Possible role of midcrustal igneous sheet intrusions in

cratonic arch formation

J. K. Welford,1 E. H. Hearn,2 and R. M. Clowes2

Received 24 July 2006; revised 23 March 2007; accepted 13 June 2007; published 9 October 2007.

[1] Factors controlling widespread cratonic archformation across western North America from theEarly Paleozoic to the Middle Mesozoic remain poorlyunderstood. While a number of causes, such as mantlehot spots, lithospheric contraction, mantle flow, andlithospheric flexure due to surface loading, have beensuggested to explain the localized uplift of basementblocks on otherwise tectonically quiescent margins, avariety of mechanisms may be at work. Here, we testthe hypothesis that seismically detected packages ofdiscrete midcrustal igneous sheet intrusions impartrheological contrasts within the crust, which act asseeds for cratonic arch formation in the presence ofweak intraplate compression, using finite elementmodeling of intraplate deformation. We find that theseismically resolved sills can generate significantsurface uplift in the presence of modest strain ratesover reasonable orogenic timescales. Cratonic archformation would be enhanced in the presence ofadditional thin, seismically unresolvable sills. Whilemidcrustal sheet intrusions may be just one of manyfactors influencing cratonic arch formation, theirpresence in northern Alberta, Canada, can helpexplain the asymmetric configuration of the well-studied Peace River Arch. Citation: Welford, J. K., E. H.

Hearn, and R. M. Clowes (2007), Possible role of midcrustal

igneous sheet intrusions in cratonic arch formation, Tectonics, 26,

TC5012, doi:10.1029/2006TC002023.

1. Introduction

[2] For over 300 Ma, from the Middle Ordovician to theMiddle Jurassic, the cratonic platform underlying the present-day Western Canada Sedimentary Basin was a network ofuplifted arches and intervening basins (Figure 1a) [Porter etal., 1982]. These features had a strong influence on sedi-mentation patterns and geometries of the arches and dura-tions of their uplift have been estimated from the stratigraphicrecord. The cause of the uplift of the arches, or epeirogenesis,over such long periods of time remains a topic of active

research. Proposed driving forces for epeirogenesis includemantle hot spots [Crough, 1979], lithospheric contractiondue to cooling [Sleep and Snell, 1976], mantle flow[Pysklywec and Mitrovica, 2000], lithospheric flexure dueto surface loading [Price, 1973; Beaumont, 1981] andhorizontal intraplate stresses [Cloetingh, 1986; Heller etal., 1993].[3] On the basis of the regionally coincidental occurrence

of the Peace River Arch in northern Alberta, Canada and asequence of bright laterally continuous midcrustal reflectorson LITHOPROBE multichannel seismic reflection data,which have been interpreted as Proterozoic doleritic igneoussheets [Ross and Eaton, 1997], Eaton et al. [1999] proposeda link between the existence of dolerite sills within thecrystalline crust and the development of cratonic arches.Citing the higher yield strength of mafic rocks relative toquartzofeldspathic rocks [Ord and Hobbs, 1989], it wasargued that the sills served to stiffen the crust relative to theadjacent sill-free crust. According to finite element model-ing results from Heller et al. [1993], the juxtaposition ofsuch zones of high and low strength can lead to uplift in thepresence of weak intraplate stresses. We expand on theseresults to test whether discrete igneous sheets like thoseimaged by LITHOPROBE can provide the rheologicalcontrasts needed to instigate cratonic arch formation.

2. Paleozoic Cratonic Arches in Western

Canada

[4] The uplift of Paleozoic cratonic arches on the passivemargin underlying the present-day Western Canada Sedi-mentary Basin fundamentally impacted sedimentationpatterns for over 300 Ma. Consequently, these featuresplayed a key role in the early evolution of the sedimentarybasin and in the distribution of oil and gas reserves inAlberta. Despite their importance, fundamental questionsremain about the structure and formation of cratonic arches.How high did these ancient features stand above sea level?How long were they subareal? How long did their formationtake? What were the mechanisms involved in their uplift?[5] The net amount of uplift experienced by individual

Paleozoic cratonic arches cannot be measured directly, dueto uncertainties in the amount of subsequent erosion, and isgenerally inferred from offsets and unconformities in thestratigraphic record. Within Alberta, arch height estimatesspan several orders of magnitude. For instance, in north-western Alberta, the Peace River Arch was a topographichigh from the Late Proterozoic to the Early Paleozoic[O’Connell, 1994; Eaton et al., 1999]. It rose to a maximumof 1000 m above basement at its westernmost extent and to

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1Department of Earth Sciences, Memorial University of Newfoundland,St. John’s, Newfoundland, Canada.

2Department of Earth and Ocean Sciences, University of BritishColumbia, Vancouver, British Columbia, Canada.

