Degassing of stratified magma by compositional convection

A new model is proposed for passive degassing from sub-volcanic magma chambers. The water content in stably stratified shallow magma chamber will be equated to its solubility at the upper boundary by convection. Water from a lower layer high in water content can enrich the contact zone of the upper layer and lead to further convective overturn of this boundary layer. A complete set of equations describing convection with bubble formation and dissolution is reduced to a simplified form by assuming a small bubble content. The development and pattern of flow driven by vesiculation is modeled numerically in a 2D magma chamber for relatively low Raleigh numbers (5×10⁵). Bubbles rising from the magma will collect near the roof in a layer of 8–10 vol% and then escape upward to fumaroles. The Stokes flux of bubbles escaping from an andesitic magma with viscosity 10⁴ P and a top surface of about 500×500 m corresponds with observed total magmatic water fluxes of 35 kg/s. Pressure within the chamber is buffered by elastic (and local visco-elastic) deformations in the solid rocks bounding the chamber to the range between ambient and close to lithostatic values. In a chamber closed to fresh magma inputs, the decrease in volume due to such gentle volatile escape lowers the reference pressure. Bubbles flux from the lower layer induced by variation of the saturation level around stratification boundary may be efficient mechanism for the water transport between layers.     

Modelling the dynamics and thermodynamics of volcanic degassing

 The rates of passive degassing from volcanoes are investigated by modelling the convective overturn of dense degassed and less dense gas-rich magmas in a vertical conduit linking a shallow degassing zone with a deep magma chamber. Laboratory experiments are used to constrain our theoretical model of the overturn rate and to elaborate on the model of this process presented by Kazahaya et al. (1994). We also introduce the effects of a CO₂–saturated deep chamber and adiabatic cooling of ascending magma. We find that overturn occurs by concentric flow of the magmas along the conduit, although the details of the flow depend on the magmas' viscosity ratio. Where convective overturn limits the supply of gas-rich magma, then the gas emission rate is proportional to the flow rate of the overturning magmas (proportional to the density difference driving convection, the conduit radius to the fourth power, and inversely proportional to the degassed magma viscosity) and the mass fraction of water that is degassed. Efficient degassing enhances the density difference but increases the magma viscosity, and this dampens convection. Two degassing volcanoes were modelled. At Stromboli, assuming a 2 km deep, 30% crystalline basaltic chamber, containing 0.5 wt.% dissolved water, the ∼700 kg s^–1 magmatic water flux can be modelled with a 4–10 m radius conduit, degassing 20–100% of the available water and all of the 1 to 4 vol.% CO₂ chamber gas. At Mount St. Helens in June 1980, assuming a 7 km deep, 39% crystalline dacitic chamber, containing 4.6 wt.% dissolved water, the ∼500 kg s^–1 magmatic water flux can be modelled with a 22–60 m radius conduit, degassing ∼2–90% of the available water and all of the 0.1 to 3 vol.% CO₂ chamber gas. The range of these results is consistent with previous models and observations. Convection driven by degassing provides a plausible mechanism for transferring volatiles from deep magma chambers to the atmosphere, and it can explain the gas fluxes measured at many persistently active volcanoes. Received: 26 September 1997 / Accepted: 11 July 1998     

Simultaneous crystallization and melting at both the roof and floor of crustal magma chambers: Experimental study using NH4Cl–H2O binary eutectic system

