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The generation of overpressure in felsic magma chambers by replenishment
ELSEVIER
Earth and Planetary Science Letters 163 (1998) 301–314
The generation of overpressure in felsic magma chambers by replenishment A. Folch, J. Martı´ * Institute of Earth Sciences, CSIC, Lluis Sole´ Sabarı´s s=n, 08028 Barcelona, Spain Received 24 February 1998; revised version received 9 July 1998; accepted 24 August 1998
Abstract Evidence of magma mixing is common in the products of explosive felsic eruptions and it is generally accepted as a common mechanism for triggering such events. In order to quantify the potential for magma mixing to trigger explosive eruptions, we have developed a simple analytical model, based on previous models of magma chamber replenishment, which considers the injection of volatile-rich mafic magma into a chamber occupied by a homogeneous, volatile-rich felsic magma. We assume that the overpressure caused by the injection of new magma is not sufficient to trigger an eruption, for which additional overpressure is required. Two mixing-related mechanisms have traditionally been considered to have the potential to generate the additional overpressure: (1) exsolution of volatiles from the felsic magma during forced convection, and (2) exsolution of volatiles from the mafic magma by oversaturation during cooling and subsequent crystallization. Our calculations suggest that exsolution of volatiles from the felsic magma is not an effective mechanism to generate additional overpressure. However, significant overpressure can be achieved by volatile exsolution from the mafic magma during its cooling and crystallization. The time scale between intrusion and eruption considered in our model is of the order of a few days to a few months, which coincides with petrological and geophysical evidence obtained from magma mixing related eruptions. We also suggest that replenishment of shallow felsic magma chambers by mafic magma in most cases does not lead to large scale mixing, as eruption will occur before thermal equilibrium between the two magmas is reached, so that density and viscosity contrasts between the two magmas will remain significant. 1998 Elsevier Science B.V. All rights reserved. Keywords: magmas; explosive eruptions; volatiles
1. Introduction Magma mixing is widely accepted as a triggering mechanism for explosive eruptions of felsic magmas. This idea was introduced to explain the 1875 plinian eruption of Askja [1] and since then it has been used to explain many other eruptions such as the 1991 Ł Corresponding
author. Tel.: C34 3 330 2716; Fax: C34 3 411 0012; E-mail: [email protected]
Pinatubo eruption [2]. The products of many explosive eruptions of felsic magmas show evidence that mixing between two magmas of contrasting physical and chemical properties occurred before the eruption. In most cases, the mixing is basically physical, and does not include the formation of hybrid compositions intermediate between the mafic and felsic end members. This fact, together with records of pre-eruptive seismic activity, suggests that the time taken from the mixing episode to the eruption is
0012-821X/98/$ – see front matter 1998 Elsevier Science B.V. All rights reserved. PII: S 0 0 1 2 - 8 2 1 X ( 9 8 ) 0 0 1 9 6 - 4
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short, of the order of a few days to a few months [1– 4]. The period of repose occurring between the injection of mafic magma and the eruption also suggests that the volume of injected mafic magma is not in itself sufficient to immediately trigger the eruption, and that some secondary effect(s) associated with the injection of new magma produces the critical overpressure necessary to rupture the magma chamber and permit the subsequent volcanic eruption. When mafic magma is injected into the base of a chamber containing felsic magma, any mixing will initially be strongly inhibited by the contrasts in density, temperature and viscosity between the two magmas [5–8]. Thermal equilibration will then result in cooling of the hotter, more mafic magma which begins to crystallize, and heating of the felsic magma which will tend to cause convection and reabsortion of phenocrysts. Cooling of the mafic magma can cause oversaturation and subsequent exsolution of volatiles [2,9,10]. Superheating and decompression of parts of the felsic magma due to convection may also lead to supersaturation in volatile phases, exsolution and vesiculation [1]. Viscous coupling between the felsic and mafic magmas can then cause entrainment of mafic magma within the convecting felsic magma, thus bringing mafic magma to the top of the chamber [11] where it will decompress and may become oversaturated. As cooling of the mafic magma progresses, crystallization and the subsequent exsolution of volatiles can significantly reduce its density, permitting overturning and large scale mixing between the two magmas [7,9]. Eruption may occur at any time during this sequence of events related to the mixing process if the additional overpressure necessary to rupture the magma chamber is attained. The exsolution of volatiles from the felsic magma due to its increase in temperature or due to convection, or the exsolution of volatiles from the mafic magma during its cooling and crystallization, have all been proposed as possible mechanisms related to the injection and subsequent mixing events which could contribute to overpressurizing the chamber [1,2,9,12–15]. However, the relative importance of these processes has not yet been quantified. This paper investigates the effects of the intrusion of mafic magma into a felsic magma chamber, and quantifies the relative importance of the above
mentioned mixing-related processes in causing overpressure of the chamber and triggering an explosive eruption. We consider a situation in which the overpressure produced by the injection of mafic magma is insufficient in itself to trigger the eruption. Hence, an additional overpressure, achieved by exsolution of volatiles from either or both the felsic or mafic magmas is required. We analyse the time-scale over which these mixing-related processes occur and we compare the results with the evidence from real eruptions.
2. Physical framework We consider the intrusion of a hydrous mafic magma into the base of a shallow felsic magma chamber. The intrusion event is considered to be instantaneous. The volume fraction of injected mafic magma can be expressed as: '
Vmi Vfi
(1)
where Vmi is the volume of injected mafic magma and Vfi is the initial volume of the felsic magma filling the chamber. Previous calculations have indicated that volumes of new injected magma of approximately 0.1% of the volume of the chamber (in the absence of any gas phase; [16]), or of approximately 1% of the volume of the chamber when a gas phase is present within the felsic magma [17], are sufficient to produce the overpressure necessary to trigger an eruption. We will focus on the case where the amount of injected mafic magma is not sufficient to immediately trigger the eruption. Hence, we will assume that the upper values of ' will be 10 2 if the felsic magma is undersaturated in volatiles prior to the injection, and 10 2 if it is volatile-saturated [16,17]. We also assume that mixing between the two magmas will initially be inhibited by their strong density and viscosity contrast (cf. [5,18]), so that the injected mafic magma comes to underlie the cooler and less-dense felsic magma. Thermal equilibration will immediately initiate causing crystallization of the mafic magma and convection of the felsic magma. Mixing may of course occur after some time due to overturning of the mafic magma due to the
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density decrease produced by cooling and crystallization [5], by convective entrainment [11,19], or simply if the eruption rate is sufficiently high [20– 23]. We will now estimate the additional overpressure that can be produced by exsolution of volatiles from the felsic and mafic magmas respectively.
