ARTICLE IN PRESS

0098-3004/$ - se

doi:10.1016/j.ca

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index.htm.�CorrespondE-mail addr

(S. Dyksterhuis

(R.A. Albert), d1Present addr

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Computers & Geosciences 31 (2005) 297–307

www.elsevier.com/locate/cageo

Finite-element modelling of contemporary and palaeo-intraplate stress using ABAQUSTM$

S. Dyksterhuis�, R.A. Albert1, R.D. Muller

School of Geosciences and University of Sydney Institute of Marine Science, Edgeworth David Building (F05),

University of Sydney, NSW 2006 Australia

Received 27 August 2003; received in revised form 24 September 2004; accepted 6 October 2004

Abstract

Knowledge of the contemporaneous and palaeo-orientation of maximum horizontal compressive stress (SHmax) in the

Earth’s crust is important for the exploration and recovery of hydrocarbons and also provides insights into the

mechanisms driving plate motion and intra-plate seismicity. To date, most approaches for modelling intraplate stress

orientations have been based on applying forces to homogeneous elastic plates. However, real tectonic plates consist of

oceanic and continental lithosphere, including sedimentary basins, fold belts and cratons with large differences in elastic

properties. We have used the finite-element method as implemented in the software package ABAQUSTM along with

the optimisation software Nimrod/O to model the orientations and magnitudes of SHmax over the Indo-Australian plate

for the present and the Miocene. An elastic 2D plane stress model incorporating realistic mechanical properties for the

Australian continent was used consisting of 24,400 elements, providing a resolution of 0.21 in both latitude and

longitude. In general, modelled SHmax directions correlate well with observed contemporary stress indicator data and

reactivation histories over the NW Shelf and Bass Strait regions of the Australian continent, where Tertiary tectonic

reactivation through time is best documented. Large perturbations in SHmax orientation over the Australian continent

are shown to occur in and around regions of heterogeneous material properties.

r 2004 Elsevier Ltd. All rights reserved.

Keywords: Australia; Stress; Palaeo-stress; Modelling; Plate dynamics

1. Introduction

An understanding of the orientation of contempora-

neous maximum horizontal compressive stress (SHmax) is

e front matter r 2004 Elsevier Ltd. All rights reserve

geo.2004.10.011

server at http://www.iamg.org/CGEditor/

ing author.

esses: scottd@geosci.usyd.edu.au

), richard.albert@exxonmobil.com

ietmar@geosci.usyd.edu.au (R.D. Muller).

ess: ExxonMobil Upstream Research Co., P.O.

ston, TX 77252-2189, USA.

relevant to many areas of earth science, providing

fundamental insights into the mechanisms driving plate

motion. Knowledge of contemporaneous and palaeo

SHmax orientations and magnitudes is also useful for

improved exploration and recovery of hydrocarbons,

allowing for the creation of a predictive framework for

fault reactivation and the planning of deviated drilling.

Since SHmax data can be sparse over large areas of

continents and over geologic time, geophysical model-

ling of SHmax regimes is necessary to provide a

satisfactory understanding of the regional stress field.

Data compiled as part of the World Stress Map project

(Zoback, 1992) provide important constraints on

d.

ARTICLE IN PRESSS. Dyksterhuis et al. / Computers & Geosciences 31 (2005) 297–307298

present orientation and magnitude of SHmax regimes of

continents, and in particular data contained in the

Australian Stress Map project (Hillis and Reynolds,

2000) are used here as constraint on modelled con-

temporary SHmax orientations for the Indo-Australian

plate.

Up to now most approaches for modelling Indo-

Australian intraplate stress orientations have been based

on applying forces to homogeneous elastic plates

(Coblentz et al., 1995, 1998; Hillis et al., 1999; Reynolds

et al., 2002). While these studies model the first-order

pattern of stress over the Australian continent well,

more recently Zhao and Muller (2003) studied the

second-order effects of homogeneous material proper-

ties on the stress field of Eastern Australia, determining

through inverse analysis that inclusion of realistic

material properties improves the regional fit between

modelled and measured SHmax orientations.