Thermal and compositional evolution of magmas after emplacement of basalt into continental crust has been investigated by means of fluid dynamic experiments using a cold solid mixture with eutectic composition and a hot liquid with higher salinity in the NH₄Cl–H₂O binary eutectic system. The experiments were designed to simulate cases where crystallization of a basalt magma is accompanied by melting at both the roof and floor of a crustal magma chamber. The results show that thermal and compositional convection occur simultaneously in the solution; the thermal convection is driven by cooling at the roof and the compositional convection is driven by melting and crystallization at the floor. The roof was rapidly melted by the convective heat flux, which resulted in formation of a separate eutectic melt layer (the upper liquid layer) with negligible mixing of the underlying liquid (the lower liquid layer). On the other hand, a mushy layer formed at the floor. The compositional convection at the floor carried a low heat flux, so that the heat transfer at the floor was basically explained by simple heat conduction. The thermal boundary layer in the lower liquid layer at the interface with the upper liquid layer became thicker with time and subsequently temperature decreased upward throughout the lower liquid layer. Compositional gradient with NH₄Cl content decreasing upward formed by compositional convection in the lower liquid layer. The formation of these gradients resulted in formation of double-diffusive convecting layers in the lower liquid layer. The upward heat transfer was suppressed when compared with the case where the liquid region is homogenized by vigorous convection.These experimental results imply that, when a basalt magma is emplaced in continental crust, floor melting does not always enhance the cooling of the magma, but it may even reduce the total heat loss from the magma to the crusts due to suppression of convection by formation of a stabilizing compositional gradient.     

Variation of volatile concentration in a magma system of Satsuma-Iwojima volcano deduced from melt inclusion analyses

Chemical analyses of 30 melt inclusions from Satsuma-Iwojima volcano, Japan, were carried out to investigate volatile evolution in a magma chamber beneath the volcano from about 6300 yr BP to the present. Large variations in volatile concentrations of melts were observed. (1) Water concentration of rhyolitic melts decreases with time; 3–4.6 wt.% at the time of latest caldera-forming eruption of Takeshima pyroclastic flow deposit (ca. 6300 yr BP), 3 wt.% for small pyroclastic flow (ca. 1300 yr BP) of Iwodake, post-caldera rhyolitic dome, and 0.7–1.4 wt.% for submarine lava eruption (Showa-Iwojima) in 1934. (2) Rhyolitic melts of the Takeshima and Iwodake eruptions contained CO₂ of less than 40 ppm, while the Showa-Iwojima melt has higher CO₂ concentration of up to 140 ppm. (3) Water and CO₂ concentrations of basaltic to andesitic melt of Inamuradake, a post-caldera basaltic scoria cone, are 1.2–2.8 wt.% and ≤290 ppm, respectively.Volatile evolution in the magma chamber is interpreted as follows: (1) the rhyolitic magma at the time of the latest caldera-forming eruption (ca. 6300 yr BP) was gas-saturated due to pressure variation in the magma chamber because the large variation in water concentration of the melt was attributed to exsolution of volatile in the magma prior to the eruption. Iwodake eruption (ca. 1300 yr BP) was caused by a remnant of the caldera-forming rhyolitic magma, suggested from the similarity of major element composition between these magmas. (2) Volatile composition of the Showa-Iwojima rhyolitic melt agrees with that of magmatic gases presently discharging from a summit of Iwodake, indicating the low pressure degassing condition. (3) The degassing of the magma chamber by magma convection in a conduit of Iwodake during non-eruptive but active degassing period for longer than 800 years decreased water concentration of the rhyolitic magma. (4) Geological and petrological observations indicate that a stratified magma chamber, which consists of a lower basaltic layer and an upper rhyolitic layer, might have existed during the post-caldera stage. Addition of CO₂ from the underlying basaltic magma to the upper gas-undersaturated (degassed) rhyolitic magma increased CO₂ concentration of the rhyolitic magma.     

Melt inclusion analysis of the Unzen 1991–1995 dacite: implications for crystallization processes of dacite magma

Dacitic magma, a mixture of high-temperature (T) aphyric magma and low-T crystal-rich magma, was erupted during the 1991–1995 Mount Unzen eruptive cycle. Here, the crystallization processes of the low-T magma were examined on the basis of melt inclusion analysis and phase relationships. Variation in water content of the melt inclusions (5.1–7.2 wt% H₂O) reflected the degassing history of the low-T magma ascending from deeper levels (250 MPa) to a shallow magma chamber (140 MPa). The ascent rate of the low-T magma decreased markedly towards the emplacement level as crystal content increased. Cooling of magma as well as degassing-induced undercooling drove crystallization. With the decreasing ascent rate, degassing-induced undercooling decreased in importance, and cooling became more instrumental in crystallization, causing local and rapid crystallization along the margin of the magma body. Some crystals contain scores of melt inclusions, whereas there are some crystals without any inclusions. This heterogeneous distribution suggests the variation in the crystallization rate within the magma body; it also suggests that cooling was dominant cause for melt entrapment. Numerical calculations of the cooling magma body suggest that cooling caused rapid crystal growth and enhanced melt entrapment once the magma became a crystal-rich mush with evolved interstitial melt. The rhyolitic composition of melt inclusions is consistent with this model.Editorial responsibility: H Shinohara     

