From Segregation, Transport, and Emplacement of Magmas,

to the Solid State Deformation of Granitoids:

Microstructures, Fabrics, and Finite Strain Fields.

I- Introduction

II- Crustal Anatexie and Crystallization of Magmas

II-1 Effect of temperature
II-2 Effect of H2O
II-3 Effect of CO2
II-4 Effect of fO2

III-The Physical Properties of Magmas and Partially Molten Rocks

III-1 Rheological behaviour of silicate-liquids
III-2 Rheological behaviour of dilute suspensions
III-3 Rheological behaviour of dense-suspensions
III-3-1 First and Second Rheological Threshold and the CMF
III-3-2 The concept of contiguity (Miller et al., 1988)
III-4 Viscous flow in dense to hyperdense-suspensions

IV- Mechanism of Melt Segregation

IV-1 Melt extraction mechanism in between the FPT and the SPT
V-1-1 Gravitational compaction
IV-1-2 Compaction by textural maturation (Miller et al., 1988)
IV-1-3 Ascent and collection of small volumes of liquid
IV-1-4 Deformation-assisted segregation
IV-1-4-1 Extensional fracturing
IV-1-4-2 Segregation during continuous deformation
IV-2 Melt extraction mechanism at or above the SPT
IV-3 Competition between different melt extraction mechanism

V- Magma Mobility and Magma Transport

V-1 Magma mobility and thermal convection
V-2- Magma transport: diapirism vs fracture
V-2-1 Diapirism
V-2-2 Fracture transport

VI- Pluton Emplacement Processes

VI-1 Ballooning
VI-2 Stoping
VI-3 Cauldron subsidence
VI-4 Geometry of intrusions and controlling factors

VII- Rheology and Fabrics

VII-1 Below the FRT
VII-2 Between the FRT and the SRT
VII-3 Above the SRT

VIII- Granite Emplacement, and their Related Finite Strain Fields

VIII-1 Methodology
VIII-2 Strain trajectories in granite intrusions: conceptual and field models
VIII-3 Archaean finite strain fields: The examples of the Murchison Province (Yilgarn Craton, WA) and Dharwar craton (South India)
VIII-4 Finite strain field of the Lower Proterozic Saraya Batholith (Eastern Senegal)
VIII-5 Finite Strain Field of the Lower Proterozic Halls Creek Belt (W.A.)



I- Introduction

Partial melting of rocks is the main mechanism responsible for the petrological differentiation of the Earth's continental crust.  Understanding what triggers partial melting, what controls the segregation of melt, and at the other end of the chain, what controls the transport and the emplacement of magmas is a prerequisite to the understanding of the differentiation of the Earth's crust.  These are the aims of the first part of that course.
In the second part, we focus on the structures that develop during the transport and the emplacement of felsic plutons.  We will see plate boundary forces assist melt and the magma to flow away from their source zones.  We will see that buoyancy forces play also a major role in the emplacement of felsic pluton in the upper crust.  Structures that develop during the transport and emplacement of felsic plutons result from the interaction between body forces and boundary forces on a volume of magma whose rheology is continuously changing.  In many case, the finite strain field in and around a granite pluton corresponds to the interference between emplacement and tectonic fabric.  We will see that incremental strain field interferences can lead to very complex structures too often and wrongfully interpreted in terms of superimposition of discrete phase of deformation (finite strain field superimposition).


II- Crustal Anatexie and Crystallization of Magmas

Viscosity of magma is the primary parameter controlling the segregation, transport and emplacement of magma. In addition to temperature, the viscosity of silicate melts is controlled by its SiO2 content (high SiO2 ->high viscosity) and by the amount of dissolved volatiles which is dominated by H2O (high H2O content -> low viscosity). Other volatiles have different effect and for example high fraction of CO2 will increase the viscosiy of melt.  Another very important parameter that affect the viscosity is the amount of crystals and also the shape of the crystal.  The Einstein-Roscoe equation (see Pikerton and Stevenson, 1992; Lejeune and Richet, 1995) is an empirical equation showing that the higher the crystal content the high the viscosity. Interestingly some parameters compete against each other. Indeed magma viscosity will tend to increase as crystallinity increases during cooling, whereas the magma viscosity will tend to decrease due to build-up in melt of H2O content during crystallization of hydrous granitic magmas.

II-1 Effect of temperature

The minimum temperature required to trigger partial melting is about 650ºC. In these conditions, water saturated meta-pelites reach their solidus and produce a melt of granitic composition. The geotherm of a "standard" phanerozoic lithosphere is such that the temperature at the moho is the range of 500-600ºC (Figure 1a and b) making anatexie impossible in the crust.

Figure 1a: Partial melting of pelitic rocks.

Figure 1b: Partial melting of basalt.

For crustal anatexie to occur in the crust one needs to perturbate the continental geotherm and therefore on needs a source of heat. In Phanerozoic lithospheres, orogenic processes such as crustal thickening, lithospheric mantle thinning and underplating of mafic magma can perturbate the geotherm towards higher temperature to produce partial melting. However melting of the crust must be restricted to the mid to lower crustal levels and only extraordinary geotherms would allow anatexis to occur at depths less than 10-15 km. Post-thickening extension following thermal relaxation a the thickened crust, combined or not with mantle delamination or convective thinning, can lead to a such HT-LP geotherm (Figure 2).

During Archaean times however, it is possible that for steady-state conditions the Moho temperature was in the range of 750 to 950ºC (Figure 1). For such conditions, partial melting would have existed without any relation to orogenic or mantellic processes. Considering a water saturated basaltic composition for the Archaean crust, partial melt would have existed from a depth of 25 km down to the moho.

Figure 2: Orogenic geotherms

II-2 Effet of H2O

Water exerts profound influence on melting in granitic systems because it controls the degree of melting to be expected at a given temperature. Figures 3a and 3b show the amount of melt generated at a particular H2O content for muscovite granite and tonalite respectively.

Figure 3a: Role of water in the production of melt: The example of a Muscovite bearing granite.  This space corresponds to Muscovite-bearing granitic magma.  A point in that space corresponds to a magma for which its abscisse and ordinate give its H2O content (% weight) and melt fraction respectively.  The space is contoured for temperature (curve in red) and viscosity (curve in blue, viscosity in Pa.s).

Figure 3b: Same as above but for Tonalitic magmas.

Note that the amount of melt stays constant for all water contents in excess of the water saturation boundary. Both diagrams indicate that very high temperatures are required to generate substantial melt if the water content of the system is low. Although Figures 3a and 3b represent melting of only two specific lithologies at 10 kbar (granite and tonalite), the general features are likely to be similar for melting of other rock types at lower pressures.

II-3 Effet of CO2

Over the temperature range between Tliquidus and Tsolidus, crystallization does not follow a linear function. For a hydrous magma, melt fraction decreases slowly to reach 70% after 95% of cooling. For such a magma, most of the crystallization occurs near the solidus temperature. Because CO2 favours the production of crystals, crystallization of H2O-CO2-bearing magmas will reduce the melt fraction to 80% after 60% of cooling, then to 10% after 95% of cooling. Figure 4 illustrates that point (Scaillet et al., 1997).

Figure 4.Crystallization of CO2-H2O-bearing magmas

Therefore, the effect of CO2 on the rheological properties of magmas is to increase bulk viscosity, in some instances by as much as several orders of magnitude compared to hydrous magmas.

II-4 Effet of fO2

Experimental work shows that fO2 has a profound influence not only on the stability of ferro-magnesian phases but also on iron-free phases such as tectosilicates (Dall’Agnol et al., 1994). As a general rule, for a given temperature and H2O content, oxidized conditions correspond to higher crystal/melt ratio than reduced conditions (Figure 5, Scaillet et al., 1997).

Figure 5. Effect of oxidation at constant melt H2O content on melt fraction

III- The Physical Properties of Magmas and Partially Molten Rocks

Of key importance for fabric development, and to most models of magma segregation, transport, and emplacement is knowledge of bulk-system physical properties, in particular viscosity. Bulk viscosity varies by about 6 to 10 order of magnitude from the solidus up to the liquidus depending on the chemistry of the magma, the percentage of solid particles, the fluid composition, and oxidation state. The whole material behaves as a single phase at the onset of melting, as two separate phases when melt segregates from the matrix, as a liquid with solid suspensions when magma is transported. Despite this complexity the macroscospic rheological behaviour of magmas can be described by three classic laws: Newtonian, pseudoplastic or Bingham (Figure 6) depending mainly on the crystal fraction and the strain rate.


