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3D relationships between sills and their feeders: evidence from the Golden Valley SillComplex (Karoo Basin) and experimental modelling

Christophe Y. Galerne a,!, Olivier Galland a, Else-Ragnhild Neumann a, Sverre Planke a,b

a Physics of Geological Processes, University of Oslo, Norwayb Volcanic Basin Petroleum Research, Oslo Innovation Park, Oslo, Norway

a b s t r a c ta r t i c l e i n f o

Article history:Received 7 October 2010Accepted 19 February 2011Available online 21 March 2011

Keywords:Feeder dykesSaucer-shaped sillsGolden ValleyField observationsGeochemistryExperimental modelling

In this paper, we address sill emplacement mechanisms through the three-dimensional relationshipsbetween sills and their potential feeders (dykes or sills) in the well-exposed Golden Valley Sill Complex(GVSC), Karoo Basin, South Africa. New !eld observations combined with existing chemical analyses showthat: 1) the contacts between sills in the GVSC are not sill-feeding-sill relationships, and 2) there are, however,close structural and geochemical relationships between one elliptical sill, the Golden Valley Sill (GVS), and asmall dyke (d4). Such relationships suggest that GVS is fed by d4 and that the linear shape of d4 may havecontrolled the elliptical development of the GVS.To test this hypothesis, we present preliminary results of experimental modelling of sill emplacement, inwhich we vary the shape of the feeder. In the !rst experiment (E1) with a punctual feeder the sill develops asub-circular geometry, whereas in the second experiment (E2) with a long linear feeder the sill develops anelliptical geometry. The geometrical relationships in E2 show that the elliptical shape of the sill is controlledby the linear shape and the length of the linear feeder. The experiment E2 presents strong similarities with theGVS–d4 relationships and thus supports the proposition that d4 is the feeder of the GVS. Our experimentalresults also indicate that the feeders of the other elliptical sills of the GVSC may be dykes.

© 2011 Elsevier B.V. All rights reserved.

1. Introduction

Extensive sill complexes are common features in large igneousprovinces, for example in the Karoo Basin, South Africa (Chevallierand Woodford, 1999), the Møre–Vøring Basin off W Norway (Plankeet al., 2005), the Parana Basin, Brazil (Bellieni et al., 1984, andreferences therein) and the NW Australian shelf (Symonds et al.,1998). In these settings, large sills commonly exhibit saucer shapes(e.g., Polteau et al., 2008b), consisting of axis-symmetrical "at innersill connected outward and upward to transgressive inclined sheets,ending in a "at outer sill (e.g., Planke et al., 2005; Polteau et al., 2008b;Galland et al., 2009). The relationships between sills (and saucer-shaped sills) and their feeders are crucial for understanding themechanisms of sill emplacement, and the relationship between sillcomplexes and "ood basalts. However, such relationships are poorlyknown because the connections are rarely exposed (e.g., Hyndmanand Alt, 1987). Because of the lack of geological evidence for feeder-to-sill relationships, the mechanisms of sill and saucer-shaped sillemplacement are largely debated on the basis of theoretical models.

Some models propose that saucer-shaped sill intrusions formalong the level of neutral buoyancy of the magma, and the feeders areexpected to be located below the outer sill at one side of the saucer(Fig. 1a; e.g., Bradley, 1965; Francis, 1982; Chevallier and Woodford,1999; Goulty, 2005). Other models propose that saucers are fed frombelow through a central feeder dyke (Fig. 1b; e.g., Pollard and Johnson,1973; Hansen et al., 2004; Malthe-Sørenssen et al., 2004; Thomsonand Hutton, 2004; Hansen and Cartwright, 2006; Kavanagh et al.,2006; Galerne et al., 2008; Goulty and Scho!eld, 2008; Menand, 2008;Polteau et al., 2008a, 2008b; Galland et al., 2009). In these models, thefeeders are expected to be situated below the central part of the innersills (Fig. 1b).

Inbothmodels, sill feeders are considered to bedykes (e.g., Gretener,1969; Hyndman and Alt, 1987; Kavanagh et al., 2006; Valentine andKrogh, 2006; Goulty and Scho!eld, 2008; Menand, 2008). However,most theoretical models do not account for the three-dimensionalrelationships between sills and linear feeders. In two-dimensionalmodels (e.g., Pollard and Johnson, 1973; Malthe-Sørenssen et al., 2004)the punctual sill feedersmay be either dykes or pipes. In contrast, three-dimensional models are mostly axi-symmetrical and consider a centralfeeder pipe (e.g., Fialko et al., 2001; Murdoch, 2002; Bunger andDetournay, 2005; Bunger et al., 2005). In their theoretical studies, bothPollard and Johnson (1973) and Goulty and Scho!eld (2008) assumedthat elliptical sills develop from central feeder dykes, but they did nottake the shape of the feeder dyke into account in their mechanical

Journal of Volcanology and Geothermal Research 202 (2011) 189–199

! Corresponding author at: Now at: Geodynamics/Geophysics, Steinman Institute,University of Bonn, Germany. Tel.: +49 228732466; fax: +49 228732508.

E-mail address: [email protected] (C.Y. Galerne).

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analyses. In addition, most geological observations provide only two-dimensional relationships between sills and their feeders (e.g.,Valentine and Krogh, 2006).

Three-dimensional information on the relationships between sillsand their feeders are essential for a better understanding of sillemplacement mechanisms. One way of obtaining three-dimensionalinformation on sill morphologies is through seismic surveys. In theNorth Sea outside Norway (Hansen et al., 2004; Cartwright andHansen, 2006; Hansen and Cartwright, 2006) and the Rockall Troughof W Scotland (Thomson and Hutton, 2004; Thomson, 2005, 2007),recent seismic surveys show that:

1. Large sill complexes show physical connections between individ-ual saucer-shaped sills, i.e. some inner sills are connected with theinclined sheets of underlying sills. Such connections have beeninterpreted as feeding connections, leading to the model ofinterconnected sill-feeding-sill networks (Cartwright and Hansen,2006).

