Journal of Petrology | Volume 39 | Number 4 | Pages 633-661 | 1998
© Oxford University Press 1998
The Skaergaard Layered Series. Part IV. Reaction–Transport Simulations of Foundered Blocks
1 Earth Sciences Division, Lawrence Berkeley National Laboratory, University of California, MS90-1116, Berkeley, CA 94720, USA
2 Department of Geological Sciences, University of Oregon, Eugene, OR 97403, USA
Received May 27, 1996; Revised typescript accepted November 14, 1997
 |
ABSTRACT |
|---|
 TOP ABSTRACT IntroductionOccurrence and CompositionNumerical ModelingSimulationsDiscussionConclusionsReferences |
|---|
During the middle stages of crystallization of the Skaergaard Layered Series large numbers of blocks became detached from the Upper Border Series and settled into the mush of crystals on the floor. It has been recognized for some time that these blocks now have compositions and textures that differ markedly from those of the units from which they came. They tend to be more plagioclase rich and seem to have lost mafic components to the surrounding gabbro. Numerical simulations coupling crystallization, melting, and heat and mass transfer for a multicomponent system show how the blocks reacted with the mush in which they were emplaced. Enhanced cooling and crystallization of a compositionally stratified mush adjacent to the blocks resulted in patterns of melt compositions similar to those of layering around the blocks. Volume changes during crystallization and melting induced convection of the interstitial melt leading to changes in the bulk compositions of the blocks and the surrounding mush. Inhomogeneities such as inclusions are likely to facilitate the onset of compositional convection in a chemically stratified solidification zone.
KEY WORDS: assimilation; convection; reaction–transport modeling;; Skaergaard Intrusion; solidification zones
|
Introduction |
|---|
|
TOPABSTRACTIntroductionOccurrence and CompositionNumerical ModelingSimulationsDiscussionConclusionsReferences |
|---|
Various types of inclusions are found in the Skaergaard Intrusion, but the most conspicuous are angular blocks that settled into the crystallizing Layered Series (Fig. 1). It was clear even to the earliest workers (Wager & Deer, 1939
; Wager & Brown, 1968) that these blocks must have fallen from the zone of crystallization under the roof. The Upper Border Series has large missing sections at levels that correspond to those parts of the Layered Series in which most blocks are found. On closer examination, however, several puzzling anomalies were recognized. First, the plagioclase-rich blocks have densities substantially less than that of the magma through which they must have fallen. Moreover, their compositions differ in important ways from those of the units from which they came, namely UBS-
and UBS-β (Table 1). They have lost FeO*, TiO2, and P2O5, and their minerals no longer have their original compositions but are closer to those of their host rocks. In view of the density differences, these changes must have occurred after the blocks had reached the floor. This interpretation is reinforced by the textural characteristics of the blocks. Although their angular outlines appear sharply defined in outcrops, under the microscope one sees no discontinuity at the boundary of the blocks other than a change in modal proportions. Foliation, which is especially strong in plagioclase-rich blocks, has the same orientation as that of their host and crosses the boundary without any apparent deflection (McBirney & Hunter, 1995). Most baffling of all, a large block in middle zone has a set of four or five layers that appear to be prolongations of a corresponding set in the adjacent gabbro (Fig. 1b).
|
|
We have attempted to explain these anomalies as the results of a vaguely defined process of metasomatism (McBirney & Sonnenthal, 1990
; McBirney, 1995) but until now could not offer a plausible quantitative model. An improved understanding of reaction–transport mechanisms associated with porous flow, together with the development of numerical codes to treat flow and reaction in porous media now permit us to analyze the evolution of these blocks in a more convincing way.
We have already described the general features of the intrusion in earlier parts of this series (McBirney, 1989; Boudreau & McBirney, 1997; McBirney & Nicolas, 1997). In the pages that follow we first elaborate on the geological setting and compositional relations of the blocks then model the physical and chemical processes by which they evolved.
|
Occurrence and Composition |
|---|
|
TOPABSTRACTIntroductionOccurrence and CompositionNumerical ModelingSimulationsDiscussionConclusionsReferences |
|---|
Of all the inclusions in the intrusion, by far the most numerous are the anorthosites and felsic gabbros that fell in swarms into the lower part of the Layered Series. A few blocks of basalt have been found but xenoliths of the gneiss and amphibolite that form most of the lower margins of the intrusion are very rare (Kays et al., 1981
), probably because they are now altered beyond recognition. Ultramafic xenoliths are locally abundant but only near the base of the intrusion (Kays & McBirney, 1982).
The blocks that are our main concern here are concentrated in the Lower and Middle Zones; they are rare in Upper Zone a and none at all have been found in Upper Zone c and the upper part of Upper Zone b. In their study of the stability relations of a zone of crystallization under a roof, Brandeis & Jaupart, (1986) concluded that fragments and individual crystals would become detached and sink through the magma in widely spaced clusters. Beneath the blocks the layering is depressed, and at the edges it is truncated and deflected (Fig. 2a). Layering draped over the blocks appears to have been laid down after they had come to rest (Fig. 2b). Some of the blocks, particularly large ones, split on impact with the floor. The cracks are filled with iron-titanium oxides, pyroxene and olivine but little if any plagioclase. The gabbro caught between large blocks is also very mafic and has a strongly laminated fabric (Fig. 3).
|
|
A very large block of anorthosite in Middle Zone has a set of four or five layers that appear to be the prolongation of a similar set in the adjacent gabbro. The faint internal layers are apparent only when seenfrom a distance and in the most favorable light. Because the block is exposed high in the near-vertical wall of a glacial cirque, we have not been able to examine it closely.
The gabbro within and around swarms of blocks tends to be more mafic than the average for the zone to which it belongs. It is also more strongly layered. This layering is thought to be due in large part to the disturbance and compaction that resulted from the blocks falling into the crystal mush (Boudreau & McBirney, 1997).
Individual blocks tend to be structurally and compositionally homogeneous but they may differ markedly in texture and composition from close neighbors in the same swarm (Table 2; Fig. 4). Most are anorthosites, and although some are more mafic, few if any approach the bulk composition of their mafic host rock. The mineral compositions are closer to those of the host gabbro than to the original units of the Upper Border Series from which they are thought to have fallen. The average composition of plagioclase is An56.2, as opposed to An43.8 for the corresponding part of the Upper Border Series, and their Mg ratio is 0.352, whereas that of the original rocks of the UBS is 0.236. Part of the mafic fraction missing from the anorthosites can be accounted for in the iron-rich selvages and veins in and around the blocks (Fig. 5; Table 1). The remainder may be in the large areas of unusually mafic layered rocks surrounding the blocks.
|
To determine whether the compositional changes are reflected in internal gradients, we collected and analyzed samples across the largest accessible block in the Layered Series (Fig. 6a). Exposed near the western shore of Kraemers Island, the block measures about 250 m by 500 m. The line of samples follows the long axis, which was close to horizontal before the intrusion was tilted. Apart from a small increase of SiO2, Al2O3 and Na2O, and a corresponding decrease of CaO, FeO* and MgO at the edges, the major elements are remarkably constant (Fig. 6b). Trace elements are less regular. Sr is the only element that seems to be relatively enriched at the margin, but most of the compatible transition elements are depleted next to the contact, even though the abundances in the adjacent gabbro are much greater.