Modelling of the stress regime of the Indo-Australian

plate was carried out here using ABAQUSTM, an

engineering industry standard finite-element modelling

software package, in conjunction with the distributed

optimisation software Nimrod/O. A 2D plane-stress

elastic finite-element model was created consisting of

24,400 elements allowing for a spatial resolution of 0.21

of both latitude and longitude (Fig. 1). While the

assumption of elastic rheology, which precludes any true

time dependence, is an oversimplification it is justifiable

Fig. 1. Mesh of ABAQUSTM contemporary Indo-Australian plate mo

giving a resolution of roughly 0.21 in both latitude and longitude.

for the modelling of such large scale, low order tectonic

stresses. Forces applied to the models are averaged over

a lithosphere of 100 km thickness.

2. Modelling method

Finite-element modelling of the Indo-Australian and

Australian plate for the present and geologic past was

carried out utilising the software packages ABAQUSTM

and Nimrod/O. ABAQUSTM is a robust, industry

accepted finite-element modelling program and allowed

for simple creation and alteration of model geometries

and parameters using the program ABAQUSTM

CAETM (Complete ABAQUSTM Environment). Imple-

menting ABAQUSTM in conjunction with Nimrod/O

allowed for extensive exploration of parameter space

through automated execution of thousands of models

using intelligent optimisation techniques (Abramson et

al., 2000; Lewis et al., 2003).

In order to compare modelled results a residual misfit

value was calculated between modelled stress orienta-

tions and measured stress orientations contained in the

Australian Stress Map database (Hillis and Reynolds,

2000). In order to calculate the residual misfit, modelled

SHmax orientations were averaged over a small window

whose centre corresponded to the location of an average

SHmax orientation as determined by Reynolds et al.

del used in analysis. Model contains 24,400 plane stress elements

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Fig. 2. Mechanical provinces implemented in models. YL ¼

Yilgarn Craton; PB ¼ Pilbara Craton; AR ¼ Arunta Block;

MUS ¼ Musgrave Block; NC ¼ Northern Cratons; MI ¼ Mt:Isa Block; GA ¼ Gawler Block; NEB ¼ North East Block;

CB ¼ Central Block; MD ¼ Murray–Darling Basin; OT ¼

Otway Basin; LN ¼ Northern Lachlan Fold Belt; SN ¼

Southern Lachlan Fold Belt; NE ¼ New England Fold Belt;

CS�NW ¼ North�West Continental Shelf; CS� E ¼

Eastern Continental Shelf; CS� S ¼ Southern Continental

Shelf; White areas represent Basin. Values for mechanical

properties are listed in Table 1.

S. Dyksterhuis et al. / Computers & Geosciences 31 (2005) 297–307 299

(2002) for various regions over the Australian continent

and continental shelf. The difference between azimuths

of the average modelled and average measured SHmax

orientations then determined the residual misfit.

Modelling using the ABAQUSTM program is divided

into modules, the framework of which will be used to

discuss model construction. The ABAQUSTM Part,

Assembly, Step, Interaction, Property, Load and Job

modules are relevant to model construction while the

ABAQUSTM Visualisation module is used for graphical

analysis of model output data.

2.1. Parts and partitions

Geometrical models of the plates in the study were

constructed as sketches within the ABAQUSTM Part

module by projecting the latitudes and longitudes along

the model boundaries into Cartesian coordinates using

the Generic Mapping Tools (GMT) software (Wessel

and Smith, 1991). The projected latitude/longitude data

were interpolated along the plate boundary to obtain an

even sampling distribution. The data were then filtered

to remove high frequencies. ABAQUSTM python sketch

files were then created using the projected, smoothed

Cartesian coordinate data. The python sketch files can

then be easily imported into the ABAQUSTM environ-

ment using the ABAQUSTM CAETM Sketch module.

Regions representing areas within the model with

differing rheological properties were also created within

the ABAQUSTM model using the process outlined

above. These regions, however, were created as so-called

‘partitions’ within the model. Interaction between

ABAQUSTM model parts was set to a tie constraint

where a ‘master’ and ‘slave’ surface is defined with all

degrees of freedom for the nodes on the ‘slave’ surface

being eliminated, allowing for the joining of all parts in

the model to form one tectonic plate.

