Gondwana Research 24 (2013) 838–848

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Gondwana Research

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Intracratonic geodynamics

Weronika Gorczyk a,⁎, Bruce Hobbs a,b, Klaus Gessner a,c, Taras Gerya d

a University of Western Australia, Center for Exploration Targeting (UWA, CET), Australiab Australian Commonwealth Scientific and Research Organisation (CSIRO), Australiac Geological Survey of Western Australia, Department of Mines and Petroleum, Australiad Swiss Federal Institute of Technology Zürich (ETHZ), Switzerland

⁎ Corresponding author. Tel.: +61 8 64 88 26 75.E-mail address: weronika.gorczyk@uwa.edu.au (W.

1342-937X/$ – see front matter © 2013 International Ahttp://dx.doi.org/10.1016/j.gr.2013.01.006

a b s t r a c t

a r t i c l e i n f o

Article history:Received 31 August 2012Received in revised form 16 January 2013Accepted 21 January 2013Available online 18 February 2013

Keywords:Intra-plate deformationTectonicsNumerical-modellingMantle lithosphere

Geodynamic concepts of deformation and metamorphism of continental lithosphere are dominated by the ef-fects of subduction, accretion or collision along themargins of continental lithospheric blocks. Yet it is becomingincreasingly apparent that suture zones, presumably representing fossil subduction zones, but occurring far fromambient continent boundaries, play a key role in intra-cratonic deformation. In such zones the crust is stronglysheared and mantle lithosphere metasomatised. Reworking of such settings reveals a surprisingly large rangeof instabilities that develop in compressed/extended lithosphere with lateral heterogeneities inherited from fos-sil subduction settings. Structural complexity ariseswhich is quite sensitive to the pre-existing geometry and tec-tonic setting. This influences localization of deformation, topographic evolution, melt generation and fluid flowpatterns. We recognise a class of instabilities, labelled acceleration instabilities, of which the classical Ray-leigh–Taylor instability is one example. In many cases shown in this paper such instabilities are responsible fortriggering most of the response of the lithosphere. In an elastic-plastic material a necessary condition for insta-bility is that thematerial reaches the yield point; thus not only density contrasts betweenmedia drive instabilitybut also processes induced by other forces normal to the interface. As a geological example the Petermann orog-eny in central Australia is given.

© 2013 International Association for Gondwana Research. Published by Elsevier B.V. All rights reserved.

1. Introduction

Most mountain building, basin forming and mineral depositionprocesses have traditionally been considered as resulting directlyfrom the plate margin process. In intracratonic settings where thereis no indication of subduction related processes resort is commonlymade to a mantle plume hypothesis to explain these features. Unfor-tunately not all intraplate processes can be explained by the occur-rence of deep mantle plumes. Campbell (2005) has characterisedthe main features required from topographic changes and melt occur-rence in order to connect the observed processes to a mantle plumemechanism. As the key features he points to: (1) plume heads shouldflatten to form a disk 2000 to 2500 km in diameter at the top of theirascent; (2) plume heads should remain hot for at least 300 Ma and beseismically detectable for ca. 100 Ma; (3) flood volcanism should bepreceded by domal uplift of ca. 1000 m in amplitude at the centreof the dome; (4) both heads and tails of the plume should producehigh-temperature magmas; (5) the temperature excess at theplume head is predicted to be appreciably hotter (by ca. ×3) at thecentre of the head than at the margin; and (6) picritic magmas should

Gorczyk).

ssociation for Gondwana Research.

be produced early during melting of a plume head, be most abundantnear the centre of the head and less abundant towards the margin.

When these criteria are not met an alternative tectonic scenario is re-quired to explain deformation, metamorphism and melting occurring inan intraplate setting. Under various guises scenarios such as delamination,underplating or Rayleigh–Taylor instabilities are proposed. In this paperweconcentrate on various kinds of instabilities of which the strict Rayleigh–Taylor instability is one and relate the development of such instabilities tothe underplating and delamination concepts; we also link the develop-ment of Rayleigh–Taylor instabilities to the far field effects of subduction.The concept of Rayleigh–Taylor instabilities developing at the base of themantle lithosphere has been investigated by a number of authors (i.e.:Elkins-Tanton, 2007; Gogus and Pysklywec, 2008; Faccenna and Becker,2010; Gerya, 2012; i.e.: Houseman and Molnar, 1997; Neil andHouseman, 1999;Molnar et al., 2001; Stern andScholl, 2010). Recent geo-logical interpretations for intraplate crustal deformation suggest muchmore extensive development of compressional and metamorphic pro-cesses thanwould be expected from the classical view of Rayleigh–Taylorinstabilities (i.e.: Wyman et al., 2007; Zhao et al., 2011; Ueda et al., 2012).The characteristic example of intra-plate plate orogeny is observed in cen-tral Australia (Korsch et al., 1998; Hand and Sandiford, 1999), where theNeoproterozoic to Palaeozoic Musgrave, Petermann and Alice SpringOrogenies are interpreted as intraplate, and the deformation is localisedat the boundaries of micro-plates that have amalgamated during the Pro-terozoic or Archean.

Published by Elsevier B.V. All rights reserved.