2. Some saucer-shaped sills have developed lobate morphologiesalong their outer boundaries. These lobate structures have beeninterpreted as indicators of magma "owing outwards and upwardsfrom a central source (dyke or pipe) beneath the inner sill.However, the seismic data have not revealed the location or shapeof the feeder, the reason probably being that thin sub-verticalstructures are rarely visible on seismic images.

The best way to constrain the three-dimensional relationshipsbetween sills and their feeders is clearly through detailed, multidis-ciplinary studies of well-preserved and well-exposed sill complexes.Recently, much work has been focused on the Golden Valley SillComplex (GVSC), Karoo Basin, South Africa (Fig. 2), which is a unique!eld laboratory for studying the relationships between saucer-shapedsills and associated dykes in a large sill complex. The quality of theoutcrops allowed detailed mapping of the three-dimensional struc-tures of the sills. AMS work and macroscopic "ow-indicatorscharacterised the "ow pattern of magma within sills (Polteau et al.,2008a). Additionally, extensive geochemistry aimed to address thegenetic relationships between the sills (Galerne et al., 2008) and thedifferentiation processes within single sills (Aarnes et al., 2008;Galerne et al., 2010). However, none of these studies have addressedthe potential connections between sills and dykes in the GVSC.

In this paper, we use geological and geochemical data on sills anddykes of the GVSC to investigate the relationships between sills andtheir feeders. We subsequently integrate our !eld observations andgeochemical data with preliminary results of experimental modelling.Our study demonstrates that 1) the contacts between some sills of theGVSC do not necessarily imply a feeding relationship, and 2) themajorsaucer-shaped sills in the GVSC are fed from below, and that theirfeeders are likely to be linear dykes.

2. Golden Valley Sill Complex, Karoo Basin, South Africa

2.1. Geology

The Karoo Basin consists of Late Palaeozoic–Early Mesozoic sedi-ments deposited in a foreland setting (e.g., Catuneanu et al., 1998). TheKaroo Igneous Event, which sealed the end of the foreland cycle of themain Karoo Basin (i.e., prior to tectonic uplift: Catuneanu et al., 1998;Catuneanu, 2004) resulted in (1) the intrusion of numerous saucer-shaped sills anddykes all over the basin, and (2) the eruption of the largeLesothoFloodBasalt Plateau (Erlank, 1984, and references therein).Mostof the Karoo Igneous Event occurred about 180 Ma ago (Jourdan et al.,2005, 2007);work in progress restricts the age range to b1 Ma, between182.3 and 183.0 Ma (Svensen et al., 2007; Polteau et al., 2010). DuringMesozoic–Tertiary, the basin was uplifted with the Gondwana Breakup,and the resultingerosion exposeda largepart of the intrusive complexes.No signi!cant post-Gondwana Breakup deformation or regional meta-morphism has affected the Karoo Basin. The exposed sill complexes arethus exceptionally well preserved and represent a unique !eldlaboratory to study the emplacement of sill complexes.

The GVSC, located SW of the Lesotho Plateau, consists of four majorelliptic saucer-shaped sills (Fig. 2a; Aarnes et al., 2008; Galerne et al.,2008; Polteau et al., 2008a). The saucers were emplaced at twostratigraphic levels: the Morning Sun Sill (MSS) and the Harmony Sill(HS) at the deeper level, and the Golden Valley Sill (GVS) and the GlenSill (GS) at a slightly higher level (Fig. 3). Each sill at the higher level islocated above a sill at the lower level (Fig. 3). The saucers at the lowerlevel have parallel long axes that trend NW–SE. At the upper level, thelong axes of the GVS and GS trend N–S and NNW–SSE, respectively(dashed lines in Fig. 2). A minor, circular, relatively "at sill (MV Sill, orMVS) is in direct continuity with the north-western limb of the GVS(Fig. 2a–b; Galerne et al., 2008). We consider the MVS to be part of theouter sill of the major GVS. The GVSC area also includes the majorGolden Valley Dyke (GVD; Fig. 2) locatedwest of the GVS (!15 m thick,17 km long) and several small dykes (d1–d4, Figs. 2 and 4a) and shortsill segments (e.g., L2 and L3, Fig. 2).

The sills at the upper level are on average ~100 m thick but may beup to 150 m thick (Galerne et al., 2010). The sills at the lower level are20 to 50 m thick. Drill-cores from different parts of the Karoo Basinshow several sills at different depths (Neumann et al., in press). Thissuggests that, although only two levels of saucers are exposed in theGVSC area, there may be unexposed saucers at deeper stratigraphiclevels (e.g., Chevallier andWoodford, 1999; Galerne, 2009; Galland etal., 2009).

2.2. Former studies

This section summarised the main results of previous studiesperformed on the GVSC (Galerne et al., 2008; Polteau et al., 2008a;Galerne, 2009; Galerne et al., 2010). These studies questionedwhether the sills of the GVSC were fed by a single batch of magmaor by several individual batches. The !rst hypothesis would imply thatthe sills fed each other, meaning that the feeders of the sills wereunderlying sills, whereas the second hypothesis would imply that thesills were fed by other conduits that need to be identi!ed.

Geochemical differences and similarities between the six majorunits (MSS, HS, GVS, MVS, GS and GVD) in the GVSC were tested

1

2 2

1: Inner-sill2: Outer-sill

Horizontal Discontinuity

1

2

LNB

1: Outer-sill2: Inner-sill

LNB: Level of Neutral Buoyancy

Buoyancy Controla

b

Fig. 1. Existing models of saucer-shaped sill emplacement mechanisms. Numbers(1) and (2) indicate the steps of emplacement. a. Model of emplacement controlled atthe level of neutral buoyancy (LNB), Modi!ed from Francis (Bradley, 1965; Francis,1982 e.g., Barker, 2000). Sills are fed laterally from one part of the outer sills. b. Model ofemplacement along horizontal discontinuity, modi!ed after Malthe-Sørenssen et al.(2004). Sills are fed radially from the inner sill. See text for more information.

