representing present-day basement geometry and crustal structure form the southwest to the northeast of Wyoming. Calculation of the model has simulated 50 Ma of post-shortening thermal uplift and the flexural isostatic response of the lithosphere to erosion to a level of 1.5 km (present-day average for region), The model shows, when compared to the equivalent profile for immediately following the Laramide shortening event (Fig. .Sb), that the region has undergone little modification during the past 50 Ma or so. The most irn~~ant changes have been a general reduction in to~graphy and a small amount of regional uplift in response to thermal re-equilibration and erosion.

iii

F-20 CL

V

A - So

401

NUMERICAL MODELLING OF LITHOSPHJZRESHORTENING

gradual heating of the lithosphere during this time (see section on Temperature perturbations). The effects of large-scale thrust-sheet erosion are illustrated by the model profiles in Figure 11. The profile of Figure llA, for reference, shows basement and crustal structure following 20 km of shortening along three thrusts with underlying regionally distributed pure shear, but assuming no erosion. The profile of Figure 11B takes the process of erosion to the extreme with all topography assumed to be eroded to sea level. The flexural isostatic response of the lithosphere to the unloading caused by this erosion has been to induce uplift (see section- on Flexural isostasy). The magnitude of this uplift is indicated by the difference between the dotted (no erosion) and solid (erosion) profiles. In the profile of Figure 11C foreland basin development is preserved by including the effects of sediment loading from material eroded from the adjacent uplifts. The model in Figure 12 shows the effects of the post-shortening re-equilibration of the temperature field and thrust-sheet erosion in the context of Laramide section A-A’ (Fig. 5a). Within the model, 50 Ma of thermal re-equilibration have been simulated (i.e. since the termination of Laramide shortening) and any uplift above 1.5 km has been eroded and the associated flexural isostatic uplift calculated. Basement geometry and foreland basin magnitudes within the model are comparable to those exhibited in Wyoming at present, where topography has an average height of about 1.5 km and the largest foreland basins are approximately 5 km deep. The crustal structure shown in the model is more realistic than that shown in the structural section, with broad flexurally induced variations imposed upon the Moho. The model suggests, when compared with the equivalent model profile for immediately following Laramide shortening (Fig. 5b), that the large-scale structure of the region has remained largely unchanged for the past 50 Ma. The most important changes that have taken place being the reduction of thrust-sheet topography due to erosion (e.g. see Wind River Range) and a regional elevation of the surrounding surface largely as a flexural isostatic response to erosion (e.g. see area analogous to Green River basin in Fig. 12).

The effect of shortening upon lithosphere strength The determinationof lithospherestrength The yield stress envelope is an effective representation of lithosphere strength. It defines either the tensile or compressive stresses that the lithosphere can sustain before it mechanically fails. The yield stress envelope differentiates the high strength, brittle sections of the lithosphere from low strength, ductile regions (Fig. 13a). The brittle yield stresses increase, more or less, linearly with depth in response to the increasing pressure of rock overburden (lithostatic pressure) and are largely insensitive to rock type and temperature. Byerlee’s law (Byerlee, 1968) has been used to calculate the brittle yield stress component. It is an empirically derived relationship with the following form: lri = 5 .03

(24)

(T1= 3.1 * u3 + 210

(25)

Equation (24) applies for a, < 110 MPa, while eq. (25) applies for a, > 110 MPa. Because (pi is the vertical principal stress component and is given by the pressure of overburden (=prock-g *.z), the brittle yield stress (a, uJ can be easily calculated for any depth. The values of yield stress have been unrealistically maximised due to the assumption of dry conditions in the calculation of the brittle yield stresses. This is not considered important for the purpose of this study which is concerned with investigating relative variations of overall lithosphere strength. Readers are directed to the work of Brace and Kohlstedt (1980) for guidance on the calculation of more accurate yield stress values. With depth, both in the crust and mantle, the temperatures rise sufftciently to induce a ductile deformational environinent. The magnitudes of the ductile yield stresses (a, - Us) are given by a power law equation of the following form: E=C*(ul-u3)‘.e-j&

(26)

where E is strain rate, C is an empirically derived constant, which is dependent upon rock-type, IZis the shear component, Q is the activation energy,

402

S.S IGAN AND J.M IIKOUHAKI

MANTLE

b1

Temp.WOO

Y)

Stress brl00HPal

Temp.(xlOO°Cl

Stress(x100MPa)

(xlOOMPa) .