Cumulate nodules as evidence for convective fractionation in a phonolite magma chamber

The physical mechanism by which chemical zonation develops in magma chambers has been controversial partly because unambiguous geological constraints have been lacking. The 11,000 years B.P. eruption of Laacher See Volcano produced a zoned tephra deposit and also ejected crystal-rich nodules which provide a snapshot of the materials crystallising at the magma chamber margins. New data on petrography and chemical compositions of nodules, their cumulate minerals and interstitial glasses are used to deduce the chemical evolution of the phonolite melt due to fractional crystallisation of the mineral assemblages. These data, together with those on the vertical zonation of the melt in the bulk of the chamber, are shown to be consistent with a model of stratification of the chamber by convective fractionation, in which a thin boundary layer of residual melt from fractional crystallisation ascends at the chamber side and accumulates at the roof. Crystallisation could have provided buoyancy to drive convection by enriching incompatible volatile components (mainly water) in the residual melt. Available fluid dynamic studies of single- and double-diffusive boundary layers are used to assess convection in the Laacher See chamber. The boundary layer is likely to have been: (1) laminar, which implies that the density gradient in the chamber steepened upwards; (2) in the counterflow regime, in which compositional and thermal layers flow in opposite directions; and (3) thin ( 10 cm), estimated from theory for a flat wall, suggesting that wall morphology could be important in determining boundary layer characteristics. Estimates of mass transfer rates due to this mechanism suggest that the chamber could have become stratified in a time of the order of 10³ years.     

On the interaction between convection and crystallization in cooling magma chambers

We investigate the interaction of thermal convection and crystallization in large aspect-ratio magma chambers. Because nucleation requires a finite amount of undercooling, crystallization is not instantaneous. For typical values of the rates of nucleation and crystal growth, the characteristic time-scale of crystallization is about 10³–10⁴ s. Roof convection is characterized by the quasi-periodic formation and instability of a cold boundary layer. Its characteristic time-scale depends on viscosity and ranges from about 10² s for basaltic magmas to about 10⁷ s for granitic magmas. Hence, depending on magma viscosity, convective instability occurs at different stages of crystallization. A single non-dimensional number is defined to characterize the different modes of interaction between convection and crystallization.Using realistic functions for the rates of nucleation and crystal growth, we integrate numerically the heat equation until the onset of convective instability. We determine both temperature and crystal content in the thermal boundary layer. Crystallization leads to a dramatic increase of viscosity which acts to stabilize part of the boundary layer against instability. We compute the effective temperature contrast driving thermal convection and show that it varies as a function of magma viscosity and hence composition.In magmas with viscosities higher than 10⁵ poise, the temperature contrast driving convection is very small, hence thermal convection is weak. In low-viscosity magmas, convective breakdown occurs before the completion of crystallization, and involves partially crystallized magma. The convective regime is thus characterized by descending crystal-bearing plumes, and bottom crystallization proceeds both by in-situ nucleation and deposition from the plumes. We suggest that this is the origin of intermittent layering, a form of rhythmic layering described in the Skaergaard and other complexes. We show that this regime occurs in basic magmas only at temperatures close to the liquidus and never occurs in viscous magmas. This may explain why intermittent layering is observed only in a few specific cases.     

