Late-stage magma flow in a shallow felsic reservoir: Merging the anisotropy of magnetic susceptibility record with numerical simulations in La Gloria Pluton, central Chile

Authors

  • F. Gutiérrez,

    Corresponding author
    1. Advanced Mining Technology Center, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Santiago, Chile
    2. Departamento de Geología/Centro de Excelencia de Geotermia de los Andes (CEGA-FONDAP 15090013), Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Santiago, Chile
    3. Earth and Space Sciences, University of Washington, Seattle, Washington, USA
    • Corresponding author: F. Gutiérrez, Advanced Mining Technology Center, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Santiago 8370451, Chile. (francisco.gutierrez.ferrer@gmail.com)

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  • I. Payacán,

    1. Departamento de Geología/Centro de Excelencia de Geotermia de los Andes (CEGA-FONDAP 15090013), Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Santiago, Chile
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  • S. E. Gelman,

    1. Earth and Space Sciences, University of Washington, Seattle, Washington, USA
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  • O. Bachmann,

    1. Earth and Space Sciences, University of Washington, Seattle, Washington, USA
    2. Institute of Geochemistry and Petrology, ETH Zurich, Zurich, Switzerland
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  • M. A. Parada

    1. Departamento de Geología/Centro de Excelencia de Geotermia de los Andes (CEGA-FONDAP 15090013), Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Santiago, Chile
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Abstract

[1] La Gloria Pluton is a 10 Myr old epizonal intrusion located in the southern Andes. We present anisotropy of magnetic susceptibility data that indicate a magnetic fabric that is mainly oblate. We find that lineations are weak and have a N-NW trend with a nearly horizontal dip, while foliations are more pronounced, have NW trends, and have dips that vary from vertical at the walls of the intrusion to horizontal at the center and under the roof of the chamber. To interpret these magmatic fabrics, we developed a time-dependent 2-D magmatic fluid dynamic numerical simulation. Our model is calibrated with MELTS and accounts for the coupled processes of cooling, crystallization, and degassing of a magma chamber. Simulations indicate that the resulting convective flow pattern in the crystallizing reservoir is consistent with the magnetic fabric, which is largely produced in the shear zone between the convecting liquid-dominated core and the growing solidification fronts adjacent to the walls. The magnetic fabric records the last increment of strain induced by convective magmatic flow in the cooling reservoir during crystallization at the rheological magma locking point along solidification fronts. Despite the small size of the pluton, the core of the chamber remains thermally insulated from the colder host rocks, surviving up to 20 kyr above the solidus, which allows enough time for the extraction of residual leucogranitic melt and partial late magmatic reactive recrystallization. The results of the simulations are also consistent with the previously determined compositional and mineralogical zonation patterns in the pluton.

1 Introduction

[2] Both regional tectonic strain (clearly associated with shear and fault zones) and emplacement and/or magma flow-related strain can be determined through anisotropy of magnetic susceptibility (AMS) fabrics in plutons [e.g., Žák and Paterson, 2005; Archanjo et al., 2008]. Several studies have indicated that AMS data can serve as a record of strain directions in tectonically unperturbed plutons and can provide insight into the dynamics of magma reservoirs, since magnetic fabrics are thought to be produced by magma flow [McNulty et al., 2000; Parada et al., 2005; Gil-Imaz et al., 2006]. Interpretations of the AMS data as indicators of magma flow have been based on the following observations [e.g., Knight and Walker, 1988; Dragoni et al., 1997; McNulty et al., 2000; Be Mezeme et al., 2007; Archanjo et al., 2008]: (1) In many cases, magnetic fabrics within plutons do not coincide with regional host rock structures, such as fractures and shear zones; (2) lineation is concordant with measured magma flow directions in dikes and lava flows and coincides with the main elongation of plutons; and (3) foliation is generally parallel to the vertical wall showing a high foliation dip near vertical walls that incrementally decrease in dip toward the upper levels and interior of plutons, yielding a roughly concentric foliation pattern. Local vertical foliations in the pluton interior have been interpreted as magma feeder channels [e.g., Philpotts and Asher, 1994; McNulty et al., 2000].

[3] However, the regime and nature of magma flow generating AMS data remains controversial. Some studies have interpreted AMS data as a record of flow during magma emplacement [e.g., McNulty et al., 2000; Parada et al., 2005; Be Mezeme et al., 2007; Stevenson et al., 2007], suggesting that magnetic fabrics record the early stages of pluton growth. Indeed, AMS patterns in small magma bodies with high cooling rates (e.g., lava flows, sills, and dikes) are consistent with such emplacement-related flow [Dragoni et al., 1997]. However, in the case of large magma bodies, which are assembled incrementally in multiple pulses, longer solidification histories are expected [e.g., Annen, 2009; Matzel et al., 2006; Walker et al., 2007], and AMS data are likely to be affected by subsequent convective flow during the prolonged solidification stage of the magma body. These later-stage convection currents will tend to reset the emplacement-related record of AMS and magmatic fabrics, preserving only the last increment of strain during crystallization [Paterson et al., 1998]. Interestingly, the AMS tensor variations often occur on a pluton-wide scale and change incrementally from one side to the other [e.g., Stevenson et al., 2007; Archanjo et al., 2008; Coleman et al., 2012]. Such an observation points toward late-stage convection patterns in magmatic systems.

[4] This study presents (1) a new, extensive data set of AMS measurements on a small, upper crustal silicic magma reservoir in the Southern Andes and (2) a 2-D time-dependent numerical model aimed at reproducing the magma flow patterns of a similar simulated crystallizing magma chamber. Using this model, we record shear rates as a function of time for the well-constrained initial conditions derived from our case study magma chamber and relate this to the AMS data. The ultimate goal is to better characterize the underlying magma fluid dynamics associated with solidification of felsic magma reservoirs in the shallow continental crust.