Fig. 1. An interface between two materials with densities ρ2 above and ρ1 below withρ2>ρ1. The interface is perturbed by y=ξ(x) and subjected to an acceleration due to grav-ity, g. The pressure difference across the interface for perturbation ξ is Δp=(ρ2−ρ1)gξ.

839W. Gorczyk et al. / Gondwana Research 24 (2013) 838–848

Cratons are amalgams of multiple lithospheric blocks and maychange their shape over time as lithospheric blocks are added to ordetached from them (Begg et al., 2009). The amalgamated strongblocks are separated by segments, which in the past have been suturezones. They are defined by different rheological and chemical charac-teristics from surrounding continental blocks.

Focusing of mantle melts by the combination of three-dimensionalarchitecture of the sub-continental mantle lithosphere (SCLM) and thepresence of active trans-lithospheric faults explains the association oflarge igneous provinces (LIPs) and active tectonic zones adjacent tomicroplatemarginswith areas of previous tectonic history. The deforma-tion concentrates on the boundaries of the sub-cratonic blocks as zonesof weaker lithosphere are more likely adjacent to and along the cratonicmargins, while stronger lithosphere often dominates craton interiors.This provides a natural focus for deformation and focusing of fluid fluxduring extensional or compressional events.

In this paper we explore mechanisms for intracratonic tectonismthat result from pre-existing architecture (zones of weakness, in-cluding fault zones, suture zones, failed rifts, and other tectonicboundaries) and far field stress, and investigate the behaviour ofthe crust and mantle lithosphere. The significance of mantle litho-spheric delamination as the mechanism for complex intraplate pro-cesses such as orogeny, basin and ore formation is investigated. Themain focus will be put on the boundaries between amalgamated lith-ospheric blocks and smaller scale discontinuities due to former tec-tonic events. It will be shown how thermal erosion at the base ofthe lithosphere combined with far field stress influences surfaceand crustal processes.

The structure of the paper is as follows. In the next section we out-line the theoretical basis for the Rayleigh–Taylor instability and discusshow the classical model put forward by Rayleigh (1883) and Taylor(1950), where the instability is driven solely by a density contrast, ismodified by the inclusion of viscosity and plasticity in the constitutiveequations. The evolution of a Rayleigh–Taylor instability is highlynonlinear and analytical solutions exist only for the initial stages ofgrowth of the instability. Subsequent growth of the instability, especial-ly with the inclusion of elasticity, viscosity and plasticity coupled withthermal effects demands a numerical approach. Hence we follow thistheoretical section with a discussion of the numerical techniques usedin this paper and set up the boundary conditions andmodel parametersto be explored. We then explore the effect of boundary conditions(shortening and extension) on the behaviour (metamorphism, defor-mation, melting and topographical evolution) of a plastically weakzone of various widths in the intraplate lithosphere. Finally we presentan example from central Australia.

2. The Rayleigh–Taylor instability

The classical concept of the Rayleigh–Taylor instability (Sharp,1984) involves the behaviour of an interface between two inviscid,incompressible materials of different densities, ρ1 and ρ2 withρ2 >ρ1 (Fig. 1). One of the simplest and insightful analyses of the in-stability is given by Piriz et al. (2009): If we consider a perturbation ofamplitude ξ(x) as shown in Fig. 1 then a pressure difference, Δp=(ρ2−ρ1)gξ, exists across the interface and tends to deform the inter-face further. Newton's second law of motion then gives m€ξ ¼ AΔpwhere A is the area of the interface, m=m1+m2 is the mass of bothfluids involved in the motion and the double over dots representdouble differentiation with respect to time, t. It is assumed that anyinstability is a surface mode that decays away from the interface asexp(−ky) where k ¼ 2π

λ is the wave-number of the instability withwavelength, λ. Then m ¼ ρ1

Ak þ ρ2

Ak and we obtain:

ρ2 þ ρ1

k€ξ ¼ ρ2−ρ1ð Þgξ ð1Þ

or

€ξ ¼ ρ2−ρ1

ρ2 þ ρ1kgξ ¼ ATkgξ ð2Þ

with AT ¼ ρ2−ρ1ρ2þρ1

:

This can be integrated (Taylor, 1950) to give an asymptotic expo-nential amplitude growth rate of γ ¼

ffiffiffiffiffiffiffiffiffiffiffiATkg

p. AT is known as the At-

wood Number. One of the issues with instabilities driven by densitydifferences, as indicated by this expression for γ, is that the growthrate for short wavelengths is unbounded so that the problem as it isconventionally framed is ill-posed mathematically. It is found thatthis derivation is true only for small ξ, with a limit of perhaps ξ=0.1λ (Sharp, 1984). For larger ξ, nonlinear terms become importantand there are no analytical solutions available. For the lithosphere/asthenosphere contact, ρasthenosphere=1.015ρlithosphere (Artemievaand Mooney, 2001) so that according to the classical view of the Ray-leigh–Taylor instability, driven solely by density contrasts, the litho-sphere/asthenosphere interface is stable.

