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Journal of Petrology | Volume 44 | Number 11 | Pages 1961-1976 | 2003
© Oxford University Press 2003; all rights reserved
The Traigh Bhàn na Sgùrra Sill, Isle of Mull: Flow Localization in a Major Magma Conduit
DEPARTMENT OF EARTH SCIENCES, UNIVERSITY OF CAMBRIDGE, DOWNING STREET, CAMBRIDGE CB2 3EQ, UK
* Corresponding author. E-mail: marian{at}esc.cam.ac.uk
RECEIVED SEPTEMBER 2, 2002; ACCEPTED APRIL 25, 2003
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ABSTRACT |
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Field evidence points to localization of magma flowing in a Tertiary doleritic sill on the Isle of Mull, Inner Hebrides, Scotland. Regions of the sill in which flow was short-lived have chilled margins, a narrow or absent metamorphic aureole, and alignment of plagioclase crystals resulting in pronounced, flow-parallel, lineations on fracture surfaces (Type I regions). Prolonged flow resulted in blocky, coarse-grained dolerite with no chilled margins, and an extensive metamorphic aureole (Type II regions). The distribution of Type I and Type II regions shows no spatial pattern, with stagnant solidifying sections immediately adjacent to sections with contemporaneous active and sustained flow. The transition between Type I and Type II regions occurs as the sill thickness exceeds 3·5 m. Our observation that sustained flow was only possible in regions of the sill thicker than 3.5 m is consistent with previously published theoretical models which predict a critical sill thickness in the range 2·2–5 m. Regions of the sill narrower than this experienced a single injection of magma. Simple models to determine flow duration from the width of the metamorphic aureole demonstrate that progressive focusing of flow into wider parts of the conduit created discrete channels active for up to 5 months.
KEY WORDS: flow localization; magma; Mull; sill; Traigh Bhàn na Sgùrra
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INTRODUCTION |
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Fluid flow in planar conduits is an important geological phenomenon, with examples ranging from H2O-dominated fluids in fault systems (e.g. Sibson, 2000
), to the movement of magmas to form planar intrusions and feed crustal plutons or lava flows (e.g. Delaney & Pollard, 1982). Such flow phenomena are complex because of the exchange of heat and mass between the fluid and the rocks forming the fracture walls. This is particularly important for systems with significant heat transfer between the fluid and wall-rock, i.e. the flow of magma in fractures.
Many attempts have been made to understand the problems associated with such flows using simplified theoretical models (e.g. Delaney & Pollard, 1982; Huppert & Sparks, 1985, 1989; Lister, 1995; Lister & Dellar, 1996) with application to the problem of understanding the development of fissure eruptions. However, there has been little work done on applying the results of such models to exposed examples of solidified conduits. In this paper we present the results of a study of a well-exposed dolerite sill and its contact aureole, relating observations of textural development to flow localization and flow duration in the sill. Such a study permits the testing of various hypotheses arising from previously published theoretical models.
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PREVIOUS WORK |
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Magma ascending through planar conduits in the Earth's crust transfers heat by conduction into cooler country rock. In the early stages of flow, heat exchange between magma and country rock causes magma temperatures adjacent to the walls to be reduced below the solidus, with the resultant formation of a glassy chilled margin (Delaney & Pollard, 1982
; Lister, 1995). The chilled margin may grow at a rate dependent on factors such as fracture width, magma flow rate, temperature difference between magma and host rocks, distance from source, and the temperature dependence of magma viscosity (Delaney & Pollard, 1982). Huppert & Sparks (1985) showed that continued flow of magma may result in melting of this early-formed chill zone. This is because the heat flux owing to conduction into the wall-rock decreases as the walls become hotter, and it may eventually become lower than the advected heat flux from the flowing magma. Complete melting of the chill zone will lead to the development of a coarse-grained, intrusive contact. This is expected to occur most quickly for turbulent flows, as the heat transfer into the walls is much greater than that for laminar flows, in which heat loss is entirely by conduction (Huppert et al., 1984). Incomplete melting of the chill zone may lead to the development of internal contacts (Huppert & Sparks, 1989).
An extension of these theoretical models was applied to the localization of magma eruptions within vertical fissures observed in Hawaii (e.g. Richter et al., 1970) by Bruce & Huppert (1990). They showed that if the advected heat flux consistently exceeds the conductive heat flux, progressive widening of the fissure occurs by melting of the walls. In contrast, if conductive heat losses into the wall-rock dominate the heat budget, solidification causes cessation of flow (Bruce & Huppert, 1990). A dyke whose initial width is close to some critical value may become blocked in some places and widened in others, leading to localization of flow into discrete channels within a partially blocked conduit (Bruce & Huppert, 1990; Lister, 1995). Lister & Dellar (1996) related this result to a critical Peclet number that determines whether a flow ultimately blocks by solidification, or widens by melting its margins. A further development of these ideas by Wylie et al. (1999) demonstrated that the effect on flow localization of solidification as a result of heat loss is minor compared with that of the increase in viscosity during cooling. They showed that, for slow-flowing magma, the onset of a flow instability results in development of hot, fast-flowing channels forming in an otherwise cool and stagnant conduit. A consideration of time-scales for the development of this instability shows that it is a plausible mechanism for observed flow localization in fissure eruptions (Wylie et al., 1999).