Figure 6: Viscous and plastic behaviour.

III-1 Rheological behaviour of silicate-liquids

Experimental deformations of analogues and natural magmas at temperature above liquidus show that at low strain rate (about 10-5 s-1) magmas are Newtonian (linear dependence between strain rate and stress) (Dingwell, 1995; Douglas, 1963; Murasse and McBirney, 1973; Spera et al., 1988; Shaw et al., 1968; Kushiro, 1980) whereas at higher strain rate their behaviour is frequently non-Newtonian due to the polymerization of the magma (formation of chain of SiO4 tetrahedron) (Li and Uhlmann, 1970; Simmons et al., 1982; Webb and Dingwell, 1990).

III-2 Rheological behaviour of dilute suspensions

Below the liquidus temperature magmas contain suspended crystals, and therefore they can treated as a suspension. The apparent viscosity of the magma (liquid+crystal viscosity/liquid viscosity) depends not only on the solid fraction (percentage of crystals in the liquid) and the composition of the residual liquid, but also on the shape, the size and size distribution of the particles, and on the formation of aggregates. Due to variable magmatic water content, and to a lesser extent temperature, granitic magmas show a wide range in viscosity, ranging from 102 Pa.s, to 1012 Pa.s (Figure 3).

At high melt-fractions (dilute suspension) and low strain rate a silicate liquid behaves approximately as ideal Newtonian fluid (constant apparent viscosity independent on strain rate). Dilute suspensions may be simple modelled as Newtonian fluids with effective viscosity dependent solely on the melt viscosity and the fraction of suspended solids. For example Roscoe (1953) predicts the viscosity of suspensions as follows: ms/mo=(1+Rf)n

ms: viscosity of the suspension; mo: viscosity of the suspending liquid, f: volume fraction of the solid (spherical) particules; R and n: experimentally determined coefficients, with R-1 referring to the maximum crystal fraction (fmax) at which the effective viscosity becomes infinite and the suspension loses mobility. In Roscoe’s original paper R=-1.35 and n=-2.5.

Figure 7 shows the variation of the relative viscosity of suspensions with increasing volume fraction of the solid particles corresponding to spheres in hexagonal close packing (hcp), cubic close packing (ccp) and random packing (rp).

Figure 7: relative viscosity of dilute suspension.

These curves suggest little change in effective viscosity of suspensions for f<0.25. This implies that granitic magma bodies with low crystal contents (<25%) will have similar viscosities to the same crystal-free liquids. Furthermore, the viscosity is not increased by much more than an order of magnitude when f=0.5 (half crystallised magma). This relation has been shown to hold for a volume fraction of crystal lower than 50% in silicate melts (Lejeune et Richet, 1995). Indeed it can be used for more than 90% of the crystallization interval of granitic magmas (cf. Figure 4).

III-3 Rheological behaviour of dense-suspensions
III-3-1 First and Second Rheological Threshold and the CMF

Non-Newtonian behaviour appears to be the rule when f>0.3-0.35. This change in rheological properties is called First Rheological Threshold (FRT). In addition to particle volume fraction, numerous extra factors influence the effective viscosity of dense suspension, resulting in pseudoplastic behaviour (apparent viscosity dependent on strain rate). Among the more important factors relevant to geological systems are grain interactions involving the clumping of particles (aggregation), the size distribution of the particles, possible anisotropic distribution of the particles in a suspension, thixotropic effects (the time-dependent change in suspension properties resulting from deformation), and polymerization (the time-dependent change in suspension properties resulting from the formation of SiO4 tetrahedron chains). These complication may lead to Bingham-type behaviour where suspension has a yield stress (internal cohesion so, Figure 6) which must be exceeded before motion can start (above that threshold the material is Newtonian).

No analytical solutions exists for suspension properties at high particle fractions (f>0.5), and simple, semi-empirical equations shown in Figure 7 are inapplicable to such system. However, all formulas imply that effective viscosity becomes infinite when the solid particles are all in contact, marking the abrupt transition from viscous liquid to elastic solid stress-strain behaviour (Figure 8).

Figure 8: The concept of First and Second Rheological Threshold.

This transition occurs when f is in the range 0.65-0.80 and is marked by a dramatic increase by many orders of magnitude in the effective viscosity of a crystallising granitic magma (8 order of magnitude when f varies form 0.65 to 0.8 in a granitic magma, Wickam, 1987) implying a radical change in mechanical behaviour. This is the Second Rheological Threshold (SRT). Consequently, the strength of the rocks will fall suddenly as some Critical Fraction Melt (CMF, Arzi 1978; van der Molen & Paterson 1979) is reached during ongoing partial melting. The CMF is used to distinguish Second Rheological Threshold, the point at which partially melted rocks lose their suspension-like behaviour (Figure 8).

III-3-2 The concept of contiguity (Miller et al., 1988)

Clearly the CMF will vary in different rock systems with different textures, grain sizes, grain geometry and macroscopic compositional inhomogeneities. However, one approach to constraint actual value of CMF is to examine the contiguity of a system consisting of melt+crystal (Miller et al., 1988). Contiguity is the fraction of surface area of all solid grains that is shared with other solid grains. The concept of contiguity has received particular attention from materials engineers involved in the development of liquid-phase-sintered alloys. Generally, LPS alloys are two-phase materials consisting of grains of a strong, brittle, and refractory metal (W, Mo) and a proportionately smaller amount of largely interstitial, ductile, relatively low-melting metal (Cu, Ni, Co). The contiguity of the refractory grains is of critical importance to LPS alloys since it plays a major role in determining the mechanical properties of the final product. If continuity is high enough to maintain a rigid, three-dimensional skeleton of solid grains then the alloy will preserve its shape at high temperature, despite the presence of melt fractions well in excess of 50%. In addition, an LPS alloy characterised by extensive interconnectedness of the hard phase will take on bulk properties attributable to that phase. Contiguity of the solid in solid-liquid mixture is primarily controlled by the volume fraction of the solid and the average wetting angle (q), and is secondarily affected by grain size distribution. Perhaps unexpectedly, contiguity is very insensitive to surface-energy anisotropy as manifested by non-spherical grain shape. Figure 9 shows contiguity as a function of the volume fraction of liquid for wetting angles relevant for granitoid systems (q=45-60º). Assuming that the system as a whole is characterised by a wetting angle of about 50º, contiguity (C) drops rapidly form 1 to 0.45 with the first 10% melting. Subsequent decreases in C with increased melting are much more gradual such that at 50% melting C=0.2 and at 90% melting C=0.1. Experimental data on various simple systems indicate that the continuous self-supporting skeleton of solid grain breaks down when contiguity falls to a value of 0.15-0.25 (CMFabout 50% melt). There is some reason to regard this as a minimum value: The TaC-Co system- which is characterised not only by a similar value of q but also by blocky crystals reminiscent of feldspars, pyroxenes, and amphiboles- has been shown experimentally to lose solid contiguity at  about 65% melt.

Figure 9: Relationship between contiguity, melt fraction and wetting angle.

These values are considerably higher than the 10-35% proposed by Arzi (1978), and van der Molen and Paterson (1979) for the CMF. The possible consequences of the persistence of solid-phase continuity to melt fraction as high as 0.5 are numerous. Perhaps most important to mechanical properties is that the system will retain a much higher yield strength than a suspension of free-floating grains. If the behaviour in compression of LPS alloys can be taken as a reasonable model, the yield strength of the partially-molten crustal rock may be simply related to that of the solid fraction (the unmelted rocks) through the contiguity. For example, if the contiguity is 0.3 then the yield strength is about 0.3 times that of a 100% solid aggregate of the residual phases. In cases where the yield strength is never reached but a small differential stress is maintained for long time periods, a partially-molten system will exhibit viscous behaviour and deformation by melt-enhanced (i.e. solution-precipitation) diffusion creep, though keeping a high effective viscosity bearing no resemblance to that of a suspension of free-floating grains. If melt-enhanced diffusion creep can dissipate stress sufficiently fast, the yield strength of a partially molten rock may never be reached. Contiguity will be maintained under such circumstances, and the viscosity of the system would remain high (Figure 10). An interesting corollary to the above conclusion is that a flowing magma containing more that 50% suspended crystals is susceptible to ‘locking up’ (i.e. formation of a solid skeleton by establishment of contiguity) if its strain rate falls below a critical value. The magnitude of that critical value is uncertain, except in the respect that it represents the point where viscous flow of the skeleton by melt-enhanced diffusion creep can keep up with the bulk flow of the solid+liquid system. At higher differential stress, the yield strength of the bulk medium (essentially that of the solid skeleton) may be exceeded, resulting in loss of contiguity and reduction in bulk viscosity.