One can generalise the discussion tomaterials withmore complicat-ed rheological properties other than inviscid and incompressible mate-rial behaviour by thinking of the surface instabilities of the typediscussed above as acceleration instabilities (Robinson and Swegle,1989; Swegle and Robinson, 1989) where instabilities arise because ofprocesses induced by forces normal to the interface. Thus if there are idifferent forces, Fi, acting across the interface then Newton's secondlaw of motion becomes:

ddt

m1 þm2ð Þ _ξh i

¼ ρ2−ρ2ð Þkgξþ∑iFi ð3Þ

and this is the equation that now describes the initial evolution of thesurface instability. Notice that, in principle, the instability can formwhen ρ1=ρ2 when there is no density contrast across the interface oreven if ρ2>ρ1, as is proposed for the lithosphere/asthenosphere inter-face, so long as (ρ2−ρ2)kgξ b∑ iFi.

Other physical parameters that result in a force normal to the inter-face that have been explored include heterogeneity, anisotropy, surfacetension, elasticity, viscosity and plasticity (Sharp, 1984; Robinson andSwegle, 1989; Swegle and Robinson, 1989; Bierlein and Betts, 2004;Piriz et al., 2005; Lev and Hager, 2008; Piriz et al., 2009). In particularthe introduction of elasticity and viscosity tends to regularise the prob-lem so that the growth rate of small and large perturbations is reducedand in the linear approximation a single dominant wavelength is pre-ferred. Heterogeneity and anisotropy introduce nonlinearities that excitelocalised (and hence, non-sinusoidal) responses. As the introduction of

840 W. Gorczyk et al. / Gondwana Research 24 (2013) 838–848

viscosity (linear or nonlinear) has an important stabilising effect, the am-plitudes of perturbations necessary before an instability begins to groware quite large (Harig et al., 2010), of the order of twice the initial thick-ness of the layer. In this paper we explore the influence of elastic-plasticbehaviour and explore the influence of regions of lower yield stress intothe lithosphere.

The linear, small perturbation theory for elastic-plastic instabilitywith AT=0 is discussed by Swegle and Robinson (1989) and Piriz etal. (2005, 2009). The necessary condition for instability is that themate-rial yields plastically. However the sufficient condition for instability isthat the yield zone extends a distance k−1 into the material. Thus(Piriz et al., 2005, 2009) the necessary condition is:

ρgξ0=Yffiffiffi3

p� �¼ 1−ρgλ=4πGð Þ=2 ð4Þ

where Y is the yield stress and G is the elastic shear modulus. The suffi-cient condition is:

ρgξ0=Yffiffiffi3

p� �¼ 1− ρgλ=4πGð Þ

1=2

� �: ð5Þ

These two conditions are plotted in Fig. 2. If one takes the valuesY=100 MPa and G=109 Pa then the sufficient condition for instabil-ity reduces to

ξ0 ¼ 5:77� 103 1−4:9� 10−4 ffiffiffiλ

p� �ð6Þ

which is relatively insensitive to the value of λ. Thus for wavelengths of10 km ξ0 is of the order of 5.77 kmwhile for wavelengths of 100 km ξ0is of the order of 5.74 km. The initial perturbation is also proportional tothe yield stress so if Y is reduced to 10 MPa then ξ0 is of the order of0.57 km for λ=10 km. These perturbation amplitudes are substantiallysmaller than that necessary to induce instability in a viscous material.This analysis is for zero density contrast across the interface. Any in-crease in AT will further reduce the magnitude of any perturbation nec-essary to nucleate an instability whereas negative buoyancy willincrease the magnitude of such a perturbation. Although the termRayleigh–Taylor instability should strictly be reserved for instabilities

Fig. 2. Plot of stable and unstable regions for instability of an elastic-plasticmaterial. Curve(a) is the necessary condition for instability whereas curve (b) is the sufficient conditionfor instability. After Piriz et al. (2009). The dots represent the results of various computersimulations reported by Piriz et al. (2009).

generated solely by a density difference across an interface normal tothe gravity field, we (in common with much of the recent literature)use the term to refer to any instability generated at an interface arisingfrom forces normal to that interface. As indicated above, a general termfor this class of instabilities is acceleration instability (Robinson andSwegle, 1989; Swegle and Robinson, 1989).

3. Numerical technique and boundary conditions

3.1. Numerical approach

To simulate the dynamic development of Rayleigh–Taylor instabil-ities, the 2D code I2ELVIS (Gerya and Yuen, 2007; Gerya, 2010) is used.It combines a conservative finite difference method with non-diffusivemarker-in-cell techniques. In the model visco-elasto-plastic rheology ofthe rocks (Ranalli, 1995) is used.

The visco-elasto-plastic rheology is represented with the deviatoricstrain rate _ε ij and is including the three respective components:

_ε ij ¼ _ε ij viscousð Þ þ _ε ij elasticð Þ þ _ε ij plasticð Þ

where

_ε ij viscousð Þ ¼12η

σ ij; ð7Þ

_ε ij elasticð Þ ¼12η

Dσ ij

Dt; ð7aÞ

_ε ij plasticð Þ¼0 for σ II b σyield;

_ε ij plasticð Þ ¼ χ∂G∂σ ij

¼ χσ ij

2∂σ IIfor σ II ¼ σyield ð7cÞ

where Dσ ij

Dt is objective co-rotational time derivative of the deviatoricstress component σij, σyield is plastic yield strength for given rock, G isplastic potential of yielding material, σII is second deviatoric stress in-variant and χ is the plastic multiplier.