The Australian continent was subdivided into four

categories (cratons, fold belts, basins and continental

shelf) in the modelling process based on the differing

rheologies and strength of the continent as determined

by Zuber et al. (1989) and Simons et al. (2000).

Regarding terminology, note that use of the words

‘‘strength’’, ‘‘strong’’, or ‘‘weak’’, etc. within this paper

refer to relative stiffness or deformability within the

elastic regime (as governed by Young’s modulus and

Poisson’s ratio), as opposed to some measure of the

stresses or stress differences that result in an onset of

inelasticity. As we are constrained to (linearly) elastic

behaviour, we have no consideration for any departure

from that rheology. Fig. 2 shows the Australian

continent illustrating these areas. Results from seismic

tomography of the Australian continent (Kennett, 1997;

Simons et al., 1999) support the findings of Zuber et al.

(1989) and further indicate the existence of a seismically

slow, probably relatively weak zone located in central

eastern Australia (labeled CB in Fig. 2). The existence

of a weak zone in this area is also supported by high heat

flow data (McLaren et al., 2003). Simons and van

der Hilst (2002) pointed out that mechanical strength

and seismic thickness of the Australian continent do not

always match. Therefore, we only modified our

model for mechanical strength in one area in central

eastern Australia (CB in Fig. 2) where seismic tomo-

graphy and heat flow data provide strong evidence for

relatively hot and presumably weak lithosphere. The

relative strengths of the individual provinces were

implemented by altering the Young’s moduli of the

materials. Zuber et al. (1989) estimated the northern

Australian cratons to have the highest rigidity, with a

value of 2.1� 1025N/m2. Areas with this rigidity were

assigned an effective Young’s modulus of 6� 1010N/m2.

All other areas were assigned an effective Young’s

modulus scaled according to the ratio between their

rigidity and that of the highest rigidity as estimated by

Zuber et al. (1989). Table 1 lists the values of rigidity

determined by Zuber et al. (1989) and the scaled

effective Young’s moduli assigned to each of the

provinces implemented in the models.

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Table 1

Values defined for material properties used in model

Province Effective elastic

plate thickness

(km)a

Flexural rigidity

(� 1025Nm2)aScaling factor Scaled Young’s

modulus

(� 1010Nm2)

Refined Young’s

modulus

(� 1010Nm2)b

Refined rigidity

(� 1025Nm2)

Basins 64 0.25 0.12 1 1 —

Yilgarn Block 132 2 0.95 5.7 5.7 —

Pilbara Block 132 2 0.95 5.7 5.7 —

Northern Cratons 134 2.1 1.00 6 6 —

Arunta Block 88 0.61 0.29 1.74 1.74 —

Musgrave Block 88 0.61 0.29 1.74 1.74 —

Gawler Block 92 0.69 0.33 1.98 1.98 —

Mt. Isa Block 134 2.1 1.00 6 6 —

North Lachlan Fold

Belt

26 0.016 0.0076 0.046 0.06 —

South Lachlan Fold Belt 20 0.0077 0.0037 0.022 0.03 0.0105

North East Block — 2 0.9524 5.7 5.7 —

Murray–Darling Basin 29 0.022 0.0105 0.063 0.063 —

New Eng. F. B. 16 0.0036 0.0017 0.01 0.01 —

Otway Basin — — — — 0.063 0.02205

Oceanic crust — — — — 7 2.45

NW continental shelf — — — — 0.31 0.1085

Southern continental

shelf

— — — — 0.11 0.0385

Eastern continental shelf — — — — 0.031 0.01085

Central Block — — — — 0.02 0.007

aValues for effective elastic plate thickness and flexural rigidity from Zuber et al. (1989).bRefined values from stress modelling. Scaling factor determined by the ratio of the provinces value of flexural rigidity with the

highest value for flexural rigidity determined by Zuber et al. (1989).