2 La Gloria Pluton, Central Chile (33°S)

[5] La Gloria Pluton (LGP) is a 10 Myr [Cornejo and Mahood, 1997; Deckart et al., 2010] epizonal intrusion in the Southern Andes, located 40 km east of Santiago, in central Chile (Figure 1). It was emplaced during an active period of Andean magmatism (with both plutonic and volcanic units) [Vergara et al., 1988] and belongs to a N-S extending cluster of middle-late Miocene belt of quartz monzonite and granodiorite plutons [Drake et al., 1982] of about 13–10 Myr. LGP is ~20 km long, 3-6 km wide and has 2.5 km of vertical exposure, exhibiting a NW axisymmetric elongated shape [Mahood and Cornejo, 1992]. Wall rocks consist mainly of Oligocene-Miocene continental volcanic and volcaniclastic rocks (Abanico Formation) [Thiele, 1980; Nyström et al., 2003], where strata dips at the west margin are 10°W–20°W, while they are dipping 50°E–70°E at the east margin (interpreted to indicate a large-scale anticlinal structure). Although LGP was emplaced to the west of an inferred reverse north-to-south fault system (Figure 1), it exhibits no significant post-intrusion deformation [Cornejo and Mahood, 1997]. Although the floor of LPG is not exposed, the roof has been extensively preserved, including overhanging blocks of roof rocks, as well as smaller stopped volcanic xenoliths locally near the margins of the pluton.

Figure 1.

(a) Geological map of the studied area with the location of the sites of sampling. (b) Magnetic Lineation. (c) Magnetic Foliation. Modified from Thiele [1980], Cornejo [1990], and Castro [2012].

[6] LGP is a small, isolated magma body that lacks internal contacts and was emplaced shallowly (about 4 km depth) [Cornejo and Mahood, 1997; Aguirre, 1960]. Hence, it is thought to be a near closed-system magma chamber, assembled in only a few pulses, and having had a short cooling history [Cornejo and Mahood, 1997] (<1 Myr based on laser ablation inductively coupled plasma–mass spectrometry data on zircon) [Deckart et al., 2010] and limited subsolidus reequilibration (except for Fe-Ti oxides, which reequilibrated at temperatures below the solidus, ~450°C–584°C) [Cornejo and Mahood, 1997]. It shows some vertical and concentric compositional and mineralogical zonation which gave rise to lower and middle levels, both with border zones, and an upper level [Cornejo and Mahood, 1997]. The zonation pattern shows variation from quartz monzodiorite with minor granodiorite in the core, to quartz monzonite with minor granite toward the borders of the pluton. Similarly, an increase of Hb/(Hb + Bt), Or/(Or + Plag), and volatile fugacity (fO2, fHCl, and fHF) and a decrease of late magmatic reequilibration have been identified toward the roof and walls [Cornejo and Mahood, 1997]. This zonation pattern appears to be mainly a consequence of late magmatic reequilibration (while temperatures still remained higher than 720°C–750°C) due to slower cooling in the pluton interior [Cornejo and Mahood, 1997]. This is supported by textural and/or compositional mineral reactions, such as the association of subhedral biotite and magnetite with clots of actinolitic amphibole [Cornejo and Mahood, 1997].

[7] Highly differentiated leucogranite dikes and sills are ubiquitous in LGP. They range in size from centimeters to hundreds of meters in width and are hosted in both LGP and its volcanic envelope [Mahood and Cornejo, 1992]. Mahood and Cornejo [1992] suggested that these leucogranites were residual liquids generated by crystallization elsewhere in the chamber. The geometry of the leucogranite dikes hosted in the pluton varies from straight to curved, reflecting the fact that the evolved liquids were extracted and accumulated during the late-magmatic stage along cracks in the partially solidified magma reservoir (“crystal mush”), and, in some cases, were subsequently deflected by late movements of the mush.

3 AMS Data

[8] Samples for AMS measurements were collected at 46 sites distributed close to the roof, walls, and in the main body of La Gloria Pluton. Sampling covered more than 2.5 km of vertical exposure. The samples were analyzed triaxially with a Kappabridge AMS System (Model KLY-3S from AGICO) with 3 × 10−8 SI resolution in the Laboratory of Paleomagnetism, Department of Geology, University of Chile.

[9] Unblocking temperatures around 600°C during thermal demagnetization experiments, relatively high magnetic susceptibility values (K > 3 × 10−2 SI; Figures 2a and 3a), as well as microscopic observations and compositions [Cornejo and Mahood, 1997] indicate that Ti-poor multidomain magnetite dominantly controls the magnetic susceptibility signal. The magnetic susceptibility (K; Figure 2a) ranges from 2 to 10 (10−3 SI), whereas anisotropy degree values (P = L*F, where L and F are the magnetic lineation and foliation, respectively; Figure 2b) range from 1.01 to 1.17 (Figure 3a). There is an increase of K toward the upper level and walls of the chamber (Figure 2d), consistent with a roofward and wallward increase of magnetite content [Cornejo and Mahood, 1997]. Magnetic fabric is generally oblate (F > L in Figure 3b and T > 0 in Figure 3c, where T is the shape parameter, a degree to which the ellipsoid is oblate or prolate, following Jelinek [1981]). The lowest anisotropy degree values correspond to (i) prolate sites with horizontal contacts with wall rocks (typically around the roof of the pluton, Figure 3a) and in the pluton interior (Figure 2b) and (ii) oblate sites under the roof of the pluton (Figure 3c). Relatively high anisotropy degree values (P > 1.10) are in the east contact and upper levels of the pluton (Figures 2b and 2d), indicating a roofward and wallward increase of the anisotropy degree values with respect to the middle level and the center of the pluton.

Figure 2.

Distribution (contour maps and sections) of the anisotropy of magnetic susceptibility (AMS) results: (a) magnetic susceptibility (K), (b) anisotropy degree (P), and (c) shape parameter (T) [Jelinek, 1981]. Contours representing biharmonic spline interpolation (Sandwell 1987) of mean values. Only interior and walls values are considered in Figure 2c. Sections are normalized to the pluton width in a direction N60°E.