Copyright 2007 by the American Geophysical Union.0278-7407/07/2006TC002023$12.00

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several tens of meters at its easternmost extent (Figure 1b)[O’Connell, 1994]. Farther to the south, Montania, a pale-otopographic high from the Upper Cambrian until the UpperDevonian [Deiss, 1941], is believed to have stood anincredible 8 km above sea level [Porter et al., 1982], whilemore typical uplifts of 600 m were experienced by theSweetgrass Arch in southeastern Alberta and northernMontana [Kent and Christopher, 1994].[6] Duration of deformation is a difficult parameter to

isolate since there is no stratigraphic method of determining

how long the deformation lasted to produce the uplift, apartfrom bounding the deformation to broad geological epochs.For instance, the uplift of the Peace River Arch is thought tohave occurred during the latest Proterozoic [O’Connell,1994], a time span of over 300 Ma. Beyond this broadconstraint, it is not known how long deformation enduredand how quickly the arch was formed. Farther south, theSweetgrass Arch is known to have been a positive featurefor 80 Ma prior to the Devonian [Kent and Christopher,1994], which limits its duration of uplift to no more than

Figure 1. (a) Map of Canada showing the locations of Paleozoic cratonic arches (long axes as blacklines), present-day Western Canada Sedimentary Basin (light gray shaded area), and occurrences ofinferred Proterozoic midcrustal igneous sheet intrusions imaged on LITHOPROBE multichannel seismicprofiles (numbered dark gray areas; 1, Head-Smashed-In Reflector, 2, Winagami Reflection Sequence;3, Wollaston Lake Reflector), adapted from Porter et al. [1982]. (b) Location and topographic map of thePeace River Arch (PRA), northern Alberta, Canada. (c) Multichannel seismic reflection evidence forinferred midcrustal igneous sheet intrusions from seismic profiles 12 and 13 (highlighted in Figure 1b)over the Peace River Arch (PRA) (data plots were obtained from http://www.litho.ucalgary.ca/atlas/atlas.html); approximate depths computed from two-way traveltimes using a velocity of 6000 m s�1. InFigure 1a, only the arches discussed in this manuscript are labeled: M, Montania; PRA, Peace RiverArch; SA, Severn Arch; SW, Sweetgrass Arch; WAA, Western Alberta Arch. In Figure 1b, the elevationcontour lines (meters) for the PRA were estimated based on geometrical constraints provided byO’Connell [1994]. The areal extent of the Winagami Reflection Sequence (WRS) and anomalously thickPrecambrian to Devonian sediments are also plotted for reference [O’Connell, 1994]. In Figure 1c, thehighlighted sediments are those of the Western Canada Sedimentary Basin.

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80 Ma. In the absence of tighter constraints on duration ofdeformation, we assume that arch formation takes a maxi-mum of tens of million of years to occur and likely occursmuch more quickly.[7] The Peace River Arch in northern Alberta is arguably

the best studied in Canada because of its direct influence onsedimentary stratigraphy in a region of significant oil andgas exploration. The arch is well recognized as a long-standing paleotopographic high with a northeast trendingaxis [Cecile et al., 1997]. The dimensions of the arch assummarized by O’Connell [1994] outline an asymmetricalfeature 750 km long and 140 km wide with a steep (�0.65�from horizontal) northern flank and a more gently dipping(�0.35� from horizontal) southern flank (Figure 1b).Sedimentary layers from the Precambrian to the Devonianare several hundred meters thicker to the north of the archthan to the south [O’Connell, 1994]. Given the configura-tion of the Peace River Arch that is well known fromseismic and stratigraphic thermal and tectonic regime inthe region at the time of arch formation, not one of theexisting mechanisms for arch formation has yet been able toaccount for all of the specific geometric details of the PeaceRiver Arch [O’Connell, 1994].

3. Occurrence of Midcrustal Igneous Sheet

Intrusions

[8] From crustal-scale multichannel seismic reflectioninvestigations, instances of anomalously bright midcrustalreflections in otherwise nonreflective crust have beenimaged at a number of locations around the world. Becauseof the strength and character of the reflections and theiroverall geometries, several of these packages have beeninterpreted as resulting from dolerite sheets intruded intocrystalline basement [e.g., Litak and Hauser, 1992;Mandlerand Clowes, 1997; Papasikas and Juhlin, 1997; Ross andEaton, 1997; Mandler and Clowes, 1998; Hajnal et al.,2005]. Seismically, these sequences are generally charac-terized by horizontal to subhorizontal discrete bands ofbright coherent reflections that extend for tens to hundredsof kilometers and are confined within the mid to uppercrust. The inferred lateral extents of some of these inter-preted deep igneous complexes are comparable to theworld’s large Phanerozoic igneous provinces and representan important and underappreciated contribution of materialto the crust.[9] In Canada, two packages of bright midcrustal reflec-

tors, interpreted as igneous sheets, coincide geographicallywith Paleozoic cratonic arches. In southern Alberta, the6000 km2 Head-Smashed-In reflector (1 in Figure 1a)[Mandler and Clowes, 1998] is completely contained withina block that corresponds geographically with Montania. Incentral Alberta, the 120,000 km2 Winagami reflectionsequence (2 in Figure 1a) [Ross and Eaton, 1997] isbounded to the west by the Western Alberta Arch and tothe north by the Peace River Arch. Figure 1c shows portionsof the seismic lines containing the Winagami sequence,which is characterized by one to five bands of brightcoherent reflections confined within a depth range of 9 to

24 km. These reflective bands extend across several Pre-cambrian basement domains and show no spatial correlationwith the distribution of those domains [Welford and Clowes,2006]. Emplacement of the Winagami sills is inferred tohave occurred between 1890 and 1750 Ma based oncrosscutting relationships with dated faults and domainboundaries [Ross and Eaton, 1997]. The thermal impactof sill emplacement is not thought to have had an impact onarch formation since the arches were formed 1 billion yearsafter emplacement. A third sequence of midcrustal reflec-tors, the Wollaston Lake Reflector sequence, imaged innorthern Saskatchewan (3 in Figure 1a) [Mandler andClowes, 1997], is of unknown lateral extent due to thelimited deep seismic coverage but could extend to the easttoward the Severn Arch in northern Manitoba. Whereas thespatial correspondence of these features may be purelycoincidental, they may also indicate a direct link betweenthe presence of midcrustal igneous complexes and theformation of cratonic arches.