Convective instabilities in a variable viscosity fluid cooled from above

Whether in the mantle or in magma chambers, convective flows are characterized by large variations of viscosity. We study the influence of the viscosity structure on the development of convective instabilities in a viscous fluid which is cooled from above. The upper and lower boundaries of the fluid are stress-free. A viscosity dependence with depth of the form ν₀ + ν₁ exp(?γ.z) is assumed. After the temperature of the top boundary is lowered, velocity and temperature perturbations are followed numerically until convective breakdown occurs. Viscosity contrasts of up to 10⁷ and Rayleigh numbers of up to 10⁸ are studied.For intermediate viscosity contrasts (around 10³), convective breakdown is characterized by the almost simultaneous appearance of two modes of instability. One involves the whole fluid layer, has a large horizontal wavelength (several times the layer depth) and exhibits plate-like behaviour. The other mode has a much smaller wavelength and develops below a rigid lid. The “whole layer” mode dominates for small viscosity contrasts but is suppressed by viscous dissipation at large viscosity contrasts.For the “rigid lid” mode, we emphasize that it is the form of the viscosity variation which determines the instability. For steep viscosity profiles, convective flow does not penetrate deeply in the viscous region and only weak convection develops. We propose a simple method to define the rigid lid thickness. We are thus able to compute the true depth extent and the effective driving temperature difference of convective flow. Because viscosity contrasts in the convecting region do not exceed 100, simple scaling arguments are sufficient to describe the instability. The critical wavelength is proportional to the thickness of the thermal boundary layer below the rigid lid. Convection occurs when a Rayleigh number defined locally exceeds a critical value of 160–200. Finally, we show that a local Rayleigh number can be computed at any depth in the fluid and that convection develops below depth z_r (the rigid lid thickness) such that this number is maximum.The simple similarity laws are applied to the upper mantle beneath oceans and yield estimates of 5 × 10¹⁵?5 × 10¹⁶ m² s^?1 for viscosity in the thermal boundary layer below the plate.     

Conduit convection,magma mixing,and melt inclusion trends at persistently degassing volcanoes

Magmas progressively exsolve volatiles as they ascend towards the Earth's surface, such that their volatile content is a function of pressure. Water and carbon dioxide concentrations measured in melt inclusions from degassing volcanoes rarely coincide with modelled degassing trends. I show that observed melt inclusion trends can be reproduced through mixing of magmas, either during convection within the volcanic conduit, or within a subterranean magma reservoir. No fluxing gas phase or post-entrapment loss of water need be invoked. A permeable network allowing gas transport is still required to avoid fragmentation of magma at shallow depths.     

Textural and geochemical constraints on eruptive style of the 79 <Emphasis Type="SmallCaps">ad</Emphasis> eruption at Vesuvius

The 79 ad Plinian eruption of Vesuvius produced first a white pumice fallout from a high steady eruptive column, and then a grey pumice fallout originating from an oscillatory eruptive column with several partial column collapse events after which there was a total column collapse. This first total collapse was followed by renewed Plinian activity and produced the last grey pumice (GP) fallout deposit of the eruption. Textural characteristics (vesicularity and microcrystallinity) of a complete sequence of the pumice fallout deposits are presented along with the major element compositions and residual volatile contents (H₂O, Cl) to constrain the degassing processes and the eruptive dynamics. Large variations in residual volatile contents exist between the different eruptive units. Textural features also strongly differ between white and grey pumices, but also within the grey pumices. The degassing processes were thus highly heterogeneous. We propose a new model of the 79 ad eruption in which pre-eruptive conditions (H₂O saturation, magma temperature and viscosity) are the critical controls on the diversity of the syn-eruptive degassing processes and hence the eruptive dynamics. Cl contents measured in melt inclusions show that only the white pumice and the upper part of the grey pumice magma were H₂O saturated prior to eruption. The white pumice eruptive units represent a typical closed-system degassing evolution, whereas the first grey pumice one, stored under similar pre-eruptive saturation conditions, follows a particular open-system degassing evolution. We suggest that the oscillatory regime that dominated the grey pumice eruptive phase is linked to pre-eruptive water undersaturation of most of the grey magma, and the associated time delays necessary for H₂O exsolution. We also suggest that the high residual H₂O content of the last grey pumice, deposited after the renewal of Plinian activity following the first total column collapse event, is due to syn-eruptive saturation of GP magma and reduced H₂O exsolution efficiency resulting from speciation of dissolved H₂O in the melt.     