3. Overpressure by exsolution of volatiles in the felsic magma We first consider the possibility of creating additional overpressure by the exsolution of volatiles from the felsic magma due to heating and convection, as suggested by Sparks et al. [1]. Felsic magmas have temperatures typically within the range of 700 to 900ºC, while temperatures of 1200ºC are typical of mafic magmas. The presence of hot, newlyinjected mafic magma at the base of the chamber will heat the felsic magma while the mafic magma itself will cool, so that after some time the magmas will attain thermal equilibrium. To estimate the equilibrium temperature and the time duration necessary to reach it, we assume that there is no heat-loss through the walls of the chamber, so that the total heat released from the mafic magma is absorbed by the felsic magma [24]. If mixing is neglected, temperature variations in the felsic and mafic magmas at thermal equilibrium are given by: ∆Tf D
'²m Cm .Tmi '²m Cm C ²f Cf
Tfi / > 0
(2a)
²f Cf .Tfi Tmi / > 0 (2b) '²m Cm C ²f Cf where Tmi and Tsi are respectively the initial temperatures of the mafic and felsic magmas, Cm and Cf their specific heat capacities, ²m and ²f their densities, and ' is the volume fraction of injected magma. Table 1 contains all the symbols used in the paper and typical values for all of the parameters are given in Table 2. The increase in temperature (predicted by Eq. 2a) of the felsic magma layer as a function of ' and for different values of Tmi is shown in Fig. 1. The temperature of the felsic magma increases only a few degrees at thermal equilibrium because the heat capacities of both magmas are similar and the value of ' is constrained. Thus, although the solu∆Tm D
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Table 1 Notation Symbol Latin a Radius of a gas bubble b Bulk modulus C Heat capacity d Width of the feeder dyke g Gravity acceleration m Mass n Exponent of the solubility law Q Gas constant P Pressure s Solubility constant T Temperature v Stokes terminal velocity V Volume w Velocity of the injection x Mass fraction of crystals in the mafic layer Greek Þ Coefficient of thermal expansion ∆P Pressure increase ∆T Temperature increase Solubility ' Volume fraction of injected mafic magma Viscosity ¼ Rigidity of surrounding rocks Ratio between the chamber expansion and its initial volume ² Density The subscripts ‘m’, ‘f’, ‘g’, ‘d’ and ‘c’ refer to mafic magma, felsic magma, exsolved gas, dissolved gas and crystals respectively. If it exists, the second subscript ‘i’ or ‘f’ in any variable refers respectively to the initial and final stages shown in Fig. 2. Thus, for example, Tmi is the temperature of the mafic magma at the initial stage.
bility of volatiles in felsic magmas decreases with increasing temperature, the exsolution of volatiles by heating of the felsic magma does not appear to be an effective mechanism to create the required additional overpressure. In the lowermost part of the felsic layer, where the temperature increase before reaching thermal equilibrium would be greater, the greater lithostatic pressure will prevent exsolution. Moreover, the increase in pressure produced by the injection of new magma will also tend to prevent the exsolution of volatiles. The intrusion of hot mafic magma will produce a thermal gradient between the upper and lower parts of the chamber which will in most cases induce con-
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Table 2 List of values used in calculations Units
Value
a bm bf Cm Cf g n
m GPa GPa J k 1 kg J k 1 kg ms 2
1
Pi Q
MPa J k 1 kg
1
Tmi Tfi Þm ¼
k k k 1 Pa s GPa
²m ²c ²f
kg m kg m kg m
1–10 µm a 30 b 56 c 1200 1000 9.81 1.0 for CO2 in basalt d 0.7 for H2 O in mafic magma e 100 188.86 for CO2 461.66 for H2 O 4.4 ð 10 12 for CO2 in basalt d 6.8 ð 10 8 for H2 O in mafic magma e 1473 b 1123 b 1.5 ð 10 5 104 –106 10–20 b ¼ ! 1 for rigid walls 2700 b 3000 b 2300 b
3 3 3
1
a Toramaru
[36] and Hurwitz and Navon [28]. Tait et al. [10]. c Murase and McBirney [37]. d Stolper and Holloway [38]. e Hamilton et al. [39].
Stokes terminal velocity v: P 2 2a g ²f 2a 2 g∆² QTf D (3) vD 9 9 where a is the radius of the bubble, ∆² is the density contrast between the gas phase and the liquid magma, g is the acceleration due to gravity, P is the pressure, and Q is a gas constant. In Eq. 3 we have assumed that the gas phase behaves as a perfect gas [10] which is in thermal equilibrium with the host magma. Considering typical viscosities of D 104 –106 for the felsic magma and a bubble size of a few µm [27,28], Eq. 3 predicts extremely low values for the relative velocity between the magma and the bubbles of v ³ 10 10 –10 12 ms 1 . This suggests that the bubbles cannot escape from the uprising parcels of magma within which they form over timescales of weeks or months. Thus, the exsolution of volatiles due to convection in the felsic magma does not seems a plausible mechanism to create some additional overpressure, contrary to the suggestion of Sparks et al. [1].
b
vection in the felsic magma layer [1]. If convection occurs, it leads to felsic magma moving from the lower parts of the chamber towards the top, where the pressure is lower. This upwelling magma may eventually exsolve volatiles, contributing to the internal pressure of the chamber. However, in order to ensure mass conservation, an equivalent volume of felsic magma from the top of the chamber must move downwards, re-dissolving most of the exsolved gas back into the magma in the downward limb of the convective cell. Although the rate of solution may not exactly compensate the rate of exsolution [26], this would result in no significant net increase in pressure, unless the exsolved gas is able to leave the felsic magma to form a foam layer at the top of the chamber, above the exsolution level. As a first approximation, the velocity of bubbles of exsolved gas relative to the magma can be estimated from the
4. Overpressure by exsolution of volatiles from the mafic magma Here we consider the possibility of creating an additional overpressure due to the exsolution of volatiles from the mafic magma during its cooling and crystallization [2,9]. We aim to derive an expression to relate the overpressure produced by the exsolved gas to the volume fraction of injected magma and its degree of crystallization. Tait et al. [10] derived an expression to calculate the chamber overpressure as a function of the degree of crystallization. However, they considered the chamber as a closed system, while we consider a two-layered open system, in which only the lower mafic layer crystallizes, so that the overpressure must also depend on the volume fraction of injected magma. Note also that the timescales involved in both processes are different by orders of magnitude. In closed-system magma chambers, magma cools significantly more slowly by losing heat through the chamber walls [10], while in the present case, the initial temperature contrast between magma layers is the reason for
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Fig. 1. Increase in the temperature of the felsic magma layer after attainment of thermal equilibrium with mafic magma, as a function of the volume fraction of injected mafic magma. Three different initial temperatures for the mafic magma are considered. The initial temperature of the felsic magma is 850ºC. The greater the amount of injected magma the greater the increase in the temperature of the felsic magma layer. However, the temperature in the felsic layer increases only a few degrees because the value of ' (the volume of injected mafic magma) is constrained.