4. Finite Element Modeling of Intraplate

Deformation

[10] Finite element modeling of horizontal compressionof elastic plates was carried out by Heller et al. [1993] todetermine whether inhomogeneities in the crust could causesurface uplift and impact the stratigraphic record. Inhomo-geneities were modeled as blocks within the crust whichhad differing Young’s moduli from the surrounding mate-rial. By applying a compressional horizontal load to a two-dimensional 500 km wide by 20 km deep plane strainelastic plate model containing a 25 km wide by 10 km deepblock of strong material in the lower central part of the platethat is surrounded by weaker material, surface deflections ofa few meters over several hundreds of kilometers weregenerated within 0.25 Ma. These results were cited byEaton et al. [1999] as evidence that the discrete midcrustalsheet intrusions imaged by LITHOPROBE may havecaused the uplift of nearby cratonic arches. To test whetherthe Eaton et al. [1999] hypothesis is plausible, we firstendeavored to reproduce the general results from Heller etal. [1993], and then refined this model to account forinelastic deformation and geometrical constraints on thesills. As with Heller et al. [1993], our computationswere performed using the finite element modeling code,TECTON [Melosh and Williams, 1989].[11] To reproduce the results from Heller et al. [1993], we

used the same two-dimensional plane strain cross section ofan elastic plate with constant thickness as used by Heller etal. [1993], although we only considered half of the modeldue to the symmetry of the problem (Figure 2). The strongmidcrust was modeled as a 12.5 km wide by 10 km deepblock in the bottom right corner of the model with a higherYoung’s modulus (E) than the surrounding material.Winkler restoring forces [Williams and Richardson, 1991]were applied to both the top and bottom of the elastic plateto account for isostasy. These restoring forces were com-puted for a density contrast of 2650 kg m�3 at the top of theplate and 350 kg m�3 at the base, assuming that the plate

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was resting on the lower crust. The lower crust wasassumed to exert no resisting shear stresses on the base ofthe model. To better relate these results to more realisticEarth lithologies, we also computed surface deflections fora strong block of material (dolerite) at the base of the platethat differed in E as well as density and Poisson’s ratio fromthe surrounding material (granite); see Figure 3 caption forparameter values. To account for density contrasts withinthe plate, Winkler springs were placed within the platealong the top of the strong block.[12] The right edge of the elastic plate was fixed with

respect to horizontal motion while a horizontal displacementof 197 m was applied to the left model boundary. Theresulting strain across the modeled region (7.88 � 10�4) isequivalent to a strain rate of 10�16 s�1 acting for 0.25 Ma.[13] The results for contrasts in E between the block and

its surroundings of 20 versus 10 GPa and 100 versus 10GPa exactly reproduce the results from Heller et al. [1993](Figure 3 curves A and B). Note that the deflections areplotted relative to the height of the top left corner of theplate. The amplitude of the net surface deflection from themodel using more realistic Earth properties (Figure 3, curve C)is intermediate to the examples produced by Heller et al.[1993], whereas the shape of the deflection is broadened.Models without density and Poisson’s ratio variationswithin the plate (not shown) yield essentially identicalresults, indicating variations in E are the dominant sourceof surface deflections in these examples.

4.1. Elastic Models of Arch Formation

[14] To better relate the elastic finite element modelingresults of Heller et al. [1993] to arch formation, we opted tomodel the relationship between the Peace River Arch andthe interpreted Winagami midcrustal sill complex in theadjacent crust (Figure 1b). In order to gauge any success in

modeling the Peace River Arch, a number of criteria mustbe met. First, the model must produce arch heights similarto those inferred from the stratigraphic record, tens ofmeters to 1000 m [O’Connell, 1994]. Second, the widthof the computed subareal arch must be consistent with the140 km width of the Peace River Arch. Last, the modelingmust reproduce the asymmetry of the arch.[15] The simple upper plate model used by Heller et al.

[1993], while informative, is not geometrically appropriatefor capturing the features of interest in the formation of thePeace River Arch. First, the limited horizontal dimension oftheir strong block is significantly shorter than the hundredsof kilometers over which the seismically imaged sillsextend. Second, the shapes of their computed surfacedeflections appear to favor the development of deep narrowbasins rather than broad arches (Figure 3). In order toconstruct a more appropriate model for the developmentof the Peace River Arch, the model used by Heller et al.[1993] was extended to 600 km with the strong block takingup 50% of the model’s lower crust (Figure 4a).[16] The boundary conditions from the simpler Heller et

al. [1993] model were scaled such that a horizontal dis-placement of 473 m was applied to the left model boundaryto generate a strain across the modeled region (7.88 � 10�4)equivalent to a strain rate of 10�16 s�1 acting for 0.25 Ma.[17] The surface deflection results for the new model,

using the same rheological variations as the simpler model(Figure 3), demonstrate several improvements (Figure 4a).First, in addition to a basin, the models generate a topo-graphic high of several meters. Second, the models are ableto generate arches of comparable width to that measured forthe Peace River Arch. Third, the resultant arches areasymmetric with a steeper flank adjacent to a deep basin.