Figure 10: Relative viscosity versus melt fraction for high and low strain rate.

III-4 Viscous flow in dense to hyperdense-suspensions

Hyperdense-suspension may developed because strong preferred orientation of anisotropic crystals reduces the fraction of liquid which is necessary for suspension flow (Longhi and Jurewicz, 1995). Indeed, in granitic melt, hyperdense suspension (f=0.80) may arise if flat crystals such as plagioclase develop a strong preferred orientation induced by magmatic flow. Suspension flow well above the SRT is possible if impingements between moving crystals (locking up) are reduced by melt-enhanced deformation (chemical dissolution or melting at their contact) (Dell’Angelo and Tullis, 1988; Rushmer, 1991, Nicolas and Ildefonse, 1996). This may explain the flow like structures observed in some highly crystallised magma. This suggests that magma mobility can occur when there is sufficient melt (10 to 20%) to occupy the grain boundaries. In that case, magma flow is a response to the applied stresses, not to buoyancy, and probably occurs by grain rotation and liquid flow, grain-boundary sliding processes, grain-boundary dissolution and melt-enhanced diffusion creep. Hyperdense-suspension may show a whole range of behaviour: brittle behaviour at high strain rate, ductile behaviour and viscous flow at low strain.  The following pictures illustrate a natural and experimental example of melt-enhanced deformation.   You can see field examples of this process on this virtual field trip...



IV- Mechanism of Melt Segregation

An interesting, yet poorly understood aspects of granitoid magmatism is the mechanism by which partial melts are extracted from their residues. Melt segregation refers to the separation of the melt fraction from its restite and source during partial melting, whereas magma mobility is the movement of the melt plus its restite (in whole or in part) from its source region. Melt segregation mechanism depends on the permeability of the source region. Melt forms first at grain boundaries and corners between the reactant phases (Figure 11).

Figure 11: Illustration of the concept of average wetting angle.

The melt pockets enlarge as melting progresses and eventually coalesce to form an interconnected network of melt channels along the grain edges. In granitic systems, the dihedral angle where the melt of two grains meet is in the range 44-60º, implying that the liquid will form an interconnected intergranular film, theoretically capable of extraction by intergranular flow. If the dihedral angle were greater than 60º the melt would not be connected and extraction would be impossible.

Once this interconnected network forms, the source is permeable and melt can theoretically migrate, this is the First Percolation Threshold (FPT, Vigneresse et al. 1991), reached at f=0.90-0.98 (2 to 10% melt). Once the FPT is reached, felsic melts migrate only if there is both a driving force and a site into which the melt can move. If melting continues and melt accumulates in the source, then the Second Percolation Threshold (SPT) equivalent to the CMF is reached (for f=0.65-0.8).

IV-1 Melt extraction mechanism in between the FPT and the SPT

At low melt-fraction the extraction of the liquid from the melted rock to form of body of magma is critically dependent not only on the viscosity of the melt and on the geometry of the melt with respect to the crystals (McKenzie, 1984) but also on the existence or not of deformation.

IV-1-1 Gravitational compaction

Partially molten material can compact only if the melt is interconnected, and if the density of the melt differs from that of the matrix (Figure 12). Both these criteria are satisfied during crustal anatexis.

Figure 12: Illustration of the concept of gravitational compaction.

McKenzie (1984) has developed a physical model describing the separation of melt from a partially molten rock at low melt-fraction by gravitational compaction. The conclusion of that model is that even for the lowest viscosity granitic melts, separation by compaction is likely to be very limited in space and incapable of generating large kilometre-sized bodies over reasonable time scales (McKenzie 1985).

IV-1-2 Compaction by textural maturation (Miller et al., 1988)

Niemi and Courtney (1983) observed that after the establishment of a continuous, self-supporting skeleton of solid grains during LPS, a cylindrical sample of 1-2 cm in length will, over a long period of time (hours to days) at constant temperature, expel some portion of its melt fraction to the top. The solid skeleton must undergo compaction for this segregation to occur, yet the gravitational forces acting upon it are far too small to cause mechanical deformation. Niemi and Courtney concluded that this compaction mechanism was a natural consequence of the textural evolution of the sample driven by surface energy minimisation. This refers to the tendency for large grains to grow at the expense of smaller ones. As this coarsening proceeds in the interconnected solid network of a partially molten material, occasional detachments of individual grains occur, and such grains are momentarily free to settle a short distance through the intervening liquid. Over time this process leads inexorable to densification at the bottom of the system and expulsion of the liquid at the top. The geological efficacy of this compaction process is completely uncertain.

IV-1-3 Ascent and collection of small volumes of liquid

Buoyant ascent of small (centimetre-sized) pockets of melt is possible is the viscosity of the country rocks is low enough (Fyfe, 1970; 1973). For a sphere moving under gravity in a viscous medium, the velocity (v) of the sphere is given by:


where g is the gravitational acceleration, r is the radius of the sphere, Dris the density contrast between the sphere and the medium and h is the viscosity of the medium. This implies that for a 10 cm radius drop of liquid to rise 1 km in 106 years, the viscosity of the ‘country rock’ must be less than 3.1011 Pa.s. The Fyfe model suggests that a partly melted zone would have such a low viscosity and that small centimetre-sized ‘blobs’ of melt would rise through it and collect at its junction with overlying sub-solidus rocks, where effective viscosity increases enormously. Eventually, enough liquid would accumulate for a large blob to ascend in the upper crust. The main criticism is that at viscosity as low as 1011 Pa.s any partially melted zone greater than 1 km in size would become instable to convection motion. Convection would interfere with the ascent of discrete pockets of liquid and would tend to homogenise the whole region. It seems likely that an anatectic zone will be either too viscous to allow ascent of small bodies of liquid, or that melt-fraction will be high enough to favour convection, which will overwhelm buoyant ascent of small bodies.

IV-1-4 Deformation-assisted segregation

IV-1-4-1 Extensional fracturing

Fracturing can occur in low melt-fraction rocks, provided the strain rate, pore fluid pressure and the differential stress are high enough. During extensional fracturing, large local hydrostatic pressure gradients develop between the fracture and the surrounding rock, promoting melt flow towards the fracture, and providing a potential segregation mechanism. In granitic systems at low water activity, there is a positive volume change during melting, which will favour high melt hydrostatic pressure and promote extensional fracturing. The efficiency of melt extraction into extensional fractures depends on the magnitude of the pressure drop, the permeability of the rock and the time during which the fracture remains open.

Wet melting at pressures <15 kbar involves the opposite effect, a decrease in the volume of the reactants; hydrostatic pressure will depend on the rate at which deformation, or the flow of aqueous fluids or silicate melt into the low pressure region can accommodate the negative volume change and will probably not become high until substantial melt has formed (>5%).

IV-1-4-2 Segregation during continuous deformation

Filter pressing

Ductile deformation of layers of differing viscosity can theoretically separate melt form low melt-fraction rocks. This situation is similar to that involved in boudin formation. Alternate layers have differing effective viscosities and therefore will suffer different stress, more competent layers supporting higher differential stress. In such system any pore pressure will tend to migrate to the more competent layers. Unlike the extensional fracture scenario, hydrostatic pressure gradients set up in this way are maintained for long periods of time which would favour segregation. The situation becomes more complicated if melt is being generated. Melt generation in competent layers may reduce the hydrostatic pressure gradient and inhibit flow. However, the physics of melt movement within an individual layer are the same as in the gravitational compaction model and therefore this process appears incapable of causing large scale separation of granitic melt from residual crystal.

Dilatant attractors

If continuous heterogeneous deformation occurs during partial melting, strain rate gradient develops in the source region. This instability creates pressure gradients that drive the melt into dilatant attractors such as shear bands, and inter-bouding zones and pressure-shadows. Thus any melt formed in excess of the FPT is squeezed out of the high-stress contacts in the deforming solid matrix and sucked into nearby low-pressure dilatational sites.

