intraplate tectonics: feedback between radioactive thermal...

Intraplate tectonics: feedback between radioactive thermalweakening and crustal deformation driven by

mantle lithosphere instabilities

Russell N. Pysklywec a;�, Christopher Beaumont b

a Department of Geology, University of Toronto, Toronto, ON, Canada M5S 3B1b Department of Oceanography, Dalhousie University, Halifax, NS, Canada B3H 4J1

Received 16 July 2003; received in revised form 12 January 2004; accepted 28 January 2004

Abstract

Two-dimensional viscous^plastic numerical experiments show that weak radioactive crust may be susceptible tosignificant tectonic activity by the effect of Rayleigh^Taylor-type instability of the sub-crustal lithosphere below acontinental interior. In particular, crust having a localized or regional enrichment of radioactive elements can respondto an underlying mantle lithosphere downwelling by initial subsidence then thickening and uplift owing to the positivefeedback among thickening, heating, and weakening. Such models may later undergo orogenic deflation asspontaneous crustal extension/thinning and surface subsidence occur while mantle downwelling continues. Stronghomogeneous crust subsides dynamically above mantle downwellings and undergoes essentially no internaldeformation. A uniform distribution of radioactive elements through the crust, or a concentration at depth, ismuch more effective in causing thermal weakening of the crust and subsequent intraplate deformation than withradioactive material concentrated nearer the surface. For wide regions of high heat production in the crust the lengthscale of the intracrustal tectonic zone is controlled by the width of the mantle downwelling in contrast with narrowheat production regions which control their own length scale. In general, the numerical experiments demonstrate thatthe presence of radioactive elements may make the crust vulnerable to intraplate tectonic deformation and represent aprimary control on the way the strength of the crust evolves during sub-crustal forcing. The results may explain first-order features of intraplate tectonics including the subsidence mechanism for intracontinental basins, orogenic crustalcontraction, thickening and surface uplift, and subsequent extension and crustal deflation. The processes haveparticular implications for regions of high radioactive heat production and juvenile crust which would more likelyhave a higher concentration of radioactive elements in the lower crust.4 2004 Elsevier B.V. All rights reserved.

Keywords: intraplate tectonics; Rayleigh^Taylor instabilities; radioactive heating; numerical modeling; mantle lithosphere

1. Introduction

Although large-scale tectonic deformation ofthe lithosphere is largely con¢ned to the plateboundary regions, signi¢cant deformation can

0012-821X / 04 / $ ^ see front matter 4 2004 Elsevier B.V. All rights reserved.doi:10.1016/S0012-821X(04)00098-6

* Corresponding author. Tel. : +1-416-978-4852;Fax: +1-416-978-3938.E-mail addresses: [email protected]

(R.N. Pysklywec), [email protected] (C. Beaumont).

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Earth and Planetary Science Letters 221 (2004) 275^292

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also occur in plate interiors. The continentalplates contain sedimentary basins, for example,that have developed far from plate margins. Sim-ilarly, episodes of intraplate crustal uplift andorogeny are evident in the geological record.The tectonic evolution of these intraplate featuresmust either be caused by forces transmittedthrough the lithosphere from plate boundariesor by a mechanism that is independent of plateboundary forces. Here we investigate the secondtype of mechanism.

Recent geodynamic work suggests that crustaltectonic events in a continental interior may beintimately linked to large-scale dynamics in theunderlying mantle. For example, it has beenshown that large-scale de£ections of the litho-sphere may be a result of underlying mantle con-vective £ow. That is, £ow in the viscous mantlecan induce signi¢cant normal stresses at the sur-face, which may lead to transient events of surfaceuplift/depression or ‘dynamic topography’ [1,2].This link between surface topography and mantledynamics has provided an important mechanismthat explains various episodes of observed large-scale continental uplift [3,4] and subsidence [5^8].However, models of these processes generallyadopt only a rudimentary thermal lithosphereand, in particular, neglect the presence of a de-formable crust. Moreover, the dynamic topogra-phy is computed a posteriori as the instantaneousresponse of the lithosphere to the computed nor-mal component of hydrodynamic stress at the topsurface of the mantle £ow models. Thus, this typeof approach precludes the investigation of time-dependent lithospheric deformation induced by£ow stresses tangential to the base of the litho-sphere.

Numerical modeling applied to tectonics on Ve-nus provided some of the ¢rst insights into thecoupled interaction between mantle convectionand crustal dynamics [9^12]. One of the common¢ndings among these studies was that, dependingon the rheology of the overlying crust, mantledownwelling may drive crustal thickening (and in-ferred plateau formation), rather than subsidence.Since plate tectonics is not active on Venus, it wassuggested that such a process may be importantfor driving crustal deformation and uplift.

A similar mechanism may be responsible forinducing crustal tectonics in intraplate regionson Earth. Various studies have considered crustaldeformation and the evolution of surface topog-raphy during episodes of gravitational instabilityof the lithosphere [13^15]. Neil and Houseman[15] calculate the in£uence of isothermal Ray-leigh^Taylor (RT) instabilities of layered linearviscous lithosphere models on crustal deforma-tion. They show that mantle lithosphere (i.e.,sub-crustal lithosphere) downwellings can inducecontinental crust to contract and thicken, andthat such events may be interpreted as intraplateorogenies which may occur without any horizon-tal plate boundary forcing. However, the rheologyof the mantle lithosphere and crust must be rela-tively weak (viscosity of V1021 PaWs for the man-tle lithosphere; and 6 13 times greater than thisfor the crust) for viscous RT instability and crus-tal thickening to occur [15].