Figure 2. Boundary conditions used for all of the finiteelement calculations in this manuscript. Circles along thetop and bottom of the plate represent free horizontaldisplacements or velocities, circles along plate edgesrepresent free vertical displacements or velocities, trianglesat the right edge of the plate represent fixed horizontaldisplacements or velocities, and the black arrows along theleft edge represent the prescribed horizontal displacement orvelocity boundary condition. The springs at the top andbottom of the plate represent Winkler restoring forces usedto account for buoyancy forces arising from deflection ofdensity contrasts. The elastic plate model shown was usedto reproduce results from Heller et al. [1993].

Figure 3. (top) Surface deflections after 0.25 Ma for amodel containing a strong block (bottom) within a platecomposed of weaker material. The different surfacedeflection curves represent contrasts of curve A, Young’smodulus (20 versus 10 GPa); curve B, Young’s modulus (100versus 10 GPa); and curve C, dolerite (density 3000 kg m�3;Poisson’s ratio 0.28; Young’s modulus 85 GPa) versusgranite (density 2650 kg m�3; Poisson’s ratio 0.20; Young’smodulus 50 GPa); based on the works by Haas [1981] andCarmichael [1989]. A horizontal strain rate of 10�16 s�1

across the region was assumed.

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[18] The discrepancy between the computed arch heights(approximately meters) and those inferred for the PeaceRiver Arch itself (�1 km) likely results from the use of anelastic model, which is not appropriate for the timescalesrelevant to arch formation. We address this issue below. Wefirst address the question of whether a strong block ofmaterial occupying the lower crust produces results thatbear any resemblance to those produced by discrete thicksills.

4.2. Strengthening Due to Thick Sills?

[19] From seismic modeling of the reflections from theWinagami sequence [Ross and Eaton, 1997; Welford and

Clowes, 2006], the thickness of the top reflective sheet isestimated to be �100 m. These seismic modeling results areincorporated into the finite element model shown inFigure 4b. Four 100 m thick sills, extending 300 km fromthe right model boundary and with a vertical spacing of3.2 km, are added to the lower part of the plate (Figure 4b).This simple model is a variation on the model used inFigure 4a to allow for comparison with those results whilealso capturing features observed in the seismic section(Figure 1c). To account for the density contrasts associatedwith the individual sills, Winkler springs were placed withinthe model along the top and bottom of each sill. In order toensure that individual sills were at least four elements thick

Figure 4. Elastic modeling results. (a) (top) Surface deflections after 0.25 Ma for a model containing astrong block (bottom) within a plate composed of weaker material. Property contrasts are as shown inFigure 3. (b) Surface deflection after 0.25 Ma (black line) for a granite plate containing four discrete100 m thick dolerite sills; deflection for a granite plate containing a solid block of dolerite is shown as adashed gray line for reference. (c) Surface deflections after 1 Ma for model in Figure 4b. (d) Surfacedeflections after 0.25 Ma for a range of models in which intermediate material equivalent to 40, 80 or160 minisills (10 m thick) exists between each of the four 100 m thick sills. (e) Surface deflections after1 Ma for model in Figure 4d. The across-strike width of the Peace River Arch (PRA) is shown across thetop for comparison. A horizontal strain rate of 10�16 s�1 across the region was assumed.

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and that elements throughout the model did not exceed a5:1 aspect ratio, the blocky parameterization of the elasticplane strain model used for Figures 3 and 4a required amuch larger number of small elements. A variable meshmodel had to be created to allow finer sampling in certainregions of the model without exceeding the computermemory allocation limits. The resulting variable meshconsisted of 125 m wide by 25 m deep elements withinand bordering each individual sill with the vertical dimen-sion of elements away from the sill borders increasing by afactor of 1.1 to a maximum element height of 136 m. Thehorizontal dimension of all elements was kept fixed at 125 mwide. The resultant mesh contained 1.248 million elements.[20] A horizontal displacement of 473 m was applied to

the left model boundary to generate a strain across themodeled region (7.88 � 10�4) equivalent to a strain rate of10�16 s�1 acting for 0.25 Ma. This boundary condition isidentical to that used for the block model.[21] The results for the model containing four 100 m

thick sills (Figure 4b) clearly shows that the observed sillsdo not provide enough strengthening to generate anyappreciable uplift in 0.25 Ma using an elastic model and astrain rate of internal deformation of 10�16 s�1. Deflectionsare only slightly more pronounced after 1 Ma (Figure 4c).