S. Dyksterhuis et al. / Computers & Geosciences 31 (2005) 297–307300

The mechanical strength of the Australian continental

margin remains relatively poorly constrained. However,

it cannot exceed that of the continental lithosphere since

the continental margins are extended and thinned

continental lithosphere, and it cannot exceed that of

the adjacent, cool and relatively strong oceanic litho-

sphere. Modelled SHmax directions on the continental

shelf and within the continental interior are dependant

on the strength of the continental shelf. In order to

determine the strength of the continental shelf we have

compared two approaches. The first approach was to

assume that stretched continental crust thermally

reheated in the Late Mesozoic/Cenozoic has remained

mechanically weak (effective Young’s Modulus of

1� 108N/m2) since breakup, following the suggestion

by Fowler and McKenzie (1989) that thinned continen-

tal crust does not regain its elastic strength similar to

ageing oceanic lithosphere. This produced a model with

large residual misfit and poor correlation with observed

stress data (Table 2). The second approach was to

assume that the elastic strength of the continental shelf

has grown equivalent to ageing oceanic lithosphere

(Karner et al., 1983) and the continental shelf was

divided into three regions corresponding roughly to the

last age of thermal reactivation (Fig. 2). Values for the

strength of the individual regions were prescribed an

effective Young’s modulus range of 1� 108–1� 1010N/

m2. Final material property values in the model were

determined by minimising the residual misfit with

measured stress orientations through extensive explora-

tion of parameter space using Nimrod/O. The results

(Table 2) indicate that a continental shelf with varying

material properties best represents the strength of the

Australian continental shelf. This novel approach

demonstrates that stress orientation data can be used

for constraining the relative strength of continental

shelf, therefore helping to resolve the long-standing

controversy whether or not stretched continental litho-

sphere regains its strength like oceanic lithosphere in

principle.

2.2. Load definition and boundary conditions

Primary forces applied to models in this study

(Table 3) were the topographic forces of ridge push

and slab pull and the forces created at collisional

boundaries. A basal traction force was not implemented

due to the poor understanding and relatively uncon-

strained nature of this force. In the case of the

contemporaneous Indo-Australian Plate the dominant

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Table 3

Forces applied to contemporary and Miocene models

Location Contemporary Miocene

Mid-Ocean ridge 1.90 1.10

Australia–Antarctic Discordance 2.1 (3.1)a 1.7 (2.5)a

Papua New Guinea 3.80 —

Banda Arc �0.50 —

Java �0.30 �0.30

New Hebrides 1.00 —

Solomon 1.20 —

Sumatra 2.00 2.00

New Zealand 2.40 2.40

Southern New Zealand Alps 2.80 2.80

Tasman Sea 1.25 1.20

Carol — �0.60

Ontong Plateau — 2.50

Positive forces are directed towards the interior of the plate.

Note: Force magnitudes are 1� 1012N/m which is equivalent to

a stress of 10MPa across a plate of thickness 100 km.aForce applied where the effects from the Australia–Antarc-

tic Discordance were not included.

Table 2

Residual misfit between average predicted and average measured stress orientations

Provincea Homogeneousb Best Fitc No Australia

Antarctic

Discordanced

Uniform Continental

Margine

Amadeus 68.1 12.5 106.2 53

North Bonaparte 14 4.8 24 92.2

South Bonaparte 0.6 1.1 11 68.9

Bowen 143.1 92.3 95.4 74.15

Canning 21.7 11.5 33.8 44.7

Canarvon 1.8 7.9 16.8 5

Cooper 46.1 6.7 65.2 3

Gippsland 6.5 1.0 4.5 1.1

Otway 3.5 6.5 6.4 102.4

Perth 37 2.9 28 24.6

Total Residual Misfit 342.4 147.2 391.3 469.05

aAs defined by Coblentz et al. (1998) and Reynolds et al. (2002). The Models have the following differences:bhomogeneous material properties (Fig. 5);cmodel producing best fit with observed stress data (Fig. 6);dresidual misfit of model where effects of the Australia–Antarctic Discordance were not implemented;eresidual misfit of model with a uniform continental margin with an effective Young’s Modulus of 1� 10�8N/m.