~x100MPal 2 ..........

..........

km

Fig. 13. (a) Diagrammatic representation of a yield stress envelope for a section of lithosphere. The linearly with depth and give the lithosphere its strength. With depth, both in the crust and mantle, interrupted as the temperatures rise sufficiently to induce ductile behaviour and, as a consequence, effects of temperature (b) and crustal thickness Cc) upon lithosphere strength. A raised geotherm lithosphere strength.

R is the universal gas constant and T is temperature. The magnitudes of the ductile yield stresses, which are relatively pressure-insensitive (Goetze and Brace, 19721, are determined mainly by temperature such that the increase in temperature with depth causes a reduction in the ductile yield stress component. For modelling purposes the lithosphere has been simplified compositionally into a crust composed entirely of the mineral dry quartz, while the mantle lithosphere is represented by the mineral olivine. This highly simplified compositional representation of the litho-

brittle yield stresses increase the brittle environments are the yield stresses drop. The and thickened crust reduce

sphere has been chosen partly due to the limited availability of data predicting the rheological behaviour of minerals and also this paper is concerned with investigating the relative strength or weakness of shortened lithosphere, which is not affected by the compositional fidelity with which the lithosphere is represented (Egan, 1991). Reference to specific values of lithosphere strength are avoided due to possible limitations in the experimentally derived fracture and power law equations when extrapolated to lithosphere conditions (Go&e and Evans, 1979; Rutter and Brodie, 1991).

403

NUMERICAL MODELLING OF LITHOSPHERE SHORTENING

Equations (24) and (25) have been used to calculate the brittle yield stresses, while the ductile yield stress of dry quartz is given by (Koch et al., 1980):

for the base of the lithosphere (z = 125 km). Temperature-depth distributions were calculated in 5 Ma-increments and an approximate surface heat flow, Q, calculated from:

18245 E

=0.126.e-T

(27)

* (a, -cT~)~‘~

A constant, intermediate strain rate of lo-“s-’ has been assumed. The ductile yield stress of olivine at a given temperature can be calculated from (Bodine et al., 1981): 53030

-T*(a1-U3)3

e=7X101°*e

(28)

This equation applies for (a, - ~~3)< 2 kbar where creep occurs by a dislocation mechanism, whereas the following equation applies for (a, - ~~3)> 2 kbar where Dom Law creep applies:

l=5.7XlOll.e

The

55556 (q -r~~)~

[

-T’-

85

1

(29)

strength of the lithosphere is controlled by temperature and crustal thickness (Kusznir and Park, 1987). Temperature controls the depth to the brittle-ductile transition in both the crustal and mantle lithosphere, while crustal thickness determines the proportion of relatively weak quartz-dominated compositions (crust) to stronger olivine-rich compositions (mantle). Geotherms and associated yield stress envelopes have been defined for “hot” and “cold” lithosphere, respectively (Fig. 13b). The values of temperature for each depth within the lithosphere have been calculated by representing the lithosphere temperature field as a one-dimensional set of equally spaced nodes. Each node within the temperature field was initially (time = 0) set to 1333°C. The cooling of the lithosphere over time, t, was then modelled by using the following equation for heat loss due to conduction: dT -=-.dt

k

d2T

pa

dz2

(30)

where T is temperature, k is thermal conductivity, z is depth, u is specific heat and p is density. This second-order differential equation has been solved using the finite difference method with constraint from the following boundary conditions of 0°C for the surface (z = 0) and 1333°C