Mechanical properties of the rocks used in the models arepresented in Table 1. The effective creep viscosities of rocks are repre-sented as a function of temperature and stress by experimentally de-termined flow laws. Viscosity for dislocation creep depending onstrain rate, pressure and temperature is defined in terms of deforma-tion invariants as (Elliott et al., 1997; Hawkesworth et al., 1997):

ηcreep ¼ _ε IIð Þ1−nn F ADð Þ−1

n expE þ VPnRT

� �ð8Þ

where _ε II ¼ffiffi12

q_ε ij _ε ij is the second invariant of the strain-rate tensor, and

AD, E, V and n are experimentally determined flow law parameters(Table 1). They are respectively the pre-exponentmaterial constant, ac-tivation energy, activation volume and stress exponent. F is a dimen-sionless coefficient depending on the type of experiments, uponwhich the flow law is based and used for conversion of experimentallydetermined rheology to model stress states. The plastic strength of arock is determined as:

σyield ¼ cþ P sin φð Þ ð9Þ

sin φð Þ ¼ sin φdry

� �λfluid ð10Þ

where c is the cohesion,φ is the effective angle of an internal friction,φdry

is for dry rocks, P is the dynamic pressure, and λfluid=1−Pfluid/P is thepore fluid pressure factor. The pore fluid pressure Pfluid reduces theyield strength σyield of fluid-containing porous or fractured media. Fordry crystalline rocks, sin(φdry) typically varies from 0.2 to 0.9, depending

Table1

Materialp

rope

rtiesus

edin

2Dnu

merical

expe

rimen

ts.Q

L—

latent

heat;H

r—

radiog

eniche

ating;

E—

activa

tion

energy

;n—

stress

expo

nent;A

D—

materialcon

stan

t;V—

activa

tion

volume;

C—

cohe

sion

;Φ—

friction

angle;

Cp=

1000

Jkg

−1K−

1 ,α=

3×10

−5K−

1 ,β=

1×10

−5MPa

−1fora

llrock

type

s.1=

Turcotte

andSchu

bert(200

2),2

=Bittne

rand

Schm

eling(199

5),3

=(C

laus

eran

dHue

nges

(199

5),4

=Schm

idta

ndPo

li(199

8),5

=Ra

nalli

(199

5)an

dreferenc

estherein,

6=

Gerya

etal.(20

08).

Material

ρ 0 kg/m

3k W

(mK)

Tsolidus

KTliquidu

sK

QLkJ/kg

Hr

μWm

3Flow

law

E kJ/m

oln

AD MPa

−ns−

1V J/(M

Pamol)

C MPa

Sin(

φ)

Continen

talu

pper

crus

t,sedimen

ts28

00(solid)

2500

(molten)

[0.64+

807/(T+

77)]×ex

p(0

.000

04PMPa

)88

9+

17,900

/(P+

54)+

20,200

/(P+

54)2

atPb

1200

MPa

,831

+0.06

Pat

P>12

00MPa

1262

+0.09

P30

01.0–

5.0

Wet/dry

quartzite

154

2.3

10−

3.5

03 1(for

wea

kzo

ne)

0.15

0.1(for

wea

kzo

ne)

Continen

tallow

ercrus

t30

00(solid)

2900

(molten)

[1.18+

474/(TK

+77

)]×ex

p(0

.000

04PM

Pa)

973−

70,400

/(P+

354)

+77

,800

,000

/(P+

354)

2at

P>

1600

MPa

,935

+0.00

35P+

0.00

0006

2P2

atPb16

00MPa

1423

+0.10

5P38

00.25

Plag

ioclase

An7

523

83.2

10−

3.5

03 1(for

wea

kzo

ne)

0.4

0.2(for

wea

kzo

ne)

Lithosph

ere–

asthen

osph

ere

dryman

tle

3300

[0.73+

1293

/(TK

+77

)]×ex

p(0

.000

04PM

Pa)

0.02

2Dry

olivine

532

3.5

104.4

83

0.6

0.3(for

wea

kzo

ne)

Referenc

es1,

23

44

1,2

15

55

51,

56

6

841W. Gorczyk et al. / Gondwana Research 24 (2013) 838–848

on pressure, temperature, and mineralogical compositions (Braceand Kohlstedt, 1980; Moore et al., 1997). After Gerya et al. (2008)we use high plastic strength of dry mantle (sin(φdry)=0.6) andlow plastic strength of rocks in the pre-deformed zone (sin(φ)=0–0.3, Table 1). For very low values of the sin(φ) material behaves asa pressure/temperature insensitive, perfectly plastic material.

For the computation of the gravitational effect of the terrain masseswe used the formula of Banerjee and Das Gupta (1977), which con-siders gravitational attraction of right rectangular prism.

gz ¼ γρ

x ln yþffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffix2 þ y2 þ z2

p� �þy ln xþ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffix2 þ y2 þ z2

p� �

−y tan−1 x

zffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffix2 þ y2 þ z2

p

266664

377775

x2x1

�������� y2y1

���� z2z1 : ð11Þ

Eq. (11) expresses the vertical component of gravity for a rightrectangular prism. The dimensions of the rectangular parallelepipedextend from x=−∞ to ∞, y=0 to 1 and z=z1 to z2, where z isin downward direction. The gravitational calculations are takenfrom the topographical surface to the depth of 60 km.