Magma dynamics, crystallization, and chemical differentiation of the 1959 Kilauea Iki lava lake, Hawaii, revisited

Using constraints from an extensive database of geological and geochemical observations along with results from fluid mechanical studies of convection in magma chambers, we identify the main physical processes at work during the solidification of the 1959 Kilauea Iki lava lakes. In turn, we investigate their quantitative influence on the crystallization and chemical differentiation of the magma, and on the development of the internal structure of the lava lake. In contrast to previous studies, vigorous stirring in the magma, driven predominately by the descent of dense crystal-laden thermal plumes from the roof solidification front and the ascent of buoyant compositional plumes due to the in situ growth of olivine crystals at the floor, is predicted to have been an inevitable consequence of very strong cooling at the roof and floor. The flow is expected to have caused extensive but imperfect mixing over most of the cooling history of the magma, producing minor compositional stratification at the roof and thermal stratification at the floor. The efficient stirring of the large roof cooling is expected to have resulted in significant internal nucleation of olivine crystals, which ultimately settled to the floor. Additional forcing due to either crystal sedimentation or the ascent of gas bubbles is not expected to have increased significantly the amount of mixing. In addition to convection in the magma, circulation driven by the convection of buoyant interstitial melt in highly permeable crystal-melt mushes forming the roof and the floor of the lava lake is envisaged to have produced a net upward flow of evolved magma from the floor during solidification. In the floor zone, mush convection may have caused the formation of axisymmetric chimneys through which evolved magma drained from deep within the floor into the overlying magma and potentially the roof. We hypothesize that the highly evolved, pipe-like ‘vertical olivine-rich bodies’ (VORBs) [Bull. Volcanol. 43 (1980) 675] observed in the floor zone, of the lake are fossil chimneys. In the roof zone, buoyant residual liquid both produced at the roof solidification front and gained from the floor as a result of incomplete convective mixing is envisaged to have percolated or ‘leaked‘ into the overlying highly-permeable cumulate, displacing less buoyant interstitial melt downward. The results from Rayleigh fractionation-type models formulated using boundary conditions based on a quantitative understanding of the convection in the magma indicate that most of the incompatible element variation over the height of the lake can be explained as a consequence of a combination of crystal settling and the extensive but imperfect convective mixing of buoyant residual liquid released from the floor solidification front. The remaining chemical variation is understood in terms of the additional influences of mush convection in the roof and floor on the vertical distribution of incompatible elements. Although cooling was concentrated at the roof of the lake, the floor zone is found to be thicker than the roof zone, implying that it grew more quickly. The large growth rate of the floor is explained as a consequence of a combination of the substantial sedimentation of olivine crystals and more rapid in situ crystallization due to both a higher liquidus temperature and enhanced cooling resulting from imperfect thermal and chemical mixing.     

Phenocryst-hosted melt inclusions record stalling of magma during ascent in the conduit and upper magma reservoir prior to vulcanian explosions, Soufrière Hills volcano, Montserrat, West Indies