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statistically by a Principal Component Analysis (named ForwardStep-Discriminant Function Analysis FS-DFA, StatSoft©, 2007) on thebasis of 46 major and trace elements in 233 rock samples (Galerne etal., 2008). The statistical analysis showed that the major saucer-shaped sills and the GVD of the GVSC form four distinct geochemicalgroups (shown by distinct colours in Fig. 2; Galerne et al., 2008). Thefour groups are (i) the sills at the upper stratigraphic level (GVS–MVSand GS), (ii) the HS and (iii) the MSS at the lower level, and (iv) theGVD. The different geochemical signatures imply derivation fromfour separate magma batches: the GVS–MVS–GS, the HS, the MSS,and the GVDmagma batch (Figs. 2 and 4; Figs. 10–12 of Galerne et al.,2008). This result is now con!rmed by Sr and Nd isotopic analyses,which notably show that the sills at the upper stratigraphic level(GVS–MVS and GS) are derived from a common source (Neumannet al., in press).

The saucer-shaped sills in the GVSC are locally in physical contact(Galerne et al., 2008; Polteau et al., 2008a; Galerne, 2009). At thesouthern tip of the GVS the southwestern limb of the MSS climbs intocontact with the GVS (L4b in Figs. 2 and 4). The two sills are in contactfrom L4b to L4a (Fig. 4a–b) where the MSS disappears. At L4b there isno chilled margin between the two sills but further west thesuperposed sills are separated by a thin chilled margin (L4a, Fig. 4d)at the transition between the dolerites of MSS and GVS geochemicalcompositions (Fig. 4d). These observations clearly show that theemplacements of the MSS and GVS were not coeval.

At locality L7 (Fig. 2) two sills lie above one another, separated by athin zone (a few centimetres thick) of low-grade hornfels; at locality L8two superposed sills are separated by a ca. 100 m. thick zone ofsedimentary rocks. Their geochemical signatures have identi!ed thesills at L7 as GS (upper) and MSS, and at L8 as GS (upper) and HS

26.1 (E) 26.2 (E) 26.3 (E) 26.4 (E)

32.0 (S)

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Harmonyar Sill (HS) (

Glen Sill (GS)

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Golden Valley Dyke (G

VD)

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L3

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L8

Fig. 4

Unstudieddolerite

Minordykes

GVD

HS

GVS, MVS, GS

MSS

Studied doleriteSills Dykes

Fig. 2. Simpli!ed geological map of the Golden Valley Sill Complex (GVSC), Karoo Basin, South Africa, modi!ed after Galerne et al. (2008). The map shows the major sills and theGolden Valley Dyke (coloured !elds), minor dykes d1–d4 (grey circles with orientations), and dolerites ignored in this study (light grey !elds). The acronyms and the colourscorrespond to chemically distinct magma batches (Fig. 4; Galerne et al., 2008): GVS–MVS–GS (Golden Valley Sill–MV Sill–Glen Sill); MSS (Morning Sun Sill); HS (Harmony Sill); GVD(Golden Valley Dyke). Straight lines indicate cross sections A–A" and B–B# of Fig. 3. The rectangle locates the map of Fig. 4.

191C.Y. Galerne et al. / Journal of Volcanology and Geothermal Research 202 (2011) 189–199


(Galerne et al., 2008). Furthermore, in locationswhere sills appear to besuperposed and in direct contact (L4b), chemical pro!les show verysharp geochemical transitions between two domains of almost constant

compositions, each domain corresponding to one sill. Such transitions inthe chemical pro!les show that themagmasof the sills in contact did notmix (Galerne et al., 2008, 2010).

AMS (Anisotropy of Magnetic Susceptibility) studies combinedwith macroscopic magma "ow indicators (ropy "ow structures andtube-like undulations) indicate outwardmagma "ow directions in thedifferent sills, implying that their feeders were located beneath theinner sill "oors (Polteau et al., 2008a). Polteau et al. (2008a) also foundindications in the AMS data of backward "ow, but concluded that thisresulted from compaction after the magma supply had stopped.

The existing geological and geochemical data indicate that the sillsof the GVSC were not fed by a single batch of magma, but by several.This implies that the feeders of the upper level sills were not the sillsof the lower level. Nevertheless, at that stage, it was still not possibleto identify the nature of the feeders of the sills of the GVSC. Moredetailed observations are therefore required.

2.3. New observations on minor dykes

The GVSC area includes four minor dykes (d1–d4 in Fig. 2). Dyke d1crops out ~8 km west of the GVD, striking NW–SE. This ~1-metre thick

Fig. 4. a. Highlight of the geological map of the southern GVSC. The colours, indicating the distinct magma batches involved in the GVSC, are the same as in Fig. 2 (Galerne et al., 2008).Themap indicates the localities L4a and L4b (see text for explanation). b. Panoramic photograph of the southern tip of the GVS (see location on Fig. 2). It shows that the MSS climbingsheet is in contact underneath the GVS. c. Photograph of the metre thick dyke d4. d. Photographs of the contacts between the underlying MSS to the above GVS at localities L4a andL4b. At L4a, a chilled margin separates the MSS and the GVS. At L4b, no chilled margin indicates the contact between the MSS and the GVS. The location of the contact between thetwo sills was only possible on the basis of different geochemical signatures (Galerne et al., 2010).

? ?? ?

MVS GVS GS

HSMSSG

VD

a

? ?

GVSMSS

GV

D

b

B'B'B

0 4

km

AA'A'

A''A'' A'''A'''

Fig. 3. a. Geological cross section A–A". b. Geological cross section B–B#. See Fig. 2 forcolour legend.



dyke is exposed over a distance of ~8 km. Dykes d2 and d3 are located NandNWof theGVS.Dyked2 is ~5 mthick and strikesNE–SW,whereasd3is only ~1 m thick and strikes NNE–SSW. Also d2 and d3may be followedfor a few kilometres. Finally, we found a N–S striking 1-metre thick dyke(d4) exposed in a 5- to 10-metre large outcrop beneath the southern tipof the GVS, i.e. below the GVS and above the MSS (Figs. 2 and 4).