3.2. Initial and boundary condition

The model spatial coordinate frame is 1500×300 km. Continentalcrust consists of (1) 20 km of upper continental crust, (2) 20 km oflower continental crust and is underlain by (3) 70 km of continentalmantle lithosphere (bulk rock properties as in Gorczyk et al. (2012)).Mantle lithosphere and crust are considered to be dry (as this is thecase for many intracratonic orogens (Smithies et al., 2011). Free slipconditions are implemented at all boundaries except for themodel bot-tom, which is free to move in both downwards and upwards directions(Gorczyk et al., 2007). Infinite-like external free slip conditions alongthe bottom imply free slip at 1200 km depth. Similar to the usual freeslip condition, external free slip allows global conservation of mass inthe computational domain.

The compression/extension regime is prescribed by imposing locallyconstant velocities at x=150 km of Vx=±0.5 and ±1 cm/yr and1350 km Vx=±0.5 and ±1 cm/yr. A weak zone is prescribed with alower plastic strength with respect to the surrounding rocks (Table 2).

3.3. Partial melting and mineral phase equilibria

A stablemineralogy for each lithology is obtained by free energymin-imization (Christensen and Yuen, 1985) as a function of pressure andtemperature from thermodynamic data. For this purpose, phase relationswere resolved on a gridwith a resolution of 5 K and 25 MPa. Examples ofphase diagrams computed for different lithologies are discussed byConnolly and Petrini (2002) and Kerrick and Connolly (2002).

3.4. Topography

Above the continental crust, a 10 km thick low viscosity layer (η=1018 Pa·s) representing the atmosphere (ρ=1 kg/m3) is imposed. Highcontrast in viscosity between the upper weak layer and the crust causesminimal shear stress (b104 Pa). The position of the surface of the crustis dynamically calculated as a free surface and changes spontaneously asit is affected by erosion and sedimentation processes specified by thetransport equation, solved at every time-step on the Eulerian coordinates:

∂yes∂t ¼ vy−vx

∂yes∂x −vs þ ve ð12Þ

where yes is the vertical position of the surface as a function of the hori-zontal distance x; vy and vx are the vertical and horizontal componentsof the material velocity vector at the surface, y is positive downwards,

Table 2Run descriptions.

Run Compressionrate [cm/a]

Extensionrate [cm/a]

Weak zonewidth [km]

Topography Crust

T_50T_50_f

12

50 Symmetric high mountain range flankedwith basins

Symmetric thickening of the weak zone

T_50_extT_50_ext_f

12

50 Symmetric basin, filled with volcanic andsediments

Symmetric thinning of the weak zone

T_100T_100_f

12

100 Mountain range flanked with basins Primary symmetric thickening of theweak zone, until development crustalscale reverse fault

T_100_extT_100_ext_f

12

100 Basin, filled with volcanic and sediments Thinning of the weak zone

T_200T_200_f

12

200 Asymmetric mountain range flanked bybasins of variable depth

Development of reverse crustal scalefault, along which thickening of the crusttakes place

T_200_extT_200_ext_f

12

200 Basin development at one of the flanks ofthe weak zone, above thinning crust,filed with volcanic

Thinning of the crust at the flank of theweak zone, lost of at least 20 km of themantle lithosphere along the weak zone.

T_400T_400_f

12

400 Basins development on the sides of thedelaminating mantle lithosphere, whichjoin in one big basin after delamination.

Development of reverse crustal scalefault on a flank of the weak zone, alongwhich thickening of the crust takes place.Thinning of the mantle lithosphere dueto delamination. Crustal buckling

T_400_extT_400_ext_f

12

400 Wide basin developing above the weakzone with multiple drips of mantlelithosphere, narrow basins on the flankof the weak zone above thinning crustfilled whit volcanics.

Thinning of the crust at the flank of theweak zone lost of at least 20 km of themantle lithosphere along the weak zone.

842 W. Gorczyk et al. / Gondwana Research 24 (2013) 838–848

y=0 (at the top of the calculation domain); vs and ve are the sedimenta-tion and erosion rates respectively, in the relation:

vs ¼ 0 mm=a ve ¼ 0:09 mm=a for yb10 km

vs ¼ 0:09 mm=a ve ¼ 0 mm=a for y > 11 km:

The increased sedimentation rates vs=1 mm/a account for slopeinstabilities in regions with steep slopes.

4. Model description

This study provides insights into the response of the continental lith-osphere–asthenosphere system to shortening and extension under lat-erally inhomogeneous strength conditions.

The mode of lithospheric deformation under such circumstances andrelated mountain/basin building processes is investigated as a functionof three essential parameters: (i) lateral extent of the weak zone, (ii) tec-tonic regime— compression/extension and (iii) the rates of compression/extension. The models described here contain no water as many intra-plate orogens described in the literature have been multiply reworkedand represent rather dry environments (Smithies et al., 2011).