|
A small block of basaltic composition in the same area shows similar effects, but in this case iron migrated from both the gabbro and interior of the block to form a dense layer of magnetite at the contact (Fig. 7). Even though the gabbro contains more iron than the original basalt (about 14% vs 9% FeO), iron was depleted from the margins of the xenolith and enriched at the contact with its host. The explanation for this apparent anomaly lies in the role of oxygen. At the time the basaltic rock entered the magma it must have been highly oxidized by hydrothermal alteration. The anomalously low 18O–16O ratios and their increase from the center of the block outward indicate that meteoric water had affected the basalt when the latter was near the surface, and that oxygen was redistributed after the block sank to its present position. The oxidizing effect of the block on the adjacent liquid led to increased precipitation of magnetite, which in turn produced chemical potential gradients down which iron, zirconium, and other mobile elements were transferred toward the contact from both the block and adjacent liquid.
|
Taylor & Forester, (1979)
determined the oxygen isotopic ratios of more than a dozen gabbroic and basaltic rocks in the Layered Series and reported that ‘in virtually every case, the 
18O of the plagioclase in the block is lower than that of the plagioclase in the adjacent Layered Series’. They attributed this difference to hydrothermal alteration of the roof rocks before they sank into the Layered Series. Wherever Taylor & Forester, (1979) analyzed samples taken around large blocks, they found that the ratios rise toward the margins but gradients extending several meters into the host gabbro indicate that oxygen continued to be exchanged after the gabbro was largely solidified.
Although the blocks may originally have contained hydrous minerals, by the time they settled to the floor of the Layered Series they could have had less water than the surrounding magma, which, by this stage of differentiation, would have been nearly saturated with volatiles (Sonnenthal, 1992). If so, the composition of the melt produced by initial heating of the blocks would have been altered by an infusion of water from the adjacent gabbro. Increased PH2O would have reduced the relative stability of plagioclase and left residual crystals of a more Ca-rich composition (Baker & Eggler, 1987). Once the system began to cool and crystallize, the plagioclase overgrowths would have become more albitic.
However this may be, the increased proportions of plagioclase in the final compositions of blocks can be attributed to extraction of a cotectic melt from an original rock slightly richer in plagioclase, leaving a residue even richer in plagioclase (McBirney, 1995). Even though the textures, bulk compositions and mineral compositions appear to have been strongly modified, there is still abundant evidence for a metasomatic process which was not fully completed before the final solidification of the blocks. Plagioclase grains have sieve-like resorption and reprecipitation textures with large compositional contrasts between different zones (Fig. 8). The patches of replacement have fine oscillatory zoning with much more Ca-rich compositions (up to An76.8) than plagioclase in the zones from which the blocks came or in the gabbros in which they now reside (Fig. 9). Dissolution of Ca-rich clinopyroxene could have supplied the excess Ca required for precipitation of anorthitic plagioclase, because the concentrations of CaO in the blocks are not much greater than in the original UBS rocks. The bulk-rock Al2O3 content, however, is much greater; it can be explained by either an influx of new melt displacing melt in the blocks or by expulsion of mafic liquids during deformation of the blocks. The angular form of the large blocks seems to discount the possibility of large volume changes.
In the following sections we address the major thermal and fluid dynamical constraints and compositional evolution of the blocks after their emplacement.
|
Numerical Modeling |
|---|
|
TOPABSTRACTIntroductionOccurrence and CompositionNumerical ModelingSimulationsDiscussionConclusionsReferences |
|---|
Just as experimental petrology is an essential tool for testing theoretical concepts, numerical simulations provide a way of testing complex thermal and compositional relations. They can also yield unexpected insights into a variety of magmatic processes.
This section summarizes the equations and parameters used in our numerical simulations of blocks after their emplacement; a more complete description of the equations and numerical techniques will be presented elsewhere (E. L. Sonnenthal, in preparation). The simulations were performed using the code RCTMAG (reaction–transport in magmas), based on the code RCTSED for transport, chemical compaction, hydrofracturing, sedimentation and subsidence in sedimentary basins (Sonnenthal et al., 1992; Sonnenthal & Ortoleva, 1994). The model presented here differs from other numerical models coupling porous flow with transport and reaction (Shirley, 1986, 1987; Iwamori, 1993; Steefel & Lasaga, 1994). First, the equations are left in their dimensional form, thus eliminating the many simplifications required for nondimensionalization, such as treating the thermal properties as uniform. Second, instead of assuming incompressible flow and using the velocities calculated using a stream function, we determine velocities by solving the mass-conservation equations for compressible multicomponent transport. The resulting equations are solved on a two-dimensional grid that is deformable and may shrink or grow as solidification advances. A summary of the numerical methods used in RCTMAG is presented in the Appendix.
Recent modeling of multicomponent reaction-transport over the entire range of crystallization (Spera et al., 1995) has helped to clarify the coupling of equilibrium reactions with convection in two-dimensional domains. Although we consider only the region of crystallization that can be described by Darcy flow, it is in this region that our model can describe the flow regime more fully, as it includes the strong effects of crystallization and melting on volumetric and density relations, the effect of pressure on the melt density, and the variation in mineral densities with composition and temperature.
We have ignored certain important aspects of the problem, such as the thermodynamics of mineral-melt reactions (although heats of fusion are utilized in the thermal model) and the kinetics of stress-mediated reactions (i.e. pressure solution) causing compaction. We also neglect the kinetics of nucleation and crystal growth and processes leading to textural equilibration. Eventually, of course, compaction and reaction kinetics in magmas must be taken into account in modeling the complex evolution of solidification zones.
Given these simplifications, we believe that much of the relevant physical behavior of the near-rigid regime of solidification zones and the assimilation of inclusions is described by the following set of conservationequations.
Conservation and transport equations
Conservation of mass and velocity of the melt
The conservation of mass for the bulk melt is given by
 |
f and s are the mass densities of the liquid and solid matrix, v is the melt velocity, and 
the melt volume fraction (McKenzie, 1984; Richter, 1986). The solid matrix density is given by the sum of the individual mineral densities times their respective volume fractions. The pressure in the melt is obtained by combining the equation for the conservation of mass of the fluid and Darcy's Law. The latter yields the macroscopic melt velocity including the motion of the rock matrix u:
 |
is the permeability (here taken to be isotropic), µ is the melt dynamic viscosity, and g is the downward-directed gravity vector (assumed constant and equal to the acceleration due to gravity, –g). Detailed discussions and derivations of this form of the fluid velocity equation have been given by Bear, (1972) and Ene, (1990). It is important to note that v is the mean velocity, as the velocities of each component differ as a function of dispersion and diffusion. However, because transport by diffusion is typically less than bulk transport for the simulations of advection–diffusion reaction shown here, at a given time step the bulk fluid velocity (as given by the Darcy Law) is approximately equal to the mass-average velocity for a multicomponent system (Bear, 1972).
Permeabilities are calculated using a form of the Carman-Kozeny equation (Spera, 1980), although consideration of the varying pore throat-size with reaction yields permeabilities closer to measured values for sandstones (E. L. Sonnenthal, in preparation). Meaningful use of such texture-based permeability equations in magmas will require consideration of the kinetics of crystal growth and nucleation, as well as textural equilibration.