Figure 3.

(a) Anisotropy degree versus (P) magnetic susceptibility (K). (b) Magnetic lineation (L) versus magnetic foliation (F), indicating that most of the AMS tensors of the La Gloria Plutons are oblates, but they are rarely prolates (anisotropy degree is given by foliation rather than lineation). (c) Anisotropy degree (P) versus shape parameter (T) [Jelinek, 1981]. (d) Dip of magnetic foliation from the west to the east side of the La Gloria Pluton in direction to N60°E, perpendicular to the main elongation of the pluton (N30°W). Dashed lines show a perfect linear trend from vertical at walls to horizontal at the center and best linear fit, respectively. Error bars represent 95% of confidence (2σ error).

[10] Magnetic lineations have a N-NW trend (Figure 4a), a subhorizontal dip, and low mean values (L, given by the direction of maximum anisotropy) between 1.00 and 1.05 (Figure 3b). Magnetic foliations (F, plane whose pole is the minimum anisotropy axis) have a NE-SW trend (Figure 4b), with mean F values ranging from 1.00 to 1.14 (Figure 3b). The foliation dip changes regularly from vertical at the walls to horizontal at the center of the LGP (Figures 2c, 3c, and 4b). This tendency produces a linear trend with respect to the width of the pluton, and it is present at almost all sites (Figure 3d), with the only exception of some sites that are directly under the roof (sites 22, 23, 25, 26, 27, 28, and 35). The dip angle of F increases up to 89° ± 12° (2σ error) from the core to the wall of the LGP (linear correlation coefficient R of 0.92). Because the pluton is wider southward, the observed variation of the dip angle of F with distance across the pluton varies southward from 50°/km (R value of 0.96) to 34°/km (R value of 0.86).

Figure 4.

Lower hemisphere Schmidt projections of (a) K maximum, representing lineation directions, and (b) K minimum values, representing perpendicular directions to foliation planes. Arrow represents the main direction of elongation of the La Gloria Pluton. Contour intervals are 2σ. Maximum values in the rose diagram are 10.9% between 331° and 340° (coinciding with the main direction of elongation of N30°W) and 15.2% between 231° and 240° for K1 and K3, respectively. Projections were obtained by using Stereonet [Allmendinger et al., 2012] including the contours (Kamb) and rose diagrams.

[11] La Gloria Pluton was emplaced in an anticline with a N30°W direction (Figure 1) [Cornejo, 1990], indicating that the elongated shape of the pluton in the N-S direction is controlled by the local tectonic stresses. However, the absence of deformation post solidification and the axisymmetry of both the pluton shape and the concentric magnetic fabric suggest a magmatic origin of the magnetic fabric [Paterson et al., 1998]. Magnetic lineation parallel to the main elongation axis of the pluton and concentric magnetic foliation has been reported in classical studies in dikes and sills where the magmatic origin is unquestionable [e.g., Knight and Walker, 1988; Tauxe et al., 1998] and can be also found in very large batholiths [e.g., McNulty et al., 2000] completely decoupled from structures of the wall rocks.

4 Numerical Modeling of the Late-Stage Fluid Dynamics of the Crystallizing LGP

4.1 Thermodynamic Constraints on Phase Equilibria and Physical Properties

[12] In order to assess the role of the magma dynamics and/or magma flow during the final cooling of silicic plutons, we present a numerical model based on an adaptation of the time-dependent fluid dynamic and thermodynamic modeling of a basaltic chamber [Gutierrez and Parada, 2010] to a felsic and larger reservoir that simulates the LGP. This model is based on the crystallinity, viscosity, and density dependence of temperature and composition obtained using MELTS [Ghiorso and Sack, 1995; Asimow and Ghiorso, 1998] considering the following: (1) pressures of 1 and 2 kbar, representing pressures from the roof (1.2 and 2.3 kbar for the lower-level border zone of the LGP and in mafic enclaves, respectively, based on amphibole geobarometry [Cornejo and Mahood, 1997]) and at 4 km depth as indicated by the estimated thickness of the volcanic and volcanoclastic cover at the time of intrusion [Aguirre, 1960]; (2) oxygen fugacity of QFM + 2, as suggested by Cornejo and Mahood [1997] for amphibole-biotite equilibrium [Carmichael, 1967]; (3) initial magma composition (62.8 wt. % of SiO2) of the middle level according to Cornejo and Mahood [1997]; and (4) initial water contents of 2.5 and 4.0 wt. % of H2O (considering initial water undersaturated and saturated conditions). We also ran simulations using the new MELTS calibration for silicic magmas (Rhyolite-MELTS) [Gualda et al., 2012]; the two calibrations yielded very similar results for the LGP magma compositions (see supplementary material for comparison between MELTS and Rhyolite-MELTS results).

4.1.1 Composition

[13] The main body of LGP is dominantly a monzodiorite with a composition of 63 ± 2 wt % SiO2. The leucogranitic dykes and sills are more evolved, with compositions around 76–78 wt % SiO2 (Figure 5). MELTS and Rhyolite-MELTS liquid compositions show the same liquid composition trends, despite variable assumptions in crystallization pressure and variations in water content (see supplementary material). Compositions of leucogranites are similar to the calculated melt composition (Figure 5) at above ~60% crystallization (Figure 6a). At 700°C, MELTS overestimates calcium (Figure 5d) and phosphorus because MELTS does not stabilize adequately apatite, which is a ubiquitous accessory phase. This suggests that leucogranites can be produced by crystallization from the bulk magma body, representing liquid compositions.

Figure 5.

Major element composition of the La Gloria Pluton determined by Mahood and Cornejo [1992] with a 95% level of confidence (error bars) and the compositional trends of residual liquids derived from MELTS [Ghiorso and Sack, 1995; Asimow and Ghiorso, 1998] considering pressures of 1 and 2 kbar and saturation and undersaturation water conditions, between 2.5 and 4.0 wt % of H2O in the initial composition. Note that most of the curves reach the composition of the leucogranites. Error bars represent 95% of confidence (2σ error).