4.1. Compressional regime

When the weak zone is narrow=50 km (Fig. 3.1, Table 2)decoupling between the weak zone and its foreland plate promotes de-formation by thrusting along the decoupled boundary. Under such con-ditions uplift is dominantly confined to the regions above the decoupledboundaries and subsidence of the foreland and indenter plates, whichare loaded by the evolving orogen, leads to the development offoreland-type basins. The corresponding topographic profiles are trian-gular in shape and symmetrically distributed with respect to the flanksof the orogen. Plastic delamination develops at the base of the weakermantle lithosphere, prior to the influence of the compression, as a resultof small-scale thermally driven convection that leads to minimalperturbance (initial ones have wavelengthsb5 km) at the lithosphere/

asthenosphere interface; this ultimately results in development of ac-celeration instability. This delamination is aidedby overall compression,which is mainly responsible for thickening the crust within the weakzone and symmetric orogeny development. A symmetrical negativegravity anomaly is observed as a result of thickened crust.

When the weak zone is wide=400 km (Fig. 3.4, Table 2, Figs. 5, 7)strong coupling between weak and strong plates or parts of plates fa-vours deformation by buckling of the weak lithospheric domain. Theprocess of buckling controls topographydevelopment resulting in alter-nating, narrower uplifting and broader subsiding regions. As in the sit-uation for a narrow zone small thermally driven convection developsat the base of the lithosphere. As the plasticity has a non-linear charac-ter the instability is localised and hence asymmetric; this triggers thedevelopment of crustal scale thrusting (Fig. 5C). The fault occursobliquely to the zone of major lithospheric mantle removal (Fig. 5B).After 10.5 Ma from the beginning of the deformation, the offset on themain fault reaches 6 km. The bucking and thrusting leads to a visibleperturbation at the Moho and this corresponds to the main structuresdeveloped at the surface (interfering sinusoidal curves).

The runs with intermediate widths (Figs. 3.2, 3.3) of the weakzone are mostly driven by delamination of the weakened mantle lith-osphere, and as they increase in width asymmetry is observed. Thetopographic response is as for the zone of 50 km width; howeverthe topographic response is less conspicuous — the topographic re-sponse decreases in height and the flanking basins shallow, especiallythe one developing above the main crustal fault. It seems that the oneabove the main crustal fault is deeper than the other.

Compression rates play an insignificant role on the development ofthe described structures, in both cases: 1 cm/a and 2 cm/a compressionrates the crustal structures and topography are controlled by delamina-tion of the lower part of the mantle lithosphere and buckling for wideweak zone. The visible difference is observed in the timing of deforma-tion (Table 3). The time difference of structure development increasesfor the runs with the same width as the compression rate increases.

Gravity profiles have been calculated from the models at 10 Mafrom the density profiles at that time. As these calculations include den-sity contrasts to the depth of 60 km theymainly respondnegatively due

Fig. 3. Compilation of compressional results at 2 cm/a compression rate from 4 runs with variable width after 10 Ma: 1–50 km (run T_50_f in Table 2), 2–100 km (T_100_f), 3–200 km (T_200_f), 4–400 km (T_400_f); A— Gravityprofile, B — Topography, C — Composition.

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Fig. 4. Compilation of extensional results at 2 cm/a compression rate from 4 runs with variable thickness after 10 Ma: 10 Ma: 1–50 km (run T_50_ext_f in Table 2), 2–100 km (T_100_ext _f), 3–200 km (T_200_ext _f), 4–400 km (T_400_ext _f);A — Gravity profile, B — Topography, C — Composition.

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Fig. 5. Compositional and thermal (white isotherms) evolution in run T_400_f (400 kmwide weak zone at 2 cm/a compression rate).

Fig. 6. Compositional and thermal (white isotherms) evolution in run T_400_ext_f (400 kmwide weak zone at 2 cm/a extension rate).

Fig. 7. Localization of strain showed in form of second strain rate invariant of A: runT_400_f, B: run T_400_ext_f after 10 Ma.

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to thickening of the continental crust and development of deep faultstructures (Fig. 3A).

4.2. Extensional regime

All the extensional models presented here are characteristic for“narrow rifting” that in nature are represented by the East African RiftSystem, the Rio Grande Rift, the northern Red Sea, and the Baikal Rift(Walter and Gorter, 1994; Camacho et al., 1995; Clarke et al., 1995;Shaw et al., 1996). All the presented models (Fig. 4) display similarcharacteristics: localised crustal and mantle extension is observedwhich gives rise to narrow regions of intense normal faulting and as-thenosphere decompression melting that results in flood basalts at thesurface, and eventually opening of a new ocean. As in compressionalmodels acceleration instabilities are initiated by initial small-scale con-vection that develops at the base of the weak zone with perturbationsamplitudes of an order of 5 km.

Similar trends are developed for compressional and extensionalmodels. For narrowweak zones (b200 km, Figs. 4.1 and 4.2) the exten-sion is localised in the middle part of the weak zone and leads to sym-metrical faulting, basin subsidence, and decompression melting. Onthe other handwith increase in thewidth of theweak domain— the de-formation processes exhibit asymmetric behaviours and while one endlocalises all the extension (Fig. 4.4 and Fig. 6), normal faulting, basinsubsidence, and melt production, the other part is affected by smallscale convection cells that lead to removal of the base of the lithosphereand substantial thinning of the mantle lithosphere. Small drips of the

lithospheric mantle do not directly influence the structures in thecrust; however this lithospheric thinning brings hot asthenospherecloser to the Moho. This thinning of the lithosphere may destabilizethe system and lead to strong deformation during the next tectonicevent.

In all extensional runs strong coupling between the weak zone andthe plate is observed — all the deformation is localised within theweak zone and no additional shearing or failure is present at the contactbetween the weak and strong plate.