These theoretical models provide a series of hypotheses that can be tested by observation of now-solidified intrusions exposed at the Earth's surface. For laminar flow, which dominates most basaltic eruptions (e.g. Delaney & Pollard, 1982), the rate of heat transfer to the wall-rock may not be sufficient to create a contact metamorphic aureole around the conduit. Nevertheless, if an aureole is present, it provides an opportunity to constrain the heat flow into the conduit walls, and thus the flow duration. Textural information from the solidified intrusion may provide further information on the heat-flow history and the flow regime (either turbulent or laminar) within the conduit. Such an opportunity is provided by the Tertiary Traigh Bhàn na Sgùrra sill, Isle of Mull, Inner Hebrides, which was a major conduit for magma flow (Wartho et al., 2001; Holness & Watt, 2002).
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GEOLOGICAL SETTING |
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The Loch Scridain Sill Complex (LSSC) is a suite of high-level, inclined, Tertiary, sheet-like intrusions that crop out along the south coast of the Isle of Mull (Fig. 1). The intrusions vary in composition from basic to acidic, and were intruded predominantly into Palaeocene lavas. Some sills intrude Precambrian Moine Schists and Mesozoic metasediments.
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The LSSC has been studied intensively (e.g. Preston, 1996
; Preston et al., 1998, 1999) and is believed to have formed by the intrusion of magmas from shallow magma chambers beneath the central complex on Mull, in which assimilation of the Moine metasedimentary country rock accompanied fractional crystallization (Preston et al., 1998). The sills of the LSSC contain abundant xenoliths of partially melted metasediments and cognate gabbroic to ultrabasic xenoliths from the base of the fractionating chambers. The sills of the LSSC range in thickness from 1 to 14 m. In most places they have sharply chilled margins with little or no metamorphism evident in the walls. Locally, the sills have a coarse-grained margin associated with the development of an extensive contact aureole (Kille et al., 1986; Preston et al., 1999; Wartho et al., 2001; Holness & Watt, 2002). At Traigh Bhàn na Sgùrra, a dolerite sill is emplaced into steeply dipping to sub-vertical Moine pelites and psammites (Fig. 1). Sill thickness varies from 2·5 m to >10 m, although for most of its outcrop it is 3–4 m thick. The gently dipping contacts of the sill define a shallow, elongate, bowl, with its lowest point SE of Scoor House (Fig. 2). The contacts everywhere truncate the metasediments at a high angle. A prominent nose is developed on the promontory Port na Mean-faochaige, where the sill has a well-defined edge (Fig. 3).
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The sill is composed of olivine-poor or olivine-free tholeiitic dolerite; groundmass plagioclase shows a compositional range between An66 and An56 (Preston et al., 1998
). The other main constituent is augite, which occurs as ophitic grains surrounding plagioclase laths and is commonly associated with Fe–Ti oxides. Phenocrysts (<3 vol. %) of plagioclase are rare.
Kille et al. (1986) suggested that the local absence of chilled margins and the presence of a wide contact aureole indicated a high heat flux into the wall-rock, consistent with locally turbulent magma flow. Wartho et al. (2001) showed, using Ar diffusion in micas in pelitic wall-rock at Locality A (Fig. 2), that the heating of the walls could not have been caused by an instantaneously emplaced sill. They calculated that active flow within the conduit lasted 5–6 months. The metamorphic reactions in the aureole at this locality are also consistent with a 5 month flow duration (Holness & Watt, 2002).
We report further observations and mapping of the Traigh Bhàn na Sgùrra sill and show that flow was highly localized within the conduit, with active channels of prolonged flow alternating with regions of little or no sustained flow. We suggest that the Traigh Bhàn na Sgùrra sill probably represents the shallow roots of a now solidified conduit feeding a fissure eruption, in which localization of flow took place during its 4–5 month lifetime.
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SAMPLING AND METHODS |
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The thickness of both sill and aureole (defined by the position at which breakdown of muscovite is visible in the pelitic metasediments at hand-specimen scale) was measured to within a few centimetres at closely spaced localities along the length of the sill outcrop. Muscovite breakdown is evident in the field as the development of a dull pink colour to the previously shiny grey mica grains, but at Locality A this is apparent in thin section some 20 cm further from the contact than the point at which it first becomes visible in hand specimen (Holness & Watt, 2002
). The distance at which it is visible using a transmission electron microscope is further away still (Brearley, 1986). This dependence of detected position of the reaction on the scale of observation introduces a significant error in aureole width determinations. From the profile of Holness & Watt (2002), a field-based aureole width measurement of 3·5 m corresponds to a width of 4·0 m determined from thin-section observations. Using this, we assigned an error bar of 14% to all other field-based measurements of aureole widths. Note was taken of the presence or absence of chilled margins and their thicknesses. Oriented samples were collected every 10–20 cm in a series of vertical profiles across the sill and its host rocks (see Fig. 2 for locations). Distances from the sill margin were measured to the nearest few centimetres.