The coupled crustal response to thermaldownwelling in a convecting mantle shows similarresults. Zhong [16] considered relaxation of crus-tal topography in a crust^mantle model usingnon-linear visco-elastic rheologies. The resultssimilarly show that time-varying over-compen-sated topography can develop under the in£uenceof sub-lithospheric loading, but the analyses im-pose a constant mantle buoyancy load and con-sequently neglect the in£uence of time-depen-dent convection in the underlying mantle. Three-dimensional isoviscous simulations of time-dependent mantle convection that include a buoy-ant overlying crust demonstrate variable crustalaccumulation and thickening above regions ofdownwelling mantle £ow [17,18]. The resultinghigh positive topography is not in (Airy) iso-static equilibrium, as the crustal thickening is dy-namically supported by the time-varying mantle£uid £ow. Thermal convection models whichtest the response of various crustal rheologies(Newtonian viscous) to time-dependent £ow ¢ndthat a crustal viscosity of 6V1023 PaWs is re-quired for the crust to deform appreciably by£ow-induced shear stresses at the base of the crust[19].

In general, these studies suggest that intraplatecrustal tectonics may be driven by mantle £ow

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dynamics if the crust is relatively weak. However,modern thermally stable continental crust as awhole is strong (e.g., [20]). This is clear from therigid behavior of the plates which tend to resistlarge-scale deformation except in high stress re-gimes, such as plate boundaries. Localized weak-ening of the crust, however, may make it suscep-tible to focussed deformation in a plate interior.In particular, regions in which crustal radioactiveheat production is anomalously high can be sig-ni¢cantly weaker than normal crust, and as a re-sult may be vulnerable to deformation driven byunderlying mantle forcings.

As an example, Australia represents a region ofhigh past and present heat £ow having a relativeabundance of radioactive heat-producing elementsin its crust [21]. Furthermore, since the Paleopro-terozoic the continent has experienced a signi¢-cant number of episodes of intraplate tectonic ac-tivity (e.g., [22^25]). It has been proposed thatthere may be a causal relationship between theradioactive heating/weakening and certain phasesof intracratonic deformation [21,26^28]. In addi-tion, changes in the distribution of the radioactivematerials during progressive evolution of the crustmay result in various phases active/inactive tec-tonism [28].

Here we use thermomechanical numerical mod-els to consider the evolution of intraplate crusthaving regions of locally enriched radioactiveheating during an episode of mantle downwelling£ow. The purpose is to investigate the feedbackbetween thermal weakening of the radioactivecrust and crustal deformation in response to atime-dependent mantle forcing. In particular, asa driving mechanism we model the developmentof RT-type instability of the mantle lithospherehaving temperature-dependent density and tem-perature-dependent, power-law viscosity.

We conduct experiments having various con¢g-urations of radioactive heating in the model crust.The evolution of surface topography is tracked inthe models as a primary observable associatedwith the crustal response to the underlying mantle£ow. In addition, the style of internal deformationof the crust is investigated in detail to determinehow time-dependent variations in crustal strengthcontrol its behavior.

2. Numerical experiments

2.1. Model set-up

Numerical geodynamic experiments were con-ducted to investigate the coupled evolution ofthe lithosphere and mantle during an episode ofRT-type instability of the mantle lithosphere. Theequations governing the thermomechanical behav-ior of incompressible viscous^plastic media inplane strain are solved using arbitrary Lagran-gian^Eulerian (ALE) ¢nite element techniques[29].

The model is set up as an idealized representa-tion of the upper mantle and crust (Fig. 1; Table1). The lithosphere is composed of a 30 km thickbuoyant crust and a 120 km thick region of man-tle lithosphere, and the remainder comprises thesub-lithospheric mantle. The uppermost 30 km isa chemically distinct, buoyant crust. The crust isde¢ned as a frictional plastic material that alsodeforms below the yield stress with a non-lineartemperature-dependent viscous £ow law based onthe experimental results of Gleason and Tullis [30]for wet quartzite (Fig. 1). A nominal value ofP=15 is used for the angle of internal frictionthat determines the plastic yield stress. Whilethere are large associated uncertainties, this valueis an estimate (e.g., implicitly assuming the in£u-ence of approximately hydrostatic pore £uid pres-sure) based on applied Coulomb wedge and crus-tal modeling [31,32].

The rheology of the mantle in the model is alsoplastic^viscous with thermally activated power-law creep, using viscous £ow parameters for adry olivine based on the experimental results ofHirth and Kohlstedt [33]. Although the modelmantle is chemically homogeneous, rheologicaldi¡erentiation (i.e., into lithospheric and astheno-spheric mantle regions) occurs in the models as aresult of dynamic variations in the system (T, _OO ).In particular, due to the temperature dependenceof rheology, a stronger mantle lithosphere regiondevelops in that portion of the mantle with a tem-perature of 6 1350‡C. The initial thermal struc-ture for the model was calculated based on a con-ductive equilibrium geotherm, and the base of thelithosphere (i.e., which we de¢ne with the 1350‡C

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isotherm) was set at a depth of 150 km (Fig. 1).This initial temperature pro¢le was laterally con-tinuous across the computational domain, exceptwhere regions of radioactive heating were intro-duced into the crust (see below).