IV-2 Melt extraction mechanism at or above the SPT

When melt fraction is above the SPT, segregation can also occur when the melt body can rise buoyantly by diapirism. Diapirism occurs when the buoyancy forces exerted by the melt body are large enough to overcome the yield strength of the wall rocks. Strictly a critical melt mass is relevant here and this may not be reached until the SPT is reached.

IV-3 Competition between different melt extraction mechanism

These conditions for melt segregation are sequential. Provided the source is subject to differential stresses during melting, then the melt will be extracted at the FPT. On the other hand accumulation of melt and subsequent diapirism will develop only if the rate of melt production is greater than the rate of melt extraction. Therefore the particular mechanism by which melt separates from its source depends, largely, upon the interplay between melt-generation rate (broadly related to thermal input) and melt-extraction rate (broadly related to externally applied stresses). If crustal melting is subject only to gravitational compaction, then the melt will probably not leave the source at the FTP but will remain until a sufficiently large volume has accumulated so that diapirism can occur. The rapid production of voluminous melt might raise the melt-generation rate above the extraction rate and allow diapirism swamping the deformation-assisted melt-segregation mechanism. An alternative to diapirism in proposed by Clemens and Mawer (1992). They state that melt accumulates until the increasing pore-pressure induces fracturing, which allows the melt to escape from its restite by buoyant rise before the SPT is reached, thus preventing diapirism.


V- Magma Mobility and Magma Transport

V-1 Magma mobility and thermal convection

Temperature gradient or a gradient of melt fraction may induce an inverted density gradient in a partially melted layer (density of granitic magma 2400 kg m-3) that may become sufficiently unstable that gravity drives a viscous flow. In uniform layers of incompressible homogeneous Newtonian fluids the tendency for thermal convection to occur depends on the non-dimensional Rayleigh number (Ra) where:

Ra= g.a.b.d4/(k.m)

In this relationship the driving force and the destabilising factors in the numerator are g, the gravitational acceleration; a, the coefficient of volumetric expansion, b the vertical thermal gradient, and d the thickness of the fluid layer being considered. In the denominator the retarding factors are k, the coefficient of thermal diffusivity; and m, the kinematic viscosity of the fluid. Convection occurs when the Rayleigh number exceeds a critical value (Racrit) which depends upon the boundary conditions. For free but inflexible top and bottom boundary conditions, convection starts when the Rayleigh number exceeds 657. If one boundary is free and the other is fixed (no slippage occurs along it) the Rayleigh number needs to exceed 1700 for convection to occur. If both boundaries are fixed (isothermal rigid planes) Rc=1708. Magmas are not incompressible homogeneous Newtonian fluids and only rough approximation of their Rayleigh number can be made.

Such a magma flow is restricted to inside magmatic layer. Therefore, even if convection can not account for magma transport across solidus boundary it can account for magma transport in a partially melted lower crust or in large granitic bodies. Large batholiths for example are commonly form by the coallescence of small bodies of different chimical composition. The transport of these "bubles" can be controlled by convection. Bubles of light and hot magma may form in the lower part of a melted layer and rise through the partially melted layer as small diapirs.

V-2- Magma transport: diapirism vs fracture

Numerous plutonic bodies have been emplaced within shallow sedimentary cover. The simple fact that magmas are emplaced within the upper structural level where temperatures are far below solidus indicates that magmas have travelled through the crust. Different model for ascent and emplacement of granitic bodies have been proposed and discussed (Figure 13). Magma transport can be treated as a Mass Transfer Process (MTP, Paterson and Fowler, 1993) where the upward movement of magma is balanced and accommodated by movement of the country rocks. If we exclude from this discussion processes such as in-situ melting, zone melting and metasomatism where no displacement of the country rocks is involved, and if we exclude processes such as cauldron subsidence, stoping, doming, and ballooning that are emplacement processes, we are left with diapirism, and fracture injection as the main candidates for magma transport through the crust.

Figure 13: Mechanism for magma transport and magma emplacement.

V-2-1 Diapirism

A layer of viscous fluid of uniform density overlying a compositionally less-dense layer is unstable. Small perturbation in the horizontal interface become amplified at a rate which depends on the thickness, density and viscosity of the two layers, size of initial perturbation and time elapsed. Diapirism is the result of such mechanical instability also named Rayleigh-Taylor instability. Diapirism ascent of granitic magma is attractive because it is a thermomechanically efficient mechanism that requires no external stresses on the body of magma other than gravity and, in theory, can operate in a range of tectonic scenarios. In contrast to thermal convection there is no critical parameter that controls the onset of Rayleigh-Taylor instability. However the Rayleigh-Taylor number (Rt) measures the vigour of Rayleigh-Taylor instability and its capacity to advect heat:

Rt = Dr g.d3/(k.m)

where D is the density contrast at the interface; g is the gravitational acceleration; d the total thickness of the layer; k the thermal diffusivity; and m the dynamic shear viscosity.

The relative dominance of Rayleigh-Taylor instability or thermal convection can be expressed by a number representing the following ratio:

Rt/Ra = Dr / (r.a.b.d)

Where this ratio is less than one, the overturn is dominated by heat-induced density contrasts and by thermal convection. Where this ratio is greater than one, the overturn is dominated by compositional density contrasts and by Rayleigh-Taylor instability.

Diapirism as a magma transport process is suggested by (1) the circular section of many granitoids from few kilometres to one hundred kilometres in diameter, (2) the shape and finite strain field analogy with salt diapiric intrusion, and (3) simple analogue modelling. However, recent numerical modelling suggests that granitic bodies 1-10 km in diameter, segregated and collected at crustal depth of 25-40 km, at an initial temperature of 800-1000ºC, will solidify and stop moving up at depth >15km. Those numerical models show that the ascent velocity (U) will largely depend on the viscosity within a softened contact zone, revealed in nature by the narrow, highly deformed innermost aureoles of many diapirs:


Dr is the density contrast between the diapir and host, g is gravity acceleration; d is the width of the softened layer (thermal boundary layer), m1 is the smallest viscosity value in the aureole, and A is an exponential factor of viscosity variation (m(x)= m1.exp(A(x)/d); A is in the range of 10 to 35).

The figure 14 presents the temperature contour around a hot sphere at temperature Ts with a radius "a" and vertical velocity U, rising in a fluid of constant viscosity at a temperature To (Daly and Raefsky, 1985). The three experiments correspond to three different value of the Peclet number (Pe). The Peclet number provides a measure of the relative importance of advection to diffusion. For a constant diffusivity and a sphere of radius "a" the Peclet number increases linearly with the vertical velocity of the sphere. For a low vertical velocity the heat loss is dominated by conductive transport and isotherms are approximately radially symmetric, the hot sphere will freeze before significant displacement has occurred. In contrast for a high vertical velocity a very narrow thermal boundary layer developed.

Figure 14: Numerical modelling of a hot sphere travelling in a viscous medium.

However, it seems that the drag which develops during ascent (even for temperature-dependent viscosity) will seriously impede movement, and only the previous warming of the conduit will allow such a hot blob rise.

Therefore diapirism seems unlikely for magma transport in the upper crust.

However, this model may be valid for magma transport in the lower crust where the viscosity of rocks is 2 or 3 orders of magnitude lower than that of the upper crust. Also this model is likely valid for Archaean time when crustal temperatures where higher, viscosity lower, and volume of magma bodies more important than that of Phanerozoic times.

In centrifuge experiments and numerical modelling (Figure 16) three stages can be distinguished in the evolution of the diapir:

(1) and exponential, slow-growth phase corresponding to a doming phase;

(2) a linear, rapid phase during which a trunk is formed by convergent flow of the sinking layer towards the base of the diapir. This convergent flow is balanced by the lateral spreading of the buoyant carapace of the diapir (Figure 15).

Figure 15: Analogue experiment of Dixon (1975)

Such a flow is considered as a wall-effect in analogue experiment and therefore as a laboratory artefact. However, it is of great relevance to explain the origin of ballooning in supracrustal granite plutons. Indeed, horizontal shortening, acting during emplacement can be compared with the convergent sinking of the overburden.