S. Dyksterhuis et al. / Computers & Geosciences 31 (2005) 297–307 301

plate driving forces are the ridge push, slab pull and

collisional forces originating at collision zones north of

the Indo-Australian plate. The ridge push force (FRP)

arises due to elevated topography at mid-ocean ridges

(MOR), and is a distributed pressure gradient that acts

normal to the strike of the mid-ocean ridge (Wilson,

1993). The force contribution from the subsiding

oceanic lithosphere created at the MOR is given by the

relationship (Turcotte and Schubert, 2002 ):

FRP ¼ grmavðTm � T0Þ 1þ2

prmavðTm � T0Þ

ðrm � r0Þ

� �kt; (1)

where gravity (g) is 10m/s2, the densities of the mantle

ðrmÞ and water ðrwÞ are 3300 and 1000 kg/m3, respec-

tively, thermal diffusivity (k) is 1mm2/s, the temperature

difference between the mantle and the surface (Tm and

T0, respectively) is 1200K, the thermal expansion

coefficient (av) is 3� 10�5/K and t is the age of the

lithosphere in seconds.

The ridge push force was implemented in the

modelling process as a pressure applied along a

boundary representing the location where ridge push

force would be maximum, for example, if the ridge push

force was calculated for a mid-ocean ridge with a

spreading age of 45Ma, the pressure would be applied to

the 45Ma isochron boundary in the model. Figs. 3 and 4

illustrate the locations where forces were applied to the

contemporaneous and Miocene models, respectively.

The Australia–Antarctic Discordance is an area south of

the Great Australian Bight that is characterised by

bathymetry 800m deeper than the surrounding spread-

ing ridge (Gurnis et al., 1998), resulting in a relatively

diminished ridge push force. The exact difference in the

ridge push force arising from the Australia–Antarctic

Discordance is not well constrained, since factors

effecting the potential ridge push force from the

Australia–Antarctic Discordance do not merely rely on

the elevation of the ridge, but also the chemistry of the

underlying mantle (Gurnis et al., 1998), but has been

modelled here as a force 23that of the calculated RPF.

ARTICLE IN PRESS

Fig. 3. Forces applied to contemporary model are also illustrated; HYM ¼ Himalayas (fixed boundary); SUM ¼ Sumatra Trench;

JAVA ¼ Java Trench; BA ¼ Banda Arc; PNG ¼ Papua New Guinea; SOL ¼ Solomon Trench; NH ¼ New Hebrides; CT ¼

Continental Topographic Force; TS ¼ Tasman Sea; NZ ¼ New Zealand; SNZ ¼ Southern New Zealand Alps;

AAD ¼ Australia–Antarctic Discordance; MOR ¼ Mid-Ocean Ridge. Boundary between light grey area along which MOR and

AAD force arrows are located is region along which ridge push force was applied for contemporary model. Note that force arrows are

not drawn to scale.

S. Dyksterhuis et al. / Computers & Geosciences 31 (2005) 297–307302

The slab pull force (FSP) originates from the negative

buoyancy of the down-going dense oceanic lithosphere

at subduction zones and is proportional to the excess

mass of the cold slab in relation to the mass of the

warmer displaced mantle (Spence, 1987). The force

contribution can be given by the relationship (Turcotte

and Schubert, 2002):

FSP ¼ 2rmgavbðTc � T0Þkl2pu0

� �12

0@

1A

þ2ðTc � T0Þg Dros

rm

kl2pu0

� �12

0@

1A; ð2Þ

where b is the slab length, l is 4000 km, u0 is 50mm/yr, gis 4MPa/K, DrOS is 270 kg/m3, other parameters are

described in Eq. (1).

For fast moving plates (5–10 cm/yr) the subducting

slab attains a ‘terminal velocity’ where forces related to

the negative buoyancy of the slab are balanced by

viscous drag forces acting on the slab as it enters the

mantle and the net force experienced by the horizontal

plate is quite small (Forsyth and Uyeda, 1975). The

amount of net force actually transferred to the

horizontal plate, however, is still quite controversial.