Topographic response to crustal extension is mainly observed in theareas of strain localizations and leads to development of the basin abovethe rifting crust (Fig. 4B). The time of asthenospheric decompressionmelting ismarked in the history of basin sedimentation by interlayering

Table 3Time when the top of the lithospheric drip reaches a depth of 170 km.

Run Time of drip detachment [Ma]

T_50 2.13T_50_f 3.02T_100 3.34T_100_f 4.51T_200 4.88T_200_f 6.71T_400 7.82T_400_f 10.21

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of mafic volcanics what precedes outburst of basaltic flow lavas (LIP)that fill the basin.

The gravity profiles obtained from the models show anomalousbehaviour only in the area of extension, crustal thickening, decom-pression melting and volcanism (Fig. 4A).

5. Geological application

Extensive regions of continental lithosphere were formed throughthe assembly of allochthonous geological provinces or terranes. Defined

Fig. 8. A— Evolution of a numerical run_50 with snapshots at: A1: 12 Ma, A2: 15 Ma A3:22 Ma. C— sketch of crustal transect (after Korsch et al., 1998; Hand and Sandiford, 1999)showing the locus of deformation (reactivation) during Petermann orogeny withinMusgrave block. Similar localization can be observed with the model — snapshot A3.

as ‘fault-bounded’ blocks of the Earth's crust characterised by a geolog-ical history distinct from that of ‘adjacent’ blocks (Friend et al., 1988).The cratonic blocks are buffered by low yield stress zones— f.e.: ‘mobilebelts’ (Lenardic et al., 2003). These zones localise most of the stressesthat act on the continental lithosphere and are first to deform, focusmelting and fluid migration. For example a number of postcollisionalgranites in Sveconorvegian Province are related to major terraneboundaries (Andersson et al., 1996).

Here as a case study we consider the deformation history of a part ofcentral Australia which is dominated by two major crustal blocks, thePalaeo-proterozoic to Meso-proterozoic Arunta Block and the Meso-proterozoic Musgrave Block which amalgamated sometime in theMeso-proterozoic (by 1100 Ma; Clarke et al., 1994; Myers et al., 1996;Shaw et al., 1996). The blocks separate the Intracratonic Officer,Amadeus, Ngalia and Georgina Basins (Hand and Sandiford, 1999). Cen-tral Australia provides an intriguing record of intraplate deformationresulting in the development of a number of extraordinary orogensresulting in multiple reworking of the area (Goleby et al., 1989;Anderson, 2005; Anderson andNatland, 2007) This is an excellent regionto study the extent to which pre-existing structures control the distribu-tion of intraplate deformation during the late Neoproterozoic to EarlyCambrian (570–530 Ma) Petermann Orogeny and the Devonian to Car-boniferous (400–300 Ma) Alice Springs Orogeny. We consider hereonly the Petermann Orogeny which was a major intraplate event thatresulted in the exhumation of the Musgrave Block from beneath theCentralian Superbasin (Walter and Gorter, 1994; Camacho et al., 1995;Clarke et al., 1995;Walter et al., 1995; Hand and Sandiford, 1999). Defor-mation during this orogeny was centred on the northern part of theMusgrave Block reactivating the Woodroffe–Mann fault system, whichwas first active during the Musgrave orogeny ca. 1200 Ma (Beyer et al.,2006). The cause of localization of strain in theMusgrave Province duringthe Petermannorogeny has been the subject of somediscussion. An earlymodel by Hand and Sandiford (1999) and Sandiford and Hand (1998)suggested thermal blanketing of an upper crust high in heat-producingelements by the thick sediments of the Centralian Superbasin as amech-anism to create anomalously weak lithosphere beneath the deepest partof the basin, which was interpreted to overlie the Musgrave Province.Hence, since then this model has been called into question on thegrounds of an emergentMusgrave Province as the source for detrital zir-cons in ca. 700 Ma to ca. 500 Ma Amadeus Basin sedimentary rocks(Sokoutis and Willingshofer, 2011). Neves et al. (2008) have proposedhigh heat production in the lithospheric mantle as a mechanism forstrain localization. As an alternative to these mechanisms, Rayleigh–Taylor instability of the lithospheric mantle (Neil and Houseman, 1999)has been proposed together with strain localization at the interface be-tween regions of contrasting mechanical strength, often related to theweakening effects of previous deformation events (Cloetingh et al.,1999; Sokoutis and Willingshofer, 2011). Here, the model we presentcombines the two proposed mechanisms, delamination of lower part ofmantle lithosphere by Rayleigh–Taylor instability as the deformationtakes place in the weaker zone (pre-worked lithosphere duringMusgrave andGiles events). Fig. 8 compares the interpretation of seismicdata (Korsch et al., 1998; Hand and Sandiford, 1999) with results of thenumerical model (run T_50, Fig. 3.1, Table 2). The striking similaritiesare the following: (1) aflower like structure developswhere reactivationof the faults takes place on both sides of the Musgrave Block during itsexhumation. This agrees with numerical runs with relatively thin weakzones (Figs. 3.1, 3.2)where strongdecoupling at the interface ofmechan-ically variable material takes place and high topography is observed dueto exhumation of the block; (2) emplacement of a wedge of lithosphericmantle within the lower crust, and its preservation for long periods oftime (of the order of hundreds of millions of years (Aitken et al.,2009)). Petermann orogenesis has led to significant lithosphericstrengthening, causing the stabilization of a previously much reworkedterrain and the preservation of its remarkable crustal architecture tothe present (Aitken et al., 2009).