Wedidnot observe direct physical connectionsbetween the sills andthe dykes. However, we noticed that the strikes of (1) the GVD and d1are parallel to the long axes of thedeeper level saucers (MS andHS), and(2) the d4 is parallel to the long axis of the GVS (Fig. 2). We also noticethat the strikes of the other dykes are different (NE–SW for d2; NNE–SSW for d3). This suggests that the state of stress at the time ofemplacement of these dykes was almost isotropic. This is in goodagreementwith the observation of Catuneanu (2004),who showed that(1) the Karoo Igneous Event sealed the end of the foreland deformationof the Karoo basin, and (2) there is no signi!cant regional tectonicdeformation that has affected the Karoo intrusive and effusive rocks.

The chemical compositions of the minor dykes d1–d4 have, so far,only been published as supplementary material by Galerne et al.(2008); they have neither been discussed, presented in !gures norcompared to the compositions of the major sills of the GVSC. Thenumber of analyses for each dyke is small, and the set of analysedelements is somewhat smaller than for the main group of samples.This makes the statistical approach used to discriminate the chemicalcompositions of themajor sills (Galerne et al., 2008) unsuitable for theminor dykes. We therefore present their compositions through plotsof strongly incompatible element ratios (Fig. 5).

In plots of ratios between pairs of incompatible elements the dykesd3 and d4 plot consistently within the GVS–MVS–GS !eld and d2within the MSS !eld (Fig. 5). We conclude that the dykes d3 and d4formed from the magma batch (GVS–MVS–GS) that gave rise to theupper level saucers,whereas the dyke d2 formed from theMSSmagmabatch (or from chemically identical magma batches). The compositionof d1 falls within the overlapping part of the MSS and GVS–MVS–GS!elds (Fig. 5), the dyke d1 thus cannot be clearly attributed to a speci!cgeochemical signature on the basis of trace elements.

Their geochemical similarities suggest a link between the dyke d1and the MSS. In addition, Galerne et al. (2008) show that a sillsegment at locality L2 is composed of MSS-type dolerites. Thepresence of these units with MSS geochemistry outside the MSSsuggests that the MSS may be part of a nested complex of two (ormore) sills formed from the same (or closely similar) magma batch(es) (Galerne et al., 2008). Similarly, the locations of the dyke d3 andthe sill segment L3, bothwith GVS–MVS–GS composition, suggest thatthe GVS–MVS–GS sill group continues (or originally continued) to thewest of the GVS (Fig. 2). However, as dykes d1, d2 and d3 are locatedfar away from the present outcrops of sills with the same chemistry,these dykes cannot be used to demonstrate feeding relationships. In

contrast to the other small dykes, dyke d4 shows a simple !eldrelationship with the GVS (Figs. 2 and 4) and it has a geochemicalcomposition that is identical to that of the GVS (Fig. 5).

2.4. Summary

In the GVSC, we found one minor dyke (d4), which geochemistry,location and orientation suggests a genetic link to the GVS althoughthere is no visible connection between the two. The location,orientation and geochemical composition of the dyke d4 relative tothe GVS give rise to the hypothesis that the three-dimensionalelliptical shape of a saucer-shaped sill and its location are controlledby the linear shape of its feeder dyke. This hypothesis was brie"ydiscussed by Pollard and Johnson (1973) and Goulty and Scho!eld(2008) on the basis of theoretical aspects, but to our knowledge it hasnever been tested experimentally nor supported by !eld observations.In order to test this hypothesis, that is to explore how the linearshapes of feeder dykes control the elliptical shapes of saucer-shapedsills, we resorted to physical experiments.

3. Experimental modelling

3.1. Materials and scaling

In this study, we used the experimental technique developed byGalland et al. (2009). Themodel rock consisted of a compacted cohesive!ne-grained silica "our of cohesion C"350 Pa, and the model magmawas a molten vegetable oil of low viscosity !"2!10#2 Pa s.

Galland et al. (2009) described in detail and discussed the scalingof the model. The experiment-to-nature scale ratio is of the order of2!10#5, so that 1 cm in experiments represents 500 m in nature. Asthe GVS was emplaced between 1 and 2 km depth, the depth ofinjection in the experiments should be between 2 and 4 cm.

The strength of the solid material is scaled with respect to thegravitational stress, illustrated by the ratio "rgD/C, where "r, g,D and Care the rock density, the acceleration due to gravity, the depth ofemplacement, and the cohesion of the rock, respectively. Density ofnatural rocks is about 2500 kg m#3 and their cohesion spans between107 and 108 Pa (Schellart, 2000). Therefore, the gravitational stress-to-cohesion ratio for the GVSC ranges between 0.24 and 5. In theexperiments, density of the silica "our is 1050 kg m#3. Therefore, thegravitational stress to cohesion ratio is ~0.9, which is consistent withthat of the GVSC.

In our experiments, we want to test the shape and size of thefeeder. This leads to the de!nition of another geometrical scalingparameter, the ratio between the length (L) of the feeder and thedepth of emplacement. Here we consider two cases. (1) If the aspectratio L/D$1, the feeder is small with respect to the depth of

10 15 2050

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d4

d1

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d3d4

d1d2

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d1

d2

d

Fig. 5. Plots of strongly incompatible element ratios (Ti/Zr versus Zr/Nb, Ti/Zr versus P/Zr, and Zr/Y versus P/Zr) in dolerites from the GVSC (modi!ed from Galerne et al., 2008). Datapublished in Fig. 15 of Galerne et al. (2008, contoured !elds) are completed with the data published as supplementary material by Galerne et al. (2008, un-contoured !elds). Thecoloured !elds represent the distinct magma batches involved in the emplacement of major sills and dykes of the GVSC (Galerne et al., 2008; see also Fig. 2). Compositions of minordykes (white !elds) are also plotted.



emplacement, so that it can be considered as punctual. (2) In contrast,if this L/D%1, the feeder is long with respect to the depth ofemplacement, and can be considered as linear. In this paper, wepresent one experiment of each case.