Schellart (2004) suggests as little as 8–12% of slab pull

force is transferred to the horizontal plate while Conrad

and Lithgow-Bertelloni (2002) suggest as much as

70–100% may be transmitted. Magnitudes of slab pull

forces were varied over a range of 1� 107 to

�1� 10�7N/m with final force magnitudes constrained

by the resulting fit with the measured stress directions

contained in the Australian Stress Map database (Hillis

and Reynolds, 2000), as were the forces at collisional

boundaries. The collisional boundary between the IAP

ARTICLE IN PRESS

Fig. 4. Miocene model setup illustrating forces applied. CA ¼ Carol Trench; refer to Fig. 3 for more details on other plate boundary

names.

S. Dyksterhuis et al. / Computers & Geosciences 31 (2005) 297–307 303

and Eurasian plate at the Himalayas was modelled as a

fixed boundary in the modelling process in order to

maintain mechanical equilibrium.

2.3. Visualisation

The ABAQUSTM CAETM Visualisation module is

used to view the model results, however, it was found to

be limited in its capabilities of data representation. In

order to have more control over the data visualisation

the *El Print and *El File options in the analysis input

file were used to output variable data from the analyses

into the analysis data and results files. The ABAQUSTM

fprin subroutine was then used to calculate the elemental

stress values and also the direction of the stress vectors.

These data were then plotted using the GMT software,

allowing for more flexibility in data visualisation.

2.4. Palaeo-modelling method

A palaeo-stress model (Fig. 4) for the Miocene

(20Ma) was created using reconstructed plate boundary

configurations (Heine et al., 2004; Hall, 2002) and the

age–area distribution of ocean crust around Australia

(Muller et al., 2000) to obtain estimates of spatial

distribution and magnitude of ridge push and slab pull

forces, while estimates of forces acting at other

boundaries were extrapolated using results of contem-

porary stress modelling. Values for material properties

were held constant with the values used in and obtained

from the contemporary stress analysis.

3. Results

3.1. Contemporary

Our results show that spatially significant rotations of

the SHmax direction can be modelled as a consequence of

perturbations of SHmax in areas of juxtaposed strong and

weak rheologies. The materials with higher values of

rigidity deform only slightly under a given loading, and

so place relatively small displacements on the bound-

aries of adjacent, weaker materials. This results in

ARTICLE IN PRESSS. Dyksterhuis et al. / Computers & Geosciences 31 (2005) 297–307304

deviation of stress trajectory directions within higher

rigidity materials around weaker materials. Large

differences in both magnitude and direction of SHmax

can be seen around areas in the Australian continental

lithosphere where there are juxtaposed strong and weak

rheologies. Fig. 5 shows the predicted SHmax regime for

a model with homogeneous material properties while

Fig. 6 shows the ‘‘best fit’’ model obtained out of many

thousands of model runs using heterogeneous material

properties. It is clear that the stress pattern predicted by

a model with heterogeneous material properties shows

more variance in SHmax direction and magnitude than

that of a model with homogeneous material properties.

This is best illustrated over the western margin of the

Yilgarn Craton (marked YL in Fig. 2) where there is up

to roughly a 901 rotation of the stress direction over an

area roughly 200 km in diameter. The model also

emulates the observed 891 rotation in SHmax orientation

between the Amadeus and Cooper basin stress provinces

defined by Reynolds et al. (2002) well with reasonably

low residual misfits in the Amadeus and Cooper basins

of 12.5 and 6.7, respectively. Such spatially rapid

Fig. 5. Modelled contemporary maximum horizontal compressive str

properties. Filled grey lines indicate compressional stress while filled bl

a circle show measured stress orientations of A–C quality taken from

variation in SHmax directions is not present in the

homogeneous model. While the value of residual misfit

for the heterogeneous model in the Bowen Basin is quite

high (Table 2), modelled SHmax magnitudes are lowest in

this region indicating that local sources of stress may

play a dominant role in controlling the orientation of

SHmax (Zoback, 1992).

3.2. Miocene

Forces applied to the boundaries of the Miocene

(20Ma) model are illustrated in Fig. 4 and listed in

Table 3. Docking of the Australian plate with the

Ontong–Java plateau had begun in the early Miocene

(Hall, 2002), however, collision with Papua New Guinea

had not yet been initiated; instead the Australian plate

was subducting beneath the Caroline plate (Hall, 2002).

Forces along the plate boundary at New Zealand were

similar to those at present with the inception of the

Alpine Fault occurring at 23Ma (Kamp, 1986).

