Zhao Muller GSA SpecPub2003

INTRODUCTION

Studies of intraplate stresses show that most intraplateregions are characterised by compressive stress regimesand crustal seismic activity (Zoback et al. 1989) and thatthe inferred maximum horizontal principal-stress orienta-tions are roughly parallel to the directions of ridge-pushforces. On the basis of the analysis of earthquake focalmechanisms, in situ stress measurements and surfacedeformation, Denham et al. (1979) have shown that theAustralian continent is in a state of substantial horizontalcompression. However, the maximum horizontal compres-sion measured in situ and inferred from seismic sourcemechanism solutions is approximately normal to the east-ern passive margin (Denham et al. 1979), which is not inagreement with the absolute velocity trajectories of theAustralian Plate (Richardson 1992; Zoback 1992).

Numerical modelling of the tectonic forces applied tothe Indo-Australian Plate (Figure 1) has been performedwith the finite-element method. Cloetingh and Wortel

(1986) investigated the tectonic stress field in the Indo-Australian Plate with a two-dimensional finite-elementmodel. Five types of tectonic forces were included in theiranalysis: slab pull, ridge push, resistant force, trench suc-tion force and drag force. The combination of the forces intheir model resulted in a concentration of the compressivestresses of the order of 300–500 MPa in some parts of theplate (e.g. the Ninetyeast Ridge). Using a similar 2D finite-element model, Coblentz et al. (1998) reinvestigated thetectonic forces acting on the Indo-Australian Plate. Thestress indicators from the World Stress Map Project(Zoback 1992) were used to constrain their numerical mod-els. They found that: (i) the ridge-push force is likely the pri-mary force in controlling the first-order stress pattern in theIndo-Australian Plate; (ii) if imposing resistance along theHimalaya, Papua New Guinea and New Zealand colli-sional boundaries to balance the ridge-push force, thenmany of the first-order stress patterns of the observed stressfield can be explained without including either subductionor basal-drag forces; and (iii) the observed maximum hori-

Geological Society of Australia Special Publication 22, 65–83

CHAPTER 6—Three-dimensional finite-element modelling of the tectonic stress field in continental Australia S. ZHAO1, 2 AND R. D. MÜLLER1*

1 School of Geosciences, University of Sydney, NSW 2006, Australia.2 Japan Marine Science and Technology Center, Yokosuka 237-0061, Japan.Corresponding author: [email protected]

Traditionally, intraplate stress orientations have been modelled using an isotropic elastic plate. Forthe Australian Plate this method has been applied successfully to model the first-order pattern ofstress orientations. However, the distribution of intraplate earthquakes and the juxtaposition ofstrong, cold with hotter, younger lithosphere in many areas suggest that the spatial variation inmechanical strength of the plate may result in substantial regional anomalies in stress orientationsand magnitudes. We explore this idea with a three-dimensional finite-element model to investigatethe regional response of the Australian continent to tectonic forces. The model covers the area of–40 to –10° (S) and 111 to 155° (E) with a spatial resolution of 90 x 90 x 50 km. The relative magni-tudes of the ridge push and boundary forces, which act on the Australian continent, are estimatedthrough an inversion analysis of in situ stress data. The differences between modelled andobserved stress orientations are minimised in a least-squares sense. Major tectonic blocks and thedifferences in their elastic strength are included in the model, and the initial estimates of theYoung’s moduli for the tectonic blocks are adapted from a published coherence analysis of grav-ity and topographic data. The values of the Young’s moduli are adjusted in the inversion analysisto best fit the stress orientations observed on the Australian continent. The inversion analysis of rhe-ological parameters is most efficient for estimating the Young’s moduli for the Northern LachlanFold Belt, the New England Fold Belt, and the Southern Lachlan Fold Belt. The adjusted values forthe flexural rigidity are 0.040 x 1025 Nm for the Northern Lachlan Fold Belt, 0.037 x 1025 Nm for theNew England Fold Belt, and 0.040 x 1025 Nm for the Southern Lachlan Fold Belt, which correspondto an effective elastic thickness of about 30 km. Based on the optimised body and boundaryforces acting on the plate, a map of maximum principal-stress distribution is constructed so thatvariations of the relative magnitude of tectonic stresses can be assessed. We find a good matchbetween predicted zones of stress concentration and the distribution of major belts of seismicity inAustralia. The results show that while the overall pattern of stress orientations in the Australian con-tinent is controlled by the forces which drive the Indo-Australian Plate, the maximum horizontalstress orientations and the pattern of the stress concentration manifested by seismicity are modu-lated by local/regional geological structures.

KEY WORDS: Australia, crustal plates, in situ stress, numerical modelling, seismicity.

zontal-stress orientations and stress-regime information inthe Indo-Australian Plate can also be explained with themodels predicting low tectonic-stress magnitudes (e.g. tensof megapascals, averaged over the thickness of the lithos-phere). This implies that the large stress magnitude (hun-dreds of megapascals) inferred by Cloetingh and Wortel(1986) for some parts of the Indo-Australian Plate is notrequired to explain the observed stress orientations andregime information. Coblentz et al. (1995) also discussedthe origins of the intraplate stress field in continentalAustralia and suggested that stress focusing effects alongthe heterogeneous convergent boundaries (implemented byfixing the boundaries) are necessary to produce the signifi-cant compression within the continent. In addition, Zhanget al. (1996) constructed a 2D finite-element model for partof the eastern Australian passive margin, although lateralstress changes could not be fully investigated because ofthe nature of the 2D elastic model, and it could not be usedto interpret the stress orientations observed in theAustralian continent.

The main tectonic forces acting on the Australian conti-nent that have been identified in previous studies are shownin Figure 1. The ridge-push force from the mid-oceanic ridgewas inferred to be the dominant force of driving the Indo-Australian Plate northwards (Coblentz et al. 1998). In theeast, the Australian continent may be affected by the sub-duction of the Pacific Plate near New Zealand. The forcetransferred from the subduction zone, which is over 3000km away from the Australian continent, was considered tohave only a secondary effect (Coblentz et al. 1998). In thenorth, the boundary between the Indo-Australian, Eurasianand Pacific Plates is very complex. At the Java Trench, theAustralian Plate is subducting beneath the Eurasian Plate,while the Eurasian Plate is subducting under the Australian

Plate at the Banda Arc. At the Solomon Trench, theAustralian Plate is subducting beneath the Pacific Plate,while the Pacific Plate is subducting beneath the AustralianPlate at Papua New Guinea.

Although the results from the previous studies havegreatly improved our understanding of the relative magni-tudes of the tectonic forces and their role in controlling thetectonic stress field in the Australian continent, there areseveral important factors that could not be addressed bypreviously applied methodologies,

(1) The Australian continent is assumed to be homoge-neously rigid in most of the previous models. Recent studieson lithospheric structures from a seismic tomographic analy-sis of the Australian continent reveal that the lithosphere isnot homogeneous in elastic strength, but heterogeneous(Simons et al. 1999; Simons & Van der Hilst 2002). Manysurface geological structures (e.g. cratons and basins) in theAustralian continent have extensions in the upper mantle interms of seismic velocity anomalies (Kennett 1997). The for-mation of the elastically/seismically inhomogeneous struc-tures is closely associated with the stress-evolution processin the lithosphere. Since some of the geological structures inthe Australian continent are quite large, up to a width of 800km for some cratons, their effect on spatial changes in stressorientations and magnitude is probably significant. Theseelastically inhomogeneous structures were not considered inany previous stress modelling for the Australian continent.

(2) Two-dimensional finite-element modelling wasemployed in all of the previous models. In the 2D models,vertical stresses have been ignored in the plane stressapproximation used in these studies.

(3) Crustal seismicity has occurred throughout theAustralian continent, and the origin of these intraplateearthquakes are still puzzling (Denham 1988; Denham &

66 S. Zhao and R. D. Müller

Figure 1 Map showing the location of the Australian con-tinent and the geometry of the Indo-Australian Plateboundaries (inset). MOR, Mid-Ocean Ridge; J, Java Trench;B, Banda Arc; PNG, Papua New Guinea; SM, SolomonTrench. Arrows indicate the directions of the major tectonicforces (not to scale). FL, the boundary force from the west;FR, the boundary force from the east; FC, the collision andsubduction-related forces from the north; FP, the ridge-push force from the south. Inset (bold lines are plateboundaries): EU, Eurasian Plate; PA, Pacific Plate; S,Sumatra Trench; NH, New Hebrides; TK, Tonga–KermadecTrench; NZ, New Zealand.