(3) a logarithmic stationary phase during which the diapir reaches a limiting height and spreads laterally causing horizontal shortening of the surroundings. At this

late stage, ring synclines may develop as a consequences of the vertical collapse of the denser layer which is plastically deformed by drag around the rising diapir.

Figure 16: Numerical modelling showing the growth of a diapir.

It is particularly interesting to note that the final volume of a mature diapir is entirely acquired in the doming phase or at the beginning of the linear rapid phase (see figure), in other terms, the upper carapace is not alimented trough the trunk. The horizontal elongated shape of the "canopy" is the result of a change in shape from an original spherical diapir. Consequently, in nature, ballooning plutons can be the result of a change in shape induced by a regional horizontal shortening instead of a process resulting from the continued injection of buoyant materials into the central part of the pluton.

V-2-2 Fracture transport

Effective tensile stresses develop during partial melting from positive DV of fluid absent melting reactions. High volumetric strain rates (10-7) and maintenance of the solid framework of the rock would result in the development of high pore fluid pressures in melt pockets, lowering of effective normal stresses, and thus brittle failure. Syn-melting deformation can only increase this tendency towards fracturing. Stress concentration at the fracture tips will be more that adequate to overcome the tensile strength of any crustal rock type. The nets of fractures developed in the partially molten rocks would rapidly become melt-filled veins. The driving force for vein filling would be the pressure difference between the opening vein and the surrounding rock. Since the melt outside the veins will form a continuous, three-dimensional network, and melt-filled porosity will be relatively high (up to 50%), porous flow into the veins will be rather efficient. If the melt generation zones are actively deforming, then the deforming solid skeleton would be "squeezing" melt into the "sucking" veins. Melt flows small distances (few meters) by porous flow, into mesoscopic veins. These may intersect to form larger veins and/or be tapped by dykes that ascend through the overlying crust. Other discontinuities that could play roles as melt sinks and transport paths include shear zones, shear bands and lithological contacts. However, most important would be the interactions between fracture formation, porous flow and matrix compaction. Once formed, dykes filled with granitic magma will be self-propagating. The density contrast between magma and rock will produce a buoyancy drive. Ascending hydrous magma will expand, in response to decompression. As pressure decreases, the magma will tend to wedge apart the dyke walls, further increasing the tensile stress concentrations at the dyke tip. Calculation for buoyancy-driven elastic fracture propagation show that a single dyke 1 km long and 3 m wide could propagate 20 km in about 8 months and inflate a 2000 km3 batholith in under 900 years (Clemens and Mawer, 1992). That’s speedy!!! A critical requirement for successful transport of magma through a fracture system is that its rate of ascent be fast enough to prevent thermal conduction (to the wall rocks) from causing solidification of the magma. That requirement seems to be verified for fractures 3-4 meters wide.

Since batholiths might be fed by a number of dykes, it appears that fracture propagation is a remarkably efficient means of rapidly transporting large volumes of granitic magma through the crust. Marsh (1984) concluded that a given volume of the same magma flowing through a dyke must move about 104 times as fast as an equivalent volume of the same magma moving as a sphere (diapir), in order to reach a given emplacement depth, from the same starting depth, at the same temperature. Mahon et al (1988) showed that granitoid diapirs probably ascent no faster than about 10-8 m s-1. For a 3-m-wide dyke ascent velocity would be about 10-3 m s-1 around 105 times faster than the diapir. The model of fracture transport is supported by the fact that basal feeder dykes have been observed in some batholiths (LeFort, 1981, John, 1988).

The formation of plutons in the upper structural level of the crust requires the cessation of the upward propagation. The upward propagation will cease when:

• the dyke intersects a highly ductile zone such as a marble, limestone or shale, or a water saturated horizon. This should stop the fracture by converting and dissipating the fracture propagation energy directly to anelastic strain;

• the dyke will intersect a very brittle, isotropic zone; this would cause a large process zone to develop around the fracture tip, thus robbing the parent fracture of its propagation energy;

• the dyke will intersect a roughly horizontal mechanical discontinuity (bedding plane, foliation, compositional layering). In front of the travelling tensile fracture there are two tensile stress concentration, one operating perpendicular and a second oriented parallel to the fracture. That second tensile stress concentration will certainly exceed the tensile strength of any horizontal discontinuity (Figure 17).

Figure 17: Cook-Gordon mechanism

This is known as the Cook-Gordon mechanism (Cook and Gordon, 1964). This model predicts that granitoids plutons should commonly be laccolithic or flattened/tabular in shape. This appears to be common among well-exposed examples, and supported by geophysical investigation. Figure 18 shows plausible pluton shapes and attendant syn-intrusion wall-rock structures developed according the Cook-Gordon mechanism.

VI- Pluton Emplacement Processes

Ballooning, stoping, and cauldron subsidence are the principal emplacement mechanisms of magmatic intrusion. Emplacement processes can be inferred from the structural character of the intrusion: (1) 3 dimensional shape of the pluton, (2) internal structure of the intrusion, and (3) structure of the host rock.

VI-1 Ballooning

Ballooning is a concept proposed by Ramsay (1981) for the emplacement of the Chindamora batholith. Ballooning can solve the classical "room problem" for granite emplacement, i.e. most of the volume for pluton accommodation can be supplied by deformation of the thermal aureole during the in-situ radial inflation of the magma chamber. The inflation of the magma chamber has two possible origins: (1) continuous feeding of the magma chamber through dykes, and (2) the hotter "tail" continues to rise whereas the upper part of the system has ceased its upward ascent. The origin of the stress responsible for wall-rocks deformation is an interesting problem. Assuming no volume change, the average vertical stress (s) from an ascending pluton is given by:

s = Dr.g.a

with a: radius of the body; g: gravitational acceleration and Dr: density contrast. Assuming a density contrast of 400 kg/m3 and a radius of 5 km, a value of 20 bars is obtained; far too small to produce the large deformation associated to ballooning plutons. The ballooning process observable in the diapiric models by Dixon (1975) may be due to a wall-effect and not due to the centrifuge forces. From these considerations it appears that ballooning is the result of a syn-kinematic emplacement. The pluton reaches its final emplacement level and forms an upper reservoir with a funnel-shaped geometry; if during emplacement a regional deformation acts, the pluton is pushed upwards and spreads laterally, acquiring the structural pattern of ballooning pluton. The following characters have been used to support ballooning:

• circular or elliptical shape in horizontal sections;

• concentric zoning of plutonic facies, the central facies generally being more acidic in composition and later with respect to the marginal facies;

• a planar fabric parallel to the contacts and more intensely developed at the border zones where it appears as a gneissic solid-state foliation;

• a planar fabric parallel to the contacts in the host rocks. This is due to pure shear increasing towards the plutons’s contact from unaffected zones;

• synkinematic growth of metamorphic minerals in the thermal aureole.

However, many of these features are permissive but not diagnostic. As mentioned by Cruden (1988) and Schmeling et al. (1988) many of the features used in support of ballooning can form around piercement diapirs.

VI-2 Stoping

Magmatic stoping implies thermal shattering induced by a hot magma in the host rocks and the invasion of fractures by the magma with sinking of the shattered blocks. Fracturation is primarily caused by thermal stress (4 kbar per 100º of heating!!!). The importance of magmatic stoping in magma transport is believed to be very limited because loss of host rocks xenolith sinking in the magma will contribute to its cooling and to the obstruction of the ascent conduit.

VI-3 Cauldron subsidence

Cauldron subsidence is an emplacement mechanism characteristic of anular complexes and has been classically considered as a special case of magmatic stoping. The magma compositions are typically basic (gabbros, diorite). Once emplaced at high crustal levels the basic pluton cools and sinks, favouring the intrusion of other melted materials (granitic) along ring fractures or along the contact with the host rocks. How can a basic magma ascend through a less dense crust? If we assume that rigid crust is buoyant over a partially melted basaltic material, we can then explain the ascent of basic magmas in terms of isostatic re-adjustment. In this sense, the magma can ascend via fractures until at an equilibrium height.

VI-4 Geometry of intrusions and controlling factors

Independently of the mechanism controlling their emplacement, plutons are generally classified into concordant intrusions when the boundary of the pluton is parallel to the structure of the host rock, and discordant intrusions when the pluton is secant on the host rock structure. Sills, laccolith, and lopolith are concordant intrusions whereas dykes, ring dykes and plugs are discordant intrusions. Domes and diapirs can either be concordant or discordant. For intrusions emplaced in the upper part of the crust, the shape of plutons depends upon four main factors:

• viscosity of the magma,

• thickness of the overburden,

• nature of the host rock,

• tectonic context.