Image analysis of digital photomicrographs was performed using the public domain NIH Image program on a Macintosh computer (developed at the US National Institutes of Health and available on the Internet at http://rsb.info.nih.gov/nih-image/). Lengths of plagioclase crystals were used both to determine the average grain size of each sample, to constrain the crystal size distribution (CSD; Marsh, 1988), and to determine the degree of alignment of crystals. Between 150 and 350 crystals were measured for each sample. The major errors in determining the characteristics of crystal populations are the difficulty in detection of the smallest crystals, and correction for their three-dimensional (3D) shape and preferred orientation. Conversion of the two-dimensional (2D) measurements to the correct 3D size for the CSD was made using the method of Higgins (2000) assuming a plagioclase aspect ratio of 1:3:5. No correction was made of measurements of 2D crystal lengths for the determinations of the average grain size. No correction was made for any preferred alignment, although in certain samples a circular variance as low as 0·6 was measured.
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FIELD RELATIONS |
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Metamorphic aureole
The edge of the thermal aureole at Traigh Bhàn na Sgùrra is visible in outcrop as the onset of muscovite breakdown. This is not always evident east of Traigh Bhàn na Sgùrra, where the country rock is either the psammitic Lagan Mor Formation or Upper Shiaba Psammite (Fig. 1), neither of which contains appreciable muscovite. In these lithologies the limit of the contact aureole is difficult to define in the field. Details of the reactions in the contact aureole at Locality A have been given by Holness & Watt (2002)
, and a summary is provided here.
The onset of metamorphism in psammitic lithologies is marked by replacement of muscovite by biotite, K-feldspar, spinel, corundum and aggregates of mullite needles (Brearley, 1986). Reaction initiates along cleavage planes. The next reaction is melting of quartz and feldspar in the presence of H2O released during breakdown of mica. Closer to the sill, reacted muscovite grains are replaced by a fine-grained mullite aggregate surrounded by a thick, polycrystalline feldspar rim. Clusters of euhedral, pinitized cordierite nucleate in the central parts of the muscovite pseudomorphs and all feldspar grains are surrounded by thick, granophyric rims indicating H2O-absent melting on quartz–feldspar grain boundaries. The reaction nearest the contact is the inversion of quartz to tridymite, evident as plate-like quartz paramorphs after tridymite in the melt rims.
In the pelitic lithologies, muscovite breakdown is also the lowest temperature reaction. Thick, granophyric rims on quartz–feldspar grain boundaries as a result of H2O-absent melting develop at the same time as the original biotite grains are replaced by smaller, red– brown biotite grains oriented parallel to the original lattice. A significant increase in the amount of melt is related to the replacement of biotite by aggregates of spinel, ilmenite and magnetite. At higher grades still, garnet is replaced by hercynitic spinel, pyroxene and plagioclase, and the reacted muscovite grains are replaced by radiating mullite needles and spinel aggregates. At the contact, the amount of melt is estimated as 70 vol. %, with a few remaining polycrystalline quartz aggregates.
Type I and Type II characteristics
In the field, two distinct sets of characteristics can be distinguished within the sill itself. Type I regions have well-developed chilled margins, which may be glassy, with a clearly defined increase in grain size towards the centre of the sill. Locally the chilled margin shows a layered structure in thin section, with grain size coarsening slightly towards the top of each layer. The sill is well jointed and tends to fracture along planar or sub-planar surfaces sub-parallel to the sill margins. Pristine muscovite is generally present immediately adjacent to the contact. Although a narrow aureole may be developed, the (field-determined) width never exceeds 0·65 m. Metasedimentary xenoliths are locally present but cognate xenoliths are absent. A striking feature of this facies is the common presence of lineations on the planar fractured surfaces. These lineations form 
1 cm wide, flat-topped, parallel-sided ridges a few millimetres high (Fig. 4). They are seen only in the centre of the sill, and never on the margins.
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Regions of the sill with Type II characteristics have no chilled margins. Instead, the contact with the country rock is coarse grained, often irregular and poorly defined, with pronounced weathering. The sill is massive and blocky with poorly defined jointing. Both metasedimentary and cognate xenoliths are common, as isolated blocks or as accumulations at the top and base of the sill. An aureole is invariably well developed, reaching thicknesses of up to 3·5 m. The lineations so prevalent in Type I regions are generally absent, although in two places poorly defined, widely spaced lineations are present.
Contact-parallel layers of vesicles, up to 12 mm in diameter, are occasionally observed within both Type I and Type II regions.
Sill thickness and aureole thickness
Figure 5 shows the relationship between measured sill thickness and the width of aureole, with distinction made between Type I and Type II areas. Because of compositional constraints, aureole width was obtainable almost exclusively in the pelites of the Ardalanish Striped and Banded Formation and the Scoor Pelitic Gneiss.
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The data from the two types fall into two distinct fields in terms of sill thickness and aureole thickness. A sharp transition between Type I and Type II regions occurs at a sill thickness of
3·5 m. There is also a distinct boundary between types in terms of aureole width: Type I regions do not develop aureoles wider than 0·65 m, whereas Type II areas invariably have aureoles wider than 1·4 m. The spatial distribution of the two types (Fig. 2) shows no obvious pattern.
Cognate xenoliths
Cognate xenoliths in the Traigh Bhàn na Sgùrra sill are spherical to sub-spherical and up to 0·4 m in diameter. The xenoliths are regressively weathered, coarse grained (2–3 mm) and olivine rich, varying from feldspathic peridotite with cumulus olivine, to gabbro (Preston & Bell, 1997). From major and trace element data and Sr–Nd isotope data, they are inferred to represent cumulate portions of the same magma chamber that supplied the Traigh Bhàn na Sgùrra flow (Preston & Bell, 1997). They are found only in regions of the sill exhibiting Type II characteristics and tend to cluster within the basal metre of the conduit, although not actually at the base.