Windsor 1991). Because of the limitations inherent in theprevious 2D finite-element models, the spatial distributionof the tectonic stress in the Australian continent, as well asthe origins of the intraplate seismicity, have not been inves-tigated. In order to assess the spatial pattern of the tectonicstresses (such as the distribution and relative magnitude) inthe Australian continent, three-dimensional modelling isessential.

(4) A trial-and-error method was used in the previousmodelling studies and the calculated stress orientationswere visually compared with the observed stress orienta-tions, which is not technically efficient. The studies weremainly qualitative or semiquantitative so that a formal fitbetween the observed and modelled stress orientationscould not be achieved. While recent improvement has beenmade through some refined strategies in forward stressmodelling (Reynolds et al. 2003), an inverse approach forestimating model parameters from observed stress orienta-tions would improve our ability to find the best-fit model.

The present study is an extension of previous modellingefforts of the tectonic stress field in continental Australia(Coblentz et al. 1995). Our work differs from the previousstudies mainly in the following aspects: (i) it is focused oncontinental Australia, and the area covered by the model isabout 45 x 31° (in longitude and latitude) with a spatial res-olution of about 90 x 90 x 50 km; (ii) heterogeneous fea-tures of the Australian continent are included in ouranalysis, which are associated with the differences in theelastic strength for different geological domains, such asmajor tectonic provinces and fold belts; and (iii) since awide range of boundary conditions can be configured tomatch the observed intraplate stress field, the non-unique-ness of the problem is investigated. In this study, an inver-sion method is used to estimate the relative magnitudesand directions of the tectonic forces associated with theAustralian continent from stress orientation data.

Previous studies demonstrated that the gravitationalpotential energy difference across the boundary betweencontinental and oceanic crust may significantly affect the

regional stress field at a plate scale (Coblentz et al. 1994;Sandiford et al. 1995). In this study, the contribution oftopography and gravity potential energy differences to alocal/regional stress field is not simulated, partly because aquantitative simulation requires a detailed crustal/lithos-pheric (density) structure model, which is not presentlyavailable. Ignoring the effect of the gravity potential energydifferences in the Australian continent will affect ourresults, especially at the continental margin, and will bediscussed later.

TECTONIC BLOCKS AND FLEXURAL RIGIDITYOF THE AUSTRALIAN CONTINENT

The Australian continent, which is geologically and tecton-ically complex, can be divided into several crustal blocks.Each block has its own distinctive tectonic style and repre-sents a significant stage in the evolution of the Australiancontinent (Plumb 1979a, b). Figure 2 shows the main tec-tonic units in the Australian continent. The yellow areas arethe cratons, which are geologically stable; the dark greenareas are fold belts; and the blank area in the continent iscomposed of basins and smaller blocks, which will betreated indiscriminately as continental crust/lithosphere,and assumed to have a mechanical strength less than thatof the cratons and larger than that of the fold belts for ourmodelling.

The flexural rigidity of the tectonic blocks in theAustralian continent has been investigated by Zuber et al.(1989) and Simons et al. (2000) on the basis of the analy-sis of Bouguer gravity and topography data. The flexuralrigidity values estimated by Zuber et al. (1989) for the New England Fold Belt and Southern Lachlan Fold Belt (~ 1022 N m) are about three orders of magnitude lowerthan those (~ 1025 N m) of cratons. A revised estimate ofthe effective elastic thickness for central Australia is abouta factor of two less than that of Zuber et al. (1989) (Simonset al. 2000). This suggests that there are large uncertainties

3D Modelling of Australian stress field 67

Figure 2 Map showing the main geologicalblocks in continental Australia. YB, YilgarnBlock; MUB, Musgrave Block; GB, GawlerBlock; ARB, Arunta Block; MB, Mt. Isa Block;Hodg. F. B., Hodgkinson Fold Belt; N. LA. F.B., Northern Lachlan Fold Belt; New Eng. F.B., New England Fold Belt; S. LA. F. B.,Southern Lachlan Fold Belt; Adel. F. B.,Adelaide Fold Belt. B5, B11, B9 and B13 areisolated blocks (see Table 1).

in the estimated effective elastic thickness and the flexuralrigidity of the tectonic blocks in Australia, depending on themethod used. In this study, we are mainly concerned withthe relative values of rigidity among the tectonic blocks;therefore uncertainties in the absolute values of the flexuralrigidity will not affect our results in terms of stress orienta-tions. We use the relative values of the rigidity of the tec-tonic blocks estimated by Zuber et al. (1989) to scale therheological parameters associated with the elastic strengthand as initial input for our model. In addition, the values ofrheological parameters will be adjusted in the inversionanalysis of the observed stress orientations. The age andestimated flexural rigidity for the main tectonic blocks usedhere are outlined below.

Yilgarn and Pilbara Blocks

The Yilgarn and Pilbara Blocks in Western Australia formedabout 3500–3100 Ma. This region is geologically stable(Plumb 1979a). The largest Moho depth here is estimatedto be ~50 km (Clitheroe et al. 2000). The flexural rigidity forthis area was estimated to be 2.0 x 1025 N m (Zuber et al.1989).

Arunta and Musgrave Blocks

The Arunta and Musgrave Blocks are located in centralAustralia, which consists of heavily faulted Proterozoicblocks and basins. Moho offsets with amplitude variationsmore than 20 km have been inferred from gravity modelling(Lambeck 1983a) and the analysis of seismic travel timeanomalies (Lambeck 1983b; Lambeck & Penney 1984).The flexural rigidity for this region is estimated to be 6.1 x1024 N m (Zuber et al. 1989).

Gawler Block

The Gawler Block in South Australia formed during theLate Archaean to Palaeoproterozoic (Plumb 1979a). Theflexural rigidity for the block is estimated to be 6.9 x 1024 Nm (Zuber et al. 1989) and the Moho depth is about 40 km(Clitheroe et al. 2000).

Mt Isa Block and Northern Craton

To the north of the Arunta Block, the entire region (includ-ing B5 and B9 in Figure 2), containing the Mt. Isa Block, issimply called the Northern Craton (Zuber et al. 1989;Plumb 1979b) and consists of Palaeoproterozoic blocksbounded by Mesoproterozoic orogenic belts. The flexuralrigidity for this region is estimated to be 2.1 x 1025 N m(Zuber et al. 1989) and the Moho depth is estimated to be~40 km (Clitheroe et al. 2000).

Eastern Highlands

The Eastern Highlands consist of several Palaeozoic foldbelts along the Australian coast: the Hodgkinson Fold Beltand Northern Lachlan Fold Belt in the northeast, and theNew England Fold Belt and Southern Lachlan Fold Belt inthe southeast. Southeastern Australia is characterised bythe highest seismicity on the continent (Lambeck et al.1984), anomalously high heat flow (Cull 1991), and highmantle conductivity (Lilley et al. 1981). The Moho depth inthe Eastern Highlands varies from about 32 km in the northto 52 km in the south (Clitheroe et al. 2000). The flexuralrigidity is estimated to be 1.6 x 1023 N m for the HodgkinsonFold Belt and the Northern Lachlan Fold Belt, 3.6 x 1022 Nm for the New England Fold Belt, and 4.4 x 1022 N m for theSouthern Lachlan Fold Belt (Zuber et al. 1989).


Table 1 Flexural rigidity and Young’s Modulus for the major tectonic blocks in the Australian continent.

no. (x 1025 Nm) Estimatedc Adjustedd (x 1025 Nm)

1 Basins – – 3.0 – –2 Adelaide Fold Belt – – 0.113 – 0.0403 Yilgarn Block 2.0 0.95 5.7 – –4 Pilbara Block 2.0 0.95 5.7 – –5 Block 5 (B5) 2.1 1.0 6.0 6.656 2.3306 Arunta Block 0.61 0.29 1.74 1.970 0.6907 Musgrave Block 0.61 0.29 1.74 – –8 Gawler Block 0.69 0.33 1.98 – –9 Block 9 (B9) 2.1 1.0 6.0 – –

10 Mt. Isa Block 2.1 1.0 6.0 – –11 Block 11 (B11) 0.69 0.33 1.98 – –12 Southern Lachlan Fold Belt 0.0011 0.00052 0.0031 0.113 0.04013 Block 13 2.0 0.95 5.7 – –14 Hodgkinson Fold Belt & 0.0016 0.00076 0.0046 0.113 0.040

Northern Lachlan Fold Belt15 New England Fold Belt 0.0036 0.0017 0.01 0.106 0.03716 Oceanic crust – – 5.7 – –17 Continental shelf – – 0.21 – –

a From Zuber et al. 1989.b Obtained after dividing the flexural rigidity values by the maximum flexural rigidity value (2.1 x 1025 Nm).c Assign a Young’s modulus value of 6 x 1010 Pa for Blocks 5, 9 and 10, which have the maximum flexural rigidity and then estimate

the Young’s modulus values of other blocks based on the scaling factor.d Estimated from the inversion analysis.