The mechanics of explosive eruptions influence magma ascent pathways. Vulcanian explosions involve a stop–start mechanism that recurs on various timescales, evacuating the uppermost portions of the conduit. During the repose time between explosions, magma rises from depth and refills the conduit and stalls until the overpressure is sufficient to generate another explosion. We have analyzed major elements, Cl, S, H₂O, and CO₂ in plagioclase-hosted melt inclusions, sampled from pumice erupted during four vulcanian events at Soufrière Hills volcano, Montserrat, to determine melt compositions prior to eruption. Using Fourier transform infrared spectroscopy, we measured values up to 6.7 wt.% H₂O and 80 ppm CO₂. Of 42 melt inclusions, 81 % cluster between 2.8 and 5.4 wt.% H₂O (57 to 173 MPa or 2–7 km), suggesting lower conduit to upper magma reservoir conditions. We propose two models to explain the magmatic conditions prior to eruption. In Model 1, melt inclusions were trapped during crystal growth in magma that was stalled in the lower conduit to upper magma reservoir, and during trapping, the magma was undergoing closed-system degassing with up to 1 wt.% free vapor. This model can explain the melt inclusions with higher H₂O contents since these have sampled the upper parts of the magma reservoir. However, the model cannot explain the melt inclusions with lower H₂O because the timescale for plagioclase crystallization and melt inclusion entrapment is longer than the magma residence time in the conduit. In Model 2, melt inclusions were originally trapped at deeper levels of the magma chamber, but then lost hydrogen by diffusion through the plagioclase host during periodic stalling of the magma in the lower conduit system. In this second scenario, which we favor, the melt inclusions record re-equilibration depths within the lower conduit to upper magma reservoir.     

Probing the magma plumbing of Erebus volcano,Antarctica, by open-path FTIR spectroscopy of gas emissions

Gas emissions from Erebus volcano, Antarctica, were measured by open-path Fourier transform infrared spectroscopy to understand degassing of its magmatic system. Two degassing phonolite lava lakes were present in the summit crater during observation in December 2004. We report analyses of H₂O, CO₂, CO, SO₂, HF, HCl and OCS, (in order of molar abundance) in the plumes. Variations in the proportions of these species strongly reflect the dynamics of degassing, and sourcing of gas from different depths in the magmatic network. The highest observed ratios of CO₂ and H₂O are consistent with gas extracted from the melt at a depth of up to ∼ 2 km below the lava lakes. Magma degassing above this depth contributes to a higher H₂O/CO₂ proportion in the airborne plume. The ratio therefore reflects the balance of deeper vs. shallower contributions of volatiles and, possibly, a combination of closed- and open-system degassing. We observe a strong contrast in HF content in emissions from the two lava lakes, which we attribute to differing levels of magma ascent and/or cooling and crystallization of the magma supply. Fluxes of all gas species were determined using independent SO₂ flux determinations and measured gas ratios. In the case of CO₂ and water, ∼ 1 and ∼ 0.4 m³ s^− 1, respectively, of parental basanite magma are required to sustain the calculated output. The discrepancy between the two figures is readily explained by sequestration of part of the magma supply at depth such that it only partially degasses its complement of water.     

Non-volatile vs volatile behaviours of halogens during the AD 79 plinian eruption of Mt. Vesuvius, Italy

Pre-eruptive conditions and degassing processes of the AD 79 plinian eruption of Mt. Vesuvius are constrained by systematic F and Cl measurements in melt inclusions and matrix glass of pumice clasts from a complete sequence of the pumice-fallout deposits. The entire ‘white pumice’ (WP) magma and the upper part of the ‘grey pumice’ (GP) magma were saturated relative to sub-critical fluids (a Cl-rich H₂O vapour phase and a brine), with a Cl melt content buffered at ~ 5300 ppm, and a mean H₂O content of ~ 5%. The majority of the GP magma was not fluid-saturated. From these results it can be estimated that the WP magma chamber had a low vertical extent (< 500 m) and was located at a depth of ~ 7.5 km while the GP magma reservoir was located just beneath the WP one, but its vertical extent cannot be constrained. This is approximately two times deeper than previous estimates. H₂O degassing during the WP eruption followed a typical closed-system evolution, whereas GP clasts followed a more complex degassing path. Contrary to H₂O, Cl was not efficiently degassed during the plinian phase of the eruption.

This study shows that F and Cl behave as incompatible elements in fluid-undersaturated phonolitic melts. H₂O saturation is necessary for a significant partitioning of Cl into the fluid phase. However, Cl cannot be extracted in significant quantity from phonolitic melts during rapid H₂O degassing, e.g. during plinian eruptions, due to kinetics effects. Halogen contents are better preserved in volcanic glass (melt inclusions or matrix glass) than H₂O, therefore the combined analysis of both volatile species is required for reliable determination of pre-eruptive conditions and syn-eruptive degassing processes in magmas stored at shallow depths.     