Metasedimentary xenoliths
Abundant metasedimentary xenoliths are found within Type II regions of the sill, and rarely within Type I regions. These xenoliths are predominantly psammitic, with angular edges, and in the psammitic country rock are commonly found just below the upper wall of the conduit (Fig. 6). The xenoliths have been removed from the conduit walls as coherent blocks, in a process of mechanical erosion, aided by pre-existing fractures and joints in the walls. The rarer pelitic xenoliths have undergone extreme partial melting (Preston et al., 1999). Estimates that 10–15% contamination of the flow occurred by assimilation of country rock during fractional crystallization (R. J. Preston, personal communication, 2002) suggest that other pelitic xenoliths may have been completely consumed.
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Where the sill reaches its maximum thickness (in the vicinity of Locality A, Fig. 2), abundant metasedimentary xenoliths are concentrated into clast-supported, lens-shaped masses at the upper boundary of the sill (Wartho et al., 2001
). The relatively low-density xenoliths are thought to have floated to the top of the conduit and accumulated there as the flow waned (Kille et al., 1986). |
GRAIN-SCALE TEXTURES IN THE SILL |
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 TOPABSTRACTINTRODUCTIONPREVIOUS WORKGEOLOGICAL SETTINGSAMPLING AND METHODSFIELD RELATIONS GRAIN-SCALE TEXTURES IN THE... FLOW REGIME IN THE...FLOW LOCALIZATIONSUMMARY AND CONCLUSIONSREFERENCES |
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The average grain size of plagioclase crystals was determined as a function of position within the sill across each of three perpendicular traverses of the sill. The first (Traverse X) was taken across a 3·1 m wide region of the sill with a well-developed chilled margin and no aureole (Type I). The second (Traverse Y) was taken across a 3·25 m wide region with a well-developed chill and an aureole 0·65 m wide. This also belongs to Type I. The final traverse (Traverse Z) was taken across a 3·5 m wide region of the sill showing the coarse-grained margin and wide contact aureole that are characteristic of Type II.
Average grain size (as observed in thin section, i.e. uncorrected for 2D sections through 3D crystals) is plotted as a function of height in the sill in Fig. 7. There is a clear distinction between types. The part of the sill with Type II characteristics (Traverse Z) shows a generally coarser grain size and much less variation in average grain size with position in the sill than the parts of the sill with Type I characteristics (Traverses X and Y). Traverse Z also shows a smooth variation in average grain size with distance across the sill, forming a parabolic profile. For Traverses X and Y the average grain size shows a greater scatter from a parabolic profile, which itself is much more pronounced than that developed in Traverse Z. It is slightly asymmetrical with coarser grain size near the base of the sill. The maximum grain size reached by the Type I profiles is similar to the minimum Type II grain size, despite a similarity in sill thickness.
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Orientations of plagioclase laths were measured in thin section for the same three traverses. The circular variance (a measure of the departure of a population of orientations from a single orientation) is shown in Fig. 8 as a function of position within the sill. A circular variance of zero signifies that all grains are aligned, whereas a variance of one signifies completely random orientations. The extent of alignment is generally very low across the Type II traverse, with a slight increase in alignment near the margin. The same pattern is observed in Traverse Y (Type I with a small aureole). However, Traverse X (Type I) shows a relatively strong alignment, even within the central part of the sill.
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The extent of crystal alignment within a strongly lineated Type I sample was investigated. Three mutually perpendicular sections were examined. In the plane perpendicular to the lineated surface, but parallel to the lineations themselves, the rock contains distinct partings
5 mm apart. These partings form 1 mm thick regions of strongly aligned plagioclase crystals with circular variance of 0·45. Between these partings the circular variance averages 0·68, the larger crystals being more strongly aligned. A plagioclase alignment with circular variance of 0·79 occurs in the plane of the lineated surface, whereas in the plane perpendicular to both the lineated surface and the lineations themselves, the plagioclase crystals are only poorly aligned (circular variance 0·90). The lineations therefore represent elongate chains of well-foliated crystals. The macroscopic orientation of the lineations is thought to represent magma flow direction and can be mapped throughout the sill (Fig. 2).
Further information can be obtained from an analysis of the CSD within the solidified intrusion. Quantification of crystal growth and residence times is possible from analysis of the CSD. Following Marsh (1988), using the method of Higgins (2000), the population density, n, for plagioclase crystals in the sill, was calculated from L (the crystal length) and the measured number of crystals in any length group. A plot of ln(n) vs L can then be used to constrain one of either plagioclase growth rate, G, or growth duration, 
, as the slope of a straight line is given by -(G)-1. Figure 9a shows the distribution of sizes of plagioclase phenocrysts in the glassy chilled margin of the sill at Traverse X (Type I). The CSD plot is concave-upwards, suggestive of two distinct populations of phenocrysts in the magma on eruption (see Higgins, 1996a, 1996b). This may indicate magma mixing or accumulation of large crystals by crystal settling. Two straight lines fitted to the data yielded residence times in the magma chamber of 14–44 years for the population of smaller crystals and 87–260 years for the population of larger crystals, using a plagioclase growth rate of 1 x 10-10 to 3 x 10-10 mm/s (Cashman, 1992, 1993; Higgins, 1996a, 1996b; Cashman & Marsh, 1988). This compares with the residence times of 6–13 years and 24–96 years calculated for a dacite from Thera (Higgins, 1996a), and of 30–75 years for Mt. Taranaki, New Zealand (Higgins, 1996b).