the sudden cooling and crystallization of the lower mafic layer [5,9]. Let us consider the scenario depicted in Fig. 2, with an initial stage just after the injection of mafic magma, and a final stage after some arbitrary time t. Just after the injection event, the chamber contains an upper layer of felsic magma occupying a volume Vfi and a lower layer of aphyric mafic magma occupying a volume Vmi D 'Vfi . For simplicity, we consider that the upper felsic layer is volatile undersaturated, leaving for latter discussion the possible effects of the presence of an exsolved gas before the injection. Heat transfer between the mafic and felsic magmas causes the mafic magma to cool and crystallize, eventually producing volatile oversaturation and the exsolution of a gas causing a pressure increase ∆P. At this stage, the lower mafic magma layer comprises
a volume of gas Vg , a volume of crystals Vc and a volume of liquid which has been compressed to a volume Vmf in response to the increase in pressure. Whether the exsolved gas remains at the interface between the two magma layers [12], or rises through the convecting upper felsic layer within blobs of mafic magma [29] does not affect substantially the results that are obtained. The increase of pressure also compresses the upper felsic layer to a volume Vff and expands the walls of the chamber by some fraction . This leads to the following equation: .1 C /.Vfi C Vmi / D Vff C Vmf C Vg C Vc
(4)
In order to solve Eq. 4, we need to characterise the values of the main physical parameters during the initial and the final stages. (i) The final and initial volumes of the felsic and
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Fig. 2. Just after the injection, at t D 0, the chamber contains an upper felsic magma layer at temperature Tfi occupying a volume Vfi , and a lower mafic magma layer at temperature Tmi occupying a volume Vmi D 'Vfi . The upper layer is assumed to be volatile undersaturated prior to the injection. The initial pressure Pi is the lithostatic pressure plus an overpressure produced by the mafic magma injection. The difference in temperature between layers induces a heat flow from the mafic to the felsic layer, which induces convection and cools the lower layer. The mafic magma crystallizes, becoming oversaturated in volatiles and exsolving gas, which causes a rise in pressure ∆P. After some time t, and in response to the pressure increase, the felsic magma is compressed to a volume Vff , and the chamber walls are expanded. The lower mafic layer now comprises a volume of gas Vg , a volume of crystals Vc , and a volume of liquid magma of Vmf .
mafic magmas are related by: ∆P Vff D Vfi 1 bf Vmf
D Vmi 1
∆P C Þmb .Tmf bm
(5) ½
Tmi / .1
Vc D x/ (6)
where bf and bm are the bulk moduli of the felsic and mafic magmas respectively, Þm is the coefficient of thermal expansion of the mafic magma, Tmf and Tmi are the final and initial temperatures of the mafic magma respectively, and x is the mass fraction of crystals in the mafic magma. Note that we have neglected in Eq. 5 the changes of volume in the felsic magma due to variations in temperature. (ii) The final temperature of the mafic magma Tmf is related to the amount of crystallization. Following Huppert et al. [9] we consider the following relationship between temperature and crystal content: T D 1373
200x
which is derived from crystallization models for calc-alkaline magmas. (iii) The volume of the crystals is given by:
(7)
x²m 'Vfi ²c
(8)
where ²c is the mean density of the crystals. (iv) Assuming that the chamber walls are elastic, the chamber expansion is proportional to the pressure variation: D
∆P ¼
(9)
where ¼ is the rigidity of the surrounding rocks. (v) We also assume that the gas bubbles behave as a perfect gas in thermal equilibrium with its surrounding mafic magma [10]. At the final stage, after gas exsolution, we have: m g QTmf ¾ m g QTmf ∆P 1 (10) Vg D D Pi C ∆P Pi Pi
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where m g is the mass of gas, Q is a gas constant and Pi is the initial pressure. In Eq. 10 we have assumed ∆P − Pi . Note that Pi is the pressure just after the injection, before the exsolution of gas. Hence, Pi will equal the lithostatic pressure plus the overpressure already produced by the injection. (vi) We need also to relate the mass of gas exsolved m g to the mass fraction of crystals. We consider the following solubility law: D s.1
(11)
where is the solubility and s and n are constants which depend on the composition of the magmatic volatiles. In most natural cases, the mafic magma will initially be volatile undersaturated, so that it will require some time to cool and crystallize sufficiently to become volatile oversaturated. However, for simplicity we here consider that the mafic magma is initially volatile saturated, so that: i D s Pin D
m di m mi
(12)
where m di is the mass of volatiles initially dissolved within the mafic magma, and m mi is the initial mass of mafic magma. In our final stage, after some cooling and crystallization, we have: f D s.1 x/.Pi C ∆P/n m df m df ¾ m df D D D m mf m mi m c m mi .1 x/
(13)
where m df and m mf are respectively the mass of dissolved volatiles and the mass of mafic magma, after some time t. In Eq. 13 we have imposed the mass conservation m mi D m mf C m c C m g neglecting the contribution of the gas. Imposing an equality for the conservation of the volatile species, i.e. m di D m df C m g , using the identity m mi D ²m 'Vfi , and substracting Eq. 12 from Eq. 13 we get: mg D
s Pin
1
.1
Eq. 4 we obtain: ½ ∆P '.1 x/ 1 Þm .1373 200x Tmi / bm Q ∆P ²m C .1373 200x/ 1 s Pin C 'x ²c Pi Pi ½ ∆P n ²m ' ð 1 .1 x/2 1 C Pi ∆P ∆P .1 C '/ D 0 (15) bf ¼ which allows us to relate implicitly the overpressure ∆P to the volume fraction of injected mafic magma and the mass fraction of crystals formed during its cooling. Fig. 3 shows the overpressure produced by the exsolution of H2 O from the mafic layer for different values of ' as a function of the amount of crystallization and assuming that the chamber has rigid walls. As this overpressure must be added to the overpressure caused by the injection of new magma, values of ∆P below the tensile strength of the surrounding rocks could be able to fracture the chamber and trigger an eruption. Note also that we are in effect overestimating the effect of the gas because we have assumed that the injected magma is volatile saturated when the crystallization starts. If the injected magma were not saturated in volatiles, the amount of crystallization required to achieve a given overpressure would be greater. The greater the volume of injected magma, the less crystallization is required to achieve a given overpressure. The results predicted by Eq. 15 tend to converge on those predicted previously by Tait et al. [10] when the value of ' is progressively increased. The contractional effect of crystallization is also reflected in Fig. 3. As shown by Tait et al. [10], the crystallization contraction reduces the overpressure of the chamber and creates space for the gas. The greater the value of ' the more important is the effect of crystallization contraction. Fig. 4 shows the same results as Fig. 3, but reflects the effect of the elastic deformation of the chamber walls. Expansion of the chamber walls has an important effect because it relieves pressure creating more space for the exsolved gas. In consequence, more crystallization is required to obtain a given overpressure. Although both chamber expansion and the contraction due to crystallization tend to restrict the '
x/P n
x/
2
∆P 1C Pi
n ½
²m 'Vfi (14)
which relates the mass of gas to the amount of crystallization. Finally, substituting the above expressions into
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Fig. 3. Overpressure produced by the exsolution of H2 O in the mafic layer as a function of the mass fraction of crystals. Results for three values of ' compatible with the values of Blake [16]: (1) ' D 10 3 , (2) ' D 5 ð 10 4 , (3) ' D 10 4 . The overpressure ∆P produced by the injection, according to the model of Blake [16], is also shown. The expansion of the chamber walls is not considered .¼ ! 1/. The temperature in the mafic layer is given by Eq. 7. The three solid curves are for no crystal contraction, i.e. ²c D ²b D 2700 kg m 3 , while the three dashed curves are obtained considering crystal contraction with ²c D 3000 kg m 3 . The greater the volume of injected magma, the less crystallization is required to achieve a given overpressure. The crystallization contraction reduces the overpressure by creating more volume for the gas phase.