STRESS ORIENTATION DATA ON THE AUSTRALIAN CONTINENT

The stress data used in this study are from the World StressMap website (Mueller et al. 2000). The dataset is compiledfrom borehole breakouts, hydraulic fracturing measure-ments, earthquake focal mechanisms, drilling-induced frac-turing, and fault orientations through the Australian StressMap Project (Hillis et al. 1998, 1999; Hillis & Reynolds2000). A total of 386 orientations (the maximum horizontalcompressive-stress directions) are plotted in Figure 3. Thestress orientations on the Australian continent do not forma uniform direction, although there is some noticeable uni-

formity in several regions (abbreviations in round bracketsrefer to Figure 3): (i) in northwest Australia there are twodominant stress orientations: 140–150°N, 80-90°N (NW1)and 30–50°N (NW2 and BONA); (ii) in west Australia(WA), there is a trend for the 130–140°N stress orientationbut east–west orientations also appear and the scatter inthe stress directions is apparent; (iii) in central Australia,the north–south stress orientations are dominant (CA1),and east–west orientations are also present at some points(CA2); (iv) in northeast Australia, north-northeast stressorientations dominate (EA1); (v) in southeast Australia(EA2), there are two dominant stress orientations,130–140°N in the southernmost part and north–south


Figure 3 Stress orientations (solid linesfor the maximum horizontal compressivestress directions) at 386 points in theAustralian continent, compiled from theAustralian Stress Map Project (Hillis &Reynolds 2000; Mueller et al. 2000).Also shown are the major tectonic blocksin the Australian continent (see alsoFigure 2). NW, northwest Australia;BONA, Northern Bonaparte Basin; WA,western Australia; CA, central Australia;SA, south Australia; EA, easternAustralia.

Figure 4 Stress orientations at the 163sample points which are used in theinversion analysis. The solid linesdenote the observed maximum horizon-tal compressive stress orientations,which is a subset of the stress orienta-tions shown in Figure 3. Also shown arethe major tectonic blocks in theAustralian continent (see also Figure 2).

stress orientations are displayed at some points in thenorthern part of the region, although the stress orientationsin almost every direction were observed in this area; and(vi) in south Australia, the dominant stress orientation isabout 130–140°N near the coast (SA2) and further inlandnear the Adelaide fold belt it is quite scattered, from130–140°N to east–west (SA1).

In this study, we use the stress orientations with qualitylevel A–B exclusively, because of their relatively high relia-bility (Zoback & Zoback 1991; Zoback 1992). There are atotal of 163 stress orientations with a quality level A–B(Figure 4). Comparing Figures 3 and 4, we can see that themain pattern of the stress orientations is still maintained inthe dataset containing only level A–B stress indicators.

NUMERICAL MODELLING

Stress changes and related phenomena, such as fault activ-ity or earthquakes, are associated with the action of varioustectonic forces, which are usually not directly observable.Therefore, the relationship between stress observations andtectonic forces is mainly investigated through modellingstudies. The tectonic forces acting on the Australian conti-nent, model assumptions and strategy used in this studyare discussed below.

Major tectonic forces acting on the Australiancontinent

RIDGE-PUSH FORCE FROM THE MID-OCEAN RIDGE

Mechanically, the ridge-push force results in a slide forcealong the ridge-spreading direction (Lister 1975). The hori-zontal component of the slide force can be viewed as acomponent of the gravitational force, which is subparallelto the topographic slope. Therefore, the slide force, whenaveraged over the plate thickness H, can be expressed as(Lister 1975):

fR = g r a k T /(vH) (1)

where g is the gravitational acceleration, r is the density, ais the thermal expansion coefficient, k is thermal diffusivity,and v is the average half-spreading rate of the ridge. T is thetemperature at which the mantle material becomes suffi-ciently weak such that the lithosphere is decoupled fromthe asthenosphere. T is usually assumed to be about900–1000°C for olivine rheology (Goetze & Evans 1979).

The Australian continent is located over 3000 km northof the mid-ocean ridge (Figure 1), therefore the horizontalcomponent of the slide force along the ridge-spreadingdirection (south–north) can be taken as constant through-out the entire continent. The average half-spreading rate forthe mid-ocean ridge is about 30 mm/y (Müller et al. 1997).Using typical rock property values a = 4 x 10–5°C–1, r =3300 kg m–3, k = 8 x 10–7 m2 s–1 and T = 950°C, we havefRH = 1.03 MPa. For the interior of the Australian Plate,which is about 3000 km from the ridge, this force integratesto 3.03 x 1012 N/m. We use a body force (slide force) to rep-resent the ridge push in 3D, and this value is adjusted inthe inversion analysis. As defined by a 950°C isotherm, the

thickness of the oceanic lithosphere increases from nearlyzero at the crest to about 30 km at the age of ca 10 Ma. Theslide force is estimated to be FR = 51 N/m3 for oceaniclithosphere with an average thickness of 20 km near theridge. This body force is considered to act uniformlythroughout the Australian continent and drives the conti-nent northwards.

BOUNDARY FORCES

In the northern part of the Australian continent, as a resultof the interaction among the Indo-Australian, Eurasian andPacific Plates, the geometry of boundaries between theplates is very complex. At the Java Trench, the Indo-Australian Plate is subducting beneath the Eurasian Plate.At the Banda Arc and Papua New Guinea, the Eurasianand Pacific Plates are subducting beneath the AustralianPlate, and at the Solomon Trench, the Australian Plate issubducting beneath the Pacific Plate (Figure 1). Since theproperties of the forces acting at the northern boundary ofthe Australian Plate are not clear, we assume that theircombined effect is to exert a resistant force (relative to theridge-push force) along the plate boundary near northernAustralia (FC in Figure 1). Along the eastern boundary ofthe Australian Plate, there might be a possible boundaryforce (FR in Figure 1) transferred from the (New Zealand)subduction zone where the Pacific Plate is subductingbeneath the Australian Plate. In west Australia, it is notclear whether there is an equivalent boundary force trans-mitted from the west (see later). In previous models(Coblentz et al. 1995), the magnitude of the boundaryforces for both the northern and eastern boundaries of theIndo-Australian Plate was taken to be ~6 x 1012 Nm–1.

DRAG FORCE

Basal drag is the shear traction that the asthenosphereapplies to the base of the lithosphere. The direction of thebasal drag is usually assumed to be opposite to the direc-tion of the absolute plate motion, but the actual direction isdifficult to assess. The magnitude of the basal drag is likelysmall and of the order of 10–2–10–1 MPa (Richardson1992). Coblentz et al. (1995) estimated a torque value forthe basal drag that is about 50% of the torque of the ridge-push force for the Indo-Australian Plate. In our study, wechoose to ignore the effect of the basal drag on stress mod-elling because: (i) its magnitude is probably small and itsother properties (such as its distribution over the base ofthe lithosphere) are unknown; and (ii) the direction of thedrag force, if resisting the plate motion of the AustralianPlate, is oriented north–south, which is the same (oppositein direction) as that of the ridge-push force. Therefore, it isnot possible to distinguish its presence or absence from thestress orientation data used in this study.

Finite-element model

We used a two-layer elastic model to simulate the responseof the Australian continent to various tectonic forces(Figure 5). The use of the elastic rheology in the stressanalysis for the Australian continent is an oversimplifica-tion, as recognised by Cloetingh and Wortel (1986) and


Coblentz et al. (1995; 1998). However, an elastic rheologyis a justifiable approach for investigating the first-order tec-tonic stresses in continental Australia, especially when wehave insufficient data to constrain a more complicated rhe-ology, such as a viscoelastic model, which would be moresuitable for investigating stress-relaxation processes in thecrust/lithosphere (Lambeck 1983a; Stephenson & Lambeck1985).