The CSDs for two samples from the central part of the sill at Traverse X are shown in Fig. 9b, with the CSD from the central part of Traverse Z (Type II) for comparison. No corrections were made for crystal alignment in the Type I samples. The two Traverse X samples, spaced 20 apart, are the most coarse-grained samples collected from the traverse, with the greatest extent of mineral alignment. The two samples were collected from 190 cm and 170 cm from the base of the sill, and have circular variance of 0·59 and 0·75, respectively. The two CSDs are very similar, and lie on a straight line, with G 
0·20, indicating a single crystal population, and no apparent effect of the difference in crystal alignment. The CSD from Traverse Z is distinct, with fewer smaller crystals and a shallower slope, with G 0·29. Because the wall-rocks of Type II regions were significantly hotter than those in Type I regions, it is unlikely that the shallower slope reflects a faster growth rate. The undercooling was likely to have been less in Type II regions, and so the associated growth rate is likely to have been slower. We consider that the difference in CSD is primarily due to a longer time available for crystal growth in Type II regions.
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FLOW REGIME IN THE SILL |
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The existence of differing flow regimes in the sill is one possible explanation for the distinct distribution of characteristics between Type I and Type II. Kille et al. (1986)
suggested that the regions of the sill with no chilled margin and a wide contact aureole (our Type II) were those in which flow was turbulent. However, theoretical models predict that these features could also be found around a solidified magma conduit in which flow was laminar, provided that flow was sufficiently prolonged to result in both melt-back of the early-formed chill and significant heating of the conduit walls (e.g. Huppert & Sparks, 1985; Bruce & Huppert, 1990; Lister & Dellar, 1995). Information about the flow regime can be obtained from grain-scale textures and calculations of Reynolds number.
Grain-scale characteristics
Characteristics of the Type I margins are consistent with a short-lived, laminar flow regime. The laminar flow initially creates a parabolic temperature profile (Kay & Nedderman, 1985) because of more rapid cooling near the margins, leading to a strong dependence of grain size on distance from the contact. Shearing of the magma results in foliation and alignment of plagioclase laths suspended in the flow, indicating that crystallization in the centres of the sill started before cessation of flow. This is consistent with a rapid cooling rate.
In the case of Type II, a distinction between laminar and turbulent (or transitionally turbulent) flow is not so straightforward. Although the absence of chilled margins and the much coarser grain size are consistent with the greater heat flow associated with turbulent flow, they could also be a consequence of prolonged laminar flow. The coarser grain size compared with Type I regions demonstrates a longer period of crystallization, consistent with prolonged heating of the wall-rocks. As the crystal load is unlikely to vary between Type I and Type II regions, the absence of alignment or foliation of plagioclase in the latter is consistent with solidification occurring in static magma, after cessation of flow, consistent with slow cooling rates.
Reynolds number for the flow
The Reynolds number for a Newtonian fluid in a parallel-sided conduit of half-width h is given by
 | (1) |
 | (2) |
 | (3) |
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Using the parameter values given in Table 1, with the range of
P/z of 460–1400 Pa/m used by Wartho et al. (2001), values of Re and associated mean flow velocities calculated using equations (2) and (3) are shown in Table 2.
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Re is highly dependent on
P/z, the pressure gradient driving the flow, which is poorly constrained. The values we used are based on an initial excess pressure in the magma chamber, P0, of (2·9 ± 0·6) x 107 Pa (Wartho et al., 2001), which is greater than accepted values for rock strength (5–10 MPa). However, recent theoretical studies (Pinel & Jaupart, 2000; Pinel, 2002) indicate that magma overpressures may be considerably greater than the tensile strength of the host rocks, as a result of the compressive stress imposed by a surface load such as a shield volcano. As Mull was a shield volcano, this high value of P0 is perhaps plausible, but gives us values of Re that are almost certainly at the high end of the plausible range. Therefore the very narrowest width at which transitional turbulence would occur in the sill is about 4 m. As the pressure gradient driving the flow will decrease exponentially on emptying the magma chamber (Stasiuk et al., 1993), Re will decrease during the eruption. This means that any early turbulent flow would evolve to laminar as the eruption progressed, and may therefore have accounted for only a short period in the early stages of flow.
Summary
The textures of Type I regions are consistent with laminar flow with crystallization occurring during flow. The textures in Type II regions are consistent with prolonged flow (either laminar or turbulent), resulting in considerable heating of the wall-rock, which meant that crystallization occurred slowly once flow had ceased. The calculated values of Re are consistent with laminar flow in the narrower parts of the sill, with transitional turbulence possible in the widest parts during the early stages of the eruption. Thus the difference between Type I and Type II regions cannot be entirely attributed to a difference in flow regime.
The presence of cognate xenoliths only in Type II regions could be simply a result of a short time of active flow in Type I regions (see next section), precluding transport of cognate xenoliths from a chamber thought to be 25 km away (Wartho et al., 2001), or it may be indicative of a significant difference in flow regime in Type II compared with Type I regions. We suggest that some of the Type II regions saw transitionally turbulent flow at least during the early stages. Later laminar flow, as a result of a decrease in flow rate associated with a drop in magma chamber pressures, would then account for the planar arrays of vesicles and the rare occurrences of flow lineations found in Type II regions.