Q=k*

Tz,- Tz, z2 -21

(31)

where z2 and z1 represent depths of 10 and 0 km, respectively. The temperature with depth profiles in Figure 13b representing “hot” lithosphere correspond to an approximate surface heat flow of 75 mW * m-*; a value associated with areas flanking presently active rifts such as the Rhine graben or the Palaeozoic erogenic crust of western Europe (Kusznir and Park, 1984). The associated yield stress envelope has been calculated using equations (24)-(29). A high strength, brittle region occurs in the upper crust, while the higher temperatures at depths greater than about 10 km induce a ductile environment, and the yield stresses drop sharply to negligible values. Within the top of the mantle there is an increase in the yield stresses as the mineral olivine is strong enough to endure the high temperatures and maintain some strength. The temperatures soon rise sufficiently, however, to reduce the strength of the olivine to zero. The temperature-depth distribution representing cooler lithosphere (Fig. 13b) gives a surface heat flow of 45 mW * mB2; a value typical of continental shield areas such as the Baltic and Canadian shields (Pollack and Chapman, 1977). The cooler temperatures at all depths increase the thickness of the high strength, brittle region in both the crust and mantle. It can be concluded, therefore, that the cooler the lithosphere the greater is its overall strength. In Figure 13c yield stress envelopes are shown for lithosphere composed entirely of mantle (olivine) and crust (dry quartz), respectively, while the temperature-depth distribution has been kept constant for both examples. The compositional representation of the lithosphere by a single mineral produces a stress envelope with a single-layer vertical stacking of brittle and ductile yield stress components. The model predictions show clearly that the crustal (dry quartz) lithosphere is much

404

S.S. EGAN

weaker than the mantle (olivine) lithosphere. This is due to the fact that quartz is a much, weaker mineral in terms of its resistance to high temperatures and is ductile at much shallower depths than olivine. Lithosphere with a thickened crust is, therefore, relatively weak.

effects will induce weakening and strengthening components, respectively. The question arises, therefore, as to whether the lithosphere is overall weakened or strengthened following compressional tectonics? In order to answer this question quantitative constraint is required for both the post-compressional crustal thickness and temperature field. The model profile shown in Figure 14a has been generated by the lithosphere shortening model described above and represents 30 km of shortening along a single thrust with squashing of the underlying lower crust and mantle lithosphere. Both the post compressional crustal thickness and temperature field predicted

The evolution of lithosphere strength following compressional tectonics

Lithosphere subjected to large-scale shortening experiences a thickening of the crust and cooling of the geotherm (see above). The results described in the previous section suggest these a)

AND J.M. UKQUHARI

3wrl

20

f--__,

km 0 -20 -40 -60 0

b) km

50

100

150

/

/

A

B

200

\

C

250

300

\ II

km IxlOOMPaI

2

0

SO

m-

100

200

100

300

Distance (km) Fig. 14. (a) Model results for 30 km of shortening along a m&r thrust fault. (b) The crustal thickness and temperature field predicted by the model in (a) have been used to calculate yield stress envelopes at various positions. Stress envelopes R, C, and D representing shortened lithosphere show an increase in strength in both the crust and mantle when compared to the reference yield stress envetope A. (c) Integration of the yield str@aseswith respect to depth for each point across the model produces a two-dimensional strength profile which shows &arty that the whole. region of shortctig is relatb& strong.

405

NUMERICAL MODELLJNG OF LITHOSPHERE SHORTENING

by this model have been incorporated into the yield stress equations described in the previous section. A constant strain rate of 10-‘5s-1 has been used for the calculation of the ductile yield stress component. The effect of changing strain rate has not been addressed in this study. Although this might be considered as too simplistic, Vink et al. (1984) suggest that the effect of strain rate upon lithosphere strength is relatively unimportant compared to temperature. Yield stress envelopes have been calculated for selected positions across the model (Fig. 14b). Stress envelope A has been taken from undeformed lithosphere for reference purposes, while B, C and D represent sections of lithosphere that have experienced varying combinations of shortening by thrusting and pure shear. The stress envelopes show that the strength of the crust has been increased due to the thickening of the surface brittle layer. The yield stresses have also been increased in the mantle lithosphere due to the depression of the geotherm induced by both thrust-sheet emplacement and pure shear. A two-dimensional strength distribution is obtained by integrating the yield stresses with respect to depth for each point across the model (Fig. 14c). The profile shows that the region of shortening is strengthened relative to flanking areas. The perturbations caused to the lithosphere temperature field by shortening gradually reequilibrate over a time span of the order of 100 Ma. The lithosphere heats back to its original state by both the lateral and vertical conduction of heat. The magnitude of the thermally induced uplift resulting from this heating is illustrated in Figure 15a and is shown by the difference between the dotted and solid line profiles. Strength profiles (Fig. 15b) show the evolution of lithosphere strength at selected times during the thermal re-equilibration process. The lithosphere is strengthened immediately following shortening (0 Ma), whereas after compression a gradual weakening occurs, which is most rapid in the region coincident with simple shear deformation. This pattern of weakening occurs because thrusting causes temperature disturbances that are relatively localized and at shallow depth. As a result