The fluid overpressure, 
, is given by the difference of the total fluid pressure P and the ‘hydrostatic’ component Ph,
 |
 |
The integral in equation (4) is evaluated from the top of the melt column (zt) to the base of the system (zb). The top of the melt column is actually above the top of the simulation domain (Fig. 10). The second term is the pressure exerted by a hypothetical column of overlying rock of density r with its thickness given by the difference between the surface depth (zs) and zt. The last two terms are the pressure exerted by a body of overlying water, if present, of density w and depth dw and the atmospheric pressure at sea level, PSL.
|
Energy conservation and heat fluxes
The heat transport equation, including conduction and advection, has been given by Bear, (1972)
. Neglecting energy dissipation by dispersive forces and adding a term for the latent heat of fusion, it is
 |
T is the combined fluid–solid thermal conductivity, Lm is the latent heat of fusion for mineral m, m the mass density of mineral m, and fm the volume fraction of mineral m, for a total number of minerals, nm. The material derivative DT/Dt has been introduced, so that we can follow the temperature of a moving rock matrix, and in general,
 |
 |
s/DT is a given relation between the temperature change and mass of total solid crystallizedor melted per cm3 (f is the total volume fraction of minerals).
Conservation of mass and fluxes for chemical components
Taking the equation for conservation of mass of a chemical component and the solid matrix (Bear, 1972) and adding a reaction term for dissolution and crystallization gives
 |
Although the chemical diffusion model treats each component independently, they affect each other by their effect on the bulk composition and density. Through sequential iteration each component is modified by the diffusion of all other components. So-called ‘uphill diffusion’ is possible with this model. A better description of multicomponent diffusion would be to solve the full cross-diffusion matrix (Hofmann, 1980; Zhang et al., 1989), but this substantially increases the difficulty of the problem. For the spatial and time scales of interest, crystallization or melting and advective transport have an overwhelming effect on the melt compositions, so this simplification has little effect on the results. In addition, the component having the greatest diffusivity, H2O, may not be strongly coupled to the diffusion of other oxide species (Zhang & Stolper, 1991).
We have also ignored the effect of diffusion in the solid grains, although it is possible to add this, as was shown by Iwamori, (1993) or Wang, (1993). In the case of plagioclase, the well-preserved, major-element zoningin crystals of slowly cooled gabbros suggests thatreequilibration for the major elements is sluggish and that diffusion can be ignored, at least initially. Clearly, the opposite is true for olivine, which equilibrates rapidly and could be considered instantaneous on the time scales of flow and diffusion in the melt.
Equations of state and transport parameters
Melt and solid densities
The melt density f is given as a function of temperature, composition and pressure in the following form:
 |
C,T is the density as a function of composition and temperature (Bottinga & Weill, 1972) at the reference pressure P0(1 bar), and β is the isothermal coefficient of melt compressibility (here set constant at 7.0 x 10–6/bar; Murase & McBirney, 1973).
Mineral densities are calculated as a function of composition and temperature using end-member molar volumes and thermal expansion relations given by Niu & Batiza, (1991). The relatively small effect of pressure on mineral densities in shallow magmatic systems is neglected.
Melt viscosity
Melt viscosities were calculated as a function of temperature and composition using the method of Shaw, (1972). The viscosities used were about an order of magnitude lower than the original model predicts, but we believe these values are better, because the older calculation does not take into adequate account the effects of water and halogens (Baker, 1996; Dingwell et al., 1996), which had unusually large concentrations in the magma at this stage. The effect of pressure on the viscosity is much smaller than that of composition or temperature and is therefore not considered.
Thermal parameters
Heat capacities of melts differ little with composition and for our purposes can be taken to be constant (1.59 J/g °C; Robie et al., 1978). Mineral heat capacities are given as a function of composition and temperature assuming perfect mixing and using end-member molar heat capacity coefficients and the polynomial expressions of Ghiorso et al., (1983), with additional data on apatite from Zhu & Sverjensky, (1991).
The thermal conductivity of the melt (kT,f) is set to a constant (1.3 x 10–2 J/cm °C s; Murase & McBirney, 1973). End-member molar thermal conductivities are used to calculate mineral values (kT,m), assuming perfect mixing, with data from Robie et al., (1978) and the Basaltic Volcanism Study Project, (1981). The bulk matrix–melt thermal conductivity (kT) is approximated as follows:
 |
but modified to use the thermal conductivity of each mineral.
Heats of fusion for each mineral are calculated assuming perfect mixing using end-member molar data from Robie et al., (1978), the Basaltic Volcanism Study Project, (1981), Ghiorso et al., (1983), and Zhu & Sverjensky, (1991). Although this is an over-simplification of the thermodynamics of mineral dissolution and crystallization, for the mineral assemblage and compositions modeled here it yields bulk heats of fusion in the ranges commonly cited (300–400 J/g).
Chemical diffusion and dispersion
The effect of diffusion of major and trace elements is small (McBirney, 1995), considering the time and spatial scales of this study. Although it would be possible to provide approximate diffusion coefficients for each component, charge balance considerations would make calculations much more difficult (Lichtner, 1993; Steefel & Lasaga, 1994). Therefore, all oxide components except water are given a diffusion coefficient of 1x10–8 cm2/s. The much greater diffusivity of H2O in silicate melts (Hofmann, 1980) and suggestions that it is not strongly coupled to other components give some justification for a separate treatment. Diffusion coefficients for H2O are calculated as a function of concentration and temperature using the empirical relations given by Zhang & Stolper, (1991).
The combined diffusion–dispersion coefficient is simplified as in Steefel & Lasaga, (1994),
 |
is the macroscopic molecular diffusion coefficient in the porous medium and Dh is the coefficient of mechanical hydrodynamic dispersion. In a porous medium the transport of components by diffusion in the liquid must be modified to reflect the average total path taken by each component species. We take the coefficient 
as the coefficient of molecular diffusion in the melt, Dd,f,i, divided by the matrix tortuosity, 
[assumed constant and equal to five; from Spera, (1980)],
 |
Finally, the coefficient of mechanical hydrodynamic dispersion is approximated in the following manner:
 |
Effective stress
The concept of effective stress, 
', has been used to advantage in soil mechanics and in studies of sediment pore fluid pressures (Bear, 1972). It describes the stress in a porous solid in excess of the pore fluid pressure,
 |
is the total stress. For a simple analysis of one-dimensional compaction, we can assume that the total stress is the maximum principal stress that can be given as the mean vertical component of stress zzmfrom the stress tensor [see Spera, (1980) for a discussion of relevance to magma transport]. The latter is given by the integral of the fluid and solid densities over the depth of the crystal pile plus the hydrostatic pressure at the top of the crystal pile (
) as calculated from equation (4),
 |
, so that zzm is negative for compressive stresses, should be noted. If there is a positive effective stress, conditions favor compaction, and the grains can assume a closer packing. Compaction, of course, increases fluid pressure, which in turn decreases the effective stress and impedes compaction.
|
Simulations |
|---|
|
TOPABSTRACTIntroductionOccurrence and CompositionNumerical ModelingSimulationsDiscussionConclusionsReferences |
|---|
Initially, our goal was to simulate the bulk compositional changes thought to have occurred in the blocks and surrounding gabbro. We encountered a number of unexpected phenomena that, on closer examination, proved to be consistent with the physics of the problem and with our observations in the field. In particular, we discovered that the form of layering around the blocks that seemed adequately explained by ‘draping’ of layers during sedimentation with or without compaction, could also be produced by the thermal effect of the block on a surrounding mush that is zoned in temperature, composition, and crystallinity.