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FLOW LOCALIZATION |
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An alternative explanation for the partition between Type I and Type II characteristics is that of flow localization in the conduit. Flow localization, or flow focusing, has been observed in fissure eruptions, notably in Hawaii (e.g. Richter et al., 1970
). Initially magma is erupted along the entire length of the fissure, but as the eruption continues, the flow is gradually localized to two or three discrete channels. As a record of the flow history is preserved in the metamorphosed wall-rocks, Traigh Bhàn na Sgùrra provides an opportunity to examine flow focusing in a now-solidified conduit.
It is straightforward to determine whether a part of the conduit experienced sustained flow. For a single pulse of intruding magma, taking into account the latent heat of solidification, the maximum temperature at the conduit wall is given by 0·65(T0 + T
) (B. Marsh, personal communication, 2003). The liquidus for the basaltic magma at 1 atm is estimated from its MgO content (Thompson et al., 1986) to be 1125–1175°C (Thompson, 1973). If this magma intruded country rock at 30–120°C (Wartho et al., 2001) the maximum wall-rock temperature would have been 750–842°C. The muscovite-out reaction, which marks the onset of contact metamorphism, is estimated at 610°C (Holness & Watt, 2002). Absence of a contact aureole in Type I, with (apparently) pristine muscovite immediately adjacent to the sill, demonstrates that the temperature of the conduit walls must have remained below 610°C for all but a very short time. This could only have occurred in the absence of sustained magma flow.
The junction between such a stagnant region and one of active flow is visible at GR 4229 1854. Here a section of the sill (2·7 m wide) with a well-defined chilled margin, flow lineations and pristine muscovite in the pelite immediately at the contact (Type I) is juxtaposed with a section of sill (3·8 m wide) with a coarse-grained margin, blocky texture and an aureole 3–3·5 m wide (Type II). At the junction are many small cognate xenoliths, distributed vertically across the entire sill thickness. This locality represents the edge of a channel of prolonged, localized flow, adjacent to a stagnant portion of the flow. The stagnant section (2·7 m wide) solidified very rapidly (i.e. before the walls attained the temperature of the muscovite-out reaction), whereas the wide aureole suggests that flow continued in the channel region for some time. We suggest that the xenoliths were deposited at the vertical contact between a stagnant, and crystallizing, region of the sill and an active channel.
To constrain the duration of flow in the channels (Type II) we can use a simple thermal model to reproduce the observed width of the contact aureole.
Modelling of thermal history
The position of the muscovite-out isograd, as observed in outcrop, was used to fix the point in the aureole at which the temperature reached 610°C. This was then fitted to the profile produced by a two-stage finite-difference thermal model, taking into account the latent heats of fusion of the intrusion and host rocks (which were assumed equal), and setting the melting point of the country rock to 780°C (Holness & Watt, 2002).
In the thermal model used, we assume that the initial chill that formed was eroded on a short time-scale relative to that of the total flow duration (Huppert & Sparks, 1989). For simplicity we therefore ignore this early period of chilling and erosion, and then model the thermal evolution of the flow in two stages. In the first stage, the flow is considered as a homogeneous layer of half-width h. The temperature of the layer is held at 1150°C (the magma intrusion temperature, T0) for the duration of the first stage. This reflects the expectation that early turbulent flow or prolonged laminar flow will heat the wall-rocks almost to the magma temperature, and that this boundary condition will be maintained until flow ceases. The initial boundary conditions for the first stage are thus T = T0 for x 
h, and T = T for x > h. In the second stage of the model, once flow has ceased, the whole system is allowed to cool by conduction. The temperature of the country rock at the beginning of this second stage will be dependent on the distance from the contact, and the duration of the first stage.
This method involves considerable simplifications, not least that cessation of flow will be a gradual process, rather than an instant cut-off. This means that the estimates of flow duration that we produce will be minimum estimates. It should be noted also that because the country rock reaction kinetics are unknown, it is impossible to deduce the temperature at which the muscovite-out reaction was complete. We therefore assumed that the muscovite-out reaction began at 610°C and placed an error bar of 14% on the aureole width.
Figure 10a shows the calculated flow duration (using the values of the parameters given in Table 1) as a function of aureole width. The points define a continuous array with a steadily decreasing positive slope. There is a wide variation in calculated flow duration within the sill, with some parts of the exposed sill experiencing little or no sustained magma flow, whereas flow in other regions may have lasted for up to 5 months. The flow of magma within the sill was therefore strongly focused.
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The maximum flow duration consistent with the survival of a chilled margin depends on the flow regime. For turbulent flows, chilled margins survive for a negligible time, whereas they may survive for a considerable time in laminar flows (Huppert & Sparks, 1985
). Regions of the sill with chilled margins and a contact aureole (e.g. Traverse Y) are those in which sustained laminar flow did not continue long enough to result in chill melt-back. From our model, the flow can continue for at least a day without complete melt-back. Two distinct scenarios can thus be identified in the Traigh Bhàn na Sgùrra sill. During its active lifetime the sill was made up of regions that were completely stagnant within a few days of initial magma injection, adjacent to regions in which active flow was sustained for weeks to months. The stagnant regions correspond to areas with Type I characteristics, whereas the regions of active flow correspond to areas with Type II characteristics.