4.3. Minisills Hypothesis

[22] Statistical studies of granitic and doleritic intrusionshave demonstrated scale-invariant or fractal size distribu-tions for these types of igneous structures [McCaffrey andPetford, 1997; Curtis et al., 2005]. On the basis of theseresults, features such as sill complexes would be expected tocontain sills with a broad range of lengths and thicknesses.For the Winagami complex, variable sill lengths are evidenton the seismic sections (Figure 1c), whereas sill thicknessesare more difficult to gauge directly.[23] From one-dimensional (1-D) forward modeling of

reflection response as a function of sill thickness for theWinagami sequence, Welford and Clowes [2006] deter-mined that while the topmost reflective sheet is approxi-mately 100 m thick, igneous sheets with thicknesses of atleast 30 m are seismically detectable. Meanwhile, reflec-tions from 10 m thick sills are comparable in amplitude tothe background noise. Consequently, if the Winagamicomplex consisted of a fractal distribution of sills, theresulting seismic sections underestimate the true volumeof sills present. Ross and Eaton [2002] argues for theexistence of such thinner seismically unresolvable sills, orminisills, based on the general spatial correspondencebetween the northern extent of the Winagami sequenceand a localized increase in crustal RMS velocities from6.45 to 6.7 km s�1 as determined from a seismic refractionexperiment [Zelt and Ellis, 1989]. On the basis of thesehigher velocities, estimates that up to 50% of the crust at thenorthern limit of the Winagami sequence could be intrudedwith dolerite sills are presented [Ross and Eaton, 2002]. Ifthe intrusion of the thicker sills imaged by LITHOPROBEwas also accompanied by parallel intrusion of much thinnerseismically undetectable minisills on the order of 10 m in

thickness, the bulk strength of the intruded rock could haveincreased.[24] In order to test the feasibility of the minisills

hypothesis while respecting TECTON’s model size limits,we opted for an effective medium approach to modeling theminisills. A 3.4 km wide by 3.4 km deep test model dividedinto 25 m wide by 5 m deep elements was constructed. Two100 m thick sills were placed at the top and base of themodel each extending 200 m horizontally from the rightedge. This setup mimics one set of sills in the larger modelexcept for the absence of the weaker material on top. The10 m thick minisills were two elements deep and wereinserted into the model at a regular spacing between thethicker sills. Finite element calculations were performed formodels containing 40, 80 and 160 equally spaced 10 mthick minisills, and the results were compared againstsimpler models in which the material between the 100 mthick sills was assigned intermediate properties betweengranite and dolerite. The boundary conditions used for theeffective medium modeling were scaled equivalents of thoseused in the larger model (Figure 2).[25] From these effective medium tests, we found that the

best correspondence between the results for the modeledminisills and the equivalent medium material occurred whenthe density, Young’s modulus and Poisson’s ratio valuesused in the equivalent medium were volumetrically weightedaverages of the values for granite and dolerite. We use theseintermediate values in the model in Figures 4d and 4e as aproxy for the presence of minisills.[26] Results for the large models from section 4.2 using

the intermediate material between the four 100 m thick sillsare shown in Figures 4d and 4e. By increasing the numberof 10 m thick minisills between the 100 m thick sills, greaternet surface deflections are observed. With 160 minisillstaking up 50% of the intersill space, the computed deflec-tions near those computed for a solid dolerite block.

5. Viscoelastic Modeling

[27] To this point, we have focused on elastic deforma-tion. This has been for two reasons. First, we wanted tocompare our results with those from Heller et al. [1993].Second, we were limited by computer memory and compu-tation speed. Detailed models (such as those containing the100 m thick sills) could not be run for multiple time steps.[28] We note that the elastic model results presented to

this point may be interpreted as viscous (or viscoelastic)models with contrasts in viscosity, rather than Young’smodulus. This interpretation is admissible because ourresults are insensitive to Poisson’s ratio (which should behigh for viscous deformation). The results are directlycomparable if we substitute strain rate for strain, andcompute stresses from the effective viscosity and strainrate. However, since effective viscosity contrasts in theEarth are much larger than contrasts in Young’s modulus,these proxy viscous models are too conservative in terms ofviscosity contrasts to represent conditions in the mid tolower crust.

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[29] Initially during arch formation, the Earth’s uppercrust should have behaved elastically, with deformationlocalizing at the site of the future arch as we have shown.According to Zhang et al. [1996], subsequent permanentdeformation should occur at the site of such a perturbation(if its wavelength is short enough relative to a parametergoverned by the folding layer thickness and the contrastbetween its viscosity and that of the surrounding material).Hence the elastic models presented in Figure 4 may help usunderstand how the Peace River Arch started to form whereit did, but they are not helpful for modeling the growth ofthis arch.[30] Most modelers, who address buckling of the upper

crust assume viscous or plastic rheologies [Biot, 1957;Zhang et al., 1996]. Such rheologies, as well as nonlinearviscous rheologies, yield folds with similar wavelengths andheights, but with some differences (e.g., different hingesharpnesses or levels of irregularity [Zhang et al., 1996]).Since we are just addressing gross features of the PeaceRiver arch, viscoelastic modeling is appropriate for model-ing its growth.[31] Figure 5 illustrates effective viscosity as a function

of temperature for the rock types we consider, under bothwet and dry conditions. The curves are generated assumingdeformation via dislocation creep with a strain rate of 10�16 s�1

[Caristan, 1982; Hansen and Carter, 1983; Mackwell et al.,

1998]. The curves demonstrate that effective viscositydecreases with increasing temperature, particularly in thepresence of water, and that effective viscosities of graniteare lower than those for dolerite. At higher strain rates, theeffective viscosities for all rock types will be lower.Furthermore, at low differential stresses the granite maydeform largely via diffusion creep, resulting in still lowereffective viscosities. Hence the effective viscosities inFigure 5 that we use for our modeling are upper limits.