The finite-element model (Figure 5) contains a total of4185 nodes and 2640 brick elements, and its spatial reso-lution is about 90 x 90 x 50 km (the dimension of each ele-ment). We use the Lambert azimuth projection to transformgeographical coordinates into Cartesian coordinates, inwhich the finite-element method computation is carriedout. Since the errors in delineating the boundaries of tec-tonic blocks is up to ~100 km, only tectonic blocks widerthan 100 km are included in the analysis, and small struc-tures, such as faults, are ignored in our continental-scalemodel. Figure 6 shows the distribution of the finite-elementnodes and the major tectonic blocks in the Australian con-tinent. The approximation of the geometry of the tectonicblocks is achieved by representing the irregular boundarieswith rectangles (bricks in 3D) (Figure 6). The differences inthe effective elastic thickness (and the flexural rigidity) ofthe blocks reflect their differences in elastic strength, usedhere to constrain the rheological parameters of our numer-ical model.

The geological/rheological provinces with different elas-tic strength are incorporated into the upper layer of a thick-ness of 50 km (Figure 5), which is close to the maximumMoho depth in continental Australia (Clitheroe et al. 2000).A bottom layer of 50 km is introduced as a reference layerwith a Young’s modulus of 14 x 1010 Pa (Turcotte &Schubert 1982) to reflect the fact that the elastic strength ofthe mantle (bottom layer) is higher than the crust (upperlayer). A change of the thickness of each layer affects themagnitude of the stresses, but it does not affect the relativemagnitudes and pattern (including the orientations) of thecalculated stresses. Our main objective is to estimate therelative magnitudes and the pattern of tectonic stresses,rather than estimating the absolute magnitude of the tec-tonic stresses in the Australian continent. The effect of vari-ations in the equivalent elastic thickness of the lithosphere

is indirectly included in our analysis by considering the dif-ferences in their elastic strength, as determined from thecoherence of Bouguer gravity anomalies and topography(Zuber et al. 1989).

Boundary conditions

We assume that the nodes at the bottom (depth = 100 km)of the tectonic block are fixed (Figure 5), which implies thatthe motion/deformation of the top layer (lithosphere), ifany, is relative to the fixed bottom layer. Other boundariesare free. In one of our models, the western boundary of theblock, corresponding to the west Australian coast, isassumed fixed, and its effect on modelling results is exam-ined in an inversion analysis. In all other models, bound-ary forces are imposed at the western, eastern and northernboundaries. Their typical values from previous studies(Coblentz et al. 1995) are used and adjusted in the inver-sion analysis.

Rheological parameters

The major geological structures considered in this studycorrespond to those investigated by Zuber et al. (1989),except for the Adelaide Fold Belt, which was not includedin their study. We assume that the rheological contrast inthe Australian continent can be represented by 17 groupsof material in terms of their differences in elastic strength(Table 1). We adopt a constant value 0.25 for the Poissonratio throughout the investigated area and use different val-ues of Young’s modulus to represent the difference in theelastic strength for different geological structures. The esti-mates for the rigidity of the geological structures in theAustralian continent are taken from the flexural analysisbased on the gravity and topographic data by Zuber et al.(1989) (Table 1). The initial values of the Young’s modulusfor the tectonic blocks are estimated on the basis of the rel-ative magnitude of the flexural rigidity (Table 1).

The scaled values of the flexural rigidity in Table 1 areobtained by dividing by the maximum value of the origi-nally estimated flexural rigidity (2.1 x 1025 N m). TheYoung’s modulus values of the blocks are estimated on thebasis of their scaling factors. The Young’s modulus is takento be 3.0 x 1010 Pa for the basins (the blank area in Figure2) and 5.7 x 1010 Pa for the oceanic crust/lithosphere (thearea outside the continent). In Table 1, a Young’s modulusvalue of 0.21 x 1010 Pa is used for the continental shelf,which is assumed to have a lower strength than the conti-nental crust. Inclusion of the continental shelf in the mod-elling analysis did not improve the quantitative analysis ofthe stress orientations, implying that the stress orientationsin the continent calculated by the numerical model are notsensitive to the rheological parameters of the continentalshelf. A possible reason is that we used a single value todescribe the strength of the continental shelf throughoutthe continent. Actually, the mechanical properties of thecontinental slope could be different from region to region(e.g. from the west to south Australia), but the stress orien-tation data in the continent could not resolve such differ-ences.

The flexural rigidity values of fold belts (Table 1) esti-mated by Zuber et al. (1989) are about three orders of mag-


Figure 5 The finite-element grid used in this study.

nitude lower than those of cratons. The errors in estimatingthe flexural rigidity of the fold belts from the gravity andtopographic data (Zuber et al. 1989) may be large com-pared with those of cratons because of their relatively smalldimensions (Simons et al. 2000). These errors in the esti-mated flexural rigidity are transferred to the Young’s modu-lus values used in this study. Therefore, the values of theYoung’s modulus for the fold belts are adjusted (re-esti-mated) in an inversion analysis of the stress orientationdata. The values for the adjusted Young’s modulus, and thevalues for refined rigidity in Table 1 are the resulting flex-ural rigidities for some of the tectonic blocks obtained fromthe inversion analysis of the stress orientation data and willbe discussed later.

Inversion analysis

Numerical modelling with the finite-element method can beclassified into two types: forward and inverse analyses.Forward modelling calculates the stresses (orientations) inthe continent from known tectonic forces and rheologicalparameters. Inverse modelling estimates some unknownforces and rheological parameters from observations (e.g.orientations) and some known tectonic forces and rheolog-ical parameters. Suppose that the stress orientations (Y) inthe Australian continent are a function of the tectonicforces (Fx) and rheological parameters (R):

Y = f(Fx, R) (2)

where f is an operator which expresses the relationshipbetween Y and (Fx, R). The description of the forward prob-lem is that we want to estimate Y, given Fx and R.

Unfortunately, we only have very limited knowledge ofthe tectonic forces (Fx) and rheological properties of thecontinent. In previous studies, the rheological parameter Rwas taken as a constant, and only the parameter Fx wasadjusted by visually comparing calculated stress patternwith observed stress orientations. If there are relativelyample stress observations and we wish to use the observa-tions as quantitative constraints, the problem has to beconsidered in a reverse way—the inverse problem—whichcan be described as wanting to estimate Fx and/or R, givenY (to estimate tectonic forces and rheological parametersfrom observed stress orientations):

(Fx, R) = f–1 (Y) (3)

where f–1 is an inverse operator which expresses the inverserelationship between Y and (Fx, R).

Since the stress dataset on the Australian continent isnot (mathematically) complete (we always have only lim-ited observations), the solutions of the associated inverseproblems are not unique. We need to introduce a prioriinformation into the modelling analysis. The known geom-etry of geological elements and basic information on thedirections and/or magnitude of tectonic forces from the pre-vious studies are taken as a priori information in our model.The inverse problem for estimating tectonic forces fromstress orientations, can then be expressed as:

|| Y – –Y (Fx ) || = min (4)

a1 ≤ Fx ≤ a2 (5)

where Y is the observational stress orientations (vector), –Y

is the modelled stress orientations (vector), Fx is the para-meter vector of the tectonic forces to be estimated; a1 anda2 are coefficients that are the lower and upper limits of theparameter (Fx).

The rheological parameters in model (4) are assumed tobe known. In addition, the constraints for the tectonicforces are easily obtained based on information from platetectonics or previous forward models. For example, for theridge-push force associated with the Australian continent,its direction is approximately northward (along the Y-axisin our model), so we have a1 >0 or Fx >0. We can also infera rough value (a2) for the upper limit of the ridge-pushforce.

Likewise, the inverse problem of estimating the rheolog-ical parameters from stress orientations can be expressedas:

|| Y – –Y ( R ) || = min ( 6)

b1 ≤ R ≤ b2 ( 7)

where Y is the observational vector of the stress orien-tations,

–Y ( R ) is the modelled stress orientation (vector),

which now depends on the rheological parameters (R), andb1 and b2 are the lower and upper limits of the rheologicalparameters.

The constraints for the rheological parameters are rela-tively easy to obtain. For example, we know that R >0, andfrom the results of laboratory experiments we can deter-mine approximate upper limits for the rheological parame-ters. Methods for solving geophysical inverse problemshave been presented by Menke (1984) and Tarantola(1987), and will not be discussed here.