(a) km

20

1

(b)

0th

40 20 -. 01

I

0

f

I

f

I

1

1

looMa

40 -_-_

20 01

0

50

100

150

1

I

200

250

300

Distance(km) Fig. 15. (a) Predicted basement geometry and crustal structure at 0 Ma (solid line profile) and 100 Ma (dotted line profile) folkuving shortening. During this time period the lithosphere temperature field re-equilibrates causing uplift. (b) Strength profiles shown at various stages from shortening (0 Ma) and during the re-equilibration of the temperature field. A gradual weakening occurs over the 100 Ma time period, while flanking areas are temporarily strengthened due to lateral heat movement.

re-equilibration, and therefore weakening, occurs relatively quickly. In contrast, the strengthening due to the pure shear deformation is more prolonged due to the large regional perturbation it causes to the temperature field within the mantle.

406

S.S. !LiAN

By 100 Ma after shortening the temperature field has almost completely re-equilibrated, while the permanent, enhanced crustal thickness serves to weaken the lithosphere. Orogen collapse in the Laramide erogenic province, western USA

Since about 30 Ma ago there has been a switch in tectonic regime within the Laramide province from compression to extension. There are numerous examples of extensional reactivation of previously active thrusts as well as the development of new normal faults (Love, 1978; Sales, 1983; Hansen, 19841. Evidence for this extensional activity can be seen at many localities within the Laramide region. For example, Figure 16 shows a cross-section across part of the Granite Mountains uplift in central Wyoming and shows a Miocene-Pliocene extensional basin generated by the inversion of a Laramide thrust. An interesting observation regarding the Laramide province is that there has been a time

Extensional

AND

J M. UKQUHAK

gap of 20-30 Ma between the termination of shortening and subsequent extensional collapse (Fig. 4). It is suggested that this time gap can be explained by the evolution of lithosphere strength following contractiona tectonics. To support this suggestion, the crustal thicknesses and temperature structure predicted by the models for the section A-A’ across the Laramide province (Fig. 5a) have been incorporated into the strength calculations described above. Strength profiles have been generated (Fig. 17) to represent the lithosphere at 0 Ma (Middle Eocene), 25 Ma (Miocene) and 50 Ma (Present) following shortening. The profiles show that immediately follo~ng the Laramide compressional event the region was strengthened relative to flanking areas due to the cooling of the temperature field. After shortening, however, the temperature field re-equilibrates and the associated strengthening gradually disappears so that the weakening effects caused by the thickened crust start to dominate. The weakening is demonstrated quite effectively in the strength profile representing the present,

Collapse of the Southern Margin of the Granite Mountains Uplift PI

s iNormal

fault

‘J?late Miocene/ \j Pliocene)

‘b ._-

_______E--

+++c+++++++++++++ ; Precambrian + + + + + + + + ++++++++ +++f+f++++++f+T~rrr~~~~~~-~~~+++++++++++++++++ rrrrr++++++++++++++++++ff+C++++++*++++

..,

I

.<

Pslaeotopaaraphy

3

(late Cret. 1’ mid Eocene)

11 km Adapted

from Sales (1983)

Fig. 16. Orogen collapse of the Gratdte Mountains u@ift in centrai Wyoming shawing a Miocene-Pliocene generated by the reactivation of a Laramide thrust.