Figure 6.

Physical parameters obtained by MELTS [Ghiorso and Sack, 1995; Asimow and Ghiorso, 1998] considering pressures of 1 and 2 kbar and saturation and undersaturation water conditions, between 2.5 and 4.0 wt % of H2O in the initial composition: (a) crystallinity, (b) density of the liquid and the magma, (c) viscosity of the liquid and the magma, and (d) crystallization sequence (in vol. %) considering 2 kbar and 2.5 wt % of H2O.

4.1.2 Density

[14] In MELTS simulations, the density of magma without exsolved H2O (magma = crystals + melt) only differs by less than 90 kg/m3 throughout the entire temperature range (Figure 6b) and varies almost linearly with changes in temperature and crystallinity. In contrast, magma density that accounts for an exsolved volatile component (magma = crystals + liquid + bubbles) varies more significantly (up to 680 kg/m3), especially for low-pressure conditions (1 kbar).

4.1.3 Viscosity

[15] Viscosities calculated by MELTS [using the Shaw, 2008 algorithm] are consistent with values obtained with the formulation of Giordano et al. [2008] (Figure 6c). Liquid viscosities vary nearly exponentially with temperature, whereas magma viscosities strongly depend on crystallinity. Throughout the entire temperature range, viscosity values are higher for the 1 kbar case than for the 2 kbar case; this effect is likely due to the higher solubility of water at higher pressures.

[16] To calibrate the fluid dynamics simulations, we chose the model of MELTS with 2.5 wt. % of H2O at 2 kbar (Figure 6d), based on the following criteria: (1) the lack of pervasive late magmatic and subsolidus reequilibration conditions in LGP (e.g., hornblende as reaction border on clinopyroxene), which suggests that the magma in the lower and middle levels of the pluton were not initially water saturated until late in the magmatic crystallization history of the pluton [Cornejo and Mahood, 1997]; (2) these conditions reproduce all the phases present in the LGP, including clinopyroxene, orthopyroxene, plagioclase, K-feldspar, amphibole, biotite, magnetite, rhm-oxides, quartz, and apatite; and (3) the whole compositional range (from 62.8 to 71.3 wt % SiO2) observed in the pluton is covered. Thus, for the majority of the crystallization path of LGP, the 2 kbar, 2.5 wt % H2O MELTS simulation should be the most appropriate thermodynamic model (Figure 6d). We stress that the different versions of MELTS (MELTS and rhyolite-MELTS) give very similar results (see supplementary material); hence, the choice of the given thermodynamic model will have little impact on the final results of the fluid dynamical simulations. Moreover, although MELTS does not appropriately model the stability of amphiboles (which are present in LGP), we use the thermodynamic results as a first-order constraint on (1) the physical properties of the magmas (density, viscosity) and (2) the crystallinity-temperature path. The fact that amphibole stability is delayed in the MELTS simulations will have little effect on those parameters.

4.2 Governing Equations

[17] We present a numerical model of the physical processes occurring in a magma reservoir based on the combination of the thermodynamic and fluid dynamic models, following the mixture approach proposed by Gutierrez and Parada [2010]. We solve the time- and space-dependent partial differential equations for energy, mass, and momentum in the reservoir using the finite element method (FEM) with the COMSOL Multiphysics© software.

4.2.1 Heat Transfer

[18] The conservation of energy equation solved to obtain the temperature of the magma considers conduction, convection, and latent heat and is given by

display math(1)

where ρ is the density, Cp is the heat capacity, T is the temperature, k is the thermal conductivity, qL is the latent heat, ϕc is the volume fraction of the exsolved phase, and u is the phase displacement velocity.

[19] Because temperature discontinuities along the margin of the chamber produce oscillations in FEM results, we assume that the walls are not perfect conductors. For that reason, we use a heat flux across the margin of the chamber (qr), given by the temperature difference between the magma (T) and the country rock (Tr), triggering phase exsolution and convection [Brandeis and Jaupart, 1986; Martin et al., 1987]. The heat transfer into a H2O-free country rock beyond the margin of the chamber is obtained from a similar equation, but without consideration of advective heat transfer, i.e.,

display math(2)

where□ρr is the density, Cpr is the heat capacity, Tr is the temperature, and kr is the thermal conductivity of the rock [Chapman and Furlong, 1992].

[20] The heat flux across the boundary of the magma chamber (qr) is given by the following Neumann boundary condition:

display math(3)

where n is the vector normal to the chamber boundary, and Lr is the distance of thermal effect in the country rocks from the reservoir walls of the heat flux. The heat conduction through the country rock simulates the temperature evolution of the host rock around the chamber but does not consider the possible effects of hydrothermal circulation (which are thought to be negligible in the LGP case) [Cornejo and Mahood, 1997].

[21] The initial temperature of the country rocks and the border temperature conditions far away from the chamber are given by

display math(4)

where Trº is the ground surface temperature, and Gr is the geothermal gradient. Through field observations surrounding LGP, we find that the thermal influence of the chamber is negligible at a distance of ~1–2 km away from the walls; the contact aureole in LGP (biotite-pyroxene hornfels and partially melted volcaniclastic breccias) reaches only a few tens of meters around the middle and upper levels of the pluton [Cornejo and Mahood, 1997]. Beyond this 1–2 km limit (L > Lr), the host-rock system is near adiabatic [Gutierrez and Parada, 2010].