5.1. Viscous Minisills

[32] For long-term deformation, the rheological parame-ter governing deformation in our models will be theeffective viscosity. On the basis of Figure 5, we see thatin the lower crust, the ratio of effective viscosities for sillsrelative to country rock is about 1000. Thus, even with onlya small number of sills within the lower crust, the weightedmean of the viscosities will yield a strong contrast with thecountry rock. For example, within the lowermost 5 km ofthe plate, the weighted mean intermediate effective viscosityused to represent four 100 m thick sills composed of wetdolerite within wet granite host rock is 2.3E + 23 Pa, whichis 50 times greater than the effective viscosity of wet granitealone (5.1E + 21 Pa). With the addition of an increasingnumber of 10 m thick seismically undetectable minisills, thecontrast becomes greater.[33] To model the influence of viscoelastic materials on

surface deflections, we used coarse models similar to thatshown in Figure 4a. The country rock was assigned theeffective viscosity of wet granite and the stronger block wasassigned the weighted mean effective viscosity for differentvolumes of wet doleritic sill material within wet granite hostrock. The effective viscosities used for the wet granite andto compute the weighted means were depth-dependent andcorresponded to the dashed lines in Figure 5. The higheffective viscosity values in the top 10 km of the crustshould be interpreted as representing a deformation processother than dislocation creep.[34] To incorporate the time dependence of the viscoelas-

tic solution, our horizontal displacement boundary condi-tion was replaced by a horizontal velocity boundarycondition. A horizontal velocity of 6 � 10�11 m s�1 wasimposed on the left boundary of the model to generate astrain across the modeled region (7.88 � 10�4) equivalentto a strain rate of 10�16 s�1 acting for 0.25 Ma.[35] The results of incorporating viscoelastic materials in

our modeling are shown in Figure 6. With only four 100 msills, the viscoelastic model is able to generate approximately8 m of uplift within 0.25 Ma (Figure 6a). As more and moreminisills contribute to the weighted mean effective viscosityof the intermediate block, surface deflections are enhanced.These results greatly exceed the surface deflections that canbe achieved with elastic modeling.[36] In order to generate the maximum height of the

Peace River Arch (1 km), our horizontal velocity boundarycondition must be sustained for tens of millions of years.However, during that time, the use of the viscosities fromFigure 5 can lead to stress buildup in the crust that exceeds thefailure strength of intact rock (100MPa). Although confining

Figure 5. Plot of effective viscosities versus temperature(thick lines) for both wet and dry granite and doleriteassuming deformation via dislocation creep with a strainrate of 10�16 s�1 [Caristan, 1982; Hansen and Carter,1983; Mackwell et al., 1998]. The temperature rangecorresponding to the model depths used in this study isshaded in gray, and the approximate model depths arelabeled on the right side of the plot. A geothermal gradientof 20� km�1 is assumed. Dashed lines denote the effectiveviscosity values used for both wet and dry granite anddolerite for the modeling presented in Figure 6.

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pressure at depth will increase the failure threshold of thecrustal rocks, this alone is not enough to overcome theproblem of high differential (and hence shear) stresses.[37] Excessive stress buildup in the crust can be averted

in two ways. First, we can assume lower viscosities thanthose shown on Figure 5 at all depths, by assuming differentflow laws or higher temperatures (e.g., due to a highergeothermal gradient or an insulating low-strength sedimen-tary layer) or by assuming a vertically averaged effectiveviscosity as done by England and McKenzie [1982]. Alter-nately, we can assume a lower effective viscosity in the top10 km of the crust, where the flow is more likely to begoverned by a pressure solution creep law than by adislocation creep law. Models in which we assigned aneffective viscosity of 1023 Pa to the top ten km of the crustyielded arch growth similar to that shown in Figure 6, withmaximum shear stresses well below 100 MPa. This sameeffective viscosity was used by Liu et al. [2002] to avoidgenerating thrust faults in the long-term deformation of aviscoelastic model of the central Andes.[38] We conclude that viscoelastic relaxation enhances

surface deflections such that the amount of uplift estimatedfor Paleozoic arches can be generated within tens of million

of years at low strain rates, particularly in the presence ofwater, and that the arch heights can be attained withdifferential stresses in the upper crust that are below thecompressive failure strength of the rock.