A physicochemical model for deep degassing of water-rich magma

Two powerful eruptions of Quizapu vent on Cerro Azul Volcano, Chile are used as examples to discuss the problem of effusive eruptions of magmas having high preeruptive volatile concentrations. A physicochemical mechanism is proposed for magma degassing, with the volatiles being lost before coming to the surface. The model is based on the interaction of magmas residing in chambers at different depths and on the difference between the solubility of water in the melt and the water equilibrium concentration in a magma body having a considerable vertical extent. The shallower chamber can accumulate the volatiles released from the magma that is supplied from the deeper chamber. An explanation is provided of the dramatic differences in the character of the 1846–1847 and 1932 eruptions, which had identical chemical-petrographic magma compositions.     

An experimental study of structures arising in convective roll flows of magma melts in peripheral chambers of volcanoes

The morphology and internal convective structure of continuous roll flows in magma melts were experimentally studied with regard to peripheral (shallow) magma chambers and downgoing circular gravity flows in conduits. We found properties of continuous convective mixing in a magma melt in a peripheral chamber due to convective roll flows. We investigated the mechanism that is responsible for cumulus generation at the bottom of a peripheral chamber when homogeneous and heterogeneous melts are emplaced. We conducted an experimental study of how the contact surface is formed at the cumulus-melt boundary. We made a qualitative study of the mechanism that affects the composition of magma melts over time in a peripheral and a mantle (deeper) chamber owing to crystallization, as well as the special mechanism that is responsible for cumulus generation in the peripheral chamber.     

A simple model of convection in the terrestrial planets

Abstract

In this paper we study analytically the simplest fluid mechanical model which can mimic the convective behavior which is thought to occur in the solid mantles of the terrestrial planets. The convecting materials are polycrystalline rocks, whose creep behavior depends very strongly on temperature and probably also on pressure. As a simple model of this situation, we consider the flow of a Newtonian viscous fluid, whose viscosity depends strongly on temperature (only), and in fact has an infinite viscosity below a certain temperature, and a constant viscosity above this temperature. This model would also be directly relevant to the convection of a melt beneath its own solid phase (e.g. water below ice, though in that case there are other physical complications).

As a consequence of this assumption, there is a vigorous convection zone overlain by a stagnant lid, as also observed in analogous laboratory experiments (Nataf and Richter, 1982). The analysis is then very similar to that of Roberts (1979), but the extension to variable viscosity introduces important differences, most notably that the boundary between the lid and the convecting zone is unknown, and not horizontal. The resulting buoyancy induced stresses near this boundary are much larger than the stresses produced by buoyancy in the side-wall plumes, and mean that the dynamics of this region, and hence also the heat flux, are independent of the rest of the cell. We give a first order approximation for the Nusselt number-Rayleigh number relationship.     

Replenishment of a mafic magma in a zoned felsic magma chamber beneath Rishiri Volcano, Japan

The trachytic Tanetomi lava from Rishiri Volcano, northern Japan, provides useful information concerning how a replenished mafic magma mixes with a compositionally zoned felsic magma in a magma chamber. The Tanetomi lava was erupted in the order of Lower lava 1 (LL1, 59.2-59.8 wt.% in SiO₂), Lower lava 2 (LL2, 58.4-59.1 wt.%), and Upper lava (UL, 59.9-65.1 wt.%). Evidence for mixing with a mafic magma is observed only in the LL2, in which a greater amount of crystals derived from the mafic magma occurs in rocks with higher SiO₂ content. The whole-rock compositional trend of the Tanetomi lavas is fairly smooth except for the LL2 lava composition, which scatter along the main composition trend. There is no reasonable composition of basaltic magma on the extrapolation of the LL2 composition trend, and the trend cannot be explained by a simple two-component magma mixing. Before the replenishment, the felsic magma was zoned in composition (58-65 wt.% in SiO₂) and temperature (1030-920°C) in the magma chamber located at the pressure of ~2 kbar. The compositional variation of the main felsic magma was produced by extraction of a fractionated interstitial melt from mush zones along the chamber walls and its subsequent mixing with the main magma (boundary layer fractionation). The LL1 magma tapped the magma chamber soon after the replenishment, before the mafic magma mixed with the overall felsic magma. Then the basalt magma mixed heterogeneously with the upper part of the felsic magma by forced convection as a fountain during injection. The mixing of the basalt magma with compositionally zoned felsic magma resulted in the characteristic composition trend of the LL2. The fraction of basaltic magma in the LL2 magma is estimated to be at most 10%. Despite such a small proportion, the basalt magma was mixed completely with the felsic magma, probably because the crystallinity of undercooled basalt magma was low enough to behave as a liquid.     