The viscosity of the magma also needs to be scaled. Theexperiments aim to simulate the transport of viscous "uid into adeforming Coulombmaterial of cohesion C. The propagation ofmagmainto the rock depends on the strength and viscosity of the rock and themagma, respectively. We use the cohesion to scale the strength of therock. Thus, the dimensionless number to scale the viscosity of magmais the ratio of viscous pressure dropwithin the intrusion relative to thecohesion of the country rock. For laminar "ow of a Newton "uid ofviscosity ! "owing at a velocity U, the viscous pressure drop along a

fracture of length l and thickness h is !Pv=!lU/h2, so that the suitabledimensionless ratio is !lU/Ch2 (Galland et al., 2009).

If we assume that usual magma velocity U ranges between 0.1 and1 m s#1 in 1-metre thick dykes (e.g., Spence and Turcotte, 1985;Battaglia and Bachèlery, 2003; Roman et al., 2004), the magmavelocity in 20- to 200-metre thick sills is expected to range between5!10#4 and 5!10#2 m s#1. In this paper, we only consider commonmagma types such as basaltic to rhyolitic magma, for which theviscosities range between 100 Pa s and 108 Pa s (Dingwell et al., 1993;Romano et al., 2003). In basins, saucer-shaped sill radii are typically5 km. Therefore, the viscous drop to cohesion ratio in nature rangesfrom 6.3!10#11 to 6.3!10#1, so that viscous stresses are smallcompared to the strength of the country rock. In the experiments, the

Fig. 6. a. Schematic drawing of the experimental apparatus, after Galland et al. (2009). b. 2-dimensional sketch representing the relationship between the inlet, the "exible net andthe intrusion. c. Example of excavated model intrusion (from experiment E1). It exhibits a typical saucer shape. d. Details of the injection setups used in experiments E1 (left) and E2(right). In E1, the injection inlet was punctual. In E2, the inlet was linear, like a dyke.



injection "ow rate was 40 ml min#1, within fractures of typical radiiabout 7 cm and typical thicknesses of 1–3 mm; the viscosity of the oilis 2!10#2 Pa s at 50 °C (Galland et al., 2006). Thus, the values of theviscous drop to cohesion ratio in experiments are 4.23!10#4 to1.2!10#2. Such values are in the same range as those in nature andmuch smaller than 1, which means that viscous stresses are smallwith respect to the strength of the country rock.

In their paper, Galland et al. (2009) also discussed the "ow regimeinto the sills by considering the Reynolds number. They show that theReynolds number in both nature and experiments is small, so that themagma "ow is laminar.

The buoyancy of the magma is acquired by integrating the bodyforces along the entire magmatic system, i.e. from the source to theemplacement level (e.g., Hogan et al., 1998; Gerya and Burg, 2007). Inthe experiments, we consider only the very super!cial part of amagmatic system. Whether the magma is buoyant or not depends onthe deep parts of the magma path, but not on shallow portionssimulated by the experiments. In addition, Galland et al. (2009)showed that the buoyancy forces generated at the scale of anintruding sill are negligible. The same conclusion was drawn by Listerand Kerr (1991) and Menand (2008). Therefore, we will not considerthe buoyancy forces at the scale of intruding sills any longer.

A critical parameter to scale is the rheology contrasts between thedistinct strata in sedimentary basins. In their experiments, Galland et al.(2009) showed that a horizontal mechanical layering was required tosimulate sills and subsequent saucer-shaped sills. In order to simulatelayering, they used a "exible net located right at the top of the inlet.Without this layering, the resulting intrusions were vertical dykes andcone sheets,whereas the layering controlled the horizontal spreading ofthe oil. Although such layering is crucial for the formation of sills, themechanical effect of the"exible net is hardly quanti!able, and so hard toscale properly. Nevertheless, the mechanical effect of such a layering isstrong enough to control the horizontal transport of the oil in theexperiments, such as in basins. On this basis, we assume that thelayering used in the experiments is suitable to simulate the mechanicaleffect of strata in nature.

3.2. Experimental setup

Our apparatus is a modi!ed version of that developed by Gallandet al. (2003, 2006, 2007, 2009). The models lay in a square box, 40 cmwide and with variable thickness (Fig. 6a). The silica "our ismechanically compacted to (1) reduce the porosity of the "our andthus the percolation of the oil, (2) control the density of the "our, and(3) control its cohesion (C"350 Pa; Galland et al., 2006). Thepreparation procedure consisted of measuring a mass of silica "ourthat we compacted using a high frequency compressed-air shakersold by Houston Vibrator (model GT-25). Such a procedure allows ahomogeneous, repeatable, and fast compaction of the silica "our.

Wewanted to take into account themechanical layering to simulatethe sedimentary strata. To prepare the experiments with the net(Fig. 6a), we poured a !rst layer of "our; then we shook the box to"atten the surface of the "our. Subsequently, we placed the net and asecond layer of "our. We shook the box a second time until the densityof theupper layerwas1050 kg m#3. Suchaprocedure inducedadensitycontrast of less than 5% between the lower and upper layers. Weconsider that this difference does not affect our experimental results.

In all experiments, we used the same square net of dimensions30!30 cm (Fig. 6a). We chose the size of the net so that it was muchlarger than the expected inner sills. Therefore, the size of the net did notin"uence the size and shape of the inner sills.We also chose anet slightlysmaller than the box to avoid any interaction between the net and thewalls of the box during the preparation of the experiments (Fig. 6a).

Because there is no evidence of active tectonic deformation coevalwith the Karoo Igneous Event, and because the observed dykepopulation exhibit very different orientations, we infer that the state of

stress at the time of emplacement of the GVSC was isotropic. Therefore,neither deformation nor load was applied in our experiments.

During the experiments, the pump injected the oil at constant "owrate of 40 ml min#1. Each experiment typically lasted for 1 min. Afterthe end of the experiments, the oil solidi!ed within about half an hour.Then, the intrusion was excavated (Fig. 6b), and its top surfacedigitalized using a moiré projection technique developed by Brèqueet al. (2004).