Sills, laccoliths, and lopoliths are concordant lens-shaped magmatic intrusions (Figure 18).

Figure 18: Example of concordant intrusion

The magma travels through the brittle crust in a pipe and spreads along a subhorizontal disconformity (low viscosity layer) lifting a domed roof of overburden. The viscosity of the magma and the thickness of the overburden (depth of the intrusion) partly controls the shape of the intrusion: flat intrusions characterise low viscosity magmas and thick overburden; bell-shaped intrusions characterise more viscous magmas and shallow level of intrusion. The presence of a fault can exert further control of the shape of the intrusion (Figure 19).


Figure 19: Influence of faulting on the shape of intrusions.

Both concordant and discordant contacts can be observed when an intrusion is emplaced in different lithologies. For example the Ploumanac’h pluton (Bretagne, North-West France) shows concordant contact with greywackes and discordant contact with earlier granites.

The presence of water in the host rock decreases the viscosity contrast and eases concordant contacts, whereas, CO2 freezes magmas intruding calcareous rocks promoting discordant contacts.

The geochemical composition of the magma controls its viscosity and therefore the geometry of the intrusion. Indeed, SiO2 increases the viscosity of the magma, in contrast some oxides such as TiO2 in mafic magmas contributes to lower the viscosity. Consequently, low viscosity mafic magmas spread laterally to form flat intrusions, whereas more viscous felsic magmas develop globular shapes.


VII- Rheology and Fabrics

The nature and the significance of the microstructures and fabrics that develop in partially melted rocks vary with their rheological behaviour. Because this rheological behaviour varies a great deal between the liquidus (100% melt) and the solidus (0% melt) (Figure 20) one may expect a great deal of change in the nature and significance and magmatic microstructures and fabrics.

Figure 20: Rheology of magma as a function of melt fraction.

In that chapter we will used field relationships to infer rheological properties of magmas of granite composition.

VII-1 Structure and microstructure below the First Rheological Threshold

At that stage, magmas have a Newtonian behaviour, consequently gravitational processes such as sedimentation of crystals and enclaves are favoured. Also, the low viscosity of the magma favour its mobility and therefore its convection. The structures associated are (1) schlieren (aggregates of mafic minerals such as biotite and amphibole stretched parallel to the main flow plane), and (2) magmatic layering (tectonic transposition of non-miscible magma into the main flow plane) that lead to the alternation of layers with different mineralogical composition. Those layers show a rather constant thickness and the absence of boudinage which indicate a low viscosity contrast between layers of different composition. Preferred orientation of crystals is difficult to observe in hand specimen because of the size of the particles, also the turbulent nature of the magma below the FRT may prevent the formation of intense Shape Preferred Orientation (SPO). When mafic magma intrudes felsic magma pillow-lavas form rather than dykes. Felspars from the felsic magma can move inside mafic enclaves, whereas mafic enclaves develop chilled margins. Plate A shows some structures and microstructures that develop below the FRT.

Plate A

VII-2 Between the First and Second Rheological Threshold

Above the FRT the magma is a non-Newtonian fluid, and the crystalline charge is high enough to prevent magmatic sedimentation. The flow of the melt triggers the rotation of crystals and enclaves as well as the viscous deformation of enclaves. Both processes lead to the development of a magmatic fabric marked by a rather strong SPO of anisotropic mineral such as felspar, amphibole and biotite. The fabric inside the enclave is magmatic with a strong SPO. This fabric is parallel to the fabric outside the enclaves. If a low viscosity contrast exists between the enclave and the magma then no fabric refraction or fabric deflection develops. The enclave behaves in the magma without triggering any instability. If the enclave is rigid, the fabric inside the enclaves and outsides may have a different orientation. This miss-orientation may be related to the fabric refraction across the rheological boundary (boundary of the enclave) or related to the rotation of the enclave inside the magma. If rotation occurs the fabric inside the magma should be deflected, wrapping around the enclave developing pressure shadows where melts may accumulate. Mafic magma may intrude felsic magma as dykes. However because of the low viscosity of the felsic magma their are most likely to be desegregated into numerous mafic enclaves as the felsic magma flows. Plate B gives some illustration of magmatic fabrics.


VII-3 Above the Second Rheological Threshold

Beyond the SRT, crystals form an interconnected medium that trigger an abrupt increase of the relative viscosity of the magma. In that domain the rheology of the magma is very complex and strongly dependent on the strain rate and consequently the microstructures and the fabrics that develop in that domain vary largely according to the strain rate. For example mafic magmas can emplace as dykes in felsic magma. Under such a high strain rate the felsic magma behave brittely whereas low viscosity mafic magma flow into the fractures. After the emplacement, the mafic dykes deform plastically under the viscous flow of the felsic magma. Mafic dykes can be folded, sheared and desegregated into mafic enclaves. At such a low strain rate magmatic fabric can further develop with the rotation of solid particles being accommodated by grain boundary dissolution.

Mechanical instability related to the gradient of strain rate lead to the development of folds, magmatic shear zones, and refraction of fabric across composition boundaries. Mafic enclaves may show solid-state high temperature plastic deformation, but also fractures.

At higher strain rates, micro-fractures affect rigid minerals such as felspar but do not propagate farther than a few grains. Those fractures develop because the interconnected nature of the solid phase. In that case stresses are transmitted across the magma and impingement of crystals occurs triggering their fracturing. The fractures are filled with the residual melt. Macroscopic tension gashes and shear fractures may also develop in both mafic and felsic magma, they present limited extension and develop with an high-angle to the magmatic fabric. Plate C, D, and E show some structures and microstructures that develop above the SRT.





VIII- Granite Emplacement, and their Related Strain Fields

Granitoid intrusions occur in a great variety of geodynamic environment, their emplacement is controlled by a variety of mechanism, they have variable thermal impacts on the host rock, and consequently, they show a great variety of finite strain fields. This great variability is further enhanced by the interplay between the rheology of the magma, the rheology of the host rocks, the buoyancy forces, and the ambient tectonic forces and the change of the above parameters through times. Before to comment some granite-related finite strain fields, we will briefly resume a methods to characterise regional finite strain fields.

VIII-1 Methodology

The determination of the strain field associated with intrusionsinvolves determination at the local scale of the characteristics of the finite strain ellipsoid. The finite strain ellipsoid is characterised by three orthogonal axes l1, l2 and l3 (l1>l2>l3) and their respective orientation in space. In the case of a deformed rocks it is assumed that the flattening plane (l1l2 plane) corresponds to the foliation plane, and that within this plane the stretching lineation is parallel to l1. Therefore, some of the characteristic parameters of the finite strain ellipsoid are accessible in the field.

These parameters are:

• the orientation of the l1l2 plane;

• the orientation of the l1 direction;

• the type of the finite strain ellipsoid. Five types of ellipsoid can be evaluated by looking at the relative intensity between the foliation plane and the stretching lineation:

-> S tectonites are defined by a strong planar fabric and weak or no lineation, the ellipsoid is of flattening type,

-> SL tectonites are characterised by a foliation plane and a lineation of equivalent intensity, this fabric characterises a plane strain ellipsoid;

-> L tectonites are characterised by a strong lineation and a weak or no foliation plane, this fabric characterises an ellipsoid of constriction type,

-> intermediate situations can be defined when the lineation is more developed than the foliation (L>S tectonites) or when the foliation is more developed than the lineation (S>L tectonites);

• the strain regime is determined by looking at: the symmetric (coaxial) or asymmetric (non coaxial) deflection of the fabric around rigid objects, the average vergence of asymmetric folds, the obliquity between the foliation plane and the plane where deformation accumulates, etc;

• the kinematic can be determined by looking at shear sense indicators, such as S-C-C’ obliquity and pressure shadows asymmetry around rigid objects in gneisses, S-S’ obliquity in migmatites, crystal tilling in magmas, fold asymmetry, etc;

• strain intensity can usually not be quantitatively evaluated in the field, however it is possible to estimate qualitatively the change of deformation intensity by comparing the deformation of objects (eg. measure of the elongation of mafic enclaves in magma, pebbles in conglomerate, mineral aggregates in crystalline rocks). The integration of these measurements on a map will give a qualitative understanding of the spatial variation of the intensity of the deformation.