overpressure that the exsolved gas is able to produce, the results obtained suggest that the exsolution of volatiles in the mafic magma during its cooling and crystallization is a plausible mechanism of generating overpressures of a few MPa. This overpressure could be responsible for triggering an eruption in those cases where the injection is not in itself immediately sufficient. The period of repose between the injection and the eruption would then depend on the amount of injected mafic magma and on its cooling history. For high values of ', close to the critical value, a short period of repose is expected because, as the initial overpressure due to the injection is high, less gas and therefore less crystallization is neces-
sary to create the overpressure required to trigger the eruption (Fig. 3). For low values of ', the eruption, if produced, would require a longer repose period. In this case, a large amount of exsolved gas is necessary to reach the critical overpressure, and most of the mafic magma would have to crystallize. Huppert and Sparks [24,25] showed that when a layer of ultrabasic melt is emplaced at the base of a basaltic magma chamber, the temperatures of the layers become identical over a period of a few months to a few years. The time required to cool the mafic layer is of the same order of magnitude as the repose periods observed, giving support to our conclusions.
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Fig. 4. Overpressure produced by the exsolution of H2 O in the mafic layer as a function of the mass fraction of crystals. Results for two values of ': solid curves using ' D 10 3 and dashed curves using ' D 5 ð 10 4 . In both cases the expansion of the surrounding rocks is analyzed considering rigid walls .¼ ! 1/ and an elastic deformation with ¼ D 15 GPa. The expansion of the chamber, due to the pressure increase ∆P, creates more space for the exsolved gas. In consequence, more crystallization is required to obtain a given overpressure.
In our calculations we have assumed that the felsic magma is volatile under-saturated when the mafic magma is intruded into the chamber. However, that the felsic magma is already volatile saturated before the replenishment of the chamber seems to be a common situation in shallow magma systems [10,30]. The presence of a gas phase in the felsic magma would imply greater compressibility for the resident magma so that a higher degree of crystallization would be required from the mafic magma to achieve the critical overpressure (Fig. 3). However, the presence of gas in the magma chamber prior to the injection of new magma would already imply an overpressure, so that the compressibility effect would to some extent be compensated for.
Although we have considered only the effect of H2 O in our calculations, other common volatile species in mafic magmas (CO2 , SO2 ) may be exsolved during crystallization and contribute to generating overpressures. Their effectiveness in overpressurizing the chamber will depend on their solubilities. Pallister et al. [2] suggest that exsolution of SO2 from a crystallizing basaltic magma which intruded a dacitic magma was responsible for the 1992 eruption of Pinatubo. A different situation occurs if we consider CO2 as the main volatile species. Fig. 5 shows the effect of CO2 , implying that due to its low solubility, this volatile species is not likely to be important in generating overpressures. Even when neither the contraction due to crystallization contraction nor
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Fig. 5. Overpressure produced by the exsolution of CO2 in the mafic layer for three values of ': (1) ' D 10 3 , (2) ' D 5 ð 10 4 , (3) ' D 10 4 . Neither the expansion of the chamber walls nor the crystallization contraction are considered here. The low solubility of CO2 in mafic melts prevents it from creating significant overpressures. When the amount of crystallization is lower than a critical value, the chamber may even become underpressured because the exsolved CO2 cannot dominate the thermal contraction of the mafic magma.
the expansion of the surrounding elastic rocks is considered, the chamber remains slightly underpressured until the amount of crystals reaches a critical value. When the mass fraction of crystals is lower than this critical value, the amount of exsolved CO2 is not sufficient to counteract the underpressure produced by the thermal contraction of the mafic magma and, in consequence, the chamber remains underpressured. As crystallization proceeds, the amount of exsolved gas is progressively increased and its overpressure finally dominates the underpressure produced by the thermal contraction. However, even in this extreme case, the overpressure produced by the exsolution of CO2 is small. Kress [31] has recently suggested that the 1991 Pinatubo eruption was triggered by the exsolution of SO2 from redox reactions accompanying the injection of a reduced sulphide-saturated basaltic magma
into an oxidized sulphate-saturated dacitic melt. This idea is presented as an alternative explanation to that of Pallister et al. [2] and implies the exsolution of significant amount of volatiles from both the felsic and the mafic magmas. Kress [31] presents his model as a mechanism to achieve rapid exsolution of volatiles in the absence of the extended period of time assumed necessary to generate enough gas from the crystallization of a mafic magma. However, petrological and geophysical data [32] indicate that the 15 June Pinatubo eruption occurred several months after the dacitic magma chamber was invaded by basaltic magma. This indicates that the critical overpressure was not achieved immediately after the intrusion and that exsolution of volatiles after the intrusion event triggered the eruption. Our calculations suggest that sufficient gas can be obtained in a few months after the intrusion from the
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cooling and crystallization of the mafic magma, as was suggested initially by Huppert et al. [9]. Therefore, we suggest that both mechanisms [2,31], could together have accounted for the paroxysmal Pinatubo eruption.