An experimental study on the effects of phenocrysts on convection in magmas

The effect of phenocrysts on convection in magma chambers is investigated experimentally using small heavy particles in convecting fluids. The particles are initially uniformly distributed in a fluid which is either heated from below or cooled from above. The system is allowed to evolve, and temperature and particle concentration profiles are measured as functions of time. When the concentration of particles is sufficiently small, convection is basically unaffected by their presence. When the concentration is above a critical value, however, the convective motion is considerably altered. The effect of particles on the subsequent fluid behaviour is different in the cases of heating from below and cooling from above. In the former case, there are strong convective motions confined to a sedimentary layer of decreasing thickness beneath a clear layer which displays rather weak convective motions. With time, the destabilizing increase of temperature in the lower layer overcomes the stabilizing contribution to the bulk density due to the particles and the layer overturns quite suddenly. In the situation of cooling from above, a critical condition separates a case of continual overturn from a case of no overturn at all, with the sedimentary layer falling unimpeded to the bottom. Theoretical analysis suggests that the critical value is determined primarily by the ratio of the contribution to the bulk density of the suspension due to particles to the change in fluid density due to the thermal effect. The size distribution of the particles can also modify the fluid behaviour. Applying our general results to geological situations, we suggest that the presence of relatively small concentrations of phenocrysts can critically influence the mode of convection in magmas.     

The viscosity of hydrous dacitic liquids: implications for the rheology of evolving silicic magmas

The viscosity of a series of six synthetic dacitic liquids, containing up to 5.04 wt% dissolved water, was measured above the glass transition range by parallel-plate viscometry. The temperature of the 10¹¹ Pa s isokom decreases from 1065 K for the anhydrous liquid, to 864 K and 680 K for water contents of 0.97 and 5.04 wt% H₂O. Including additional measurements at high temperatures by concentric-cylinder and falling-sphere viscometry, the viscosity (η) can be expressed as a function of temperature and water content w according to: where η is in Pa s, T is temperature in K, and w is in weight percent. Within the conditions of measurement, this parameterization reproduces the 76 viscosity data with a root-mean square deviation (RMSD) of 0.16 log units in viscosity, or 7.8 K in temperature. The measurements show that water decreases the viscosity of the dacitic liquids more than for andesitic liquids, but less than for rhyolites. At low temperatures and high water contents, andesitic liquids are more viscous than the dacitic liquids, which are in turn more viscous than rhyolitic liquids, reversing the trend seen for high temperatures and low water contents. This suggests that the relative viscosity of different melts depends on temperature and water content as much as on bulk melt composition and structure. At magmatic temperatures, rhyolites are orders of magnitude more viscous than dacites, which are slightly more viscous than andesites. During degassing, all three liquids undergo a rapid viscosity increase at low water contents, and both dacitic and andesitic liquids will degas more efficiently than rhyolitic liquids. During cooling and differentiation, changing melt chemistry, decreasing temperature and increasing crystal content all lead to increases in the viscosity of magma (melt plus crystals). Under closed system conditions, where melt water content can increase during crystallization, viscosity increases may be small. Conversely, viscosity increases are very abrupt during ascent and degassing-induced crystallization.