extensional basin

-

30

40

1

T = 50 Ma (PRESENT)

40

T = 25 Ma (MIOCENE)

88, ;o

100 I

150

2w1

____-_-____________-^___________________~~~~~~~~~~~~-~~~~~-~~~~

DISTANCE

250

(KM)

300

350

400

450

generate a significant time gap between initial shortening and subsequent tectonic reactivation.

for 0, 25 and 50 Ma after Laramide shortening based upon crustal and temperature field structures predicted by the model shown in Fig. 5b. The profiles show that the lithosphere under-lying the Laramide structures was relatively strong immediately following the shortening event, but, then progressively weakened in response to the thermal re-equilibration (heating) of the lithosphere. It is suggested that the initial strengthening is sufficient to resist gravitational and plate boundary forces and

Fig. 17.Strengthprofilescalculated

+

5

0 ‘;

F

z

z

_------..-_

*0

, A

-

30

10

-

40

T = 0 Ma (EOCENE)

500

9

3 $ d E 3

m

1

g

!z

%

3

P c

8

S.S. tGAN

which shows localities of weakness correlate closely with examples of inversion in the southwestern Wind River Range and eastern Owl Creek-Bridger mountains. There is no documented evidence of major inversion in the Bighorn mountain range, even though the model results suggest that the underlying lithosphere is relatively weak. The modelling alogorithms, however, have assumed a constant pre-shortening geotherm across the section, whereas, in reality, lateral variations in the lithosphere temperature field would be expected. Thus the section of lithosphere that was shortened to form the Bighorn mountains may have been originally cooler, therefore prolonging its strength for a greater period of time. Discussion A two-dimensional model of lithosphere shortening has been presented and applied to the Laramide erogenic province, western USA. Model results provide a realistic representation of the large-scale structure of the Laramide Province and illustrate the complex interaction between crustal shortening, thermal and flexural isostatic components. It is acknowledged, however, that the model is not a completely accurate representation of the shortening process and many of the assumptions made are described in the text. Simplifications have been made partly as an unavoidable consequence of the development of a model, but also due to the lack of geological constraint upon some of the processes being represented. For example, the model assumes that the lithosphere accommodates compressional deformation by faulting and pure shear mechanisms in the brittle and ductile environments of the lithosphere, respectively. The rational for adopting this arrangement is provided mainIy by deep seismic reflection data which suggests a confinement of faulting, and hence brittle behaviour, to crustal depths. Modelhng of the thermo-rheological behaviour of the lithosphere, as presented in the section on the effect of shortening upon lithosphere strength, however, suggests that there is a

AND

J.M. lJKOUHAK1

vertical stacking of brittle and ductile sections throughout the crust and mantle lithosphere. It is suggested, therefore, that lithosphere shortening might be a lot more complex than represented in the model presented here. An attempt has also been made to support and elaborate upon the work of Vink et al. (1984) and Glazner and Bartley (1985) by using numerical modelling techniques to show how the overall strength of the lithosphere is affected by compressional tectonics. The results presented above imply that the evolution of the strength of the lithosphere following shortening must have an important control upon the timing of subsequent tectonic reactivation. If this were not the case then there would not have been a time gap of 20-30 Ma before the extension activity in the Laramide province, but rather extension would have begun immediately following shortening under the influence of gravitational potential energy and plate boundary forces. The regional tectonic setting suggests that significant tensile stresses have been affecting the Laramide province and neighbouring regions for about the last 40 Ma. Initially the extensional activity affected most of the North American Cordillera and then, since approximately 17 Ma, became more concentrated within the Basin and Range province (Coney, 1987). Sonder et al. (1987) and Braun and Beaumont (1989) attributed the extension in the Basin and Range to gravitational collapse, while Verral (1989) has proposed that this extension has been driven by the subduction of the hot spots within the Farallon plate. His tectonic reconstructions suggest that for the last 20 Ma the Yellowstone and Socorro hot spots have migrated sufficiently beneath the North American plate to cause extension and igneous activity in both Basin and Range and Laramide provinces. The former, however, shows well developed extensional basins, whereas extension has been much more subdued in the Laramide province. It is suggested here that the greater relative strength of the lithosphere underlying the Laramide structures has inhibited the evolution of extensional basins to the same magnitude as has occurred in the Basin and Range province.