Deformation in the model is driven by thechemical and thermal buoyancy anomalies of thecrust and mantle materials. A thermal perturba-tion (of width 200 km, and amplitude 15 km) tothe base of the mantle lithosphere is introduced to

initiate an RT downwelling in the center of themodel (Fig. 2; t=0). This perturbation is not theminimum that would drive the ¢nite instability ofthe mantle lithosphere. Rather than examining theparameters that control the growth of the insta-bility as has been considered in previous studies[34^37], we assume that a su⁄cient perturbationexists to cause onset of ¢nite instability. Such aperturbation may arise, for example, from in-plane plate compression leading to minor contrac-

Fig. 1. Initial geometry of the full solution space for the numerical model. The buoyant model crust (light gray) is a chemicallydistinct material from the underlying mantle lithosphere (dark gray) and the hotter, weaker underlying mantle (asthenosphere).Power-law viscous parameters (B, n, Q ^ see Table 1) for the crust are based on experimental results for wet quartzite [30], anddry olivine for the mantle [33]. The position of the block of radioactive crust for the ¢rst numerical experiment is denoted. Un-disturbed geotherm (away from radioactive region; see text) is plotted at right. Solution space has a free top surface, re£ectingboundary conditions on the side walls, and no material £ux through the bottom boundary. Dashed box shows zoomed region ofmodel in Fig. 2. Governing equations for the system and formulation of viscous^plastic rheology in the model are shown. Inthese expressions b, u, and T represent the ¢elds of density, velocity, and temperature, respectively. The variables g, A and t aregravitational acceleration, rate of internal heat production per unit volume, and time (see Table 1 for de¢nition and values of re-maining model parameters). In the viscous^plastic model the deviatoric stress, cP, is determined at each computational node asthe lesser value of either a plastic yield stress cy or a viscous stress cv ; where p is the pressure, _OO is the second invariant of thestrain rate, and R is e¡ective viscosity.

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tion of the lithosphere, or inherent thermal insta-bility of the thermal boundary layer in the broad-er mantle convective system.

A free surface at the top of the numerical mod-el allows us to track directly the deformation ofthe crust and evolution of topography. The sidewalls and bottom boundary of the solution spaceare free slip; with zero tangential stress and nomaterial transfer across the boundaries. This con-dition is not overly restrictive because we limitour investigations to the early stages of the modelevolution when the in£uence of the bottomboundary on the deformation of the lithosphereis minimal. The temperature at the top and bot-tom of the box are held ¢xed at 20 and 1820‡C,respectively; the heat £ux out the side boundariesis zero. In the experiments we maintain a nearlyconstant geothermal heat £ux into the base of thelithosphere by signi¢cantly increasing the thermalconductivity of the sub-lithospheric mantle (to 41W/m/K; Table 1). The high thermal conductivityin the sub-lithospheric mantle maintains a verticalheat transport in this region that essentially isequivalent to a convecting mantle, without theneed to model ¢nite amplitude thermal convec-tion. This e¡ectively keeps the sub-lithosphericmantle close to the adiabatic geothermal gradientand allows us to isolate the e¡ect of the RT in-stability on the crust from other thermal convec-tive boundary layer instabilities.

The accuracy of the computational code hasbeen veri¢ed by a series of benchmarking tests.Detailed analyses of the growth of RT instabilitiesindicate that our numerical formulation is in closeagreement with other numerical and analytical

studies [35,38]. In addition, the development offree surface topography in the code is consistentwith mantle £ow-induced topography derivedfrom other free surface models [39] and a poste-riori calculations from ¢xed surface models [40].

2.2. Evolution of surface topography: in£uence ofa region of radioactive crust

In this ¢rst series of experiments, we considerthe in£uence of a region of high radioactive heatproduction in the crust on the crustal response toRT downwelling. In the ¢rst model we consideran end-member case in which the crust is given ahigh radioactive heat production of A=5 WW/m3,while the rest of the crust has no heat production.This 100 km wide radioactive block extendsthrough the full thickness of the crust and is o¡setfrom the center of the mantle lithosphere pertur-bation (Fig. 1). The o¡set is chosen such that oneside of the radioactive block is above the center ofthe downwelling. The asymmetry of the surfacetopographic response above the downwelling willtherefore provide a general comparison of the rel-ative response of radioactive and non-radioactivecrust.

To generate the initial thermal structure of themodel including the radioactive crust, a ‘thermalequilibration’ phase was run until the radioactivecrust reached a state of conductive equilibrium.For this, the thermal state of the model was ad-vanced while preventing material motion (i.e.,thermal advection) and prior to introducing theRT instability.

Fig. 2 (t=0 Myr) shows the state of the ther-

Table 1Modeling parameters/properties

Parameter Crust Mantle lithosphere Sub-lithospheric mantle

B viscosity parameter 1.1U10315 Pa3n/s 4.85U10315 Pa3n/s 4.85U10315 Pa3n/sn power exponent 4.0 3.5 3.5Q activation energy 223 kJ/mol 535 kJ/mol 535 kJ/molP internal angle of friction 15‡ 15‡ 15‡b0 reference density 2.8U103 kg/m3 3.3U103 kg/m3 3.3U103 kg/m3

T0 reference temperature 500‡C 800‡C 800‡CK coe¡. of thermal expansion 3.0U1035 K31 2.0U1035 K31 2.0U1035 K31

cp speci¢c heat 1250 J/kg/K 1250 J/kg/K 1250 J/kg/Kk thermal conductivity 2.25 W/m/K 4.86 W/m/K 41.0 W/m/K

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mal^mechanical model following the end of thethermal equilibration phase. This initial state as-sumes the presence of a mantle lithosphere pertur-bation beneath a long-lived, pre-existing region ofanomalous crustal heat production. At t=0.25Myr, the initial thermal and lithospheric bound-ary perturbation has developed into a dense man-tle lithosphere root that is descending into themantle as a gravitational instability. Elevated iso-therms indicate relative heating in the radioactivecrust while isotherms in the sub-crustal root aredepressed as the relatively colder material sinks.