5. Summary and conclusions We have investigated the consequences of the injection of mafic magma into a felsic magma chamber. Previous authors [1] have proposed that this process triggers exsolution of volatiles from the felsic magma because it heats up and convects vigorously. This implies that parcels of heated felsic magma will rise to zones of lower pressure where magma will become volatile-oversaturated and start to exsolve gas. Our calculations indicate, however, that the effect of temperature on the solubility of volatiles in magmas is relatively small compared with the effect of pressure and magma composition, so that for a homogeneous felsic magma, significant changes in volatile solubility must be related to variations in pressure. In the lower parts of the felsic magma layer, where the increase in temperature due to the transfer of heat from the mafic magma will be highest, the exsolution of volatiles will still be prevented by the higher pressure exerted on the deeper parts of the chamber. In addition, our calculations indicate that the net temperature increase of the felsic magma is only of the order of a few degrees, so that any significant changes in the volatile solubility of the felsic magma will necessarily be associated with variations in pressure. Convection induced by the intrusion of mafic magma can, in fact, account for these pressure changes, as deep parts of the felsic magma will be transported to shallower levels in the chamber. However, mass conservation implies that, at the same time, shallower parts of the felsic magma will be transported to deeper zones of the chamber thus compensating for the decompression effect. Overpressures could be created only if the gas bubbles formed when a rising parcel of felsic magma crosses the saturation limit could separate and accumulate at the top of the chamber. However, this has also been shown to be unlikely, due to the high viscosity of the felsic magma and the small size of the bubbles. Therefore, we suggest that exsolution
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of volatiles from the felsic magma is not an effective mechanism to create overpressure at the time scale of a few days to a few months after the intrusion. Exsolution of volatiles from the mafic magma due to its cooling and crystallization [9] is revealed to be a more effective mechanism for generating the additional overpressure required to trigger the eruption. Figs. 3 and 4 show the calculated overpressures produced by the exsolution of H2 O from the mafic magma for different volumes of injected magma as a function of the amount of crystallization for a rigid and an elastic magma chamber, respectively. The results confirm that the overpressure necessary to cause the rupture of the chamber can be achieved by the injection of new magma and the additional overpressure produced by exsolution of volatiles from the mafic magma on the required time scale of a few days to a few months. The study of the products of mixing-related eruptions reveals that in most cases magma mixing apparently does not occur on a large scale. In cases similar to that we have described here, where a felsic magma chamber is invaded by mafic magma, evidence of mixing is provided by the presence of small inclusions of quenched mafic magma within the felsic pumice clasts, with the total erupted volume of felsic magmas being much greater than that of mafic magma [1,11]. Moreover, the compositions of the two components are generally relatively unmodified, suggesting that the duration of the injection-mixing event has not been long enough to allow large scale chemical diffusion within the chamber. When the presence of hybrid compositions intermediate between the two end-members is observed, they represent only a small amount of the total erupted volume [2,3,33–35]. However, estimates of the volume of mafic magma involved in the mixing process, based on petrological and geophysical data, suggest much larger volumes (e.g. [2]). Therefore, over the time scale of a few days to a few months between the intrusion of mafic magma and the eruption, large scale magma mixing affecting the whole chamber seems unlikely. However, once the eruption has started, physical co-mingling of mafic and felsic magmas may occur depending on the eruption dynamics [21– 23]. Huppert et al. [5,9] proposed that overturning of the mafic magma, and consequent large-scale magma
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Fig. 6. Bulk density of the mafic layer as a function of its mass fraction of crystals. Overturn can occur when the bulk density of the mafic magma equals that of the felsic layer, here assumed to be ²s D 2300 kg m 3 . Results obtained using the Eq. A.4 for different values of ': (1) ² D 10 3 , (2) ² D 5 ð 10 4 and (3) ² D 10 4 . We have assumed that neither the crystals nor the gas are removed from the mafic layer and that the mafic magma is saturated in volatiles when the crystallization starts. Under these circumstances, the additional overpressure required to trigger the eruption will be reached before significant crystallization has occurred in the mafic magma allowing it to overturn and mix with the felsic magma (see Fig. 3).
mixing, can occur when its density and viscosity approach those of the overlying felsic magma, after some cooling and crystallization. In our case, where volatile exsolution is driven by crystallization, the additional overpressure required to trigger the eruption will be reached before the mafic magma has crystallized sufficiently to cause it to overturn and mix with the felsic magma (Fig. 6). Therefore, most of the mixing eruption products will correspond to parts of the upper part of the mafic magma layer entrained in the felsic magma layer during convection while most of the mafic magma remains at the bottom of the chamber (see [1,11]). Evidence of large scale mixing in the eruption products probably indicates that the time period between the injection of mafic magma and the eruption is much longer than the time scale considered here, suggesting that neither the intrusion, nor the exsolution of volatiles
from the mafic magma, were sufficient to cause the overpressure necessary to trigger the eruption. In this case, if new injections or further exsolution of volatiles due to fractional crystallization in the felsic magma are able to trigger an eruption, the observed mixed products may correspond to previous replenishment events. Such could be the case for very dry basic magmas.
Acknowledgements This research has been founded by the EC contract ENV4-CT96-0259 and the CICYT Project AMB96-0498-C04. A. Folch is grateful for a CIRIT research fellowship. We also thank L. Wilson and D.L. Sahagian for their constructive reviews. [RV]
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Appendix A In this appendix we derive an expression to obtain the mean bulk density of the mafic layer as a function of its crystal content, in order to envisage the possibility of having an overturning during the cooling process. At some time t, the mafic layer contains crystals, exsolved gas bubbles and the residual liquid phase, so that the mean bulk density is: ²N D
²c Vc C ²mf Vmf C ²g Vg VT
(A.1)
where VT is the total volume occupied by the mafic layer, i.e., VT D 'Vfi C
∆P ∆P Vfi .1 C '/ C Vfi ¼ bf
Using the fact that ∆P ²mf D ²mi 1 C bm
Þm ∆Tm
(A.2)
(A.3)
and the expressions Eqs. 6 and 14 we finally get: ( " ( 2 # ∆P Þm ∆Tm .1 x/ ²N D ²mi ' x C 1 bm " #)) ∆P 2 C s Pin 1 .1 x/2 1 C Pi ² ¦ ∆P ∆P ð 'C .1 C '/ C bf ¼
1
(A.4)
which gives the bulk density ²N as a function of the mass fraction of crystals. The relation between the overpressure ∆P and the mass fraction of crystals x is implicitly given by Eq. 15.
References [1] S.R.J. Sparks, H. Sigurdsson, L. Wilson, Magma mixing: a mechanism for triggering acid explosive eruptions, Nature 267 (1977) 315–318. [2] J.S. Pallister, R.P. Hoblitt, A.G. Reyes, A basalt trigger for the 1991 eruptions of Pinatubo volcano, Nature 356 (1992) 426–428. [3] D.Y. Venezky, M.J. Rutherford, Preeruption conditions and timing of dacite–andesite magma mixing in the 2.2 ka eruption at Mount Rainer, J. Geophys. Res. 102 (1997) 20069–20086. [4] K.J. Wolf, J.C. Eichelberger, Syneruptive mixing, degassing, and crystallisation at Redoubt Volcano, eruption of December, 1989 to May 1990, J. Volcanol. Geotherm. Res. 75 (1997) 19–37. [5] H.E. Huppert, J.S. Turner, R.S.J. Sparks, Replenished magma chambers: effects of compositional zonation and input rates, Earth Planet. Sci. Lett. 57 (1982) 345–357. [6] R.S.J. Sparks, L.A. Marshall, Thermal and mechanical constraints on mixing between mafic and silicic magmas, J. Volcanol. Geotherm. Res. 29 (1986) 99–124.