In this paper, we compare two experiments with different feedersizes and geometries. In experiment E1, the inlet was circular and0.5 cm in diameter; the inlet was located right underneath the "exiblenet, at 4 cm depth (Fig. 6c). In E1, the inlet represented a pipe-likefeeder and could be considered as punctual. This inlet would simulatea 500-m wide magma pipe, which is in the range of commonlyobserved magma pipes in nature (from 100 m to several kilometres,e.g. Odé, 1957). Experiment E1 has been described by Galland et al.(2009) and corresponds to a background experiment. In contrast,experiment E2 is new and is used to test the effect of linear feederdykes on the three-dimensional shape of the sills. The length of theinlet is 12 cm and its thickness is ~1 mm; it was located at 3 cm depth.The thickness/length aspect ratio is thus b10#2, which is a realisticvalue for dykes (e.g., Rubin, 1995). Simulating a 1-m thick dyke suchas the dyke d4 would require a linear inlet of 1/500 cm, which istechnically hard to achieve. However, as long as thickness/length$1,the thickness of the linear feeder has negligible effect on the !nalresult.

3.3. Experimental results

Although E1 has been already described by Galland et al. (2009),we brie"y describe it in this manuscript in order to compare it withthe new experiment E2. In experiment E1, the punctual inlet wassmall with respect to the depth; using its diameter as “L”, the feedersize-to-depth ratio is L/D=0.17. During experiment E1, oil injectionresulted in smooth doming of the model surface; the dome wascircular, and a network of sub-radial open cracks developed. At theend of the experiment, the oil erupted at the rim of the dome. Theresulting intrusion was saucer-shaped, with a horizontal inner sill,steep inclined sheets and "atter outer sills (Fig. 7a). The inner sillformed along the net and its shapewas sub-circular with a diameter of4.5 cm. The centre of the inner sill was off centre with respect to theinlet, and the inclined sheets were asymmetric (Fig. 7a).

In experiment E2, the linear feeder was long with respect to thedepth, such that the inlet size-to-depth ratiowas L/D=4.AlsoduringE2,oil injection resulted in smooth doming. However, in contrast to E1, thedome in E2was elliptical, and an open crack developed at the surface ofthe dome along its long axis. In addition, the long axis of the dome wasparallel to the linear inlet. At the end of the experiment, the oil eruptednear the intercept between the edge of the dome and the short axis ofthe dome. The intrusion in E2was also saucer-shaped, but in contrast tothat of E1, it exhibited a strongly elliptical shape (Fig. 7b); the long andshort axes of the inner sill were ~11 and 5 cm long, respectively.

The long axis of the inner sill was directly above the linear inlet.The linear inlet was slightly longer than the long axis of the ellipticalsill, as the linear inlet extended further away than the upper tip of theinner sill (Fig. 7b). In contrast, we noticed that the lower tip of theinner sill was located right above the tip of the linear inlet (Fig. 7b).

4. Discussion

4.1. Sill shape vs. feeder shape

The experiment E1 (Galland et al., 2009; Fig. 7a) showed thatinjection through a pipe-like inlet in a model with layering alwaysresults in a sub-circular saucer-shaped sill. In similar experimentsfrom Galland et al. (2009), a sub-circular sill shape was obtained for



any depth of emplacement. This suggests that the horizontal state ofstress was isotropic in the experiments.

Experiment E2 is used to test the effect of the linear shape of afeeder dyke on the three-dimensional development of sills andsaucer-shaped sills. The experiment E2 suggests that when the linearfeeder dyke is long, i.e. the inlet size-to-depth ratio is large (L/D=4),the resulting intrusion is an elliptical saucer-shaped sill (Fig. 7b). Inaddition, the long axis of the elliptical saucer in experiment E2 wasparallel to, and located directly above, the linear inlet (Fig. 7b). Thus,experiment E2 represents strong evidence that a linear feeder with alarge size-to-depth ratio controls the ellipticity of the sill intrusion.Moreover, in E2, the position of one tip of the inner sill directly aboveone tip of the linear inlet (Fig. 7b) strongly suggests that the feederalso controls the exact location and extent of the sill.

In more detail, the elliptical sill produced from experiment E2exhibits an asymmetric appendix rooted at the tip of the short axis ofthe elliptical sill. Pollard and Johnson (1973) and Goulty and Scho!eld(2008) showed that stresses generated around elliptical sills arehigher at the tips of short axis than at the tips of the long axis of anelliptical sill. This leads to the formation of lateral inclined sheetsrooted at the tips of the short axis of the elliptic sills, such as in E2. Inaddition, the theoretical study of Bunger (2005) shows that whennear-surface fractures grow, they reach a critical size fromwhich theybecome unstable and develop asymmetrical shapes. We suggest thatthis asymmetrical appendix formed as a result of such mechanicalinstabilities.

In experiment E1, the punctual feeder was located off the centre ofthe circular inner sill (Fig. 7a). This was also the case for theexperiments described by Galland et al. (2009), for which L/D$1; insome of them, the feeder was even close to the rim of the sill. In theseexperiments, the resulting intrusions were always circular althoughthe location of the feeder and the ratio L/D varied. This shows thatwhen L/D$1, the feeder was so small with respect to the depth ofinjection that its location, size and shape had no in"uence on the !nal

shape of the sill. Therefore, if a small dyke feeds a deep sill, (L/D$1),the resulting sill may develop a sub-circular shape. We thus concludethat the occurrence of sub-circular saucer-shaped sills does not implythat their feeders are pipes, but that they can be dykes which lengthsare smaller than the depth of emplacement. The feeders of the sub-circular saucer-shaped sill observed in the Karoo Basin (see Fig. 1 ofGalland et al., 2009) may thus be small dykes.