5.2. Depth of Sills

[39] In all of the modeling results presented to this point,the Winagami sills have been restricted to the bottom 10 kmof the modeled plate. This placement of the sills has beenintended to correspond to the present distribution of the sillsbeneath the Western Canada Basin as determined from theLITHOPROBE seismic reflection profiles. However, sincethe sills were intruded between 1890 and 1750 Ma [Rossand Eaton, 1997], prior to the deposition of the WesternCanada Sedimentary Basin, it is likely that they werelocated at a shallower depth during arch formation. Com-pensating for the thickness of the sedimentary cover, Rossand Eaton [2002] suggest that sill emplacement occurredbetween 6.5 and 16.5 km depth. Shallower sills, that havesince been eroded, may also have been present, in additionto any number of thin seismically undetectable sills.[40] While the ratio of effective viscosities for sills

relative to country rock remains roughly the same through-

Figure 6. Surface deflections after 0.25 Ma (gray lines) for viscoelastic models containing a block withintermediate effective viscosities between wet granite and wet dolerite within a plate composed of wetgranite where the intermediate values are the weighted averages for (a) four 100 m sills, (b) four 100 msills with forty 10 m sills between each of the thicker sills, (c) four 100 m sills with eighty 10 m sillsbetween each of the thicker sills, and (d) four 100 m sills with one hundred and sixty 10 m sills betweeneach of the thicker sills. On all surface deflection plots, the computed response for the purely elastic caseis plotted as a black line for comparison. The across-strike width of the Peace River Arch (PRA) is shownacross the top for comparison. A horizontal strain rate of 10�16 s�1 across the region was assumed(corresponding to a velocity of 6 � 10�11 m s�1 at the left model boundary).

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out our entire model (Figure 5), both granite and doleritewill be more viscous at shallow depths. To model the impactof these higher viscosities on surface deflections, we devel-oped a simple viscoelastic model consisting of a block ofwet dolerite emplaced within a plate of wet granite. Themodel was varied by placing the wet dolerite block atdifferent depths, between 10 and 20 km, between 5 and15 km and between 0 and 10 km. A further model wasconstructed using a thinned wet dolerite block confined tothe top 5 km of the plate. The effective viscosities used forthe wet granite and the wet dolerite were again depth-dependent and corresponded to the dashed lines in Figure 5.[41] As with the viscoelastic modeling in section 5.1, we

imposed a horizontal velocity boundary condition of 6 �10�11 m s�1 on the left boundary of the model to generate astrain across the modeled region (7.88 � 10�4) equivalentto a strain rate of 10�16 s�1 acting for 0.25 Ma.[42] Varying the depth of the wet dolerite block results in

a range of different surface deflections. As the wet doleriteblock is moved from the base of the plate (Figure 7a) to themiddle of the plate (Figure 7b), the surface deflection isnoticeably dampened due to the higher viscosities at theshallower depths. When the block is brought completely tothe surface (Figure 7c), the surface deflection is furtherdampened and reversed in orientation. With the shallowestthinned block (Figure 7d), the reversed surface deflection isagain produced although the surface deflection is slightlyless dampened relative to Figure 7c.[43] From these results, we conclude that the depth of the

sills can impact both the amplitude of the surface deflec-tions and their orientation. For a given rate of deformation,deeper sills can generate surface deflections more quicklythan shallower sills. Meanwhile, shallow sills will generatesurface deflections that have a reversed orientation relativeto those produced by deeper sills.

6. Discussion

[44] The strength or rheology of the continental crustdepends on a number of factors including the geothermalgradient, the presence of water, the stress rate and thecomposition. All other factors being equal, lateral variationsin rheology within the crust can lead to a contrast in theeffective flexural rigidity of the upper crust. This contrastcan impact topography even in the presence of weakhorizontal intraplate compressional forces. Here, we haveshown that it is possible for the juxtaposition of weakgranite and strong doleritic igneous sills in the middle toupper crust to generate the width, height, asymmetry andadjacent basin observed for the Peace River cratonic archwithin reasonable geological time spans.

6.1. Strain Rate of Internal Deformation

[45] The development of cratonic arches in westernCanada occurred on a passive margin. Nonetheless, thepresence of northeast trending ancestral transfer faults thatdivided the margin into three distinct blocks with differingtectonic histories, suggests that the margin was active[Cecile et al., 1997]. Three episodes of contractional defor-

Figure 7. Surface deflections after 0.25 Ma for viscoelas-tic models with a block of wet dolerite within a platecomposed of wet granite where the block is (a) at the baseof the plate, (b) in the middle of the plate, (c) at the top ofthe plate, and (d) at the top of the plate and only 5 km thick.The across-strike width of the Peace River Arch (PRA) isshown across the top for comparison. A horizontal strainrate of 10�16 s�1 across the region was assumed(corresponding to a velocity of 6 � 10�11 m s�1 at theleft model boundary).

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mation from the Middle to Late Proterozoic along themargin [Cook et al., 2004; Thorkelson et al., 2005] furtherchallenge the notion that western Laurentia consisted of aquiescent passive margin. Despite having no evidence otherthan broad temporal overlap with which to link thesetransfer faults and compressive orogens to the formationof cratonic arches, we nonetheless argue that a higher strainrate of internal deformation for the region than that consid-ered in this manuscript is not unreasonable given thepotential influence of these stresses on arch formation. Insuch a scenario, the discrete 100 m thick sills couldgenerate the uplifts inferred for the Peace River Arch inless time and the presence of any number of seismicallyunresolvable thinner sills could cause arch uplift to occurmore quickly. Deformation at a higher strain rate would notresult in unreasonable differential stresses because effectiveviscosities would be much lower than those shown onFigure 5.