In the host rocks, granitic intrusions may develop, in addition to a structural aureole, a metamorphic aureole. These aureoles may or may not correspond and it is alway interesting to map both of them. Where the two aureoles coincide metamorphic crystallisation is syn-kinematic with respect to the emplacement of the pluton. It may happen that deformation aureoles extend far away from the pluton outside the limit of the thermal aureole or that the metamorphic aureole develops in a static environment. The role of regional tectonics can be questioned in the late case. In general when regional tectonics interfere with pluton emplacement, metamorphic crystallisation related to the thermal impact of the pluton are syn-kinematic to the pluton emplacement or to regional tectonics.

VIII-2 Strain trajectories in granite intrusions: conceptual and field models

The finite strain field of diapirs is a result of the diapiric transport of the magma as well as the dynamic of the emplacement of the diapir head. Therefore, the strain field depends of the evolution stage of the diapir and the l1l2 trajectories show abrupt changes in space and through time. The Figure 21a corresponds to a granitic dome that represents the initial stage of the development of a diapir. The l1l2 trajectories changes sharply from vertical in the core and the flanks of the granite to horizontal trajectories at the roof. Statistically however, most of the fabric inside the granite is strongly dipping except at the roof. When the diapir evolves (Figures 21 b-c) this early fabric is progressively deformed, the trajectories become more complex: note the anticlinal fold developing inside the granite, and synclinal fold developing in the host rock.

Figure 21: Strain trajectories on cross-section views across a diapir. After Dixon, 1975

In three dimension, the l1l2 plane can have any dip and any direction. The direction of maximum elongation (l1) is horizontal on the roof with a radial distribution when the diapir has a circular section, and vertical in the core of the diapir. These features can be represented on diagrams where the dip of the l1l2 plane and the pitch of l1 are reported as a function of the strike of the l1l2 plane (Figure 22).

Figure 22: Variation of dip of l1l2 plane and pitch of l1 as function of l1l2 strike

The strain regime changes from coaxial at the roof to non-coaxial along the flank of the diapir.

For non-diapiric intrusions the finite strain field is a response of the inflation (the ballooning) of the magmatic chamber. The ballooning can be symmetric (Figure 23 a-b) or asymmetric (Figure 23 c), so the l1l2 trajectories. Coaxial deformation dominates when the inflation is symmetric, however non-coaxial deformation can be observed when the inflation is asymmetric.

Figure 23: Strain trajectories across non-diapiric intrusions

The l1l2 planes are defined by the preferential orientation of minerals, and also by the orientation of enclaves. Near the margin of plutons, minerals show solid-state ductile deformation. This solid state fabric evolve toward a magmatic fabric (preferential orientation of minerals without ductile deformation) in the core of the pluton. It is important to note the that fabric correspond also to a flattening plane l1l2 of the finite strain ellipsoid. It is a common mistake of interpret magmatic fabrics in terms of magmatic flow.

The finite strain fields presented are valid for single intrusion whose emplacement is not affected by regional tectonics or disturbed by other nearby intrusions. In general, intrusions are coeval with regional tectonics and frequently occurs along with other intrusions. Therefore finite strain fields represent the interference between local and regional strain field (ie., emplacement related strain field and tectonic related strain field). Figure 24 illustrates what happens when the strain field of several intrusions interfere together.

Figure 24: Finite strain field interferences between coeval intrusions

Because of the ballooning, intrusions may collide with their neighbours. Soft collisions develop flat contacts (vertical l1l2 plane, coaxial deformation, oblate finite strain ellipsoid) between the plutons whereas a foliation triple point develop where the three plutons met. Foliation triple point form because the local strain field related to each pluton deforms that of the neighbours. They develop with a triangular shape and strain is characterized by a cigar shape ellipsoid with vertical l1 axis. In the Pilbara the Shaw batholith, the Mount Edgar batholith and Corona Down Batholith developed such an interference strain pattern.

Interference also occurs with regional tectonics. For a co-axial regime the favourable direction for the expansion of the pluton are parallel to the direction of regional extension. The pluton will have an elliptic shape with a long axis parallel the regional horizontal l1 axis (Fig. 25). Along the long limbs of the plutons, the l1l2 trajectory planes in the pluton will tend to be parallel to that of the host domain. Along the hinge zones of the elliptic pluton where margins of the pluton are perpendicular to the regional l1l2 plane, the local and regional strain field compete. Inside the pluton the deformation related to the expansion of the pluton dominates, the l1l2 plane are parallel to the pluton margins. However, when one moves away form the hinge zones of the pluton, the regional and local strain field interfere in a triangular zone where the deformation becomes constrictive with a vertical l1 direction, this triangular domain is a foliation triple point (Fig. 25).

Figure 25: Expansion during regional co-axial deformation.

Moving further form the pluton the regional strain field dominates. Considering now the stretching lineation, the l1 direction in the pluton will depart from a down dip radial distribution (for a pluton with an isotropic expansion) to become parallel with the regional l1 direction. In other terms stretching lineation with intermediate dip will develop inside the pluton and near its margins.

For non-coaxial deformation, two contrasted situations will develop according to the homogeneity or non-homogeneity of the deformation. If the deformation is homogeneous, the favourable direction for expansion is the l1 direction of the incremental strain ellipsoid. This explain that the long axis of elliptic plutons is oriented with an angle to the trajectories of the regional l1l2 planes (Fig. 26). Another consequences is that the l1l2 trajectories are not parallel to the margins of the pluton when the margin are parallel to the long axis of the pluton. The general form of the trajectories are helicoidal. In the host rock, the triple points have an asymmetric distribution with respect to the long axis of the plutonic ellipse. Stretching lineation (l1 direction) are horizontal in the host rock and in the pluton near its margins, but the pitch increases toward the core of the intrusion.

Figure 26: Expansion during regional homogeneous non-coaxial deformation

If the intrusion occurs nearby a shear zone and if one of its margin is affected by the shearing the pluton will develop a coma-like shape (Fig. 27). As for homogeneous non-coaxial deformation, the favourable direction for expansion is the l1 direction of the incremental strain ellipsoid. Therefore the long axis of elliptic plutons is oriented with an angle to the regional l1l2 trajectories. Only one triple point will develop in the host rock, whereas a second triple point may develop inside the pluton where the internal deformation related to the expansion of the pluton and the regional shearing interfere.

Figure 27: Expansion during regional heterogeneous non-coaxial deformation.

As the precedent case, the l1 direction is horizontal in the host rock and in the pluton near its margins, but the pitch increases toward the core of the intrusion.

VIII-3 Archaean finite strain fields: The examples of the Murchison Province (Yilgarn Craton, WA) and Dharwar craton (South India)

In the past twenty years, contrasting models have been proposed to explain the characteristic structural features of the Archaean. For some authors, Archaean geodynamic processes were not different from that of modern times: subduction of oceanic domains and accretion of crustal material were the main mechanisms involved in the growth and structuration of the continental lithosphere (eg., Condie, 1989). For others, Plate Tectonics has no solid ground because crustal-scale nappes and thrusts, and high-pressure metamorphism are absent from Archaean terrains (eg., Kröner, 1991). As an alternative, they suggest that the emplacement of large volume of granitoid was responsible for both the structural and metamorphic characteristics of the Archaean crust (Gee et al., 1981, Collins, 1989; Hill et al., 1992b; Bouhallier et al., 1993; Jelsma et al., 1993; Bloem et al., 1997; Ridley et al., 1997). Geochemical constraints on mafic rocks from greenstone belts, support the view that magmas related to mantle plumes may have been important in building the Archaean crust (Lambert, 1981; Hill et al., 1992b; Kröner and Layers, 1992; Peucat et al., 1993; Arndt 1994; Stein and Hofmann, 1994), and providing the heat responsible for the widespread partial melting and multi-diapirism (Kröner and Layers, 1992; Hill et al., 1992b; Choukroune et al., 1997).