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6. Summary and conclusions

The acceleration instability and subsequent delamination of part ofthe lithosphere is a viable mechanism for intra-plate tectonism andmay be quite common. Some examples are the Carpathian–Pannoniansystem of Eastern and Central Europe (Ren et al., 2012), the ProterozoicNampula Complex, northern Mozambique (Ueda et al., 2012), litho-spheric delamination beneath the Alboran Sea and Rif–Betic mountains(Seber et al., 1996), lithospheric delamination in the core of Pangaea(Gutiérrez-Alonso et al., 2011), the “Great Basin Drip” in Nevada (Westet al., 2009) and lithospheric deformation in the South Island of NewZealand (Pysklywec et al., 2002). Although the Rayleigh–Taylor instabil-ity concept has been discussed many times in the literature we haveemphasised here that the plastic properties of the lithosphere are impor-tant and perhaps dominant in controlling the development of the insta-bility rather than previously emphasised viscous properties or densitycontrasts as in the strict Rayleigh–Taylor instability. Small-scale thermalconvection, which developed in all of the models in the weak zone, trig-gers theminimal bulging at the lithosphere/asthenosphere interface andleads to acceleration instabilities. Ballmer et al. (2007) have proposed asimilar mechanism – small scale sub-lithospheric convection – for theoceanic lithosphere, which may lead to extensive decompression melt-ing due to convective removal of the lowermost part of the oceanicman-tle lithosphere.

Compressional results obtained in this paper with zones of plasticweakness in the lithosphere are consistent with previous analogue andnumerical models (i.e.: Cloetingh et al., 1999; Willingshofer et al.,2005; Sokoutis andWillingshofer, 2011 and citationwithin). New obser-vations made here are: narrow weak zones are characterised bysymmetric geometrical development; widening of the zone leads toasymmetry in topographic and localization response. By simplificationof thermal structure of the lithosphere in analogue models thermal ero-sion at the base of the lithospherewas not observed, by this all the defor-mation within the weak zone was assigned to the compressive tectonicregime. As presented in this paper, thermal small-scale convection andconsequent plastic delamination of lower part of the mantle lithosphereprecede the main phase of compressional influence. On the other handfor wide weak zones the results are consistent with results obtained byCloetingh et al. (1999) for a weak crust, where buckling was observed,thus no delamination and thinning of the lithosphere.

All the extensional models presented here are characteristic for“narrow rifting”. In the case of a narrow weak zone the results are con-sistent with previous modelling (i.e.: Braun and Beaumont, 1989;Huismans and Beaumont, 2011; Brune et al., 2012) and there rifting cor-responds to necking instability (Brun, 1999). Thus, against the sametype of localization occurs for wide zones (400 km). There, as in caseof compression, the initial stage is dominated by small-scale thermalconvection at the base of the weak lithosphere, which in combinationwith non-linear behaviour of visco-plastic medium (Huismans andBeaumont, 2003), determines where localization of deformation occurs(on one side of theweak zone). Subsequent thinning of themantle lith-osphere does not assist development of “wide rifting” (Brun, 1999).

Most kimberlites seem to have been emplaced along preexistingzones of weakness that cut through the whole lithosphere (mobilezones) that were frequently reactivated (White et al., 1995). The em-placement of the kimberlites has been associated with intra-plate ex-tensional tectonics.

As indicated above, the strict Rayleigh–Taylor instability, which wasdefined, by Rayleigh (1883) and Taylor (1950) to involve only a densitycontrast as the driving force for instability has been extended forgeodynamic applications inter alia by Houseman and Molnar (1997)to include viscosity but needs to be generalised to involve plasticity aswell. The analysis of Piriz et al. (2005) indicates that smaller initialperturbations are needed than with viscosity alone. The lithosphere/asthenosphere boundary is stable (Atwood numberb0) for the classicalRayleigh–Taylor instability. However the boundary becomes unstable

for a critical (small) value of the yield stress. After the instability is nu-cleated, subsequent behaviour is controlled by the initial geometry andstructure and by the fact that the drippingmaterial is colder and denserthan the asthenosphere below the initial instability. This density con-trast remains until the drip or delaminating slab heats up to the ambienttemperature of the asthenosphere. This process, for a delaminated slab30 km thick may take 30 million years. Two forms of long term behav-iour are possible: a symmetrical drip or asymmetrical delamination.Both behaviours are associatedwith upwelling of asthenosphericmate-rial and associated decompression melting of the asthenosphere lead-ing to two forms of underplating: (1) symmetrical underplating and(2) localised or widespread underplating which evolves spatially withtime as the asymmetric delamination and associated decompressionmelting evolve and spread horizontally.

Acknowledgements

This work was supported by the Australian Research Council GrantLP100200785. Published with permission of the Executive Director,Geological Survey of Western Australia. This is contribution 248from the ARC Centre of Excellence for Core to Crust Fluid Systems.We greatly appreciate constructive reviews and very valuable sugges-tions by two anonymous reviewers.

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