The inversion analysis is conducted in a stepwise fash-ion. We first take the Young’s modulus scaled from the flex-ural rigidity analysis as initial values, and then investigatethe response of tectonic blocks to the assigned tectonicforces. Different combinations of the tectonic forces areexamined and adjusted to fit the stress orientations in theAustralian continent. We then take the estimated tectonicforces as known parameters and refine the estimates of theYoung’s modulus to fit the stress orientations. These proce-dures are repeated until the squared residuals between theobserved and modelled stress orientations reach a mini-mum, in a least-squares sense. The final estimates of thetectonic forces and the Young’s moduli can be viewed asglobal least-squares estimates.

RESULTS

Ridge-push force

An initial value of 6.0 N/m3 was assigned to the magnitudeof the slide force in the Australian continent. The refinedvalue (FP in Table 2; Figure 1) after the inverse analysis is55.8 N/m3 (0°N), which is close to the value 51 N/m3, cal-culated independently from Equation (1) based on para-meters for the Southeast Indian Ridge. To examine thepossible east–west component of the slide force, the tec-


tonic block is divided into four sections (Figure 6), and foreach of the sections, an eastward ridge-push force compo-nent is added: the resultant changes in the stress orienta-tions are not significant (Table 2).

Boundary forces

In the eastern boundary (Figure 1), there may be a force(FR) resulting from the Pacific Plate, which is subductingbeneath the Australian Plate. Similar to the value(1012–1013 Pa/m) used in previous studies (Coblentz et al.1995), we assume an initial value of 2.0 x 1012 Pa/m for themagnitude of the boundary force at the eastern boundary,and the search for the optimal value gives an estimate of >5.99 ±5.2 x 1012 Pa/m: that is, the upper limit of the mag-nitude is uncertain. The error in this estimate is significantand we interpret this as implying that the dataset is not sen-sitive to the magnitude of boundary force from the east. Forthe boundary force (FC) associated with the northernboundary, we used the same initial value as that used forthe eastern boundary. The estimated value is 11.8 ±3.2 x1012 Pa/m. The absolute values of the forces are difficult to

evaluate from the stress orientation data used in this study.The estimated values of the forces only have relative impor-tance, and they are model dependent. In other words, onlythe relative magnitudes of the tectonic forces can be con-strained by the stress-orientation data.

In order to explore the possible range of boundaryforces at the western boundary of the Australian continent,we tested three models: (i) an east–west boundary force of1.0 x 1012 Pa/m; (ii) a free boundary; and (iii) a fixedboundary. We found that none of the three models pro-duces a significant improvement in the residuals of thestress orientations. Since the western boundary of theAustralian continent is in the interior of the Indo-AustralianPlate (Figure 1), the tectonic deformation in westernAustralia associated with plate-boundary forces is muchsmaller than that in northern Australia, which supports theuse of a fixed boundary. In addition, the fixed westernboundary in the third model serves to resist any plate-tec-tonic forces from deflecting the western boundary, whichseems reasonable. Therefore, we adopt the fixed westernboundary assumption. A further test of the boundary forcevectors acting on four sub-segments of the western bound-


Figure 6 Map showing the distribution of the finite-element nodes in plan view, and the approximation for the geometry of the majorgeological structures in the Australian continent with the brick elements (50 km thick each). The areas coloured red are cratons; foldbelts are green. The yellow curve denotes the boundary of the continental shelf. The numbers represent the estimates of the effectiveelastic thickness in kilometres (Zuber et al. 1989). Arrows denote the force vectors (not to scale) considered in the modelling analysis.

ary of the block (Figure 6) did not produce any substantialimprovements on the misfit, which might suggest that thestress observations (WA in Figure 7) discussed here cannotbe fully accounted for by the continental-scale model.Possible mechanisms for the local stress field in westAustralia will be discussed later.

To test the effect of the possible oblique-type forces atthe northern boundary of the Australian continent, thenorthern segment of the tectonic block is divided into foursegments (Figure 6). For each segment, in addition to thenorth–south component of the boundary force (along the Y-axis), an east–west component (along the X-axis) is alsoassumed to be unknown in the inversion analysis. A com-bination of the two components (X and Y) constitutes aforce vector. However, the inversion fails to give a signifi-cant estimate for the east–west component of the collisionforce for all segments. This suggests that detailed charac-teristics of the tectonic-force vectors cannot be resolvedfrom the available stress-orientation data. This may indi-cate that the variations of the boundary forces along thenorthern Australian plate boundary have little effect on thestress orientations observed within the Australian conti-nent. This conclusion supports the interpretation that alarge amount of the energy associated with subductionzones may be dissipated by resistance to subduction, andtherefore a surface plate may not experience substantialslab pull (Richardson 1992; Hillis et al. 1997). However,this does not mean that the effect of the forces acting at the

plate boundary on the intraplate tectonic stress field can bedismissed. Forces originating at the plate boundary, otherthan the boundary forces considered here, could havesome significant effects on the intraplate stress field, suchas the body forces transmitted from the plate boundaries,but the properties of such forces are not very clear.

The maximum horizontal stress orientations estimatedfrom the inversion analysis (Model A1) are shown in Figure7. The estimated stress orientations (red lines) are fairly con-sistent with the observations (black lines) in the western partof northwest Australia (NW1), Northern Bonaparte Basin(BONA), central part of Australia (CA1) and northeastAustralia (EA1). While the inclusion of the geological struc-tures in our analysis has provided a reasonable fit to some ofthe observed stress orientations, there are deviationsbetween the observed and modelled stress orientations, e.g.in the southern part of west Australia (WA), the eastern partof northwest Australia (NW2), central Australia (CA2), east-ern Australia (EA2) and south Australia (SA2).

Refined rheological parameters

The stress orientations for the points near or inside a geo-logical structure are associated with the material contrastbetween the structure and its surrounding area. Therefore,the rheological parameters for some of the tectonic blocksare adjusted to obtain their optimal values by inversionanalysis of the stress-orientation data.


Figure 7 Observed (black lines) and esti-mated (red lines, Model A1) maximumhorizontal compressive stress orienta-tions. NW, northwest Australia; BONA,Northern Bonaparte Basin; WA, westernAustralia; CA, central Australia; SA, southAustralia; EA, eastern Australia.

Table 2 Estimated magnitude of the ridge push and boundary forces.

Ridge push (slide force) (FP) Northward 6.0 N/m3 55.8 ±6.1 N/m3

Eastward – not significantBoundary force (FR) Northward – not significant

Eastward 2.00 x 1012 Pa/m FC >5.99 ±5.2 x 1012 Pa/mBoundary force (FC) Northward 2.00 x 1012 Pa/m 11.8 ±3.2 x 1012 Pa/m

Eastward – not significant

INLAND BASINS

The Young’s modulus value is taken to be 3.0 x 1010 Pa forthe basins in the Australian continent (Figure 2). A changein the value of the Young’s modulus of the basins has littleeffect on the overall residuals between the observed andmodelled stress orientations, suggesting that stress orienta-tions are not sensitive to the change of this parameter. Apossible reason could be that we used a single value to rep-resent the elastic strength for all of the basins, so that thedifference among the basins, which (if any) affects the localstress distributions, could not be distinguished in the con-tinental-scale model.

FOLD BELTS

The inversion analysis indicates that the stress orientationsare sensitive to the Young’s modulus values of fold belts.Comparing the Young’s modulus values (~1010 Nm) of thecratons, the re-estimated values for the fold belts are aboutone to two orders of magnitude lower (Table 1). The re-esti-mated value of the Young’s modulus is 0.113 x 1010 Pa forthe Northern Lachlan Fold Belt, 0.106 x 1010 Pa for theNew England Fold Belt and 0.113 x 1010 Pa for theSouthern Lachlan Fold Belt (Table 1). The adjusted flexuralrigidity value is 0.040 x 1025 Nm for the Northern LachlanFold Belt, 0.037 x 1025 Nm for the New England Fold Belt,


Figure 8 Observed (black lines) andmodelled (red lines, Model A2) maxi-mum horizontal principal stress orienta-tions (after adjustment of therheological parameters of the tectonicblocks). NW, northwest Australia;BONA, Northern Bonaparte Basin; WA,western Australia; CA, central Australia;SA, south Australia; EA, easternAustralia.