4.2. Implications for the GVSC

We showed above (see also Galerne et al., 2008; Polteau et al.,2008a) that some sills of the GVSC are in contact (GVS and MSS atlocation L4, Fig. 8a; GS andMSS at location L7; GS and HS at location L8;Fig. 2). However, the geochemical data show that the magmas of thesesills originate from different magma batches, implying that thesecontacts are not feeding connections. Therefore, we do not have anyevidence of sill-feeding-sill relationships in the GVSC. Instead, the AMSanalyses and macroscopic "ow indicators of the major sills in the GVSC(Polteau et al., 2008a) imply that the magma "owed outward from thecentre of the sills. The feeders of the sills were thus located underneaththeir inner sills. The feeders could either be pipes, the inclined sheets ofan underlying sill (Polteau et al., 2008a), or dykes.

Our experiments show that in an isotropic state of stress a long linearfeeder (dyke) gives rise to an elliptical sill. This suggests that theelliptical sills of the GVSC are fed by linear feeders. In addition,experiment E2 shows that the tips of the linear feeders are likely to belocated below the tips of the inner sills, though these former can extendfurther (Fig. 7b). Therefore, if the feeders of these elliptical sills can beobserved in the !eld, we expect to !nd them at the vicinity of the tips ofthe sills. Indeed, we did !nd a dyke (d4) that ful!ls the criteria for beingthe feeder of the GVS: it crops out underneath the southern tip of theGVS, it strikes parallel with, and is located directly below the long axis ofthe GVS (Figs. 2 and 4a–b), and its geochemical composition is identicalto that of the GVS dolerites (Fig. 5). There is thus good evidence that the

Fig. 7. a. Topographic map view of the intrusion of experiment E1 (punctual inlet). The white straight line locates the cross-section underneath. The black circle locates the circularfeeder below the inner sill. The intrusion is a saucer-shaped sill with sub-circular inner sill (white dashed line). The scales of themap and colour bar are inmillimetres. b. Topographicmap of the intrusion of experiment E2. The horizontal white straight line locates the cross-section underneath. The vertical bold black line locates the linear feeder. The intrusion is asaucer-shaped sill with elliptical inner sill (white dashed line); its long axis located directly above the feeder dyke. In both cases, the horizontal net was a much larger square(30!30 cm) than the intrusions, so that we did not report it in this !gure.



dyke d4 is the feeder to the GVS and that the elliptical shape of the sill iscontrolled by the strike and extent of d4.

One major concern is that there is no evidence of potential feederdykes at the tips of the other elliptical sills of the GVSC. Nevertheless,our experiment E2 shows that a feeder dyke is essentially locatedunder the inner sill, although it can extend merely longer than thelong axis of the inner sills (Fig. 7b). Because the inner sills in the GVSCare not eroded, their feeders remainmainly hidden. This explains whywe did not observe potential feeders for the other sills of the GVSC.

Anothermajor concern is the small size of the dyke d4 (~1 m thick;Fig. 4c). Can this dyke feed a sill as large as the GVS? Experiment E2suggests that the length of the long axis of the inner sill is almost thesame as the length of the feeder dyke. The exposed part of the dyke d4at the southern end of the GVSmay represent only the tip of the feederdyke. Thus, d4 may be much wider beneath the central part of the sill.If we assume that d4 is as long as the long axis of the GVS its lengthshould be 20 km. Magma velocity estimates for ma!c dykes rangebetween 0.1 and 1 m s#1 (e.g., Spence and Turcotte, 1985; Battagliaand Bachèlery, 2003; Roman et al., 2004). Given such parameters, thetime for a 1 m thick dyke such as d4 to feed the GVS, which length,width and thickness are 20 km, ~10 km, and ~100 m, respectively, isbetween ~12 and ~115 days. These values are typical for the durationof eruptions in basaltic shield volcanoes, e.g. at Piton de la FournaiseVolcano, Réunion Island, France (see review by Peltier et al., 2009), orat Etna, Sicily, and Mauna Loa, Hawaii (Bebbington, 2008).

Experiment E2 shows that a linear feeder dyke can generate anelliptical sill with a feeder size-to-depth ratio L/D=4 (Fig. 7b). In theGVS, the estimated depth of emplacement is 1 to 2 km (Polteau et al.,2008a). If we assume that d4 is the feeder to the GVS, the feeder L/Dratio ranges between 10 and 20, which is larger than the value in E2,and so more favourable for elliptical sill formation.

The identical geochemical compositions of the GVS and the GSsuggest that theirmagmasderived froma common source. Galerne et al.(2008) proposed that these sills were connected laterally by their outersills. However, the integrated results of this study suggest that eachelliptical sill of the GVSC was fed by an individual linear feeder locatedbelow. This implies that they are fed from a common reservoir at depth.Our dataset does not allow us to decipher whether such a reservoir is amid- to lower-crustal reservoir or a shallow reservoir, e.g. a deepersaucer-shaped sill. Thus, we cannot de!nitely rule out a sill-feeding-silltype of connection.

It is well known that anisotropic horizontal stresses control theorientation and the shape of magma conduits (e.g., Hubbert andWillis, 1957; Odé, 1957; Muller and Pollard, 1977; Vigneresse, 1995).Such stresses may have in"uenced the orientations of some dykes inthe GVSC area, as well as the shape of the elliptical sills (Trude, 2004;Goulty and Scho!eld, 2008). However, the Karoo Igneous Event sealsthe end of the foreland deformation of the Karoo basin, and there areno signi!cant regional tectonic deformation that has affected the

Karoo intrusive and effusive rocks (Catuneanu, 2004). Furthermore,many of the Karoo saucers are circular (see Fig. 1 of Galland et al.,2009). Therefore, we consider the regional tectonic setting to havebeen negligible at the time of the Karoo Igneous Event, i.e. the state ofstress was essentially isotropic. This statement is in good agreementwith the scatter of the orientations of minor dykes in the GVSC(Fig. 2). We infer that the elliptic shapes of the sills of the GVSC werenot controlled by any anisotropic regional state of stress but bydifferent orientations of their feeder dykes.