The unstable root descends quickly and sets upsigni¢cant £ow in the low-viscosity sub-litho-spheric mantle, reaching velocities V2 cm/yr(t=0.75 Myr). Adjacent lower mantle lithospherematerial is laterally entrained into the developingRT downwelling. Between t=0.75 and 3.25 Myrthe £ow is at its most vigorous as the initial rootof mantle lithosphere mantle drips into the man-tle. Lithospheric deformation occurs primarily inthe lowermost regions of the mantle lithosphere.This is a result of the temperature-dependent non-linear viscosity of the mantle material which pro-motes more localized £ow in the hot regions atthe base of the lithosphere.

By t=10 Myr there is continued, but less pro-nounced downwelling of the mantle lithospherebeneath the radioactive region of the crust. Themain convective instability event has occurred butsome downwelling is maintained by a smaller,convectively cooled remnant root.

The pro¢les of surface topography across thefull width of the solution space are plotted foreach of the time frames shown in Fig. 2 (Fig.3). During the initial stages (t=0.25^0.75 Myr),a negative surface topography develops above thenon-radioactive crust above the developing RTinstability, with positive topography on the

£anks. This topography is essentially the responseof the strong crust to the normal stresses inducedat the surface by the central mantle lithospheredownwelling and associated mantle return £ow(Fig. 2). However, the symmetry of the topog-raphy is broken by a distinct, short wavelengthperturbation at the location of the block of radio-active crust. By t=3.25 Myr, this small pertur-bation has grown to a distinct positive spike intopography. At the same time, the surface subsi-dence adjacent to the spike has reached its max-imum amplitude of V500 m during the most vig-orous phase of RT downwelling. At t=10 Myrthe surface topography is dominated by the highelevation feature of V750 m amplitude above theregion of radioactive crust. Topography varia-tions in the unperturbed portions of the litho-sphere, away from the zone of convergence arecaused by the time-dependent mantle £ow (whichmay have a relatively more important e¡ect inthese closed box models than would be expectedin natural systems).

This distinctly time-dependent evolution of sur-face topography may be understood by consider-ing the e¡ect of the underlying £ow stresses onthe heterogeneous crust. The vertical componentof hydrodynamic stress associated with the evolv-ing downwelling mantle lithosphere instabilitycauses time-varying regional subsidence of thecrust. This ‘dynamic topography’ will be sustainedonly as long as there is active sub-crustal £ow. Ahorizontal forcing also acts on the crust as a re-sult of the RT mantle lithosphere downwellingwhich causes horizontal shortening of the crust.

Although most of the lithospheric deformationoccurs in the lowermost mantle lithosphere (Fig.2), the RT instability also induces signi¢cantstresses in the upper lithosphere. In general these£ow-driven shear stresses will de£ect the crust

C

Fig. 2. Progressive evolution of the ¢rst model showing development of RT mantle lithosphere instability and crustal deforma-tion; t is time relative to onset of numerical experiment. In the left column, material regions (shaded) and instantaneous velocityvectors are plotted. Contours of temperature following thermal equilibration are superimposed; contour interval is 200‡C, startingat 20‡C at the surface. In the right column, contours of the log of e¡ective viscosity, log(R) (R as de¢ned in Fig. 1) at intervalsof one for the corresponding times. Shading marks material that is in the plastic (dark) or viscous (light) regime. E¡ective viscos-ity in the model is clearly reduced in regions of radioactive heat production; radioactive crustal heating is also responsible forminor temperature inversion in the lithosphere.

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downward but are not su⁄cient to cause defor-mation of the relatively strong nominal quartz-rich crust. In this case, the response of the crustwill be governed by the instantaneous vertical vis-cous £ow stresses. However, in a region whereradioactive heating results in local weakening ofthe crust and uppermost mantle, the basal shearstresses associated with the sub-crustal £ow cancause appreciable internal deformation of thecrust. In the case of the radioactive crust locatedin a region above the mantle lithosphere down-welling, £ow-induced convergence will thicken thehot, susceptible crust. This, in turn, will result insurface uplift which has dynamical and long-termisostatic components, the latter from the net crus-tal thickening. If the thickening and uplift aresu⁄cient, there may be a net positive surface to-pography despite a simultaneous downward man-tle dynamical forcing.

The ¢rst-order character of the crustal defor-mation is evident in the deformed radioactivecrust region in Fig. 2. Essentially, the ductilelower crust, weakened by radioactive heating, isentrained horizontally towards the mantle litho-sphere downwelling, and as a whole the radio-active block undergoes shortening. Later, we ex-amine in more detail the nature of this £ow-induced crustal deformation.

In Fig. 4a we show the evolution of surfacetopography above a model crust that does notcontain a region of radioactive heating. In all oth-er respects, the experiment is the same as the pre-vious model. The formation of the RT instability

in this homogeneous crust model is essentiallythe same (i.e., in timescale and thermal character)as in Fig. 2. A negative topography developsabove the descending RT instability, and reachesa maximum depression of V800 m by t=3.25Myr. At t=10 Myr, although there is still surfacesubsidence at the center of the solution space, themagnitude is decreased as the initial mantle lith-osphere root detaches but more subdued down-welling £ow continues. Clearly the evolution ofsurface topography is very much di¡erent inthe model without local radioactive heating. Thestrength of the homogeneous crust and uppermostmantle prevents signi¢cant internal deformationby £ow-induced shear stresses lower in the litho-sphere, so the dynamic vertical response domi-nates the surface topography signal.