409

NUMERICAL MODELLING OF LITHOSPHERE SHORTENING

Conclusions (1) Thick-skinned compressional tectonics, as displayed in the Laramide erogenic province of the western USA, can be simulated effectively by a numerical model which assumes shortening by thrusting in the brittle crust giving away to a regionally distributed pure shear (squashing) deformation in the ductile environment of the mantle lithosphere. The model quantifies crustal thickening arising from thrusting, the initial cooling of the geotherm and its subsequent re-equilibration by conductive heat transfer, and the flexural isostatic compensation of tectonic loads. (2) The model shows that basement geometry and crustal structure following shortening are very sensitive to the flexural rigidity of the lithosphere. Low flexural-rigidity values generate low amounts of uplift and narrow, deep foreland basins, whereas a high flexural rigidity promotes high uplift values and shallow, deep foreland basins. Modelling of sections across major Laramide structures suggests that the flexural rigidity of the lithosphere was very low (T, = 5 km) at the time of deformation. (3) Following shortening, regional uplift is suggested to occur as a flexural isostatic response to the re-equilibration of the temperature field and large-scale thrust-sheet erosion. (4) Compressional tectonics causes a thickening of the crust and cooling of the temperature field, which induce relative weakening and strengthening of the lithosphere, respectively. Model results suggest that the lithosphere is relatively strong immediately following compression but, subsequently, weakens in response to the re-equilibration of the cooled temperature field. (5) The Laramide orogeny occurred from the Late Cretaceous to mid- to Late Eocene and caused large basement uplifts due to crustal shortening along major thrusts. About 20-30 Ma following this contractional event, many Laramide structures experienced extensional collapse. This extension, and particularly its timing relative to original shortening, can be explained in terms of the evolution of lithosphere strength following shortening, whereby the lithosphere is initially strong immediately following compression, but

then weakens sufficiently during thermal re-equilibration to be deformed by both gravitational and plate boundary forces. Acknowledgements We thank Maurice Bamford, Nick Kusznir and Graham Williams for useful discussion during various stages of completing this work. J.M.U. gratefully acknowledges funding by the Shell International Petroleum Co. Ltd. References Allmendinger, R.W., Brewer, LA., Brown, L.D., Kaufman, S., Oliver, J.E. and Houston, R.S., 1982. COCORP profiling across the Rocky Mountain Front in southern Wyoming, Part 2: Precambrian basement structure and its influence on Laramide deformation. Geol. Sot. Am. Bull., 93: 12531263. Armstrong, R.L., 1968. Sevier erogenic belt in Nevada and Utah. Geol. Sot. Am. Bull., 79: 429-458. Beaumont, C., 1978. The evolution of sedimentary basins on a &co-elastic lithosphere: theory and examples. Geophys. J;R. Astron. Sot., 55: 471-498. Beaumont, C., 1981. Foreland basins. Geophys. J.R. Astron. Sot., 65: 291-329. Berg, R.R., 1962. Mountain flank thrusting in the Rocky Mountain foreland, Wyoming and Colorado. Am. Assoc. Pet. Geol. Bull., 46(11): 2019-2032. Blackstone, D.L., 1990. Precambrian basement map of Wyoming: outcrop and structural configuration. Geol. Surv. Wyo. Map Ser., 27. Bodine, J.H., Steckler, M.S. and Watts, A.B., 1981. Observations of flexure and the rheology of the oceanic lithosphere. J. Geophys. Res., 86(B5): 3695-3707. Brace, W.F. and Kohlstedt, D.L., 1980. Limits on lithospheric stress imposed by laboratory experiments. J. Geophys. Res., 73: 4741-4750. Braun, J. and Beaumont, C., 1989. Contrasting styles of lithospheric extension: Implications for differences between the basin and range province and rifted continental margins. Am. Assoc. Pet. Geol. Mem., 46: 53-79. Brewer, J.A., Allmendinger, R.W., Brown, L.D., Oliver, J.E. and Kaufer, S., 1982. COCORP profiling across the Rocky Mountain Front in southern Wyoming, Part 1: Laramide structure. Geol. Sot. Am. Bull., 93: 1242-1252. Byerlee, J.D., 1968. Brittle-ductile transition in rocks. J. Geophys. Res., 73: 4741-4750. Coney, P.J., 1987. The regional tectonic setting and possible causes of Cenozoic extension in the North American Cordillera. In: M.P. Coward, J.F. Dewey and P.L. Hancock (Editors), Continental Extensional Tectonics. Geol. Sot. Spec. Publ., 28: 177-186.