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[7] J.S. Turner, I.H. Campbell, Convection and mixing in magma chambers, Earth Sci. Rev. 23 (1986) 255–352. [8] D. Snyder, S. Tait, Replenishment of magma chambers: comparison of fluid-mechanic experiments with field relations, Contrib. Mineral. Petrol. 122 (1995) 230–240. [9] H.E. Huppert, R.S.J. Sparks, J.S. Turner, Effects of volatiles on mixing in calc-alkaline magma systems, Nature 297 (1982) 554–557. [10] S. Tait, C. Jaupart, S. Vergniolle, Pressure, gas content and eruption periodicity of a shallow, crystallising magma chamber, Earth Planet. Sci. Lett. 92 (1989) 107–123. [11] D. Snyder, S. Tait, Magma mixing by convective entrainment, Nature 379 (1996) 529–531. [12] J.C. Eichelberger, Vesiculation of mafic magmas during replenishment of silicic magma reservoirs, Nature 288 (1980) 446–450. [13] S. Self, Krakatau revisited: The course of events and interpretation of the 1883 eruption, Geol. J. 28 (1992) 109– 121. [14] N. Thomas, S. Tait, T. Koyaguchi, Mixing of stratified liquids by the motion of gas bubbles: application to magma mixing, Earth Planet. Sci. Lett. 115 (1993) 161–175. [15] C. Mandeville, S. Carey, H. Sigurdsson, Magma mixing, fractional crystallization and volatile degasing during the 1883 eruption of Krakatau volcano, Indonesia„ J. Volcanol. Geotherm. Res. 74 (1996) 243–274. [16] S. Blake, Volcanism and dynamics of open magma chambers, Nature 289 (1981) 783–785. [17] S. Bower, A. Woods, Control of magma volatile content and chamber depth on the mass erupted during explosive volcanic eruptions, J. Geophys. Res. 102 (1997) 10273– 10290. [18] I.H. Campbell, J.S. Turner, Turbulent mixing between fluids with different viscosities, Nature 313 (1985) 39–42. [19] A. Kouchi, I. Sunagawa, A model for mixing basaltic and dacitic magmas as deduced from experimental data, Contrib. Mineral. Petrol. 89 (1985) 17–23. [20] S. Blake, G.N. Ivey, Density and viscosity gradients in zoned magma chambers and their influence on withdrawal dynamics, J. Volcanol. Geotherm. Res. 30 (1986) 210–230. [21] F. Spera, D. Yuen, J. Greer, G. Sewell, Dynamics of magma withdrawal from stratified magma chambers, Geology 14 (1986) 723–726. [22] F. Spera, Some numerical experiments on the withdrawal of magma from crustal reservoirs, J. Geophys. Res. 89 (1984) 8222–8238. [23] A. Trial, F. Spera, J. Greer, D. Yuen, Simulations of magma withdrawal from compositionally zoned bodies, J. Geophys. Res. 97 (1992) 6713–6733. [24] H.E. Huppert, R.S.J. Sparks, The fluid dynamics of a basaltic magma chamber replenished by influx of hot, dense ultrabasic magma, Contrib. Mineral. Petrol. 75 (1980) 279– 289. [25] H.E. Huppert, R.S.J. Sparks, Double-diffusive convection due to crystallization in magmas, Annu. Rev. Earth Planet. Sci. 12 (1984) 11–37. [26] A.A. Proussevitch, D.L. Sahagian, A.T. Anderson, Dynam-
314
[27]
[28]
[29]
[30]
[31] [32]
[33]
A. Folch, J. Martı´ / Earth and Planetary Science Letters 163 (1998) 301–314 ics of diffusive bubble growth in magmas, Isothermal case, J. Geophys. Res. 98 (1993) 22283–22308. A. Toramaru, Measurement of bubble size distributions in vesiculated rocks with implications for quantitative estimation of eruption processes, J. Volcanol. Geotherm. Res. 43 (1990) 71–90. S. Hurwitz, O. Navon, Bubble nucleation in rhyolitic melts: Experiments at high pressure, temperature, and water content, Earth Planet. Sci. Lett. 122 (1994) 267–280. N. Thomas, S. Tait, The dimensions of magmatic inclusions as a constraint on the physical mechanism of mixing, J. Volcanol. Geotherm. Res. 75 (1997) 167–178. S. Blake, Volatile oversaturation during the evolution of silicic magma chambers as an eruption trigger, J. Geophys. Res. 89 (1984) 8237–8244. V. Kress, Magma mixing as a source for the Pinatubo sulphur, Nature 389 (1997) 591–593. Ch.G. Newhall, R.S. Punongbayan (Eds.), Fire and Mud: Eruptions and Lahars of Mount Pinatubo, Philippines, University of Washington Press, Seattle, 1996, 1126 pp. J.A. Wolff, Zonation, mixing and eruption of silica-undersaturated alkaline magma: a case study from Tenerife, Ca-
nary Islands, Geol. Mag. 122 (1985) 623–640. [34] V. Arana, Q J. Martı´, A. Aparicio, L. Garcı´a-Cacho, R. Carcı´a-Garcı´a, Magma mixing in alkaline magmas: An example from Tenerife, Canary Islands, Lithos 32 (1994) 1– 19. [35] G.J. Ablay, G.G.J. Ernst, J. Martı´, R.S.J. Sparks, The 2020 ybp subplinian eruption of Montan˜a Blanca, Tenerife (Canary Islands), Bull. Volcanol. 57 (1995) 337–355. [36] A. Toramaru, Numerical study of nucleation and growth of bubbles in viscous magmas, J. Geophys. Res. 100 (1995) 1913–1931. [37] T. Murase, A. McBirney, Properties of some common igneous rocks and their melts at high temperatures, Geol. Soc. Am. Bull. 84 (1973) 3563–3592. [38] E. Stolper, J.R. Holloway, Experimental determination of the solubility of carbon dioxide in molten basalt at low pressure, Earth Planet. Sci. Lett. 87 (1988) 397–408. [39] D.L. Hamilton, C.W. Burnham, E.F. Osborn, The solubility of water and effects of oxygen fugacity and water content on crystallization of mafic magmas, J. Petrol. 4 (1964) 21– 39.