Pathways of least resistance
In Fig. 10b, the calculated flow duration is shown as a function of sill thickness. This diagram is effectively a remapping of Fig. 5 and shows considerable scatter. Figure 10b also shows a reversal in the positive trend, at sill thicknesses greater than 7 m. The maximum calculated flow duration is approximately 5 months, although some of the widest parts of the conduit appear to have experienced much shorter flow duration. We will return to these points later.
During localization, the preferred pathway for magma flow, and therefore the one that remains active for longest, will be the one that offers the least resistance to flow. In general, this means that the widest channels should be active for longest. However, the pathway of least resistance will not necessarily be the most direct, and may well have localized constrictions or widenings. The Traigh Bhàn na Sgùrra sill essentially represents a 2D view of a complex 3D hydraulic system, and at least some of the scatter in Fig. 10b reflects the influence of the third dimension.
Because the width of the initial crack forming the conduit in Type II regions has undoubtedly been modified by melting and erosion of the walls, the scale of initial variations in crack width is probably reflected by variations in sill thickness in the Type I regions, where erosion will have been insignificant. Figure 5 shows that a minimum width variation of nearly 2 m is plausible. Along-stream width variations are also observed in the field. With reference to the map (Fig. 2), a good example is immediately north of Locality A. Here the sill reaches its greatest thickness of 10 m, with an associated aureole width of 2 m. The outcrop immediately downstream of this (i.e. Locality A itself) has a sill thickness of 7 m and an aureole of 3–3·5 m. Interestingly, the greatest accumulations of psammitic xenoliths are found at Locality A. The rapid change in down-stream sill thickness suggests that the xenoliths accumulated at constrictions in the conduit.
Critical conduit half-width
The observations relating flow duration and sill thickness allow us to test a prediction of a previously published theoretical model, that there exists some critical conduit half-width, hcrit, below which sustained flow is impossible because of solidification of magma in the conduit (Lister, 1995). For rigid-walled conduits in which flow is laminar, hcrit is given by
 | (4) |
). The dominant parameter in equation (4) is P/z, which will decrease exponentially during an eruption (Stasiuk et al., 1993). hcrit will thus increase with time, so that successively wider parts of the sill will solidify, leading to further localization of flow. The increase in hcrit will also be enhanced by increases in viscosity as a result of cooling. This process can be illustrated by recasting the pressure term in equation (4) as P = P0 exp(-Kt) (Huppert & Woods, 2002) where K = (SA2ß)/(HµV).
Equation (4) therefore becomes
 | (5) |
 | (6) |
The form of equation (5) is shown in Fig. 11a, contoured for viscosity. Figure 11a shows that hcrit increases with time, because of the effects of both decreasing chamber pressure and increasing viscosity. The shaded arrows mark the path of hcrit as eruption progresses. Figure 11b shows how hcrit (calculated for a point 25 km from the magma chamber) varies with Kt. The value of K is uncertain because the viscosity µ, the cross-sectional area of the conduit A, and the shape factor S will all change with time. However, the value of hcrit when Kt = 0, hI, should represent the maximum thickness of sill with no aureole (i.e. the critical half-width 25 km from the chamber in the initial stages of the eruption).
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Using values of the parameters given in Table 1, which we consider to be in the middle of the plausible range, and
P0 of 23 MPa, we calculate that sustained flow is possible at Traigh Bhàn na Sgùrra in conduits wider than 5 m (Fig. 11b). This can be decreased to 2·2 m using values at the extreme of the plausible range of the parameters: T = 120°C (Wartho et al., 2001), T0 = 1175°C [from MgO contents given by Thompson et al. (1986), using the 1 atm relationships of Thompson (1973)], Lf = 8 x 105 J/kg (Huppert & Sparks, 1985, 1989), Cp = 750 J/kg per K (Huppert & Sparks, 1985, 1989), µ = 108 Pa s [using the calculations of Shaw (1972) for a temperature of 1175°C], 
= 6 x 10-7 m2/s (Delaney, 1987) and P0 = 29 MPa (Wartho et al., 2001). From Fig. 5, the sill thickness threshold for sustained flow (indicated by the presence of a metamorphic aureole) occurs at 2·7–3·5 m (hI = 1·35–1·75 m). This is well within the bounds of the critical half-width given by the upper value calculated using values of parameters in the middle of the reasonable range of parameter values and the lower value calculated using extreme values of the parameters. This suggests that Type I regions are parts of the sill where the conduit is below the initial critical half-width hI to support sustained flow. Type II regions have an initial crack width greater than hI and sustained flow is possible.
Thermal erosion of the wall-rocks
In the previous section we showed how the width of the conduit has a significant control on flow duration, and hence aureole width. We have already mentioned that some of the considerable scatter in Fig. 10b may be influenced by irregularities in the 3D geometry of the conduit. A further factor that may contribute to the scatter in the relationship between sill thickness and aureole width, and that can account for the reversal in the trend, is thermal erosion during flow.