Before examining the complex system of a stratified solidification zone with advection and diffusion, we performed several simpler simulations to examine the interaction of a small block in an unzoned, thermally uniform magma. The melt pore pressure was set to the hydrostatic value, so that heat transport was controlled solely by conduction and chemical transport by diffusion. Although crystallization and melting can change the melt composition and bulk mineral assemblage, we held the mineral compositions constant while allowing their densities to change with temperature. Although we do not know the initial temperature of the blocks, they must have had a range of temperatures characteristic of the upper solidification front, and many must have been above their solidus (Brandeis & Jaupart, 1986). Their residence times in the main magma before being enveloped by the advancing solidification front are unknown. In these simulations we assume that the blocks are above their solidus temperature and thus have some small initial proportion of melt.
Block assimilation at the sub-meter scale
In this first simulation a block 0.58 m in height and 0.8 m wide has a temperature of 1050°C and a melt mass fraction of 0.05. It is immersed in a uniform magma at 1095°C and 0.50 mass fraction of melt. The upper boundary of the computational domain was fixed at 1095°C, and the side boundaries have no heat loss. The grid dimensions are 25 vertical by 45 horizontal nodes. The simulated mush is 2 m thick by 4 m wide, and its overburden pressure is calculated assuming 1 km of overlying magma (of the same composition as the initial melt) and 1 km of overlying rock (Fig. 10). The melt composition is set as uniform and identical in the block and the surrounding magma. The mineral proportions in the surrounding magma, taken as those of MZ (McBirney, 1989), are also assumed to be the cotectic proportions that would melt or crystallize in the block and magma. The mineral proportions of the block are set initially to those of UBS-β, and their compositions are the same as in the magma (Table 3; plagioclase rim and core compositions were averaged). Four minerals are present: plagioclase, augite, magnetite, and ilmenite. The grain diameters are held constant at 1 mm in the magma and 2 mm in the block, which for these simulations is important only for calculating permeability. The change in melt volume fraction with temperature [see equation (7)] is set to 0.009/°C, on the basis of the experimental melting relations of Skaergaard rocks (McBirney, 1989), and is held constant for all simulations. The boundary conditions for chemical transport were set to prevent flux at the sides and maintain a constant melt composition at the upper and lower boundaries.
|
In this simulation, as in those to follow, we focus on the evolution of FeO*, because it illustrates best the compositional changes of interest, yet it must be emphasized that the mass-conservation equations for all oxides are calculated, using the full melt and mineral compositions given in Tables 1 and 3. The initial water content of the melt was set to 0.33 wt %.
Vertical profiles through a reacting block as a function of time are shown in Fig. 11. Thermal equilibration takes about 1 year (Fig. 11a). Cooling by the block results in crystallization of the surrounding magma and causes the interstitial melt to become more iron rich, whereas melting in the block causes its melt composition to be more iron poor (Fig. 11b). As expected, the spatial effects of chemical diffusion over several tens of years are on the order of centimeters, yet water, with its higher diffusivity, shows a stronger effect. As Fig. 11c shows, water acts as an incompatible element, initially increasing in the crystallizing melt and decreasing in the interstitial melt of the block undergoing melting. Once the block and the surrounding magma equilibrate thermally, diffusion is the sole process changing the melt compositions. As a result, the water content of the block slowly increases. In contrast, changes in the FeO concentration after thermal equilibration (from 0.9 to 20 years) are barely detectable.
|
Contour plots of the same simulation are shown in Fig. 12. As expected, volume fractions of melt after 0.9 years (Fig. 12a) have a symmetrical pattern of reaction owing to the imposition of a cooler block on the initially uniform temperature field of its surrounding magma. Figure 12b shows FeO* in the interstitial melt, from which the profile of Fig. 11b was taken. Melting of an assemblage poorer in plagioclase than the original block of UBS-β results in a substantially greater volume fraction of plagioclase in the crystalline assemblage (Fig. 12c).
|
Large blocks in a compositionally stratified magma: thermal effects
When blocks with diameters of tens to hundreds of meters sank into magma that was zoned in temperature, crystallinity, and, most likely, composition, they would have disrupted the thermal environment as just shown, but with time conduction and partial melting would cause the thermal gradients in the magma to be imposed on the blocks, eventually giving them the same thermal profiles as the surrounding magma. An important factor governing how the blocks reacted and exchanged chemical components with the magma was the degree to which these thermal gradients could equilibrate at temperatures significantly above the solidus of the block and the magma. In simulating the reaction of large blocks with a zoned magma, chemical transport is still limited to diffusion, as we are mainly interested in the thermal effects on interstitial melt compositions, through melting and crystallization. Because the spatial scale of this simulation is 100 times greater than the previous one, the effects of chemical diffusion are insignificant.
Initial conditions of temperature, melt fraction, and the concentration of FeO* are given in Fig. 13a–c. Because of the complexity and larger scale of this simulation the number of grid nodes was increased to 50 x 101. The thermal condition for the lower boundary was modified to simulate heat loss by lowering the temperature 20°C/100 years and causing the lower crystallization front to advance at a rate of roughly 20 cm/year.
|
The temperature field after 33.7 years (Fig. 14a) shows the inward progression of isotherms into the melting blocks while the surrounding magma cools. The smaller block has more nearly equilibrated thermally owing to its size and higher initial temperature. Crystallization in the magma causes the melt concentration of FeO* (Fig. 14b) to increase in the melt around the blocks, giving an appearance remarkably similar to the ‘draped’ and upturned layering seen around the Skaergaard blocks. Compositional zoning within the blocks is a function of the inward progression of melting, causing the melt in the block to become poorer in FeO*. As in the previous simulation, the block becomes much richer in plagioclase. After nearly 100 years, the large block has little compositional zoning, but the small block has begun to develop internal zoning parallel to the external isotherms. The magma at the lowermost boundary has the greatest concentrations of FeO*, because it has cooled and crystallized substantially, yet the advance of this front has not yet interacted with the blocks.
|
Thermal advection, compositionalconvection, diffusion, and reaction
Crystallization and melting induce significant volume changes that must be accommodated by flow of melt with or without deformation of its matrix. Matrix deformation by dilatation or compaction are complex mechanochemical processes that will be addressed more fully in a later paper. Nevertheless, McKenzie, (1984
, 1987) has pointed out the similarities to compaction of sediments, and several workers (Dewers & Ortoleva, 1990; Sonnenthal et al., 1992; Sonnenthal & Ortoleva, 1994) have modeled chemical compaction and transport. We refer to such processes as mechanochemical because they are chemically controlled at some level by diffusion in the melt or solid (Ortoleva, 1994). It is important to start by simulating the system under conditions of a perfectly rigid matrix, as this will indicate the magnitude of the driving forces for flow and matrix deformation. If volume changes are not accommodated by viscous flow, compression or expansion of the melt, pressure changes in the rigid matrix will cause significant deformation. For a simple analysis of the system we can observe the change in effective stress (') assuming that the maximum principal stress is vertical. (This point is discussed at greater length in a later section.) Whereas volume changes due to crystallization result in a type of forced convection, thermal and compositional convection may also be important. Because assimilation results in regions that may initially cool and crystallize, then melt again before finally crystallizing, the flow patterns and dominating phenomena will change with time, and the final compositional patterns will have a complex imprint.