6.2. Orientation of the Peace River Arch

[46] From the ENE-WSW orientation of the axis of thePeace River Arch and its position to the north of theWinagami sill complex (Figure 1b), the surface deflectionresults for the sills at their present-day depth, if overlain as across section on the map, would be oriented from left toright in a NNW-SSE orientation with maximum compres-sion coming from either of those directions. This wouldplace the deep basin to the south of the Peace River Arch,directly over the Winagami complex (Figure 1b). Whereasno southern basin has been identified from the stratigraphicrecord, a deep basin containing several hundred meters ofsediments has been identified immediately to the north ofthe arch. Thus our surface deflection results would appear tobe reversed relative to the known orientation of the PeaceRiver Arch and its adjacent sedimentary basin, providedthese two features were formed simultaneously. As shownin Figure 7, this discrepancy can be remedied by assumingthat the sills were located near the surface, an assumptionwhich is consistent with the inferred depth of the sills at thetime of arch formation. The consequence of this shallowingof the sills is that the duration of deformation would need tobe longer and/or that the rate of deformation would have tobe higher in order to achieve the same amount of uplift asfor the deeper sills. Both of these requirements are geolog-ically plausible and would still generate the maximum upliftheights for the Peace River Arch within several tens ofmillions of years. Thus, with the sills within the upper crust,both the formation of the Peace River Arch and the adjacentsedimentary basin to the north can be explained with ourviscoelastic modeling results.

6.3. Differential Arch Height

[47] Extending the results of our 2-D modeling to a thirddimension, we can begin to contemplate the areal character-istics of the Peace River Arch. As illustrated in Figure 1b,the arch achieves a maximum height at its westernmostextent and dips east-northeastward for 750 km. From ourresults, two possible explanations for this geometry can beenvisaged. First, the along-strike variation in arch height

may reflect an along-strike variation in the distribution ofsills within the crust. With many more sills in the crust inthe west, a south-southeastward trending compressionalforce could generate differential arch height. Such anincrease in the number of sills is not immediately obviouson the LITHOPROBE data (Figure 1c) but the acquisitionof more deep seismic reflection data westward of theLITHOPROBE surveys could further test this hypothesis.Alternatively, the variation in arch height may simply reflectthat the direction of maximum compression was horizontalbut was not normal to the edge of the sills. Supposing thecompression was oriented east-southeastward, a differentialcompression would be experienced by the sill complexwhich could generate the gradient in the arch heights. Thishypothesis is more difficult to test as the source of com-pression has yet to be identified, let alone its orientation.[48] One further consideration that must be taken into

account in this study is our limited knowledge of theWinagami sill complex. At present, the inferred areal extentof the sill complex is based on a series of 2-D multichannelseismic reflection profiles acquired by LITHOPROBE.Whereas some of these profiles capture the edge of the sills(Figure 1c), certain areas like the northern limit of theinferred extent are not constrained. It is possible that thesesills extend farther north through and beyond the PeaceRiver Arch. Should that be the case, the hypothesizedconnection between midcrustal sills and cratonic archeswould be disproved. The acquisition of more seismicreflection data to the north of the LITHOPROBE datawould be beneficial in confirming the areal extent of thesill complex and to supporting our hypothesis.

7. Conclusions

[49] Several causes have been proposed to explain thelocalized uplift of cratonic arches on otherwise tectonicallyquiescent margins. In this manuscript, we have tested thehypothesis that rheological variations due to seismicallyimaged midcrustal igneous intrusions in the crust can lead touplift in the presence of weak intraplate stresses. This wasachieved using finite element modeling of both 2-D elasticand 2-D viscoelastic deformation of plates containing doleriteblocks and sheets. Our results demonstrate the following:[50] 1. For the elastic models, the seismically imaged sills

are unable to generate appreciable uplift; however, thepresence of increasing numbers of seismically undetectableminisills would enhance uplift.[51] 2. Viscoelastic relaxation greatly enhances arch for-

mation, particularly in the presence of water, such that theseismically imaged sills alone can generate the maximumheight of the Peace River Arch within tens of millions ofyears at low deformation rates.[52] 3. The depth of the sills has a direct impact on how

fast arches can be formed and also on their orientationrelative to adjacent coeval basins.[53] 4. Variations in the regional configuration of the

Peace River Arch may reflect areal variations in the con-centration of dolerite sills within the crust and/or thedirection of maximum compression during arch formation.

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[54] From our simple modeling, we are able to generatethe width, height, asymmetry and adjacent basin of thePeace River Arch of northwestern Alberta, a feature whosewell documented configuration has not easily beenexplained or reproduced by other proposed causes ofcratonic arch formation.

[55] Acknowledgments. We would like to thank C. A. Williams forhis help with using the TECTON code, S. Ellis and an anonymous reviewerfor providing useful comments on an early version of the manuscript, andfinally, the two anonymous reviewers who carefully examined and com-mented on this manuscript, particularly the reviewer who stressed theimportance of treating the upper plate as viscoelastic.

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���������R. M. Clowes and E. H. Hearn, Department of Earthand Ocean Sciences, University of British Columbia,6339 Stores Road, Vancouver, BC, Canada V6T 1Z4.(rclowes@eos.ubc.ca; ehearn@eos.ubc.ca)

J. K. Welford, Department of Earth Sciences,Memorial University of Newfoundland, 300 PrincePhilip Drive, St. John’s, NL, Canada A1B 3X5.(kwelford@esd.mun.ca)

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