4.2.2 Exsolution of Phases

[22] We use the Gutierrez and Parada [2010] magma chamber model to obtain the total crystallinity (X = ϕcs) and gas water exsolution (ϕcg), where the volume fractions of the exsolved phases (ϕ j) are explicit error functions of temperature only. Because we are interested in only the latest chamber processes and because crystal-liquid separation is not expected to be efficient before ~50 vol % crystallization [Dufek and Bachmann, 2010], we assume that no crystal fractionation takes place; only exsolved water can move differentially from the magma. The exsolution rate with respect to the temperature of each j phase (solids and H2O) from the liquid is adjusted by the sum of a Gaussian probability function that depends on liquid temperature, i.e.,

display math(5)

where j designates the solid (crystallinity) or gas H2O phase, j is the number of functions needed to represent crystallinity and exsolved water, and ϕj,if, μ j,i, and σ j,i are the final volume fraction of the j phase, the mean, and the standard deviation of the exsolution temperature of each i function, respectively. The parameters ϕj,if, μ j,i, and σ j,i can be calibrated from data obtained by MELTS. The volume fraction of the overall solid phase that crystallized, or crystallinity, and the volume fraction of the exsolved water, at temperature T from each residual liquid (ϕc), are obtained by the following error function:

display math(6)

where Tm is the maximum temperature from which these parameters have been calibrated.

4.2.3 Magma Fluid Dynamics

[23] We use the incompressible Navier-Stokes formulation of conservation of momentum and mass, i.e.,

display math(7)
display math(8)

where ρm is the magma density, g is the gravity acceleration vector, math formula is the liquid velocity, p is the pressure, and μ is the dynamic viscosity. Both ρm and μ are error functions and depend on temperature. We assume that as water is exsolved, it is immediately fractionated (removed from the site of exsolution). Then, ρm is the magma density of the magma without exsolved H2O, given by

display math(9)

where ρm° and ρi f are constants, is the number of functions needed to represent density, and νρ,ι and σρ are the mean and the standard deviation of each i function for density, respectively. Following the same scheme, the dynamic viscosity is given by

display math(10)

where ν10max and ν100 are the maximum viscosity and a constant, respectively; is the number of functions needed to represent viscosity; and νi f, μν,ι, and σν are a constant, the mean, and the standard deviation of each i function for dynamic viscosity, respectively.

[24] The liquid flow along walls is controlled by the no-slip boundary condition in an insulated chamber (no volume of magma penetrates beyond the walls). In other words, we assume that the melt does not flow across the wall-liquid interface, i.e.,

display math(11)

[25] The shear dip (SD) is defined to be analogous to the dip of magnetic foliation in an image that shows west-east as right-left: dip is positive to east, or right, and negative at west, or left. The foliation dip, defined by the velocity field, is given by

display math(12)

where uy and ux are the vertical and horizontal components of velocity, respectively.

4.3 Initial Conditions

[26] The numerical model presented in this study attempts to reproduce the late-stage fluid dynamic evolution of a silicic chamber over ~10 kyr of cooling; hence, our model starts at 850°C (~47 vol % crystals). At that temperature, the reservoir is still liquid enough to allow convection along the walls; however, any previous convection currents would be likely not preserved by AMS data and, therefore, are not modeled (saving a lot of computational time). The 2-D model geometry adopted a section for the reservoir based on the shape of a N60°E section of the axisymmetric N30°W elongated LGP, which is a triangle with a stepped roof, representing overhanging walls, as described by Mahood and Cornejo [1992]. The 2-D section is 4 km wide and 2 km thick.

[27] The following initial parameters were considered in the model: (1) a geothermal gradient of 30°C/km; (2) a pressure of 2 kbar, given the minimum pressure at the roof of ~1.2 kbar, equivalent to 4 km depth (in a crust of about 2,900 kg/m3), which is the estimated thickness of the volcanoclastic cover (Abanico Formation) [Aguirre, 1960] at the time of the intrusion; (3) an oxygen fugacity of QFM + 2, as suggested by Cornejo and Mahood [1997]; and (4) an intermediate composition of the pluton [Cornejo and Mahood, 1997]. The phase diagram was obtained by MELTS, as detailed above. An extension of 1 km from the walls into the country rocks is imposed on the heat flow across the margins and is based on the observed extension of the contact aureole around LGP.

4.4 Calibration of Parameters by MELTS

[28] Variations in physical properties and compositional parameters of the LGP magma upon cooling were simulated by MELTS for the calibration of the model. The calculated compositional trends of residual liquids were compared with the compositional trends of the LGP (see supplementary material). The calibration indicates that a melt at 700°C exsolved ~10.5 vol % H2O (Figure 7b) and ~85.8 vol % of solid phases, distributed by volume as follows: 48.1% plagioclase, 18.7% K-feldspar, 9.8% quartz, 7.1% amphibole, 2.4% bitotite, 1.8% magnetite, 1.1% orthopyroxene, 0.4% clinopyroxene, 0.3% rhombohedral oxides, and 0.3% apatite. Liquidus temperature is reached at 1055°C, with the early crystallization of pyroxenes (orthopyroxene and clinopyroxene), plagioclase, and magnetite. By 855°C, amphibole, bitotite, K-feldspar, and H2O are exsolved. Below 705°C, a dramatic increase in crystallinity occurs over a small temperature interval as the system cocrystallizes quartz, K-feldspar, and plagioclase (+exsolved H2O; Figure 6d; see the sequence of crystallization at 1–2 kbar and 2.5–4 wt % H2O in the supporting information), consistent with the attainment of the haplogranite eutectic conditions.

Figure 7.

Calibration of the main physical parameters by using MELTS results with temperature: (a) crystallinity, the dashed line corresponds to the expression used by Huber et al. [2009] for comparison; (b) exsolved water (vol. %); (c) density of the liquid and magma with and without gas water; and (d) dynamic viscosity.