Earth and Planetary Science Letters 163 (1998) 301–314
The generation of overpressure in felsic magma chambers by replenishment A. Folch, J. Martı´ * Institute of Earth Sciences, CSIC, Lluis Sole´ Sabarı´s s=n, 08028 Barcelona, Spain Received 24 February 1998; revised version received 9 July 1998; accepted 24 August 1998
Abstract Evidence of magma mixing is common in the products of explosive felsic eruptions and it is generally accepted as a common mechanism for triggering such events. In order to quantify the potential for magma mixing to trigger explosive eruptions, we have developed a simple analytical model, based on previous models of magma chamber replenishment, which considers the injection of volatile-rich mafic magma into a chamber occupied by a homogeneous, volatile-rich felsic magma. We assume that the overpressure caused by the injection of new magma is not sufficient to trigger an eruption, for which additional overpressure is required. Two mixing-related mechanisms have traditionally been considered to have the potential to generate the additional overpressure: (1) exsolution of volatiles from the felsic magma during forced convection, and (2) exsolution of volatiles from the mafic magma by oversaturation during cooling and subsequent crystallization. Our calculations suggest that exsolution of volatiles from the felsic magma is not an effective mechanism to generate additional overpressure. However, significant overpressure can be achieved by volatile exsolution from the mafic magma during its cooling and crystallization. The time scale between intrusion and eruption considered in our model is of the order of a few days to a few months, which coincides with petrological and geophysical evidence obtained from magma mixing related eruptions. We also suggest that replenishment of shallow felsic magma chambers by mafic magma in most cases does not lead to large scale mixing, as eruption will occur before thermal equilibrium between the two magmas is reached, so that density and viscosity contrasts between the two magmas will remain significant. 1998 Elsevier Science B.V. All rights reserved. Keywords: magmas; explosive eruptions; volatiles
1. Introduction Magma mixing is widely accepted as a triggering mechanism for explosive eruptions of felsic magmas. This idea was introduced to explain the 1875 plinian eruption of Askja [1] and since then it has been used to explain many other eruptions such as the 1991 Ł Corresponding
author. Tel.: C34 3 330 2716; Fax: C34 3 411 0012; E-mail: [email protected]
Pinatubo eruption [2]. The products of many explosive eruptions of felsic magmas show evidence that mixing between two magmas of contrasting physical and chemical properties occurred before the eruption. In most cases, the mixing is basically physical, and does not include the formation of hybrid compositions intermediate between the mafic and felsic end members. This fact, together with records of pre-eruptive seismic activity, suggests that the time taken from the mixing episode to the eruption is
0012-821X/98/$ – see front matter 1998 Elsevier Science B.V. All rights reserved. PII: S 0 0 1 2 - 8 2 1 X ( 9 8 ) 0 0 1 9 6 - 4
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short, of the order of a few days to a few months [1– 4]. The period of repose occurring between the injection of mafic magma and the eruption also suggests that the volume of injected mafic magma is not in itself sufficient to immediately trigger the eruption, and that some secondary effect(s) associated with the injection of new magma produces the critical overpressure necessary to rupture the magma chamber and permit the subsequent volcanic eruption. When mafic magma is injected into the base of a chamber containing felsic magma, any mixing will initially be strongly inhibited by the contrasts in density, temperature and viscosity between the two magmas [5–8]. Thermal equilibration will then result in cooling of the hotter, more mafic magma which begins to crystallize, and heating of the felsic magma which will tend to cause convection and reabsortion of phenocrysts. Cooling of the mafic magma can cause oversaturation and subsequent exsolution of volatiles [2,9,10]. Superheating and decompression of parts of the felsic magma due to convection may also lead to supersaturation in volatile phases, exsolution and vesiculation [1]. Viscous coupling between the felsic and mafic magmas can then cause entrainment of mafic magma within the convecting felsic magma, thus bringing mafic magma to the top of the chamber [11] where it will decompress and may become oversaturated. As cooling of the mafic magma progresses, crystallization and the subsequent exsolution of volatiles can significantly reduce its density, permitting overturning and large scale mixing between the two magmas [7,9]. Eruption may occur at any time during this sequence of events related to the mixing process if the additional overpressure necessary to rupture the magma chamber is attained. The exsolution of volatiles from the felsic magma due to its increase in temperature or due to convection, or the exsolution of volatiles from the mafic magma during its cooling and crystallization, have all been proposed as possible mechanisms related to the injection and subsequent mixing events which could contribute to overpressurizing the chamber [1,2,9,12–15]. However, the relative importance of these processes has not yet been quantified. This paper investigates the effects of the intrusion of mafic magma into a felsic magma chamber, and quantifies the relative importance of the above
mentioned mixing-related processes in causing overpressure of the chamber and triggering an explosive eruption. We consider a situation in which the overpressure produced by the injection of mafic magma is insufficient in itself to trigger the eruption. Hence, an additional overpressure, achieved by exsolution of volatiles from either or both the felsic or mafic magmas is required. We analyse the time-scale over which these mixing-related processes occur and we compare the results with the evidence from real eruptions.
2. Physical framework We consider the intrusion of a hydrous mafic magma into the base of a shallow felsic magma chamber. The intrusion event is considered to be instantaneous. The volume fraction of injected mafic magma can be expressed as: '
Vmi Vfi
(1)
where Vmi is the volume of injected mafic magma and Vfi is the initial volume of the felsic magma filling the chamber. Previous calculations have indicated that volumes of new injected magma of approximately 0.1% of the volume of the chamber (in the absence of any gas phase; [16]), or of approximately 1% of the volume of the chamber when a gas phase is present within the felsic magma [17], are sufficient to produce the overpressure necessary to trigger an eruption. We will focus on the case where the amount of injected mafic magma is not sufficient to immediately trigger the eruption. Hence, we will assume that the upper values of ' will be 10 2 if the felsic magma is undersaturated in volatiles prior to the injection, and 10 2 if it is volatile-saturated [16,17]. We also assume that mixing between the two magmas will initially be inhibited by their strong density and viscosity contrast (cf. [5,18]), so that the injected mafic magma comes to underlie the cooler and less-dense felsic magma. Thermal equilibration will immediately initiate causing crystallization of the mafic magma and convection of the felsic magma. Mixing may of course occur after some time due to overturning of the mafic magma due to the
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density decrease produced by cooling and crystallization [5], by convective entrainment [11,19], or simply if the eruption rate is sufficiently high [20– 23]. We will now estimate the additional overpressure that can be produced by exsolution of volatiles from the felsic and mafic magmas respectively.
3. Overpressure by exsolution of volatiles in the felsic magma We first consider the possibility of creating additional overpressure by the exsolution of volatiles from the felsic magma due to heating and convection, as suggested by Sparks et al. [1]. Felsic magmas have temperatures typically within the range of 700 to 900ºC, while temperatures of 1200ºC are typical of mafic magmas. The presence of hot, newlyinjected mafic magma at the base of the chamber will heat the felsic magma while the mafic magma itself will cool, so that after some time the magmas will attain thermal equilibrium. To estimate the equilibrium temperature and the time duration necessary to reach it, we assume that there is no heat-loss through the walls of the chamber, so that the total heat released from the mafic magma is absorbed by the felsic magma [24]. If mixing is neglected, temperature variations in the felsic and mafic magmas at thermal equilibrium are given by: ∆Tf D
'²m Cm .Tmi '²m Cm C ²f Cf
Tfi / > 0
(2a)
²f Cf .Tfi Tmi / > 0 (2b) '²m Cm C ²f Cf where Tmi and Tsi are respectively the initial temperatures of the mafic and felsic magmas, Cm and Cf their specific heat capacities, ²m and ²f their densities, and ' is the volume fraction of injected magma. Table 1 contains all the symbols used in the paper and typical values for all of the parameters are given in Table 2. The increase in temperature (predicted by Eq. 2a) of the felsic magma layer as a function of ' and for different values of Tmi is shown in Fig. 1. The temperature of the felsic magma increases only a few degrees at thermal equilibrium because the heat capacities of both magmas are similar and the value of ' is constrained. Thus, although the solu∆Tm D
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Table 1 Notation Symbol Latin a Radius of a gas bubble b Bulk modulus C Heat capacity d Width of the feeder dyke g Gravity acceleration m Mass n Exponent of the solubility law Q Gas constant P Pressure s Solubility constant T Temperature v Stokes terminal velocity V Volume w Velocity of the injection x Mass fraction of crystals in the mafic layer Greek Þ Coefficient of thermal expansion ∆P Pressure increase ∆T Temperature increase Solubility ' Volume fraction of injected mafic magma Viscosity ¼ Rigidity of surrounding rocks Ratio between the chamber expansion and its initial volume ² Density The subscripts ‘m’, ‘f’, ‘g’, ‘d’ and ‘c’ refer to mafic magma, felsic magma, exsolved gas, dissolved gas and crystals respectively. If it exists, the second subscript ‘i’ or ‘f’ in any variable refers respectively to the initial and final stages shown in Fig. 2. Thus, for example, Tmi is the temperature of the mafic magma at the initial stage.