The absence of the collisional Papua New Guinean

boundary to the north of the Australian continent in the

ess (SHmax) orientations for a plate with homogeneous material

ack lines indicate tensional stress. Filled black lines marked with

Australian Stress Map database.

ARTICLE IN PRESS

Fig. 6. ‘Best Fit’ modelled SHmax orientations with realistic material properties for the Australian continent and continental shelf (see

Fig. 2 for further explanation of provinces). Filled grey lines indicate compressional stress while filled black lines indicate tensional

stress. Filled black lines marked with a circle show measured stress orientations of A–C quality taken from the Australian Stress Map

database.

S. Dyksterhuis et al. / Computers & Geosciences 31 (2005) 297–307 305

Miocene produces a dramatically different stress regime

(Fig. 7) to that of the present. The stress distribution is

more uniform with less spatially rapid variation. A

general NW–SE SHmax orientation is evident over the

Australian continent during the Miocene, whereas at

present there exists a general NE–SW trend over

Northern Australia with SHmax orientations over the

southern continent displaying more variation. Orienta-

tions of SHmax directions over the NW shelf and Bass

Straight region in particular show large differences

during the Miocene compared to present, with modelled

SHmax orientations agreeing well with fault reactivation

histories of these areas.

SHmax directions over the NW shelf have changed

from a NW–SE orientation in the early Miocene to a

general NE–SW at present. Reactivation histories of

coast-paralleling extensional basin forming faults on the

Canarvon Terrace on the NW shelf occurred during the

Miocene (Baillie and Jacobson, 1995; Muller et al., 2002)

with migration of hydrocarbons also taking place at this

time (Crostella and Boreham, 2000). This is consistent

with the results of this study which show rotation of

SHmax directions over the Canarvon Terrace from

orientations oblique to the coastline during the early

Miocene to orientations normal to the coastline at

present.

Inversion in the Torquay Embayment and Otway

Ranges of the Bass Strait region occurred in the

Miocene due to compressional reactivation of numerous

NE striking extensional faults (Hill et al., 1995).

Modelled SHmax results in this region of the Bass Strait

show a rotation from roughly EW in the early Miocene

to NNW–SSE at present, indicating a SHmax regime

conducive to compressional inversion in the Torquay

Embayment and Otway Ranges existed between the

early Miocene and present.

4. Summary

Modelling the intraplate stress regime of tectonic

plates represents a novel use for the engineering software

ARTICLE IN PRESS

Fig. 7. Modelled Miocene SHmax orientations. Filled grey lines indicate compressional stress while filled black lines indicate tensional

stress.

S. Dyksterhuis et al. / Computers & Geosciences 31 (2005) 297–307306

package ABAQUSTM that has not previously been

explored. We have developed a methodology implemen-

ted as programs and shell scripts which allows for

straightforward creation of geophysical models within

ABAQUSTM CAETM. All programs and scripts used to

create models in ABAQUSTM as part of this work can

be accessed at www.geoframework.org and are freely

available for use and alteration under the GNU license

agreement.

We have modelled the maximum horizontal compres-

sive stress regime for the Indo-Australian plate for the

present and Miocene. Methods developed allow for easy

creation of models with different geometries. The

Generic Mapping Tools software (Wessel and Smith,

1991) has been used to plot the modelled and measured

data. Modelling results show significant perturbations of

SHmax directions and magnitudes in areas of juxtaposed

weak and strong materials in the heterogenous model.

The results demonstrate that models with heterogeneous

material properties fit observed stress directions con-

tained in the Australian Stress Map database better than

models with homogeneous material properties. Rapid

spatial rotations of SHmax directions, as seen in the

observed stress data, cannot be reproduced in homo-

geneous models, only in models with heterogeneous

material properties. Modelled Palaeo-SHmax orientations

also demonstrate the dramatic changes in SHmax regime

that occurred over the Indo-Australian plate between

the Miocene and present day, with modelled SHmax

regimes agreeing well with fault reactivation histories

over the NW Australian Shelf and in the Bass Strait

region.

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Baillie, P.W., Jacobson, E., 1995. Structural evolution of the

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