The rate of heat production in an enriched ra-dioactive region of the crust may also be expectedto have a signi¢cant e¡ect on the crustal response

Fig. 4. Plot of surface topography at four time intervals for:(a) model in which radioactive region has been removedfrom the crust. The arrow indicates the lateral position ofthe radioactive block in the previous experiment. (b) Modelwith a radioactive block extending through the full thicknessof the crust with a reduced heat production of A=2.5 WW/m3.

Fig. 3. Plot of surface topography across the ¢rst model withA=5 WW/m3 at the four time frames shown in Fig. 2. Astylized crust (not to vertical scale) is illustrated to show thelocation and con¢guration of the enriched radioactive regionin the crust.

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to the sub-lithospheric dynamics. The value ofA=5 WW/m3 may correspond to continental re-gions of unusually high radioactive heat produc-tion (e.g., see discussion related to Mt. Isa region,below). In Fig. 4b, we show the results of an ex-periment that is the same as the original model(Fig. 2) except that the amount of radioactiveheat production in the anomalous crustal blockhas been reduced to A=2.5 WW/m3. Initially thecrust subsides above the mantle lithosphere insta-bility. A subtle surface uplift gradually developsat the location of the radioactive region, but nei-ther surface subsidence nor uplift strongly domi-nate by t=10 Myr. This represents an intermedi-ate model to the end-member cases where crustalthickening and uplift (Fig. 3) or dynamic subsi-dence (Fig. 4a) dominate the crustal response.

2.3. Vertical distribution of radioactive heating andevolution of surface topography

The initial model assumed that radioactiveheating was distributed uniformly through the en-tire thickness of crust in the radioactive region(Fig. 2). This situation may be applicable for ju-venile, undi¡erentiated crust, but in evolved crustcommon to most continental interiors, radioactiveelements are generally concentrated near the sur-face [41]. In Fig. 5 we show the results of twonumerical experiments which considered two al-ternative con¢gurations of crustal radioactiveheating.

In Fig. 5a, the block of radioactive crust (A=5WW/m3) is limited to the lower half of the crust.Otherwise, the model set-up is unchanged and theevolution of the sub-crustal £ow is the same as inFig. 2. A negative surface topography developsabove the mantle lithosphere downwelling duringthe initial stages of the model (t=0.25^3.25 Myr),but a localized elevation high is clearly developingabove the radioactive block. By t=10 Myr, thetopography is dominated by this uplift. As inthe original model with radioactive heating (Fig.3), the thermally weakened crust is able to deformby the e¡ect of the mantle lithosphere £ow, andthe subsequent crustal thickening and uplift over-come the dynamic subsidence of the crust.Although the surface uplift is appreciable in this

model, it is more subdued than in Fig. 3. This isobviously due to the smaller region of radioactiveheat production and, hence, reduced integratedheating/weakening over the entire crust anduppermost mantle.

A similar experiment was conducted in whichthe A=5 WW/m3 radioactive region was restrictedto the top 15 km of the crust (Fig. 5b). In thiscase, the surface topography above the downwel-ling remains negative throughout the model run.With this con¢guration of radioactive heating, thewhole crust and uppermost mantle remain rela-tively cool and strong and resist deformationinduced by mantle lithosphere £ow-induced trac-tions. Instead, the surface topography is con-trolled by the normal component of the hydrody-namic stresses, and their e¡ect on the strong crust.The pair of experiments demonstrate that, as ex-pected, deeply buried sources of radioactive heatare much more e¡ective at heating (and weaken-ing) the crust than those located near the surface.

Fig. 5. Plot of surface topography at four time intervals for:(a) model with a radioactive block in the lower half (15 km)of the crust with heat production A=5 WW/m3 ; (b) modelwith a radioactive block in the top half (15 km) of the crustwith heat production A=5 WW/m3.

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2.4. Feedback between crustal deformation andradioactive thermal weakening

The feedback between radioactive thermalweakening and deformation of the crust is a pri-mary process in controlling the response of thecrust to the mantle dynamic forcing. Here, weconsider in more detail this interaction duringevolution of the crust^mantle system.

An alternate series of models was developed inwhich the initial mantle lithosphere perturbation(i.e., as shown in Fig. 2, t=0 Myr) and crustalradioactive region were placed at the left-handside of the solution space (Fig. 6a). This con¢gu-ration takes advantage of the mirror symmetry ofthe model, allowing for a greater numerical reso-lution and facilitating interpretation by e¡ectivelykeeping the locus of deformation stationary. Theradioactive block, A=5 WW/m3, is situated in thelower half of the crust (i.e., lower 15 km) and hasa half-width of 50 km. Besides the modi¢cation ofgeometry, all other parameters of the model, suchas material rheologies, initial geotherm, thermalperturbation, and boundary conditions are thesame as shown in Fig. 1. An initial thermal equil-ibration phase is included.