Theoretical models have shown that magma flow can cause the conduit walls to melt, resulting in progressive widening (e.g. Huppert & Sparks, 1989; Bruce & Huppert, 1990). Once melting has proceeded to the point at which the wall-rock loses all strength [the rheologic critical melt percentage (RCMP) of Arzi (1978) and van der Molen & Paterson (1979)] at about 25–40 vol. %, the wall-rock would start to be eroded by the shearing effects of the flow. The widest parts of the conduit are within pelitic country rock, which is more prone to erosion because of the significant increase in amount of melt associated with biotite breakdown, suggesting that erosion may have been important in controlling final sill thickness. As flow duration is calculated from the observed final aureole width, it will be anomalously low if wall-rock erosion is significantly faster than widening of the aureole by heat conduction, and this could account for the short flow durations calculated for the wider parts of the sill (Fig. 10b).
Flow direction
A general picture of the spatial form of the focusing can be derived using the orientations of the flow lineations that are found throughout the sill (Fig. 12). A large proportion of the magma was apparently focused through the nose of the sill at the promontory Port na Mean-faochaige (Figs 3 and 12), with flow predominantly coming from the west and NW. This flow direction is contrary to expectation, as the magma is believed to have originated beneath the central complex on Mull (Preston et al., 1998), which is NE of Traigh Bhàn na Sgùrra. However, the least resistant pathways for the magma may involve considerable sinuosity, and as the available outcrops represent only c. 700 m in the direction of flow, we may be seeing an unrepresentative apparent flow direction.
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SUMMARY AND CONCLUSIONS |
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This detailed study of the Traigh Bhàn na Sgùrra sill has shown that it is possible to infer much about the flow in a magma conduit using a combination of field and petrographic evidence.
The flow in the sill was predominantly in the laminar regime, although it is possible that in places it may have been transitionally turbulent in the early stages. Type I regions correlate with instantaneous intrusion, or flow for less than a few days. This results in a chilled margin, with a narrow or absent metamorphic aureole in the walls. In the centre of the sill, planar fractures with lineated surfaces are due to a preferred alignment of plagioclase crystals formed during flow in the later stages of crystallization during rapid solidification. Average crystal size shows a strong relationship with position within the conduit, reflecting highly variable cooling rates across the sill.
In thicker parts of the conduit sustained flow was possible, with some parts of the conduit remaining active for up to 5 months. This led to the formation of wide thermal aureoles in the walls, with significant wall-rock erosion (Type II). In these regions, chilled margins are absent, and the average grain size is greater than that of Type I regions. Large numbers of xenoliths are present, including significant numbers of cognate xenoliths, congregating at the junctions with stagnant parts of the conduit, reflecting a greater ability of the flow to transport them (perhaps related to an early turbulent period) or the greater time available for transport in Type II regions. In regions of sustained flow the interior of the intrusion has a characteristic massive texture, indicative of the absence of preferred orientation of plagioclase grains, suggestive of slower solidification in a hot environment once flow had ceased.
The division of the sill into these two clearly demarcated facies reflects a strong control of conduit width on magma solidification. Sustained flow is possible only in regions of the sill exceeding an initial critical half-width hI. Below hI, solidification occurs rapidly and little or no sustained flow occurs. The critical half-width hcrit is inversely proportional to the pressure gradient driving the flow. Thus as P/z decreases during the eruption, hcrit increases, with the result that active flow is continuously focused into the wider areas of the conduit. Transitions between the two flow regimes occur over distances of <1 m, demonstrating significant flow focusing with sharp boundaries between cool, stagnant regions and hot, active channels. The 2D pattern of flow localization revealed by mapping (Fig. 2) is limited by the amount of outcrop, but there appears to be a concentration of flow within pelitic horizons. This may be a result of enhanced thermal erosion of the more fusible pelitic rock, increasing conduit width. Increased wall-rock erosion may be important in the localization process because it increases conduit thickness, creating a feedback loop. The pattern of flow lineations (Fig. 2) suggests a final concentration of flow into a narrow channel in the region of Traverse Z.
The published estimate of the total volume of magma (1750 km3) that passed through the Traigh Bhàn na Sgùrra sill is very large, representing more than 20 vol. % of the magmas thought to have erupted from the Mull volcano (Wartho et al., 2001). This is based on a 5 month flow along a 5000 m x 6 m conduit. We have shown that only very limited areas of the conduit experienced sustained flow for the full duration. A more realistic estimate of the total volume of magma assumes a conduit with a cross-sectional area of 100 m x 4 m. With an average magma flow rate of 10 m/s (Table 2) for 4 months, the Traigh Bhàn na Sgùrra sill accounts for 50 km3 or 0·5 vol. % of the total magma volume erupted by the volcano. This is much smaller than the estimate of Wartho et al. (2001) but still represents a significant eruption, consistent with the emptying of a magma chamber of 2·3 km radius.
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ACKNOWLEDGEMENTS |
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We thank Bruce Marsh, Steve Sparks and Stephen Blake for thorough and constructive criticism of a previous version of the manuscript. Steve Sparks provided criticism and help during revision. We are grateful to Herbert Huppert, John Lister and Dan McKenzie, with whom we had very useful discussions. Nigel Woodcock gave invaluable help in analysing crystal orientations. Claire Barlow and Pat Thistlethwaite kindly provided accommodation during fieldwork.
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FOOTNOTES |
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Present address: Department of Earth Sciences, University of Bristol, Wills Memorial Building, Queen's Road, Bristol BS8 1RJ, UK. 
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