Reaction of blocks in a compositionally stratified magma: Case I
Introducing the mass-conservation equations for compressible flow in an inhomogeneous medium [equation (1)], the Darcy Law [equation (2)], fluid non-hydrostatic pressure [equation (3)], the melt density [equation (9)], and melt viscosity as a function of composition and temperature allows us to examine convection and advective mass-transport in a porous rigid mush. Several factors affect the flow regime—compositional convection driven by density differences in the melt, chemical diffusion, thermal convection driven by thermal expansion of the melt, heat conduction, and volume changes as a result of crystallization or melting, thermal expansion or contraction of the solid, and compressibility of the melt.
For this simulation the system shown in Figs 13 and 14 was scaled down to 20 m x 40 m, while keeping the temperature–compositional relations and boundary conditions the same. The grid resolution was 25 vertical nodes by 45 horizontal nodes. Because the block represents a strong discontinuity in permeability (about four orders of magnitude) and temperature, starting the full flow and reaction simulation from the initial conditions does not allow for time steps large enough to see more than a few hours of reaction after many days of computational time. Therefore, the system was allowed to evolve thermally and compositionally for about 2 months, to smooth out the discontinuities, before introducing the full pressure–velocity equations. As the blocks must have equilibrated somewhat while sinking through themagma and before reaching the floor, this is notunrealistic.
Figure 15 shows the simulation after 70 days (about 10 days after turning on the pressure–velocity calculations). The isotherms shown in Fig. 15a are controlled mostly by fronts of crystallization and melting, yet some effects of advection are seen when this figure is compared with Fig. 15b, where the velocity vectors are superimposed on the non-hydrostatic pressure contours. The velocity vectors show the strong effect of crystallization on volume, especially between and below the blocks, where melt fractions were smaller and the impermeable lower boundary impeded the supply of melt to the zone of crystallization under the block. The negative non-hydrostatic pressures are strongest below the blocks, because the relative impermeability of the blocks isolates the region below from the overlying melt zone. Because there is crystallization at the lower boundary, the overall flow regime is downward, although the magnitude of this effect is much less than that of convective flow around the blocks. The maximum velocity is 17.9 cm/year. An interesting aspect of the flow patterns is the weak flow out of the zone of melting in the blocks. This can be explained by the slightly greater volume changes in the adjacent zones of crystallization where the melt is becoming more FeO rich and increasing in density, whereas the melt in the zone of melting is becoming less dense. The resulting change in volume is less for a given temperature difference (although the relative magnitudes are reversed). In addition, the lower permeability of the block results in a reduced flow velocity.
|
After 68 years the isotherms (Fig. 16a) are horizontal, indicating that the blocks have achieved thermal equilibrium. The system is still convecting slowly (with a maximum velocity of 3.2 cm/year), especially around the smaller block, because it is closer to the lower crystallizing boundary and this cooling effect is now causing the block to recrystallize, where it had previously undergone melting. The dynamic viscosity (Fig. 16b) is lower in the melt with more FeO, even though its temperature is lower. The FeO* contours (Fig. 16c) show the combined effect of melting of the blocks and convective transport; in contrast to the system where only chemical diffusion was active, the melt compositional patterns deviate from the initial shape of the block. The flow vectors in Fig. 15b show the strong flow around and eventually through the corners of the blocks, and these edge effects are apparent in the final melt compositions.
|
Reaction of blocks in a compositionally stratified magma: Case II
Even though interaction of the magma and blocks was pronounced, the surrounding magma in the foregoing simulations was relatively stable. This is what one would expect in a system in which hotter, less dense melt overlies cooler, denser melt. In the following simulation the compositional stratification has been reversed, so that hotter, denser melt overlies cooler, less dense melt, a condition that is thermally stable but compositionally unstable. The boundaries and initial conditions are the same as before, except for the lower boundary temperature, which is maintained at 1075°C, so that crystallization at the lower boundary is prohibited.
Figure 17 shows the simulation after 100 years, at which time, as in the previous simulation, the blocks were already well equilibrated thermally. Figure 17a shows the distribution of melt fractions, which reflects the outline of the blocks and their lower final melt fractions after thermal equilibration. The differencebetween this simulation and the previous one is immediately apparent from the flow vectors, which show strong upward flow through the larger block and broader descending flow from the top. The melt composition clearly shows the dense FeO-rich melt sinking while the less FeO-rich melt rises as diapirs. The maximum flow velocity at 100 years is about 30 cm/year, significantly faster than the advance of a solidification front in a slowly cooled intrusion. Recrystallization of this zone would, of course, change the melt distribution. Full crystallization cannot be traced realistically, because the mineral compositions and proportions being melted or crystallized do not change and the resulting melt compositions would tend toward extreme values.
|
Although the smaller block was given a higher initial temperature, its initial melt fraction was only slightly greater than that of the larger block, but after equilibrating thermally, the melt fraction in the smaller block was considerably less than in the larger one. The flow vectors at the top of the smaller block show a deflection of the descending melt along its upper surface, owing to its much lower permeability relative to that of the surrounding mush. The permeability of the larger block is not very different from that of its surroundings, so it does not deflect the convective flow. Differences in initial temperature, composition, crystal size, and overall dimensions will no doubt have a large effect on the patterns of convection in the solidification zone, and on permeabilities, reaction rates, and the extent of melt transport between the block and its surroundings.
|
Discussion |
|---|
|
TOPABSTRACTIntroductionOccurrence and CompositionNumerical ModelingSimulationsDiscussionConclusionsReferences |
|---|
Thermal and chemical diffusion
Our first series of simulations was designed to examine the effects of thermal equilibration and chemical diffusion on melt compositions in the absence of advective transport. They showed that thermal equilibration proceeds quickly and that, except for water, which can diffuse over distances of meters, chemical diffusion was too slow to have a significant effect at time scales of 100 years or less. As heat was transferred from the magma into the blocks it increased the proportion of melt in the blocks while causing the adjacent magma to crystallize. Crystallization of the surrounding stratified mush resulted in the draped and upturned form of the contours of melt FeO* concentrations (Fig. 14), similar to those of the layering around the blocks in the intrusion.
The most striking effect of the blocks on the surrounding magma was the marked increase in iron locally manifested in precipitation of magnetite. In the modeling we did not consider the oxidizing effects of the blocks that were responsible for the increased proportion of magnetite observed in the selvages around basaltic xenoliths. The sharp increase in Zr in the magnetite-rich selvage of the basaltic block and its decrease in the basalt (Fig. 7) implies that mass transfer must have been effective in both directions. In view of the low diffusivity of high-field-strength cations such as Zr, the main mode of transfer must have been interstitial flow of melt toward the zone of crystallization.