[29] The compositional effect on magma density (melt + crystals + exsolved H2O, Figure 7c) strongly depends on the content of exsolved phases, particularly the magnetite and H2O content. Initially, magma density (superheated melt) increases of about −0.21 kg/(m3 °C) as temperature decreases. However, the density of the melt actually decreases constantly up to 800°C because of higher dissolved water in the melt. Water exsolution (second boiling) starts at temperatures ~800°C (Figure 7b). In the interval between the liquidus temperature and 770°C, magma density changes at a rate of −0.53 kg/(m3 °C); this rate is largely controlled by crystallization of early minerals, which is more significant than the single effect of temperature (thermal expansivity). At the onset of exsolution of H2O, the rate of change of density of the magma without the exsolved gas component is about −1.84 kg/(m3 °C), indicating that magma degassing is a key factor controlling density; the removal of a low-density gas phase from the magma increases the rate of density variation more than the effect of crystallizing phases (Figure 7b). Because crystallization leads to density increase and bubble exsolution leads to density decrease (Figure 7c), bulk magma density (without the exsolved gas component) increases by about 0.50 kg/(m3 °C).

[30] Magma viscosity (Figure 7d) depends on the amount of suspended solid and gas contents and, to a lesser extent, on temperature. Viscosity of the magma increases from 9.7 103 Pa s, at the liquidus temperature, to 2.2 109 Pa s at 790°C, when crystallinity reaches 57 vol %. Magma viscosity near the solidus reaches up to 6.6 1022 Pa s.

[31] Only two error functions are needed to represent each variable (Ns = Ng =   =   = 2), reflecting the bimodal character of early and late (haplogranite-eutectic conditions) crystallization of this silicic system. We use a nonlinear least squares method to fit each variable to MELTS results.

5 Modeling Results

[32] The results presented in this paper are a simplification of an extremely complex evolution of a natural silicic system obtained from the described modeling and should be considered as nonunique because it has been derived from a model where any deviation in thermal, physical, and compositional parameters and initial conditions (given in Tables) will change the numerical results to some degree. However, we stress that it provides a useful guide to interpret AMS data and petrological variability within the reservoir by highlighting the dominant parameters controlling late-magmatic convection. These simulations are the only way to get a time-dependent picture of the magma dynamics occurring during cooling.

5.1 Thermal Structure of the Magma Chamber

[33] Temperature in magmas is controlled by the interplay of convection and diffusion. Initially, a weak thermal stratification is developed in the magma chamber, indicating that heat transfer by convection is higher than diffusion. At 2 kyr (Figure 8a), a small temperature difference of 13°C is reached between the hottest and the coolest part of the reservoir, caused by cooling magma convecting downward along the walls, and continually being replaced by rising hot magma from the center of the chamber (Figure 9a). This efficient convective mechanism prevents large temperature differences within the reservoir as a consequence of continuous circulation of hot magma along walls and magma self-mixing. As soon as nonconvecting crystalline boundary layers (“solidification fronts” defined as a region where velocities are ≤1 cm/yr) develop, after 2–3 kyr of simulation (Figures 8b and 8f, see below), these solidification fronts act as insulated rinds that affect how the magma chamber cools by (i) preventing fast cooling of the hot magma inside the chamber and (ii) allowing faster cooling of the magma adjacent to the wall rocks (magma reservoir boundaries). Differences of temperature up to 67.2°C and 137.7°C (Figure 8a) between the convecting core and the crystallized walls were obtained at 3 and 10 kyr, respectively. Simulations indicate that the center of the pluton is thermally insulated and survives above the solidus for ~20 kyr, even in the cold upper crust, as solidification fronts are formed (inset in Figure 8) against the walls.

Figure 8.

Maximum and minimum value of variables on time: (a) temperature (inset show temperature evolution up to 20 kyr, where all magma reach the solidus temperature), (b) crystallinity, (c) velocity, (d) shear rate, (e) density, and (f) viscosity.

Figure 9.

Cross section through the simulated magma reservoir after 3.5 kyr of simulation: (a) temperature, (b) crystallinity, (c) shear rate, and (d) shear dip. White dashed lines represent the capture domain of the solidification front. Arrows indicate current velocity and direction.

5.2 Magma Fluid Dynamics

[34] Magma cooling, crystallization, and degassing in a closed chamber induces a simple convection pattern before the magma becomes a mush (we refer to mush as the high-crystallinity magma that cannot convect, e.g., ~ 55 vol % crystals). In this liquid-dominated regime, magma flows down along the walls, producing the density stratification at the lower levels of the chamber, while magma from the core rises to replace the upper space at a lower velocity, reaching gravitational equilibrium (Figure 9a). High shear rates are produced in progressively crystal-rich flowing magma layers along walls and roof and/or between the magma flow and the solidification front (Figures 9b and 9c). In contrast, the shear rate is low in the hot rising magma at the center of the chamber.

[35] During the first 2 kyr of simulation, solidification fronts almost cannot form along the walls. However, dense crystal-rich magma is accumulating at the floor of the chamber, while lower density magma is rising in broad plumes at the center of the magma body. Maximum velocities (Figure 8c) and shear rate (Figure 8d) are recorded at the walls and decrease exponentially from 2207 to 335 m/yr and from 50.9 to 7.4 per year, respectively (at time t = 0 and 2000 kyr). After ~3 kyr, the cooling along the walls and roof is enough to produce solidification fronts all around the reservoir margins (Figure 9b). Consequently, velocities and shear rate in the convective core decrease at their highest rate, dropping below 10 m/yr and 0.1/yr, respectively. Nevertheless, convecting magma of the core preserves the same flow pattern, but the shear layer is now formed between the fluid magma and the boundary mush zone. After ~6 kyr of simulation, the whole magma body has become an immobile mush zone; velocities and shear rate of the magma flow are lower than 5 cm/yr and 10−3/yr, respectively. The modeled shear rate is the lowest at the center and lower levels of the simulated chamber (Figure 11a). This is consistent with the low anisotropy degree obtained in the middle and lower levels of the pluton (Figure 11c).