The mantle lithosphere instability develops as adownwelling at the left boundary of the model ona timescale similar to that shown in Fig. 2. Ini-tially, the downwelling induces contraction andthickening in the crust and entrains the thermallyweakened ductile crust towards the center of thedownwelling (Fig. 6b). This is similar to the lowercrustal lateral entrainment evident in Fig. 2, ex-

C

Fig. 6. Progressive deformation of crust in model with gravi-tational instability and radioactive crust at the left boundaryof the solution space. (a) Initial model geometry; 15 kmthick, 50 km wide radioactive region in lower crust (lightgray), A=5 WW/m3. Zoom of Lagrangian mesh and trackedmaterials (top frame) and velocity ¢eld (bottom frame) at (b)t=6.4 Myr, (c) t=16 Myr, and (d) t=25 Myr. Lagrangianmesh initially consists of regular, rectangular cells ; distortedcells indicate progressive deformation of materials in model(mesh plotted at one third actual resolution; highly deformedcells are not plotted). Bold arrows indicate relative £ow vec-tors in lower crust and isotherms (heavy black lines) at200‡C intervals, starting at 100‡C are plotted. (e) Topogra-phy along 250 km of surface, starting at left side of box.

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cept in this case the radioactive block is centeredabove the downwelling so the convergent mobilecrust accumulates and thickens at the downwel-ling. The horizontal extent of the uplifted regionis approximately 50 km, roughly equal to that ofthe radioactive zone (Fig. 6e).

The thickened radioactive crust becomes in-creasingly hot, reaching temperatures of V800‡C,thereby further weakening the ductile crust. Con-sequently, signi¢cant £ow begins in this region(Fig. 6c) and the crust thins by outward channel£ow of the hot low-viscosity lower crust above thedownwelling plume (Fig. 6c). This style of local-ized channel £ow is similar to that predicted tooccur beneath plateaus at continental collision[42] and illustrates the feedback e¡ects betweenradioactive heating of thickened crust and gravi-tationally driven channel £ow. The channel £owwould be even more pronounced were the e¡ect ofcrustal melting in lowering the bulk e¡ective vis-cosity of the hot thickened crust taken into ac-count.

The variations of the surface topography, crus-tal thickness and Moho temperature above thecenter of the downwelling and radioactive block(i.e., x=0) are plotted versus time (Fig. 7). Forthe ¢rst 5 Myr the crust remains moderatelystrong. It undergoes a short period of surface up-lift, then subsidence under the e¡ect of the mantlelithosphere downwelling. The crust is progres-sively heated, up to temperatures of V800‡C,causing weakening of the lower crust and under-lying mantle (Fig. 6c). Consequently, the basalmantle forcing entrains the ductile lower crust to-wards the downwelling, thickening the crust toV45 km and leading to surface uplift (despitethe downward mantle dynamical forcing).

The crustal thickening does not persist, but in-stead by V15 Myr the increasingly hot orogeniccrustal region begins to undergo gravitationallydriven extension and thinning (Fig. 6b,c) andfrom 20 Myr the surface subsides as the crustde£ates. The decrease in surface elevation is rela-tively modest as the mantle lithosphere downwel-ling is still actively entraining a signi¢cant amountof lower crust material towards the center of thethickening above the downwelling (e.g., note in-ward-directed £ow of crust beneath the outward

channel £ow of radioactive crust, Fig. 6c,d). Con-sequently, the de£ated crust does not return to itsoriginal thickness (30 km), but remains at a thick-ness of V40 km (Fig. 7b). Radioactive self-heat-ing of the crust causes an overall rise in Mohotemperature through the experiment while longtimescale £uctuations (i.e., the relative tempera-ture highs at V7 and 23 Myr) are due to changesin the heat £ux at the base of the crust caused bythe time-dependent mantle lithosphere downwel-ling.

Fig. 7. Time series for: (a) surface topography at x=0, (b)crustal thickness at x=0, and (c) temperature at the base ofthe crust at x=0 for radioactive crust model shown in Fig. 6.

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A similar experiment was conducted in whichthe width of the radioactive zone in the crust wasincreased to 500 km (Fig. 8). The broad zone ofradioactive crust causes thermal weakening of thecrust on a regional scale. As the mantle litho-sphere instability develops, it rapidly entrainsthe hot lower crustal material to the convergentzone, resulting in progressive crustal thickeningabove the downwelling (Fig. 8b). Crustal conver-gence also thickens the lower crustal radioactiveregion which self heats and eventually becomeshot and weak and outward £ow of the low-vis-cosity lower crust commences by 6.4 Myr (Fig.8c). In this case the overlying crust is also unsta-ble and outward Couette £ow results in subse-quent thinning of the upper crust above the man-tle lithosphere downwelling.

The progression of these events is similar to theprevious model (Fig. 6) except for two main as-pects. Firstly, the timescale for surface uplift andcrustal thickening is signi¢cantly shorter becausethe wide radioactive region provides a larger vol-ume of hot/weak lower crustal material that canbe entrained towards the mantle £ow-inducedconvergent zone. A peak topography and maxi-mum crustal thickness is reached within V5 Myrfrom the start of the experiment and crustal thin-ning begins by V5 Myr (Fig. 9). Secondly, thebroad radioactive lower crust in£uences the widthof the surface topography features that develop inresponse to the mantle^crust tectonics (Fig. 8e)because the weak crust is essentially uncon¢ned.In this model the weak crust thickens and upliftsquickly (Fig. 9) and consequently there is a sig-

C

Fig. 8. Progressive deformation of crust in model with gravi-tational instability and wide zone of radioactive crust. (a) In-itial model geometry; 15 km thick, 500 km wide radioactiveregion in lower crust (light gray), A=5 WW/m3. Zoom of La-grangian mesh and tracked materials (top frame) and veloc-ity ¢eld (bottom frame) at (b) t=3.2 Myr, (c) t=6.4 Myr,and (d) t=9.5 Myr. Lagrangian mesh initially consists ofregular, rectangular cells; distorted cells indicate progressivedeformation of materials in model (mesh plotted at one thirdactual resolution; highly deformed cells are not plotted).Bold arrows indicate relative £ow vectors in lower crust andisotherms (heavy black lines) at 200‡C intervals, starting at500‡C are plotted. (e) Topography along 250 km of surface,starting at left side of box.