Figure 9 Observed (black lines) andmodelled (red lines, Model A3) maxi-mum horizontal principal stress orienta-tions (after inclusion of the effect oflocal stress fields). The shaded barsdenote the orientations of the intro-duced local stress fields. NW, northwestAustralia; BONA, Northern BonaparteBasin; WA, western Australia; CA, cen-tral Australia; SA, south Australia; EA,eastern Australia.

and 0.040 x 1025 Nm for the Southern Lachlan Fold Belt(Table 1). The estimates correspond to an effective elasticthickness of about 30 km.

COMPARING THE OBSERVED AND MODELLEDSTRESS ORIENTATIONS

Figure 8 shows the observed (black lines) and estimated(red lines) maximum horizontal stress orientations asobtained after the adjustment of the rheological parameters(Model A2). The standard deviation of the residuals is±45.3° and ±44.5° for Models A1 and A2, respectively.Since the standard error in the observed stress orientationscould be about ±15° (Zoback 1992), the difference betweenthe two models is not statistically significant. However,considering that there are many non-statistical uncertain-ties in the quantitative analysis of observed stress orienta-tions as well as the associated tectonic forces, the resultsobtained in this study should be viewed as semiquantita-tive. Comparing the observed (black lines) and modelled(red lines) stress orientations in Figure 8, the general pat-tern of the observed stress orientations has been recon-structed by the numerical model, though deviations stillexist at some sites.

In eastern Australia, the fold belts are simulated as ‘weakzones’ in the numerical analysis, and substantial rotations inthe stress orientations occurred near these ‘weak zones’. Thevariations in the stress orientations reflect the combinedeffect of the tectonic forces and the contrast in the elasticstrength of tectonic elements on producing the intraplatestresses. For the northern part of eastern Australia (EA1),Model A2 (Figure 8) predicts two types of stress orientations:northeast and north-northeast. The stress orientations mod-elled are generally consistent with those observed. The stressorientations predicted for the southern part of the easternAustralia (EA2) are also of two types, northwest and north-east, and apparent deviations exist between the predictednorth-northeast and observed northeast orientations. For thestress indicators around the Southern Lachlan Fold Belt(Figures 2, 8), the orientations predicted by the model arelargely of two types, northwest and north-northeast, and sig-nificant deviations exist between observations and predic-tions. Model A2 could not reflect the rotations of theobserved stress orientations from northeast in the north(EA2) to northwest in the southernmost part of the region.

Stephenson and Lambeck (1985) constructed an ero-sion-rebound model for southeastern Australia to explainthe geomorphological and geological observations for theuplift that occurred since Early Cenozoic time, and pre-dicted a tensile stress field for southeastern Australia (withnorthwest orientations: Stephenson & Lambeck 1985 figure12, p. 50). Since only the regional trends of the stress ori-entations related to the continental-scale tectonic forces, aswell as the contrast in the elastic strength among major tec-tonic blocks, are simulated in our model, the local stresschanges caused by different kinematic/dynamic mecha-nisms, such as the erosion-rebound effect discussed byStephenson and Lambeck (1985), can not be directlyaccounted for. However, after superimposing a local tensilestress field (103°N: green bar near EA2 in Figure 9) esti-mated by Stephenson and Lambeck (1985) onto the

regional stress field predicted by Model A2, a hybrid model(Model A3) is obtained, and the stress orientations pre-dicted by the model are shown in Figure 9. There are somesignificant improvements on the fit between the observa-tions and predictions. For the points around the SouthernLachlan Fold Belt (Figures 2, 9), the stress orientations arenow consistent with the observations.

In northwest Australia, the east–west and northeaststress orientations (NW1 and NW2 in Figure 8) are not fit-ted by the model. As mentioned before, adjusting the distri-bution of the collision forces at the northern boundary failedto reduce the misfit. One possible cause for this misfit mightbe the effect of some local geological structures in theregion. The borehole breakout data in this area are from theCanning Basin, which is bounded by Fitzroy Trough in thenorth. The sediments in the Fitzroy Trough are about 14 kmthick (Borissova & Symonds 1997); its length is about 700km, but its width is merely about 100 km. The presence ofthe Fitzroy Trough could have some effect on the local stressfield, but it is difficult to include this effect into our analysisdue to the narrowness of the trough, for which a model with


Figure 10 Distribution of the residuals (between the observedand modelled stress orientations) for Models A1, A2 and A3. Thevertical lines indicate the one standard deviation.

a resolution of at least 50 km is required. In addition, a ten-sile stress regime has been reported in northwest Australia(Coblentz et al. 1995), which might be related to the effectof the continental shelf and deep basins in the region. Wetherefore tentatively introduce a local tensile field with itsdirection perpendicular to the coast (140°N: green bar nearNW2 in Figure 9). After inclusion of the local stress field(Model A3, Figure 9), we see that the predicted stress orien-tations are now consistent with the observations.

In west Australia (WA), for the eight stress indicators(Model A3) used in the analysis, the average deviationbetween the observed and modelled orientations is about46°, which is larger than the standard deviation of themodel (±37.6°). In addition, a test for inclusion of theboundary-force vector with different magnitudes and ori-entations on four sub-segments along the western bound-ary failed to improve the fit (Figure 6). This suggests thata further improvement on the fit between the observedand modelled stress orientations with the present model isdifficult. In previous studies, two mechanisms were pro-posed for the rotation of the local stress field in westAustralia. Cloetingh and Wortel (1986) suggested that the

state of compression in the western part of centralAustralia is induced by the action of resistant forces at theHimalayan and Banda arc collision zones (Figure 1 inset).However, as demonstrated by Coblentz et al. (1995,1998), the collision forces produce stress focusing onlynear the boundaries, and their effects on the orientationsof the stresses within the plate are secondary. Since mostof the stress orientations in central and northwestAustralia have been fitted by the present model (Figure 9),a causative mechanism for the local variations of thestress orientation in the interior of the Australian conti-nent due to regional- or plate-scale forces is not likely. Alocal mechanism for the stress changes and seismicity inwest Australia has been proposed by Lambeck et al.(1984). They suggested that: (i) there might be alocal/regional stress field resulting from the interactionbetween the Yilgarn Block (YB in Figure 2) and the nearbyDarling Fault; and (ii) the stress regime of the local stressfield could be tensile. The north–south-oriented DarlingFault (Borissova & Symonds 1997) is more than 800 kmlong, but its width is less than 50 km. Therefore, the effectof the fault and its interaction with the Yilgarn Block as


Figure 11 Principal-stress distribution in continental Australia (in units of 100 MPa). Also shown are the boundary of the major geo-logical structures (yellow), the boundary of the continental shelf (green), and epicentres of the earthquakes with magnitudes of M ≥3.0(triangles) and M ≥5.0 (stars). The blank areas represent the zones of least compression (with a compressive stress value ≤0 MPa).

well as their combined effects on the local/regional stressfield could not be simulated here, given the resolution ofthe present model.

Figure 10 shows the distribution of the residuals forModels A1, A2, and A3. The numerical model has statisti-cally fit the observed stress orientations to ±37.6° (ModelA3). More than 45% of the observed stress orientationshave been fitted by our model within ±25°. Overall, thenumerical model provides a reasonable interpretation ofthe observed stress orientations in the Australian continent.

PRINCIPAL-STRESS DISTRIBUTION AND SEISMICITY IN CONTINENTAL AUSTRALIA

Figure 11 shows the principal-stress distribution predictedin this study with seismicity in continental Australia super-imposed. Seismicity in the Australian continent is concen-trated in several zones (Figure 11).

(1) In Western Australia, earthquakes are observedmostly in the southern part of the Yilgarn Block (also seeFigure 2) and near the North West Shelf (northwestAustralia). Fault plane solutions for two earthquakes (M =6.8, 1968; 5.9, 1970) in Western Australia indicate thrustfaulting (Fitch et al. 1973). The source mechanisms for theearthquakes in the North West Shelf are not well deter-mined, as most of them occurred along the continental shelf.

(2) In South Australia, seismicity is largely confined tothe Adelaide Fold Belt and the adjacent gulf graben regions.An average depth of about 10 km is estimated for the earth-quakes recorded during 1976–77 by McCue and Sutton(1979). In addition, the source mechanism solutions of theevents indicate failure by strike-slip faulting.