Advection of melt induced by crystallization and melting
The decrease of volume during crystallization produces a flow of interstitial liquid toward the growing crystals and effectively transports components into the solidification zone. Over several tens of years, this has significant compositional effects, even without large-scale convection. In most of the gabbroic blocks from the Upper Border Series this flow was probably in both directions (Fig. 15b), because heating of the blocks caused an increase of the melt fraction, which in turn caused a volumetric expansion and increased permeability. In the case of the basaltic block, there would have been less chemical transport out of the block, because the basalt, being more MgO rich and colder, would have undergone less melting. In addition, flow through the basaltic block would have been hindered by its finer grain size and much lower permeability.
Melting of the blocks resulted in an increase in volume and melt pore pressure, which, in addition to the bulk thermal expansion of the crystal matrix, could have caused blocks to rupture along existing fractures or textural inhomogeneities. Much of the splitting of the blocks on impact with the floor could have been a result of internal stresses.
Compositional convection of interstitial melt
If the trend of liquid compositions was one that promoted compositional convection, exchange between the blocks and magma would be further enhanced by flow of the interstitial melts. As Fig. 17b shows, the blocks would serve as nuclei to initiate flow in the surrounding magma. At high melt fractions the interstitial melt in the blocks would be redistributed and replaced by the main magma, much in the manner proposed by Kerr & Tait, (1985) and by Tait et al., (1992) on the basis of numerical models and experiments using aqueous solutions. Our simulations have demonstrated this phenomenon using viscosities of silicate melts in a solidification zone with realistic permeabilities and thermal properties, pressure and temperature gradients, and time scales. The rising diapirs might have produced localized dissolution pipes. We did not observe the dissolution ‘chimneys’ seen in tank experiments, but they might have developed if we had included in our simulations the effect of water on melt proportions.
Rates of flow and equilibration
Several lines of evidence indicate that blocks up to hundreds of meters across underwent drastic changes of composition and texture after they fell from the roof and before the surrounding parts of the Layered Series were totally crystallized. The metasomatic processes involved reactive flow through the porous structure developed by partial dissolution. Brandriss et al., (1996) reached a similar conclusion. They showed that metabasaltic xenoliths in the Kap Edvard Holm Intrusion underwent an estimated 30–50% remelting followed by extraction of liquid through deformation or flow. Our models support this interpretation, and indicate that the process would proceed on a time scale much less than the total time the blocks were at temperatures above their solidus. The minimum time the blocks were in the zone of solidification can be estimated from the 1–10 cm/year rate of advance of the lower crystallization front (Norton & Taylor, 1979; McBirney, 1995). Thus, even at the more rapid rate, a block 10 m high would take 100 years to be overtaken by the solidification front.
Although the rates of reaction in the model are probably greater than those that assume diffusive transport of components away from crystal surfaces (Kerr, 1995), they are also overestimated because the heats of reaction we used take no account of non-ideality. Another consideration is the melt velocity, which is directly proportional to the permeability of the block and controls the rate of heat transport by advection. Melting is likely to have created channels larger than typical intergranular pore throats, and the bulk permeabilities and flow rates would have been significantly higher than the simple Carman–Kozeny model would predict on the basis of grain diameter and porosity alone. This would have the effect of making reaction rates somewhat greater than those used in our simulations.
Layering
The similarity between the contours of FeO* contents of the interstitial melts (Figs 14 and 15) and the layering observed around the blocks suggests that layering may be related to the compositional gradient induced by crystallization around blocks and enhanced by the transfer of components between the blocks and surrounding magma. Our modeling has demonstrated the large-scale exchange of components, and we see nothing preventing layers from passing through blocks that have also equilibrated with the adjacent thermal and compositional gradients. In fact, the strong gradients induced by the blocks should accentuate the development of modal contrasts (Boudreau & McBirney, 1997).
Gravitational stability of the blocks
The gravitational stability of a block can be determined by comparing its bulk density at an appropriate stage of melting with that of the crystals and liquid of its host magma. The initial density of a block having the bulk composition of UBS-β is about 3.07 g/cm3, whereas that of the MZ liquid was probably close to 2.91 g/cm3 and the crystal fraction about 3.17 g/cm3. Thus the block would have the same density as a Middle Zone magma with 61.5% crystals and a temperature of 1095°C. At crystallinities approaching this value, the bulk viscosity of the magma was probably too great for blocks to move at an appreciable rate through the viscous mush. It seems more likely that the rate at which blocks sank in the magma became negligible while the density of the latter was still slightly less than that of the blocks. This small difference would have the effect of increasing the stress below the blocks and aiding compaction until the surrounding magma crystallized enough to become denser than the block. At this point the block would become buoyant and press upward, possibly ‘filter-pressing’ the overlying mush, and dilation of the region below the block would tend to generate flow of melt into this zone. A possible example of a block that appears to have risen in this way is illustrated in Fig. 2b. Whether an individual block rose fast enough to escape would depend on its size, density contrast, and the rate of cooling of the host magma. In most cases, the buoyancy of the blocks must have been weak, for the example shown in Fig. 2b is the only one we know of, and we find no evidence that any escaped and floated to the roof.
Compaction
Because stresses on the crystal matrix drive compaction, they have an important influence on the flow of melt through and around the blocks. Compaction of the crystal matrix of the blocks could initially impede melt entering the blocks and enhance expulsion of their interstitial melt. The starting point for an analysis of this effect would be a calculation of effective stresses [equations (14) and (15)]. Figure 18 shows the evolution in time of the effective stress corresponding to the simulation illustrated in Figs 15 and 16. After 70 days the block has melted only at its margins and the effective stress is still higher in its interior, because melting is confined to the margins. The effective stress is not only greater in and below the block, but increased crystallization causes it to increase in the zone around the block. After 68 years (Fig. 18b) the effective stresses are now lower in and below the block because of its much greater proportion of plagioclase and its lower density relative to the surrounding mush.
|
Crystallization can increase the effective stress in two ways. First, the increased proportion of crystals raises the bulk density, and second, the volume decrease on crystallization lowers the melt pressure. In this way, compaction could be enhanced below the blocks and possibly even around the blocks. Melt would then be driven into the block, imparting to it some of the local concentration gradients of the melt. This effect might account for the propagation of layers in Fig. 1b. Some qualification is necessary, however. Because compaction in magmas may be controlled predominantly by diffusive transport at grain boundaries (i.e. Coble creep), the increased rate of crystallization, although raising the effective stress, also limits any effects dependent on chemical diffusion. In addition, the larger grain size would increase the size of grain contacts, diminishing the local stresses at the contacts and increasing the distance over which solutes must diffuse from the centers of the grain contacts to the pore fluid.
Several earlier studies have suggested that at some critical melt velocity the matrix would become fluidized (McKenzie, 1987; Shirley, 1987). Whereas this seems plausible in mushes with greater amounts of melt (
40–60%), at greater crystallinities the crystals of the interlocking framework cannot move relative to one another without deforming internally, possibly by dislocation creep, or undergoing some type of pressure solution creep. The time scales for the latter processes are certainly much greater than that of simple disaggregation, so processes in the solidification zone below a block will differ from those in a more easily deformed mush of lower crystallinity.
|
Conclusions |
|---|
|
TOPABSTRACTIntroductionOccurrence and CompositionNumerical ModelingSimulationsDiscussionConclusionsReferences |
|---|
As large gabbroic blocks fell from the Upper Border Series through the main magma and settled into the crystallizing Layered Series, they underwent marked changes of bulk chemistry, mineral composition and fabric. Reactions with their host made them more anorthositic while enriching the surrounding magma in iron and other rejected components.