[36] The shear dip (SD) is recorded at different moments inside the chamber when velocity becomes lower than 1 cm/yr (our cutoff value for magma lockup; Figures 10 and 11). This condition is reached when magma viscosity is higher than 1012 Pa s (Figure 8f) and crystallinity is higher than 55 vol % (Figure 8f). From 2 to 5 kyr, the SD changes continuously through the walls to the chamber interior. The modeled SD at lockup has a similar trend to the measurements of dip foliation observed in LGP (Figure 10). To a first order, predicted SD angles and measured magnetic foliation dip vary from subparallel along the chamber boundaries to horizontal at the center of the chamber (Figures 10 and 11). A minor perturbation in these dip trends can be attributed to heterogeneities in the shape of the pluton and/or differences of elevation at which the samples were collected, representing differences in depth inside the chamber (Figure 11). Under the roof and next to the walls of the simulated chamber, the predicted SD angles can be flatter or steeper than the regular trend inside the chamber (Figures 10 and 11b). This is consistent with samples collected under the roof and next to a wall of the chamber (gray samples in Figures 10 and 11d) that do not follow the regular dip trend.

Figure 10.

Two profiles of the dip of the measured magnetic foliation and the simulated dip of the shear orientation. The two profiles are normalized by the width of the pluton (distance to the west contact) and go across: (a) the pluton boundaries and (b) the chamber center. In both profiles, a linear variation between the dip of foliation and the pluton width is found. Note, however, that time at which foliation recorded is different in both profiles.

Figure 11.

State of the simulated magma reservoir at different times for the following parameters: (a) time of shear record (critical crystalline region advance), (b) shear rate, and (c) shear dip. Contours in Figure 11a show the evolution of the critical crystalline region of the solidification fronts over time. White and gray areas represent high and low values. Both shear rate and anisotropy degree in Figures 11b and 2b, respectively, have low values in the middle level and at the center of the chamber and the pluton, respectively. Both shear and foliation dips in Figures 11c and 10, respectively, have low dips at the center of the chamber and pluton, respectively, whereas high dips are found at the borders and near walls. Note the complex pattern of the magnetic data in Figures 2 and 10 with respect to the symmetric model. This is likely due to (1) geometrical complexities inside the pluton and (2) because we considerate all the sites (over 20 km along the pluton) projected on a single section in a N60°E direction.

[37] If the magnetic fabric records the last shear induced by convection, the SD tracks the boundary of the critical crystalline region (dashed lines in Figure 9; gray lines in Figure 11a), described by Marsh [1996] as “the relatively abrupt transition from an interlocking assemblage of some strength to a high viscosity mush.” In the simulation, the presence of a nonconvecting zone (“solidification front”) starts ~2–3 kyr after the beginning of the simulation on the roof and slightly later at the corners of the floor of the chamber (Figures 10 and 11). This is expected, since these are the areas of the magma chamber that cool the fastest. Between 3 and 4 kyr, the critical crystalline region of the solidification fronts reaches the sidewalls of the chamber (Figure 11). After ~6 kyr, we suspect that steep SD related to magma rising cannot be recorded anymore because the shear rate is below 10−3/yr everywhere in the chamber, and SD does not record flow anymore (Figure 10b; dashed line in Figure 11).

5.3 Thermal Aureole

[38] The country rocks are heated more than 100°C at the floor in the first 2 kyr but only an additional 28°C in the next 10 kyr (Figure 12a), illustrating the decreasing heat flux at the pluton boundaries due to the thermal insulation of the main magma body. Maximum temperatures occur in the lower levels of the chamber because of the influence of the geothermal gradient (hotter wall rocks). The maximum temperature is 609°C at about 12 kyr of simulation (Figure 12), when temperature has increased by ~100°C at the wall rock contact with the magma in the floor of the chamber (Figure 12). Hence, significant partial melting of the wall rocks in these upper crustal conditions is not expected. The external limit of the thermal aureole, where the temperature of the rock does not exceed 100°C above the unperturbed geothermal gradient, is located about 100 from the chamber contact surrounding the chamber.

Figure 12.

Thermal perturbation in the host rock: maximum temperature of the country rock as a function of time below the floor of the magma chamber. Inset represents the temperature of the country rock when the metamorphic peak is reached at 12 kyr.

6 Consistency Between Magnetic Fabric and Numerical Simulation of Magma Flow Pattern: A Discussion

[39] Our numerical simulations of magma chamber dynamics in LGP support the hypothesis that significant shear rate can be produced in magma chambers at crystallinities ≤55 vol % (about 800°C; Figure 7a) and that AMS data record late-magmatic flow in LGP and other plutonic bodies [Marsh, 1996; McNulty et al., 2000; Archanjo et al., 2008]. High-crystallinity solidification fronts develop along the roof and floor of an intrusion after 2–3 kyr of simulation when the magma reaches temperatures of about 800°C (Figures 8a and 8b), leading to a high viscosity and a consequent decrease in velocity and shear rate (Figures 8c and 8d, respectively). In such conditions, most of the strain is recorded at the interface between the solidification front along the margins of the reservoir and the molten core (Figures 10 and 11), which is thermally isolated by the growing nonconvecting mush in a solidification front (Figures 8a and 9a). Hence, we stress that the AMS record can allow the determination of late convection patterns in crystallizing magma reservoirs, which, in turn, can explain the following.

  1. [40] The oblate AMS ellipsoids associated with a higher degree of anisotropy which are preserved along the pluton walls (Figures 2b, 2d, and 11c), while lower values should be obtained in the central and lower parts as well as near the roof of the pluton.

  2. [41] The gradual changes in magnetic foliation from the walls to the center of the pluton (Figures 2c and 11d).

  3. [42] The horizontal lineation parallel to the main pluton elongation due to axisymmetric convection.

  4. [43] Vertical foliations at the center of the pluton, marking the upwelling zones of the convection cells, are lacking in the LGP but are found in other plutonic units [e.g., Philpotts and Asher, 1994; McNulty et al., 2000]. The absence in the LGP may be due to the following: (1) sampling dominantly in the upper and lower levels of the pluton, (2) late foliation due to compaction in the insulated core of the pluton, and (3) low strain rate in the upwelling region (Figure 11a).