410 Dickinson, W.R. and Snyder, W.S., 1978. Plate tectonics of the Laramide orogeny. Geol. Sot. Am. Mem., 151: 355366. Dixon, J.S., 1982. Regional structural synthesis, Wyoming salient of the Western Gverthrust Belt. Am. Assoc. Pet. Geol. Bull., 66(10): 1560-1580. Egan, S.S., 1991. The rheological strength of the lithosphere following extensional and compressional tectonics. In: D.G. Farmer and M.J. Rycroft (Editors), Computer Modelling in the Evironmental Sciences. Oxford Univ. Press, Oxford, pp. 161-178. Egan, S.S., 1992. The flexural isostatic response of the lithosphere to extensional tectonics. Tectonophysics, 202: 291308. Gibbs, A.D., 1983. Balanced cross-section constructions from seismic sections in areas of extensional tectonics. J. Struct. Geol., 5: 152-160. Glazner, A.F. and Bartley, J.M., 1985. Evolution of lithospheric strength after thrusting. Geology, 13: 42-45. Goetze, C. and Brace, W.F., 1972. Laboratory observations of high-temperature rheology of rocks. Tectonophysics, 13: 583-600. Goetze, C. and Evens, B., 1979. Stress and temperature in the bending lithosphere as constrained by experimental rock mechanics. Geophys. J.R. Astron. Sot., 59: 463-478. Gries, R., 1983. North-South compression of the Rocky Mountain Foreland structures. In: J.D. Lowell (Editor), Rocky Mountain Foreland Basins and Uplifts. Rocky Mount. Assoc. Geol., Denver, Co, pp. 9-32. Hansen, W.R., 1984. Post-Laramide tectonic history of the eastern Uinta Mountains, Utah, Colorado and Wyoming. Mount. Geol., 21(l): 5-29. Jordan, T.E., 1981. Thrust loads and foreland basin evolution, Cretaceous, Western United States. Bull. Am. Assoc. Pet. Geol., 65: 2506-2520. Klemperer, S. and Hobbs, R., 1991. The BIRPS Atlas. Cambridge Univ. Press, Cambridge, 124 pp. Koch, P.S., Christie, J.M. and George, R.P., 1980. Flow law of ‘wet’ quartzite in the cu-quartz field. Eos, 61: 376. Kusznir, N.J. and Egan, S.S., 1989. Simple-shear and pureshear models of extensional sedimentary basin formation: application to the Jeanne d’Arc basin, Grand Banks of Newfoundland. Am. Assoc. Pet. Geol. Mem., 46: 305-322. Kusznir, N.J. and Park, R.G., 1984. Intraplate lithosphere deformation and the strength of the lithosphere. Geophys. J.R. Astron. Sot., 79: 513-535. Kusznir, N.J. and Park, R.G., 1987. The extensional strength of the continental lithosphere: its dependence on geothermal gradient, and crustal composition and thickness. In: M.P. Coward, J.F. Dewey and P.L. Hancock (Editors), Continental Extensional Tectonics. Geol. Sot. Spec. Publ., 28: 35-52. Kusznir, N.J., Kamer, G.D. and Egan, S.S., 1987. Geometric, thermal and isostatic consequences of detachments in continental lithosphere extension and basin formation. In: C. Beaumont and A.J. Tankard (Editors), Sedimentary Basins

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AND J.M. UKOlUHAft’I

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