Coupling the equations for mass conservation of the melt and solid for a multicomponent system with 11 oxides and several minerals, the conservation of energy equation, and equations of state for the melt and solid phases, we have traced the thermal and compositional evolution of blocks of differing dimensions in a solidification zone stratified thermally and compositionally. Thermal equilibration is relatively rapid. For example, a rectangular block 40 m high by 90 m wide would equilibrate in slightly more than 100 years. For most components, chemical diffusion is much slower and has effects over distances of <1 m, but the higher diffusivity and fugacity of water in the magma could effectively increase the water content of the melt in the block. The blocks disrupt the isotherms in the surrounding magma, and alter the pattern of crystallization, causing an increased concentration of iron near the margins of the blocks. Contours of FeO* take on a form remarkably similar to that of the layering observed around the blocks.
Volume changes during crystallization and melting induce strong convection of the interstitial melt, especially at the margins of the blocks and even more so in regions between them. Crystallization in the adjacent magma increases the effective stress (the difference betweenlithostatic stress and pore fluid pressure) in the matrix by the extra mass of crystals and by decreasing the pore fluid pressure, whereas melting in the blocks has the opposite effect. Although we have not modeled compaction, the analysis indicates that compaction would initially be enhanced below the blocks, but as the blocks become more anorthositic and less dense than the surrounding mush, dilation would be possible. A reversal of density relations could make the blocks buoyant, but they probably rise too slowly to escape the advancing solidification front.
In a system where the melt is stratified with iron-rich melt overlying less iron-rich melt the blocks can initiate strong compositional convection. Iron-rich melt descends from the top of the solidification zone and return flow is in the form of narrow diapirs of less dense melt. Thermal gradients are not greatly affected, because they are buffered by crystallization and melting. Once the blocks have equilibrated thermally with the magma, convective flow could pass through blocks, provided they have sufficient permeability and the viscosity of the melt is low.
The numerical models support the conclusions based on earlier studies (McBirney, 1989; McBirney & Sonnenthal, 1990) that strong compositional changes can be the result of reactive flow of interstitial melt through the solidification zone.
|
|
|
|
|
Acknowledgements |
|---|
The preliminary work providing the basis for this study was supported chiefly by a series of grants from the National Science Foundation. We are grateful to George Bergantz and Tony Philpotts for helpful reviews.
* Corresponding author. Telephone: 510-486-5866. Fax: 510-486-5686. email: elsonnenthal{at}lbl.gov
|
References |
|---|
|
TOPABSTRACTIntroductionOccurrence and CompositionNumerical ModelingSimulationsDiscussionConclusionsReferences |
|---|
Aris R. Vectors, Tensors, and the Basic Equations of Fluid Mechanics (1962) New York: Dover.
Baker D. R. Granitic melt viscosities: empirical and configurational entropy models for their calculations. American Mineralogist (1996) 81:126–134.[Abstract]
Baker D. R., Eggler D. H. Compositions of anhydrous and hydrous melts coexisting with plagioclase, augite, and olivine or low-Ca pyroxene from 1 atm to 8 kbar: application to the Aleutian volcanic center of Atka. American Mineralogist (1987) 72:12–28.[Abstract]
Basaltic Volcanism Study Project. Basaltic Volcanism on the Terrestrial Planets (1981) New York: Pergamon Press.
Bear J. Dynamics of Fluids in Porous Media (1972) New York: American Elsevier.
Bottinga Y., Weill D. F. The viscosity of magmatic silicate liquids: a model for calculation. American Journal of Science (1972) 272:438–475.[Abstract]
Boudreau A. E., McBirney A. R. The Skaergaard Layered Series. Part III. Non-dynamic layering. Journal of Petrology (1997) 38:1003–1020.
Brandeis G., Jaupart C. On the interaction between convection and crystallization in cooling magma chambers. Earth and Planetary Science Letters (1986) 77:345–361.[Web of Science]
Brandriss M. E., Bird D. K., O'Neil J. R., Cullers R. L., et al. Dehydration, partial melting, and assimilation of metabasaltic xenoliths in gabbros of the Kap Edvard Holm Complex, East Greenland. American Journal of Science (1996) 296:333–393.
Dewers T., Ortoleva P. A coupled reaction/transport/mechanical model for intergranular pressure solution, stylolites, and differential compaction and cementation in clean sandstones. Geochimica et Cosmochimica Acta (1990) 54:1609–1625.[Web of Science]
De Zeeuw P. M. Matrix dependent prolongations and restrictions in a blackbox multigrid solver. Journal of Computational and Applied Mathematics (1990) 33:1–27.[Web of Science]
Dingwell D. B., Romano C., Hess K.-U. The effect of water on the viscosity of a haplogranitic melt under P–T–X conditions relevant to silicic volcanism. Contributions to Mineralogy and Petrology (1996) 124:19–28.[Web of Science]
Ene H. I. Application of the homogenization method to transport in porous media. In: Dynamics of Fluids in Hierarchical Porous Media—Cushman J. H., ed. (1990) New York: Academic Press. 223–241.
Ghiorso M. S., Carmichael I. S. E., Rivers M. L., Sack R. O., et al. The Gibbs free energy of mixing of natural silicate liquids; an expanded regular solution approximation for the calculation of magmatic intensive variables. Contributions to Mineralogy and Petrology (1983) 84:107–145.[Web of Science]
Hofmann A. W. DiVusion in natural silicate melts: a critical review. zone. In: Physics of Magmatic Processes—Hargraves R. B., ed. (1980) Princeton, NJ: Princeton University Press.
Iwamori H. Dynamic disequilibrium melting model with porous flow and diffusion-controlled chemical equilibrium. Earth and Planetary Science Letters (1993) 114:301–303.[Web of Science]
Kays M. A., McBirney A. R., et al. Origin of the picrite blocks in the Marginal Border Group of the Skaergaard Intrusion, East Greenland. Geochimica et Cosmochimica Acta (1982) 42:23–30.
Kays M. A., McBirney A. R., Goles G. G., et al. Xenoliths of gneisses and the conformable, clot-like granophyres in the Marginal Border Group, Skaergaard Intrusion, East Greenland. Contributions to Mineralogy and Petrology (1981) 76:265–284.[Web of Science]
Kerr R. C. Convective crystal dissolution. Contributions to Mineralogy and Petrology (1995) 121:237–246.[Web of Science]
Kerr R. C., Tait S. R. Convective exchange between pore fluid and an overlying reservoir of denser fluid: a post-cumulus process in layered intrusions. Earth and Planetary Science Letters (1985) 75:147–156.[Web of Science]
Lichtner P. C. Scaling properties of time-space kinetic mass transport equations and the local equilibrium limit. American Journal of Science (1993) 293:257–296.
McBirney A. R. Effects of assimilation. In: The Evolution of Igneous Rocks—Yoder H. S. Jr, ed. (1979) Princeton, NJ: Princeton University Press. 307–338.