4.3. Implications for sill emplacement mechanisms

The existing models for saucer-shaped sill emplacement implydistinct magma "ow patterns (Fig. 1). In the buoyancy-controlledemplacement model, the feeders are expected to be located beneaththe outer sheets, resulting in lateral magma "ow (e.g. Francis, 1982;Goulty, 2005). In contrast, in the laccolith model controlled bydiscontinuities of the country rock, the feeders are expected to belocated below the inner sill, resulting in lateral upward and outwardmagma "ow (e.g. Pollard and Johnson, 1973; Malthe-Sørenssen et al.,2004; Galland et al., 2009). In the GVSC, "ow indicators show thatmagma "ow pattern was radial, implying that the feeders of the largesills were located beneath their inner "oors (Polteau et al., 2008a).This is consistent with the location of the dyke (d4) identi!ed as thefeeder of the GVS. In contrast, we have no evidence of feeders locatedbelow the outer limbs of the saucer-shaped sills. Thus, our studysupports the laccolith model for sill emplacement. However, we haveno evidence in favour of the “neutral buoyancy” model.

As cited above, some authors argue that large sill complexesrepresent interconnected sill networks (Hansen et al., 2004; Cart-wright and Hansen, 2006). This assumption mostly results from theinterpretation of seismic 3D imaging, in which sills emplaced atdifferent stratigraphic levels appear to be physically connected,forming sill-feeding-sill networks (Hansen et al., 2004). In the GVSC,we observe similar relationships at locations L4, L7 and L8 (Figs. 2–4and 8a). In a seismic 3D image these sill–sill contacts might be takenfor sill-feeding-sill relationships (Fig. 8b). However, the combinationof detailed geological observations and geochemical analyses ofGalerne et al. (2008, 2010) are robust evidence that there is nofeeding relationship between these pairs of sills. Our study does notprovide any evidence of interconnected sill networks. Instead, ourstudy strongly suggests that the GVSC sills were fed by dykes (GVS bythe small dyke d4) located underneath the long axes of their innersills. Such small dykes would most likely be invisible on seismicpro!les. The results from the GVSC have important implications forseismic interpretation of large sill complexes: contacts between sillsdo not necessarily represent feeding relationships (Fig. 8b).

In contrast to the sill-feeding-sill model, three-dimensional lobatemorphologies imaged on seismic data have been interpreted as

Fig. 8. a. Geological cross section of the southern part of the Golden Valley Sill and the underlyingMorning Sun Sill (along B–B1 in Fig. 3). Although there is a physical contact betweenthe two sills, their different geochemistry shows that the MSS was not the feeder of the GVS. b. Example of seismic image showing contact between two saucer-shaped sills,interpreted as feeding relationship (modi!ed after Hansen et al., 2004). The comparison between this image and the geological cross section of the GVSC show remarkablesimilarities. Because our study shows that contacts between sills are not obviously feeding relationships, we propose another interpretation where each sill (highlighted in red andpurple) may represent a distinct batch of magma. Thus, in order to infer the nature of these contacts on seismic images, more criteria are needed.



channels where magma "ows outwards from central feeders, some ofwhich have been identi!ed as dykes (Thomson and Hutton, 2004;Thomson, 2007). The observations collected in the GVSC are in goodagreement with this interpretation: (1) the radial undulationsobserved in the limbs of the GVS, interpreted as magma channels,are parallel to other "ow-indicators (Polteau et al., 2008a); and (2)the radial undulations of the GVS indicate a radial "ow of magma,which is consistent with a central feeder (dyke d4). Therefore, thedata collected in the GVSC validate the use of lobatemorphologies andundulations in sills as magma "ow indicators.

5. Summary and conclusions

The main conclusions of our !eld observations, geochemicalanalyses and experimental modelling on the three-dimensionalrelationships between saucer-shaped sills and their feeders aresummarised in the following points:

1. In the GVSC, we identi!ed physical contacts between some of themajor sills (the roof of one sill in contact with the "oor of theoverlying sill). However, geochemical contrasts show that thesecontacts do not represent sill-feeding-sill relationships. Our studythus shows that a physical connection between two sills does notnecessarily imply a sill-feeding-sill relationship.

2. Magma "ow indicators in the GVSC sills, i.e. (1) radial undulations ofthe limbs of the GVS, and (2) AMS data (Polteau et al., 2008a),indicate that the magma "owed radially from the centres of the sills.

3. We identi!ed 4 minor dykes in the GVSC. One dyke, d4, hasidentical chemical characteristics to the Golden Valley Sill (GVS); itis located right below the southern tip of the GVS, and is paralleland superimposed on the long axis of the GVS.

4. The geometrical and geochemical relationships between the GVSand the dyke d4 suggest that this dyke was the feeder of the GVS.

5. To test this hypothesis, we resorted to experimental modelling. Themodels show that a sill fed by a punctual feeder develops a sub-circular saucer shape, whereas a sill fed by a long linear feeder (adyke) develops an elliptical saucer geometry.

6. The relationships between the elliptical sill and its linear feeder inexperiment E2 are very similar to those between the GVS and thedyke d4. This shows that d4 may be the feeder of the GVS. Theexperimental results also suggest that the other elliptic sills of theGVSC were fed by dykes.

7. The consistency between the radial magma "ow indicators in theGVS, based on AMS data and on the orientation of magma channels(Polteau et al., 2008a), and the central location of the feeder dyked4 con!rms that the lobate and tubular structures imaged onseismic data (see e.g., Thomson, 2007) are good criteria fordetermining sill feeding processes.

Acknowledgements

This study was supported by a Centre of Excellence grant from theNorwegian Research Council to PGP. This work was also partly fundedby the Norwegian Research Council (NFR project 159824/V30“Emplacement mechanisms and magma "ow in sheet intrusions insedimentary basins”) and by the Norwegian Young OutstandingResearcher (YFF grant 180678/V30 “Processes in volcanic basins andthe implications for global warming andmass extinctions”). We thankB. van Wyk de Vries, J. Cartrwight, G. Norini, T. Menand, O. Merle, A.Guerer, and V. Acocella for their constructive reviews.

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