[44] Based on our detailed AMS study of LGP, and with insights gained from our numerical simulations, here we can summarize our model for the construction of small and shallow plutons (<10 km width and 5 km depth) in low- and high-crystallinity stages (Figure 13). The low-crystallinity stage corresponds to the filling of the chamber when magma intrusion makes space to form the chamber by diking, deforming rocks, and disaggregating blocks of the surrounding rock [e.g., Petford et al., 2000]. During this stage, convection plays a significant role in the chamber's evolution by stirring magmas from different pulses and wall rock assimilants. In this stage, magma is fluid enough to maintain most crystals in suspension and keep the magma compositionally fairly homogeneous [Brophy, 1991; Ruprecht et al., 2008; Bachmann and Bergantz, 2008; Dufek and Bachmann, 2010; Burgisser and Bergantz, 2011; Huber et al., 2011], particularly in sill-like magma chambers [e.g., Gutierrez and Parada, 2010]. Periodic recharge of hot magma will slow down cooling and add additional stirring to keep the system homogeneous [Huber et al., 2012; Lohmar et al., 2012], although some heterogeneities can still survive as mixing efficiency varies across the reservoirs [Jellinek et al., 1999; Ruprecht et al., 2008; Huber et al., 2009; Gutierrez and Parada, 2010). Such recharge events are commonly recorded in plutons [e.g., Robinson and Miller, 1999; Wiebe et al., 2004] and volcanic products, where the refilling of the chamber, and the consequent reheating, mush defrosting, degassing, and crystal resorption tend to trigger volcanic eruptions [Murphy et al., 2000; Bachmann et al., 2002; Ruprecht and Bachmann, 2010; Matthews et al., 2012; Lohmar et al., 2012].

Figure 13.

Conceptual model of the evolution of a La Gloria Pluton magma chamber: (a) low-crystallinity stage and (b) high-crystallinity stage. Alternations between these two stages can occur.

[45] As the rate of recharge decreases, the magma reservoir will continue to progress toward total solidification, leading to the late, high-crystallinity stage. Cooling down will proceed from the wall inward, ultimately producing an immobile mushy magma. This process is expected to occur regardless of the initial conditions (even in the case of a strongly thermally stratified reservoir). This high-crystallinity stage is also supported by the presence of stopped blocks at the margins of the pluton, indicating that the magma behaved as a viscous fluid with significant yield strength [Mahood and Cornejo, 1992; Cornejo and Mahood, 1997; Miller et al., 2011]. Transition from the high-crystallinity back to the low-crystallinity state can occur if a large-enough recharge pulse enters the chamber, reheating and remobilizing the mush and possibly leading back to a whole-chamber convection stage [Huber et al., 2012; Lohmar et al., 2012].

[46] In addition to the AMS record, the large-scale mineral and chemical zonation pattern of LGP is also consistent with the cooling pattern illustrated by our simulations. As discussed above, the center of the pluton is thermally insulated as the solidification fronts progress inward (Figures 8a and 9a). As predicted by Marsh [1996] (his “silicic chaos”), two major compositional and mineralogical consequences of the thermal insulation effect at the center of the pluton are (1) enhanced late magmatic mineral reequilibration [Cornejo and Mahood, 1997] and (2) enhanced liquid extraction, producing leucogranitic dykes [Mahood and Cornejo, 1992; Dufek and Bachmann, 2010], the silicic chaos [Marsh, 1996]. Correspondingly, LGP presents a mineral zonation pattern [Mahood and Cornejo, 1992; Cornejo and Mahood, 1997], where the stratigraphically defined “middle level,” which corresponds to the simulated core of the pluton, is (a) where the late magmatic reequilibration of minerals take place more pervasively than in the border zones and the upper level of the chamber and (b) compositionally slightly more mafic than the upper and lower levels (Figure 5), suggesting a relatively higher loss of leucogranitic liquid in the core of the pluton.

7 Conclusion

[47] In order to understand the convection patterns in small, shallow, silicic magma reservoirs, we performed fluid dynamical numerical simulations of cooling magma encased in a cool upper crust. The results of those simulations were compared to the composition, mineralogy, and AMS data obtained for LGP. The numerical model is based on time-dependent partial differential equations that have been calibrated by using self-consistent thermodynamic modeling for magmas (MELTS) and a previous numerical model for magma chambers [Gutierrez and Parada, 2010]. Simulation results reproduce some of the main AMS characteristics commonly observed in plutons (including LGP in this study) and attributed to magma flow: (1) a regular change of the dip of the magnetic foliation, from vertical at the walls of the pluton (oblate fabric) to horizontal at the lower levels at the center and under the roof (prolate fabric); and (2) a lower magnetic anisotropy degree at the center in the middle and lower levels of the pluton. The model presented here posits that AMS data dominantly record late-stage convection, as magma becomes highly crystalline and develops static boundaries (“solidification fronts”) along the roof, floor, and walls of the magma chamber. The evidence for flow during emplacement and/or convection of low-crystallinity, low-viscosity magma is typically lost. A major consequence of this inward solidification model is the thermal insulation of the core of the intrusion, allowing it to remain above the solidus for a long period of time (~20 kyr for this small, shallow system). This protracted supersolidus period results in the observed late-magmatic mineralogical reactions and extraction of differentiated residual liquids.

Acknowledgments

[48] This research has been developed by the FONDECYT 11100241 and PBCT-PDA07 projects granted by CONICYT (Chilean National Commission for Science and Technology). F. Gutiérrez and O. Bachmann were supported by U.S. National Science Foundation (NSF) grant EAR-080982 during the completion of this paper. S. E. Gelman was supported by U.S. NSF grant DGE-1256082. We thank S. Gilder, G. Gualda, and J. H. Kruhl for their reviews and comments. We also thank G. Bergantz, C. Huber, P. Ruprecht, and F. Poblete for their useful comments.

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