(3) In central Australia, seismicity is relatively diffuse. Aconcentration of seismicity is observed in the Gawler Blockand near the Arunta Block (Figure 2). Source mechanismsolutions of two earthquakes (M = 6.2, 1972; 4.7, 1978) inthe Simpson Desert show failure by compression.


Figure 12 Shear-wave speed anomalies (depth = 80 km) for the upper mantle of the Australian continent (modified from Kennett 1997,2002). The letters mark the major zones of shear-wave speed anomaly in southern Australia (A), central Australia (C and C1), easternAustralia (E1 and E2), northern Australia (N1) and western Australia (W1) (see text for discussion).

(4) In east Australia, seismicity is mostly concentratedaround the southern Lachlan Fold Belt and along the coastadjacent to the Northern Lachlan Fold Belt and the NewEngland Fold Belt (Figure 2). Most of the earthquakes insoutheast Australia indicate horizontal compressive failure.

Earthquakes are indicative of where stress is concen-trated so that the brittle failure limit of the crust has beenexceeded. Therefore, a correlation between seismicity andthe predicted stress distribution is expected. Comparing thedistribution of seismicity and the pattern of the stress pre-dicted in this study, we see that such a correspondence doesexist: the seismicity in northwest and southeast Australiafalls into two bands where stress concentration is predicted.

Nevertheless, there are still several zones where the pre-dicted stress concentration is not compatible with seismic-ity observed in the continent. In southwest Australia, azone of intense seismicity in the Yilgarn Block (Figure 2)does not correspond to any concentration of stress pre-dicted by our model. Along the Great Australian Bightcoastline (south Australia), a large zone of stress concen-tration is predicted, which is unsupported by observations.

Only the eastern part of this stress concentration zone cor-responds to the seismicity near or around the Adelaide FoldBelt. The western part of the zone does not correspond toany recorded seismicity. In central Australia, the diffuseseismicity is not accounted for by the stress concentrationpredicted in this model.

To further interpret the seismicity in continentalAustralia, it is necessary to include additional informationon the contrast in elastic strength of the tectonic elements,such as results from seismic tomography (Kennett 1997,2002; Simons et al. 1999) (Figure 12). Shear-velocity anom-alies reveal the relative contrast in elastic strength amongthe tectonic elements: seismically ‘slow’ (negative anomalyin Figure 12) indicates the material in the area is of ‘lowerstrength’, and seismically ‘fast’ (positive anomaly) indicates‘higher strength’. Seismically ‘slowest’ is predicted for theSouthern and Northern Lachlan Fold Belts (marked E1 andE2), and ‘fastest’ is predicted for western (marked W1),central (C1) and northern Australia (marked N1). In addi-tion, relative small, but noticeable, seismically ‘fast’ zonesalso appear in the western part of South Australia (marked


Figure 13 Principal-stress distribution in continental Australia (in units of 100 MPa) computed after including the rheological infor-mation from seismic tomography. Also shown are the boundary of the major geological structures (yellow), the boundary of continen-tal shelf (green), and epicentres of the earthquakes with the magnitude of M ≥3.0 (triangles) and M ≥5.0 (stars). The blank areasrepresent the zones of least compression (with a compressive principal stress value ≤0 MPa).

A) and eastern part of central Australia (marked C). Thesevelocity anomalies may reflect material contrasts betweenthe cratons, basins and fold belts. We investigate thishypothesis by including these contrasts between lower andhigher strength lithospheric blocks based on seismic tomog-raphy in terms of differences in their Young’s moduli.

After inclusion of this additional information, a revisedmap of the principal stress distribution for continentalAustralia is constructed (Figure 13). A noticeable feature inthe predicted stress pattern is that the areas with the leastcompression (the blank areas in the continent) are almostseismicity free. The band of stress concentration along theGreat Australian Bight, where little seismicity is observed,has disappeared and moved further north where it nowmatches a belt of seismicity from the Musgrave Block to theYilgarn Block. The magnitude of the principal stresses is esti-mated between 10 and 40 MPa, and the deformation style islargely compressive. The predicted area with the least com-pression (blank zone) in the North West Shelf correspondsapproximately to the normal faulting stress regime inferredfrom the in situ stress data (Hillis 1991; Hillis & Williams1992, 1993a, b). The stress concentration zones predicted bythe model now correspond quite well with the areas whereconcentrated seismicity is observed. The improvements inmodel prediction by including lateral variations in lithos-pheric rheology based on seismic tomography illustrate theshortcomings of relying on surface geology and gravity/topog-raphy coherence results for estimating the spatial variation inlithospheric rigidity. However, the inclusion of informationfrom seismic tomography in our model does not contribute tofurther improvement of the fit between the observed andmodelled stress orientations on the Australian continent.Features revealed by seismic tomographic analysis have alarger length-scale and poorer resolution than those fromsurface geological investigations. As discussed before, weneed to include more information on local and small-scalestress sources into a higher resolution model in order to inter-pret the variations of stress orientations in some regions. Theextra information obtained from the seismic tomographicanalysis at the current resolution does not contribute signifi-cantly to a better and quantitative interpretation of the stressorientations observed on the Australian continent, as com-pared to the rheological model based on the coherence ofBouguer gravity and topography.

DISCUSSION

A three-dimensional finite-element model has been con-structed and used to investigate the pattern and orienta-tions of the tectonic stresses in continental Australia. Themodel, which consists of two layers (Figure 5), provides aspatial resolution of about 90 x 90 x 50 km. The major geo-logical structures such as cratons and fold belts areincluded in the analysis. The difference in the elasticstrength of the tectonic structures are initially estimated onthe basis of their rigidity values inferred from the coherenceof Bouguer gravity and topography (Zuber et al. 1989). Themajor tectonic forces which act on the Australian continent(such as ridge-push and plate-boundary forces) are investi-gated in the analysis. An inversion approach is used to esti-mate the relative magnitude of tectonic forces from the

observed stress orientations (equations 4 and 5). In addi-tion, an approach for estimating the main rheological para-meter (Young’s modulus) from the inversion analysis of theobserved stress orientations is also developed (equations 6and 7) and used to estimate the values of the Young’s mod-ulus for some of the geological structures.

Our results suggest that the slide force associated withridge push is the dominant force that controls the magni-tude and orientations of the stress field in the Australiancontinent, confirming the results of Coblentz et al. (1995,1998). The magnitude of the slide force is estimated to be55.8 N/m3, and the magnitude of the forces at the easternand northern boundaries is estimated to be >5.99 x 1012

Pa/m, and 11.8 x 1012 Pa/m, respectively (Table 2). Theestimates for the magnitude of the forces are model depen-dent and subject to many uncertainties (e.g. the assumedrheological parameters and geometry of tectonic blocks).Therefore, they may be interpreted only as semiquantitativeestimates. The boundary forces acting on the northern andeastern boundaries of the Australian continent only have asecondary effect on the overall stress pattern, and they donot significantly affect the pattern of the stress in the inte-rior of the continent.

The presence of tectonic domains with different rigidi-ties has a significant influence on the pattern of the esti-mated regional and local stresses. After combining thetectonic forces, major geological structures, and the effectof the local stress fields in the numerical model, a reason-able fit has been achieved between the observed and mod-elled stress orientations (Figure 9). The in situ stressorientations can be statistically fitted within ±37.6° by thenumerical model.

The inversion analysis of rheological parameters is use-ful for estimating the Young’s moduli for the NorthernLachlan Fold Belt, the New England Fold Belt, and theSouthern Lachlan Fold Belt. The adjusted values for theflexural rigidity are 0.040 x 1025 Nm for the NorthernLachlan Fold Belt, 0.037 x 1025 Nm for the New EnglandFold Belt, and 0.040 x 1025 Nm for the Southern LachlanFold Belt (Table 1), which correspond to an effective elasticthickness of about 30 km. These estimates are about twoorders of magnitude lower than those of the cratons (~1025

Nm). The original estimates (~1022 Nm) for the fold beltsfrom Zuber et al. (1989), which are about three orders ofmagnitude lower than those of the cratons (Table 1), mayhave been underestimated (Simon et al. 2000). It appearsthat the re-estimated values of the rigidity for the fold beltsfrom this study, which are between the maximum and min-imum of the flexural rigidity estimated by Zuber et al.(1989) and constrained by the stress-orientation data, aremore geologically plausible. Therefore, we have providedan indirect estimate for the flexural rigidity of the fold beltsin continental Australia.