The Murchison province in the Yilgarn craton (Figure 28, map A1 and A2) is a good example of an Archaean domain where such bipartisan models have been proposed. The origin of dome-and-basin patterns in granitoid-greenstone domains is at the core of the debate. For Gee et al. (1981), the occurrence of greenstone sequences as tight synforms in between large granitoid domes (Figure 28, map A1) can be interpreted in terms of diapiric rise of felsic magma and associated downward movement (sagduction) of the greenstones. Myers and Watkins (1985) have presented a fold interference model to explain the same patterns. According to this model, the dome-and-basin structures (Figure 28, map A2) are the product of two orthogonal compressional events responsible for folding of the greenstones and granitoids. These contractional events are interpreted as the far field consequences of subduction zones at the plate boundaries. The paper by Myers and Watkins (1985) is acknowledged worldwide as a classic study supporting Plate Tectonics in the Yilgarn craton. It is however worth noting that neither Gee et al. (1981), nor Myers and Watkins (1985) have presented detailed structural maps to support their views.

Insight from the Murchison Province: Finite strain field in the Yalgoo region

In the Murchison Province, a preliminary study has shown that the fold interference model, put forward by Myers and Watkins in 1985 to explain the dome-and-basin patterns, has no structural ground (Foley, 1997; Rey et al., in prep.). This model was proposed in the belief that a NS regional fabrics, axial planar to regional scale folds, was cross cutting an older EW foliation, also associated with regional scale folds (Figure 28, map A2). Our detailed structural mapping of the strain field around regional fold hinges (Figure 28, map A3 and map A4) shows that: (1) there is a unique regional fabric which presents variable orientations, (2) this regional fabric wraps around hinges of greenstone synforms and trends parallel to the granitoid/greenstone contacts, (3) the nature of this fabric progressively changes from magmatic, in the core of the granitoids, to high-temperature solid state fabric at the contact with the greenstones, (4) kinematic indicators argue for the downward displacement of greenstones relative to granitoids, (5) complex structures (refolded fabrics and small scale dome-and-basin type fold interferences) develop at foliation triple points. The characteristic of the finite strain field argue against the validity of the fold interference model and is compatible with the emplacement of granitic domes into the greenstones.

Modern geological studies in the Archaean craton of south India have revealed that the regional structure, together with the characteristics of metamorphism and plutonism are compatible with the development of craton-scale diapiric instabilities (Bouhallier, 1995; Bouhallier and Choukroune, 1995). The resemblance between the regional structure of the Murchison Province with that of the Indian craton suggests that both cratons have enjoyed a similar Archaean history (Figures 28 and 29). The main feature of these diapiric instabilities is that strain shows a large variability in space. Indeed, planar fabric develops in a domal position, plano-linear fabric develops along linear troughs in between granitic domes, and intense, linear and vertical fabric develops at foliation triple points where linear troughs merge (Figures 29). Local complexity such as the strong variability of both the shape and the intensity of the fabrics, can be interpreted in terms of progressive interference of originally independent strain fields associated with rising domes: Dome-in-dome interferences. More complexity arises from the fact that this interferences occur in the context of a regional shortening (Figure 29).

VIII-4 Finite strain field of the Lower Proterozoic Saraya Batholith (Eastern Senegal)

This study form Pons et al., in 1992 is another nice example of the power of the finite strain analysis applied at the regional scale.
In early studies the Saraya batholith (120 km long, 30 km wide) was assumed to be an homogeneous post-tectonic granitic body intrusive in the Lower Proterozoic sequences of eastern Senegal (Figure 30A). More recently Pons et al., showed that this large granitic batholith corresponds to a composite body consisting of several coalescent plutons and interfering diapirs.

The orientation of magmatic mineral fabric, compositional layering and xenoliths were recorded at more than 500 locations throughout the batholith. A foliation trajectories map of the Saraya batholith (Figure 30B) reveals that this large batholithic body is actually made of several contiguous plutons. Each of them is characterised by internal foliation trajectories displaying a concentric pattern which defines, in horizontal section, a contorted ovoid shape. The dips of foliation are generally higher in the cores of plutons and progressively decrease towards the contacts where they have a slight dip either towards the interior or the exterior of the pluton. This geometry gives a general idea of three dimensional shape of the plutons. In the outer parts of the plutons the intensity of the foliation is stronger than in the inner core. A gneissic foliation has even developed within the 100 to 200 meters of the contact around the northern half of the Saraya pluton. The granite foliation is locally oblique to the pluton boundary where the intrusives are in contact with metasedimentary country rocks. A geometric continuity between pluton internal fabric and country rock cleavage can thus be observed. This is interpreted as being the result of interference between regional and local strain fields, the latter corresponding to a pluton "ballooning" (Figure 30C) Triple points of foliation have been encountered within the country rocks and also in the interior of the Saraya pluton. They are respectively interpreted in terms of finite strain field interference between regional and local strain field, and mutual interference between growing diapirs which initially separated, come in contact, mutually deform each other and, finally fuse to form a single batholith.

The linear structures in the batholith correspond to a stretching fabric within foliation plane. It is defined by the streaking of biotite and muscovite clusters and quartz aggregates and is often more difficult to observe than planar structure. No shear criteria has been observed. The lineation, remarkably parallel to the long axis of the pluton (N040) is subhorizontal or plunger gently (never more than 20º) often northeasterly. Parallelism between these plutonic lineation and the host-rock lineation confirms the synkinematic character of the pluton emplacement. The horizontal arrangement suggests also that the stretching deformation recorded by plutonic rocks corresponds essentially to a lateral expansion, and not to an ascent of the plutons.

VIII-5 Finite strain field of the Lower Proterozic Halls Creek Belt (W.A.)

The East Kimberley (Figure 31. A-B) is part of the Barramundi Orogeny that has affected northern Australia between 1880 to 1820 Ma. The deformation and metamorphic style of this orogen have been mainly defined in the Halls Creek Mobile Zone (HCMZ) which is considered has a key region for Australia Lower Proterozoic orogeny (Hancock and Rutland, 1984; Etheridge et al., 1987).

The Halls Creek/King Leopold Mobile Zone is a linear belt several hundred of kilometer long and few tens of kilometer wide (Figure 31. A). This linear belt wrap around the Kimberley Plateau whose Proterozoic sediments are inferred to be deposited on top of an Archaean craton. Deformation, metamorphism and magmatism are strongly localised in space and time. Indeed the Barramundi deformation is inferred to have last less than 20 Ma.

The rocks formation of the Halls Creek Mobile Zone has been divided on two groups (Gemut, 1969) (Figure 31.B).

Halls Creek Group consists of Lower Proterozoic volcano-sedimentary rocks. From top to bottom (Smith, 1963): Olympio Formation (Greywacke-siltstone-shale mid-fan facies), Woodward Dolerite, Biscay Formation (volcano-sedimentary sequence), Saunders Creek (deltaic and marine facies ), and Ding Dong Down (bimodal volcanics). The upper part of Halls Creek Group overlies the 1910 Ma felsic and mafic volcanics of the Ding Dong Downs Formation and the 1910 Ma Sophie Downs Granite. Felsic volcanism has been dated at around 1870 Ma in the Biscay Formation and 1857 Ma in Olympio Formation.

Lamboo Group forms the nucleus of the HCMZ. It consists of the Tickalara Metamorphics, inferred to be the metamorphic equivalent of Halls Creek Group, intruded by mafic and felsic igneous rocks. Geochronological data indicate that the Lamboo Group developed in between 1870 and 1820 Ma. In the low grade metamorphic rocks of the Tickalara Metamorphics, the structural style is similar to the Halls Creek Group: folds and numerous small shear zones and faults are common. In the high-grade rocks the structural style is more complex, and more than one phase of penetrative deformation has been described.

Based on "cross-cutting" relationships, four phases of deformation (D1 to D4) have been defined (Hancock and Rutland, 1984). In the Lamboo Group, D1 and D2 are two "high-grade" deformation phases, whereas D3 and D4 are retrogressive folding and faulting (Figure 31. D). This approach is not sufficient in crystalline basement and can lead to the misinterpretation of the deformation history in particular when deformation is coeval with magmatism (finite strain field interference).

In fact  the fabric of the granodiorite, hitherto interpreted has ductile foliation, is a magmatic foliation developed during the emplacement of the plutons, and folding and shearing occured during magmatic state. Therefore the inferred overturned anticlinal folding (Figure 31. D) affecting an inferred composite foliation (S1-2) (Gemut, 1971, Hancock and Rutland, 1984) is likely to be related to the magmatic flow of the pluton during is emplacement. If the internal structure of the granodiorite has a magmatic origin, then the D1 to D4 phases of deformation must be revisited...



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