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ni¢cantly reduced phase of initial surface subsi-dence (e.g., compared to Fig. 7a). Taking intoaccount the symmetry of the solution space, atransient topographic high of V150 km half-width develops above the mantle downwelling(Fig. 8e). This is broader than the peak that de-veloped with the narrow radioactive zone, V50km (Fig. 6e). However, the high is signi¢cantlynarrower than the 500 km half-width of the radio-active zone. This result indicates that for wide

regions of weakened crust the length scale of de-formation and surface uplift (Fig. 8e) is controlledby the width of the mantle downwelling in con-trast with narrow regions which control their ownlength scale (Fig. 6e).

3. Conclusions and discussion

The results of the numerical experiments havethe following implications.b The presence of crustal radioactive heating may

make otherwise strong, tectonically inactivelithosphere in a continental interior susceptibleto signi¢cant deformation induced by underly-ing mantle £ow. Essentially, localized enrich-ments of radioactive elements may prepare thelithosphere for intraplate tectonic deformationand represent a primary control on the way thestrength of the crust evolves during sub-crustalforcing.

b The feedback between thermal^mechanical pro-cesses during the evolution of the radioactivecrust in response to a driving mantle downwel-ling event can cause the crust to go throughphases of: (1) dynamic subsidence of strongcrust, potentially forming intracratonic sedi-mentary basins; (2) £ow-induced contraction,thickening and uplift of the self-heating crust;and (3) orogenic de£ation as spontaneous crus-tal extension/thinning and surface subsidenceoccur. The extension may occur by channel£ow con¢ned to the mid/lower crust or mayinclude the upper crust. Strong homogeneouscrust subsides dynamically above mantledownwellings and undergoes essentially no in-ternal deformation.

b The vertical distribution of radioactive elementsin the crust is important, because buried sour-ces of radioactive heating are more e¡ective atheating/weakening the crust than those nearerthe surface.

b A broad zone of deformation and surface upliftmay develop in crust having a wide regionalconcentration of radioactive material in thelower crust, compared to a restricted topo-graphic high above a localized concentrationof radioactive elements. In the former case,

Fig. 9. Time series for: (a) surface topography at x=0, (b)crustal thickness at x=0, and (c) temperature at the base ofthe crust at x=0 for wide radioactive crust model shown inFig. 8.

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the width of the zone of high topography andthickened crust is limited by the width of thedownwelling, rather than the horizontal extentof the region of radioactive crust.The modeling results have particular implica-

tions for situations where the positive feedbackbetween crustal tectonics and radioactive heatingleading to enhanced deformation is the strongest.McLaren et al. [21] have proposed that the tec-tonic evolution of the Mt. Isa region of Australiain the Proterozoic is closely related to changes inthe thermal state of the crust. In particular, theysuggest that the burial of highly radioactive gran-ites (e.g., having a present-day regional averageA=5.2 WW/m3) beneath insulating sediments re-sulted in an increase in crustal temperature and anassociated decrease in crustal strength, leading toa phase of intraplate compression and crustalthickening during the Isan orogeny. Our numeri-cal experiments suggest that radioactive crustalheating during thickening may provide the requi-site thermal weakening feedback to permit a pro-nounced crustal contraction, thickening and sur-face uplift even when orogeny is relatively weaklydriven by lithospheric RT instabilities. In the Isanorogeny case the sediment blanketing may haveenhanced the thermal weakening but such insula-tion may not be required in general if the down-welling alone can initiate crustal thickening. Thee¡ect of thermal insulation and self-heating bysediments that would isostatically deepen and ¢llthe dynamical depressions predicted by the nu-merical experiments would, however, further en-hance the positive feedback mechanism in the in-tracratonic basinal parts of the models and maypromote basin inversion even in instances wherethe crust does not deform in the current experi-ments.

For example, in the numerical models with aradioactive lower crust the surface topographyabove the mantle downwelling undergoes an in-version from subsidence to uplift (Figs. 5a and7a). This re£ects the evolution of the crust fromthe strong end-member to a thermally weakenedstate. While the crust is strong, it resists signi¢-cant deformation and experiences intraplate sub-sidence induced by the downwelling RT instabil-ity. This process has been invoked, for example,

to account for certain phases of the formation ofintracratonic basins such as the Ordovician andSilurian development of the Canning Basin inWestern Australia [43]. Our results suggest thatlocations of crustal weakening (e.g., crust havinghigh radioactive heat production or at weak pre-existing tectonic rifts) within such a basin may besusceptible to inversion and deformation duringor subsequent to the £ow-induced regional subsi-dence.