McBirney A. R. The Skaergaard Layered Series: I. Structure and average compositions. Journal of Petrology (1989) 30:363–397.
McBirney A. R. Mechanisms of differentiation in the Skaergaard Intrusion. Journal of the Geological Society, London (1995) 152:421–435.
McBirney A. R., Hunter R. H. The cumulate paradigm reconsidered. Journal of Geology (1995) 103:114–122.[Web of Science]
McBirney A. R., Naslund H. R. The differentiation of the Skaergaard Intrusion. A discussion of Hunter & Sparks (Contrib Mineral Petrol 95: 451-461). Contributions to Mineralogy and Petrology (1990) 104:235–247.[Web of Science]
McBirney A. R., Nicolas A. The Skaergaard Layered Series. Part II. Magmatic flow and dynamic layering. Journal of Petrology (1997) 38:569–580.
McBirney A. R., Sonnenthal E. L. Metasomatic replacement in the Skaergaard Intrusion, East Greenland: preliminary observations. Chemical Geology (1990) 88:245–260.[Web of Science]
McKenzie D. The generation and compaction of partially molten rock. Journal of Petrology (1984) 25:713–765.
McKenzie D. The compaction of igneous and sedimentary rocks. Journal of the Geological Society, London (1987) 144:299–307.
Murase T., McBirney A. R. Properties of some common igneous rocks and their melts at high temperatures. Geological Society of American Bulletin (1973) 84:3563–3592.
Naslund H. R. Petrology of the Upper Border Series of the Skaergaard Intrusion. Journal of Petrology (1984) 25:185–212.
Niu Y., Batiza R. DENSCAL: a program for calculating densities of silicate melts and mantle minerals as a function of pressure, temperature, and composition in the melting range. Computers and Geosciences (1991) 17:679–687.
Norton D., Taylor H. P. Quantitative simulations of the hydrothermal systems of crystallizing magmas on the basis of transport theory and oxygen isotope datas: an analysis of the Skaergaard Intrusion. Journal of Petrology (1979) 20:421–486.
Ortoleva P. J. Geochemical Self-Organization (1994) Oxford: Oxford University Press.
Person M., Garven G. Hydrologic constraints on petroleum generation within continental rift basins: theory and application to the Rhine Graben. American Association of Petroleum Geologists Bulletin (1992) 76:468–488.[Abstract]
Richter F. M. Simple models for trace element fractionation during melt segregation. Earth and Planetary Science Letters (1986) 77:333–344.[Web of Science]
Robie R. A., Hemingway B. S., Fisher J. R., et al. Thermodynamic properties of minerals and related substances at 298.15 K and 1 bar (105 pascals) pressure and at higher temperatures. US Geological Survey Bulletin (1978) 1452:456.
Shaw H. R. Viscosities of magmatic silicate liquids: an empirical method of prediction. American Journal of Science (1972) 272:870–893.[Abstract]
Shirley D. N. Compaction of igneous cumulates. Journal of Geology (1986) 94:795–809.[Web of Science]
Shirley D. N. Differentiation and compaction in the Palisades Sill. Journal of Petrology (1987) 28:835–865.
Sonnenthal E. L. Geochemistry of dendritic anorthosites and associated pegmatites in the Skaergaard Intrusion, East Greenland: evidence for metasomatism by a chlorine-rich fluid. Journal of Volcanology and Geothermal Research (1992) 52:209–230.[Web of Science]
Sonnenthal E. L., Ortoleva P. J. Numerical simulation of overpressured compartments in sedimentary basins. In: Basin Compartments and Seals. American Association of Petroleum Geologists Memoir—Ortoleva P., Al-Shaieb Z., eds. (1994) 61:403–416.
Sonnenthal E. L., Maxwell J. M., Qin C., Ortoleva P. J., et al. Mechano-chemistry of compartmented basins. In: Proceedings of the 7th International Symposium on Water-Rock Interaction, Vol. 2—Kharaka Y. K., Maest A. S., eds. (1992) Rotterdam: A. A. Balkema. 1055–1058.
Spera F. J. Aspects of magma transport. In: Physics of Magmatic Processes—Hargraves R. B., ed. (1980) Princeton, NJ: Princeton University Press.
Spera F. J., Oldenburg C. M., Christensen C., Todesco M., et al. Simulations of convection with crystallization in the system KAlSi2O6–CaMgSi2O6: implications for compositionally zoned magma bodies. American Mineralogist (1995) 80:1188–1207.[Abstract]
Steefel C. I., Lasaga A. C. A coupled model for transport of multiple chemical species and kinetic precipitation/dissolution reactions with application to reactive flow in single phase hydrothermal systems. American Journal of Science (1994) 294:529–592.
Tait S., Jahrling K., Jaupart C., et al. The planform of compositional convection and chimney formation in a mushy layer. Nature (1992) 359:406–408.
Taylor H. P. Jr, Forester R. W. An oxygen and hydrogen isotope study of the Skaergaard Intrusion and its country rocks: a description of a 55-MY-old fossil hydrothermal system. Journal of Petrology (1979) 20:355–419.
Wager L. R., Brown G. M. Layered Igneous Rocks (1968) Edinburgh: Oliver & Boyd.
Wager L. R., Deer W. A. Geological investigations in East Greenland, Part III. The petrology of the Skaergaard Intrusion, Kangerdlugssuaq, East Greenland. Meddelelser om Grønland (1939) 105:1–352.
Wang H. F. A double medium model for diffusion in fluid-bearing rock. Contributions to Mineralogy and Petrology (1993) 114:357–364.[Web of Science]
Wessel P., Smith W. H. F. New version of the Generic Mapping Tools released. EOS Transactions, American Geophysical Union (1995) 76:329.
White F. M. Viscous Fluid Flow (1974) New York: McGraw-Hill.
Zhang Y., Stolper E. Water diffusion in a basaltic melt. Nature (1991) 351:306–309.
Zhang Y., Walker D., Lesher C. E., et al. Diffusive crystal dissolution. Contributions to Mineralogy and Petrology (1989) 105:492–513.
Zhu C., Sverjensky D. A. Partitioning of F–Cl–OH between minerals and hydrothermal fluids. Geochimica et Cosmochimica Acta (1991) 55:1837–1858.[Web of Science]
CiteULike 
Connotea 
Del.icio.us What's this?
This article has been cited by other articles:
|
|
 |
|
  A. R. Mcbirney, A. E. Boudreau, and Bruce. D. Marsh Comments on: 'Textural Maturity of Cumulates: a Record of Chamber Filling, Liquidus Assemblage, Cooling Rate and Large-scale Convection in Mafic Layered Intrusions' and 'A Textural Record of Solidification and Cooling in the Skaergaard Intrusion, East Greenland' J. Petrology, January 1, 2009; 50(1): 93 - 95. [Full Text] [PDF]
|
|
|
|
|
|
M. E. Brandriss and D. K. Bird Effects of H2O on Phase Relations during Crystallization of Gabbros in the Kap Edvard Holm Complex, East Greenland J. Petrology, June 1, 1999; 40(6): 1037 - 1064. [Abstract] [Full Text] [PDF]
|
|
| ||||||||||||||||||||||||||||||||||||||||||||||||||