Another significant result from this study is the esti-mated distribution of the principal stress in the Australiancontinent (Figure 13). We predict stress concentration innorthwest Australia, South Australia, and southeastAustralia. In addition, several zones with least compressionare also identified in the continent. Although the predicteddeformation style in the Australian continent by our modelis of compression and strike-slip faulting, it is plausible toinfer that normal faults are most likely to develop in the


areas where the least compression is predicted. It is alsonoteworthy that the concentration of seismicity is notobserved inside the predicted least compression zones, butit is mostly inside the zones of significant compression.Therefore, the principal-stress distribution predicted herehas furnished a preliminary interpretation for the seismicityobserved in continental Australia.

Considering lateral variations in lithospheric strength inthe modelling analysis by including results from shear-wavetomography proved to be essential to remove some first-order artefacts from initial model, and improve the match ofmodelled zones of stress concentration with observed beltsof seismicity. The results demonstrate that by combiningsurface geology, lithospheric rigidity estimates from grav-ity–topography coherence, and seismic tomography, wehave assembled a simple rheological model for theAustralian Plate that, together with an optimised model forplate-driving forces, accounts for the observed large-scalepatterns of intraplate seismicity in Australia.

However, like any other numerical analysis (Richardsonet al. 1979; Cloetingh & Wortel 1986; Coblentz et al. 1995,1998), there are many limitations inherent in our model.Although the estimated magnitude of the principal stressbetween 10 and 40 MPa is compatible with the value(~tens of megapascals, over a 100 km-thick layer) esti-mated by Coblentz et al. (1998), it is subject at least to thefollowing uncertainties: (i) since the magnitude of theboundary forces is actually unknown, a geologically plausi-ble value has been adapted: typically, a value of ~1012 N/mwas used; the absolute value of the forces could not be welldetermined by the analysis of the stress orientation dataalone; (ii) the absolute values of the rheological parametersof the crust/lithosphere are unknown, and a value of ~1010

Pa was used for the Young’s modulus; and (iii) the magni-tude of the stresses is estimated over a layer of 50 km thick-ness, and the effect of the rigidity layering as well as anyother depth dependent-stress changes have been ignored,which affects the magnitude of the calculated stresses.What we have estimated in this study are the relative mag-nitude and the pattern of the tectonic stresses, rather thanthe absolute magnitude of the tectonic stresses in theAustralian continent.

Our analysis shows that ignoring the effect of the grav-ity potential energy differences in the Australian continentinfluences the modelling results. Two additional stressfields required to fit the observed stress orientations innorthwest (NW1 and NW2) and southeast (EA2 in Figure9) Australia may reflect the possible contribution of thetopography or gravity potential energy difference at areasnear the continental margin. One of the mechanical effectsof the gravity potential energy difference at the continentalmargin is to produce a local stress field. The stress concen-tration reflected by seismicity near the continental marginpredicted in our model indicates that the mechanicalstrength of the continental shelf is weaker than that of con-tinental crust whose last thinning/reheating event is sub-stantially older (see Fowler & McKenzie 1989). Thisweakening effect has been incorporated in our model byincluding the continental shelf as a weak zone. However,the forces arising from the gravity potential energy differ-ence at the continental margin are not directly simulated inour study. Since the crustal structure at the continental

margin could vary from place to place, a separate analysisof the local stress field associated with the gravity potentialenergy difference or gravity instability based on a detailed(density) structure model is required in the future.

Moreover, many small- to intermediate-scale geologicalstructures are not included in our study, such as basins andfaults. For some of the basins, the depth of the sediment tothe basement is more than 10 km (e.g. the Browse Basin inthe North West Shelf: Borissora & Symonds 1997), and forsome crustal-scale faults, their length scale is up to 500 km(e.g. the Darling Fault in Western Australia). Inclusion ofgeological structures into a future model with a higher spa-tial resolution will alter the magnitude as well as the patternof the calculated stress in the areas around or close to thesestructures. Further, the present activity or reactivation offaults also influences the pattern of the local/regional stressfield (Sandiford & Hand 1998). These could be the objectsof future local or regional stress analysis, which may bedesigned to explore the effects of the local or regional geo-logical structures as well as their activity on the tectonicstress field. These factors discussed above could in partaccount for the reason that about 20% of the observedstress orientations are not well fitted by our continental-scale model.

The interaction between the lithosphere and mantle orthe upper and lower crust has not been considered in ouranalysis. The stress transferred from the lower or the uppermantle into the upper crust or lithosphere associated withpre-existing geological structures could influence the pat-tern of the local or regional stress field (Kusznir & Bott1977; Lambeck et al. 1984). However, the magnitude andproperties of the transferred stresses, which are modeldependent, are very difficult to assess. For instance, astress difference of 50–200 MPa for eastern Australia is pre-dicted by the erosion–rebound model of Stephenson andLambeck (1985), which is almost at the same magnitude asthat of the predicted regional stress field (Coblentz et al.1995, 1998). Our study has shown that a combination oflocal stress-relaxation processes associated with some dis-tinct geological structures with a continental-scale modelbetter accounts for the observed stresses. However, theincreasing uncertainties with adding more (speculative)geodynamic mechanisms into any model will furtherincrease the ambiguity of the results. Therefore, these geo-dynamic processes are currently modelled separately.

The type of deformation and the stress regime inferredfrom the in situ stress measurements, the seismic sourcemechanisms, and the numerical model experiments are alldepth dependent. The information of the deformation typeand faulting style estimated from earthquakes in the uppercrust could be different from those from the earthquakes inthe middle crust, or different from those obtained from thein situ stress measurements. Therefore, the available infor-mation on the stress regime from the in situ stress mea-surements, the earthquakes source mechanisms, and thenumerical modelling of the Australian continent is incom-plete. While the dominant deformation style in theAustralian continent inferred from this study is compres-sion, which is consistent with that from the in situ stressmeasurements, caution should be taken when extrapolat-ing the results to the state of the stress at depth because ofthe inherent uncertainties stated above.


SUMMARY

The main results from the 3D stress analysis with the finite-element method for the Australian continent are as follows.

(1) The ridge-push force is the dominant force whichcontrols the magnitude and pattern of the first-orderstresses in the Australian continent. The effect of theboundary forces are secondary and they mostly influencethe pattern of the stress in areas near the boundaries. Thereis no need to invoke the drag force to explain the first-orderstress pattern in the Australian continent partly because ofour poor understanding of the properties of the drag forceand the insensitivity of the stress orientation data to thedrag force. These results are consistent with those obtainedby Coblentz et al. (1995).

(2) Geological structures significantly affect the magni-tude and pattern of modelled stresses. Combining spatialvariations in rigidity between major geological structures(cratons and fold belts) and a tectonic-force model, bysimultaneously inverting for stress orientations and tec-tonic-force vectors, a fairly good fit has been achievedbetween the observed and modelled stress orientations.The model can explain statistically about 45% of theobserved stress orientations within ±25°, and about 62%within ±40°.

(3) The model also provides an indirect estimate of theflexural rigidity for the Northern Lachlan Fold Belt (0.040 x1025 Nm), the New England Fold Belt (0.037 x 1025 Nm)and the Southern Lachlan Fold Belt (0.040 x 1025 Nm).These estimates correspond to an effective elastic thicknessof about 30 km.

(4) A preliminary map of principal-stress distribution(Figure 13) is constructed for continental Australia, inwhich the relative magnitude of the principal stress overthe continent can be assessed. The predicted stress-con-centration zones in general correspond to the areaswhere intensive seismicity is observed. In addition, theleast compression is predicted in several zones whereearthquakes are relatively sparse, and it is also inferredthat normal faults would mostly likely develop in thesezones.

(5) While the model from this study provides a reason-able interpretation for the stress orientations and seismicityobserved in the Australian continent, about 20% of theobserved stress orientations are not well-fitted by themodel. The main reason for this could be that the distur-bances in the stress field associated with some local orregional geological structures (and their present activity)cannot be simulated in our present continental-scalemodel.

ACKNOWLEDGEMENTS

We wish to thank D. Coblentz, R. Hillis and M. Sandifordfor their constructive reviews, which improved this manu-script substantially, B. L. N. Kennett for kindly providing ushis latest shear-wave model of the Australian lithosphere,and G. Clitheroe for providing some of the data used in thisstudy. This research is supported by an ARC SPIRT grantand industry sponsorship by BHP, Santos, Shell andWoodside.

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Received 23 July 2001; accepted 29 August 2002


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