If the radioactive elements are distributedevenly through the entire crust or concentratedat depth, the crust is more prone to deformationinduced by the underlying mantle lithosphere in-stability. This situation most closely correspondsto juvenile, undi¡erentiated crust [44^46]. Fur-thermore, it may be inferred that the coupledmantle^crust processes occurring in the modelsmay play a role in the progressive cratonizationof juvenile crust in an intraplate environment.That is, crust containing a uniform distributionof radioactive elements, or a concentration atdepth, may promote intraplate tectonics throughthe feedback between mantle downwellings, crus-tal thickening, radioactive self-heating, meltingand granitic diapirism which will lead to the con-centration and upward transfer of radioactive el-ements in the crust.

In the experiments, we have made the assump-tion that the subcontinental mantle lithosphere isgravitationally unstable resulting in RT instabil-ities, thereby creating a mechanism that forcesintraplate deformation. Houseman et al. [47] ¢rstproposed that during continental plate conver-gence, dense thickened mantle lithosphere is grav-itationally unstable, and under certain conditionsmay develop as an RT-type mantle downwelling.This type of convective removal of the mantlelithosphere has been invoked to explain the geo-dynamic evolution in various tectonic environ-ments [48^53]. The development of perturbationsat the base of the lithosphere into gravitationalinstabilities requires that the rate of growth ofthe instabilities exceeds the dissipative e¡ects ofthermal di¡usion. The growth rates of RT insta-bilities can be strongly a¡ected by rheological var-iations such as temperature dependence [54,55]and non-linear viscosity [35,36]. Our models sug-

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gest that with a power-law viscous rheology basedon dry olivine for the mantle the lower portion ofthe mantle lithosphere is susceptible to RT insta-bility for the assumed thermal structure of thelithosphere (Fig. 2). Even RT instability of justthese lower regions of the mantle lithospherecan be su⁄cient to drive appreciable crustal tec-tonics in the experiments. However, in the modelswe ignore the in£uence of chemical alterations inthe mantle lithosphere and potential associatedbuoyancy e¡ects. These may be important for in-creasing the stability of the lithospheric roots[56,57] and inhibit the growth of RT instabilitiesat the base of the lithosphere.

The development of RT instabilities of themantle lithosphere also requires that at least aportion of the mantle lithosphere is more densethan the underlying asthenosphere. Recent studiesusing mantle xenoliths/xenocrysts have placedconstraints on the secular variation in the densityof sub-crustal lithosphere through Earth history[58,59]. These analyses are interpreted to implythat there has been a progressive geochemical evo-lution from depleted mantle lithosphere in the Ar-chean to a more fertile state in the Phanerozoic.Based on these measurements and assumed geo-therms at past geological times, it is suggestedthat the cratonic mantle lithosphere in the Arche-an and Proterozoic may have been less dense thanthe underlying asthenosphere and it is only sincethe Phanerozoic, and below cool cratons that themantle lithosphere is denser than the astheno-sphere. The analyses in these studies consideredthe density structure of cratonic mantle litho-sphere that has survived since the Archean andthus are inherently biased towards stable portionsof the lithosphere. Nevertheless the results suggestpotentially important implications for the secularchange in behavior of mantle lithosphere roots.

In our experiments, we have only considered amantle lithosphere instability/downwelling as theforcing for deformation of the radioactive intra-plate crust. As stated in Section 1, another mech-anism which may act independently, or in concertwith the £ow-induced deformation in a plate in-terior is the e¡ect of in-plane horizontal stressesacting on the margins of the plate. This has beenproposed as a mechanism for vertical intraconti-

nental motions as pre-existing elastic lithosphericde£ections may be ampli¢ed by horizontal com-pressive stresses, resulting in relative motions ofuplift and subsidence of disparate regions of thecontinent [60^62]. The compressive stresses areassociated with the movement of lithosphericplates and are transmitted from the margins ofthe plate to the interior. Flow-induced crustal de-formation and topography, such as demonstratedin our numerical model experiments, may contrib-ute the initial lithospheric perturbations that arethen ampli¢ed by the in-plane stresses. Compres-sive stresses within the lithosphere may be ex-pected to amplify the predicted time-dependenttopography both by plate buckling, when the lith-osphere is relatively strong, and/or by contractionand thickening of the weak radioactively heatedcrust. In addition, horizontal shortening of theplate may in£uence the growth rate and wave-length of the RT mantle lithosphere instability[34,36].

We have shown that there are potentially sig-ni¢cant feedbacks between thermal and mechan-ical processes in the crust in response to drivingby mantle downwelling. In the absence of super-imposed e¡ects from far-¢eld in-plane lithosphericstresses, the character of the tectonic response canrange from formation of intracratonic sedimenta-ry basins to crustal thickening and orogenesiswhich may be followed by outward crustal £ow.The particular response predicted for the crustabove the downwelling is very sensitive to itsstrength, which is parameterized in terms of tem-perature caused by radioactive heating in themodel experiments. Natural examples of thesame coupled processes should be characterizedby relatively short (6V10 Myr), moderate am-plitude (few km), spatially restricted (few 100 km),pulse-like, tectonic events dictated by the spaceand timescale of the RT mantle lithosphere insta-bility or zonation of weak crust/upper mantle lith-osphere, and the requirement that the lithospherebe susceptible to RT instabilities.

Acknowledgements

The work was funded by research grants to

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R.N.P. and C.B. from the Natural Sciences andEngineering Research Council of Canada. C.B.also acknowledges support through the Inco Fel-lowship of the Canadian Institute for AdvancedResearch and through the Canada ResearchChair in Geodynamics. Numerical calculationsused software developed by Philippe Fullsack.We thank the reviewers, Julian Lowman andGreg Houseman, for constructive comments onthe original manuscript.[SK]

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