bility of volatiles in felsic magmas decreases with increasing temperature, the exsolution of volatiles by heating of the felsic magma does not appear to be an effective mechanism to create the required additional overpressure. In the lowermost part of the felsic layer, where the temperature increase before reaching thermal equilibrium would be greater, the greater lithostatic pressure will prevent exsolution. Moreover, the increase in pressure produced by the injection of new magma will also tend to prevent the exsolution of volatiles. The intrusion of hot mafic magma will produce a thermal gradient between the upper and lower parts of the chamber which will in most cases induce con-
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Table 2 List of values used in calculations Units
Value
a bm bf Cm Cf g n
m GPa GPa J k 1 kg J k 1 kg ms 2
1
Pi Q
MPa J k 1 kg
1
Tmi Tfi Þm ¼
k k k 1 Pa s GPa
²m ²c ²f
kg m kg m kg m
1–10 µm a 30 b 56 c 1200 1000 9.81 1.0 for CO2 in basalt d 0.7 for H2 O in mafic magma e 100 188.86 for CO2 461.66 for H2 O 4.4 ð 10 12 for CO2 in basalt d 6.8 ð 10 8 for H2 O in mafic magma e 1473 b 1123 b 1.5 ð 10 5 104 –106 10–20 b ¼ ! 1 for rigid walls 2700 b 3000 b 2300 b
3 3 3
1
a Toramaru
[36] and Hurwitz and Navon [28]. Tait et al. [10]. c Murase and McBirney [37]. d Stolper and Holloway [38]. e Hamilton et al. [39].
Stokes terminal velocity v: P 2 2a g ²f 2a 2 g∆² QTf D (3) vD 9 9 where a is the radius of the bubble, ∆² is the density contrast between the gas phase and the liquid magma, g is the acceleration due to gravity, P is the pressure, and Q is a gas constant. In Eq. 3 we have assumed that the gas phase behaves as a perfect gas [10] which is in thermal equilibrium with the host magma. Considering typical viscosities of D 104 –106 for the felsic magma and a bubble size of a few µm [27,28], Eq. 3 predicts extremely low values for the relative velocity between the magma and the bubbles of v ³ 10 10 –10 12 ms 1 . This suggests that the bubbles cannot escape from the uprising parcels of magma within which they form over timescales of weeks or months. Thus, the exsolution of volatiles due to convection in the felsic magma does not seems a plausible mechanism to create some additional overpressure, contrary to the suggestion of Sparks et al. [1].
b
vection in the felsic magma layer [1]. If convection occurs, it leads to felsic magma moving from the lower parts of the chamber towards the top, where the pressure is lower. This upwelling magma may eventually exsolve volatiles, contributing to the internal pressure of the chamber. However, in order to ensure mass conservation, an equivalent volume of felsic magma from the top of the chamber must move downwards, re-dissolving most of the exsolved gas back into the magma in the downward limb of the convective cell. Although the rate of solution may not exactly compensate the rate of exsolution [26], this would result in no significant net increase in pressure, unless the exsolved gas is able to leave the felsic magma to form a foam layer at the top of the chamber, above the exsolution level. As a first approximation, the velocity of bubbles of exsolved gas relative to the magma can be estimated from the
4. Overpressure by exsolution of volatiles from the mafic magma Here we consider the possibility of creating an additional overpressure due to the exsolution of volatiles from the mafic magma during its cooling and crystallization [2,9]. We aim to derive an expression to relate the overpressure produced by the exsolved gas to the volume fraction of injected magma and its degree of crystallization. Tait et al. [10] derived an expression to calculate the chamber overpressure as a function of the degree of crystallization. However, they considered the chamber as a closed system, while we consider a two-layered open system, in which only the lower mafic layer crystallizes, so that the overpressure must also depend on the volume fraction of injected magma. Note also that the timescales involved in both processes are different by orders of magnitude. In closed-system magma chambers, magma cools significantly more slowly by losing heat through the chamber walls [10], while in the present case, the initial temperature contrast between magma layers is the reason for
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Fig. 1. Increase in the temperature of the felsic magma layer after attainment of thermal equilibrium with mafic magma, as a function of the volume fraction of injected mafic magma. Three different initial temperatures for the mafic magma are considered. The initial temperature of the felsic magma is 850ºC. The greater the amount of injected magma the greater the increase in the temperature of the felsic magma layer. However, the temperature in the felsic layer increases only a few degrees because the value of ' (the volume of injected mafic magma) is constrained.
the sudden cooling and crystallization of the lower mafic layer [5,9]. Let us consider the scenario depicted in Fig. 2, with an initial stage just after the injection of mafic magma, and a final stage after some arbitrary time t. Just after the injection event, the chamber contains an upper layer of felsic magma occupying a volume Vfi and a lower layer of aphyric mafic magma occupying a volume Vmi D 'Vfi . For simplicity, we consider that the upper felsic layer is volatile undersaturated, leaving for latter discussion the possible effects of the presence of an exsolved gas before the injection. Heat transfer between the mafic and felsic magmas causes the mafic magma to cool and crystallize, eventually producing volatile oversaturation and the exsolution of a gas causing a pressure increase ∆P. At this stage, the lower mafic magma layer comprises
a volume of gas Vg , a volume of crystals Vc and a volume of liquid which has been compressed to a volume Vmf in response to the increase in pressure. Whether the exsolved gas remains at the interface between the two magma layers [12], or rises through the convecting upper felsic layer within blobs of mafic magma [29] does not affect substantially the results that are obtained. The increase of pressure also compresses the upper felsic layer to a volume Vff and expands the walls of the chamber by some fraction . This leads to the following equation: .1 C /.Vfi C Vmi / D Vff C Vmf C Vg C Vc
(4)
In order to solve Eq. 4, we need to characterise the values of the main physical parameters during the initial and the final stages. (i) The final and initial volumes of the felsic and
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Fig. 2. Just after the injection, at t D 0, the chamber contains an upper felsic magma layer at temperature Tfi occupying a volume Vfi , and a lower mafic magma layer at temperature Tmi occupying a volume Vmi D 'Vfi . The upper layer is assumed to be volatile undersaturated prior to the injection. The initial pressure Pi is the lithostatic pressure plus an overpressure produced by the mafic magma injection. The difference in temperature between layers induces a heat flow from the mafic to the felsic layer, which induces convection and cools the lower layer. The mafic magma crystallizes, becoming oversaturated in volatiles and exsolving gas, which causes a rise in pressure ∆P. After some time t, and in response to the pressure increase, the felsic magma is compressed to a volume Vff , and the chamber walls are expanded. The lower mafic layer now comprises a volume of gas Vg , a volume of crystals Vc , and a volume of liquid magma of Vmf .
mafic magmas are related by: ∆P Vff D Vfi 1 bf Vmf
D Vmi 1
∆P C Þmb .Tmf bm
(5) ½
Tmi / .1
Vc D x/ (6)
where bf and bm are the bulk moduli of the felsic and mafic magmas respectively, Þm is the coefficient of thermal expansion of the mafic magma, Tmf and Tmi are the final and initial temperatures of the mafic magma respectively, and x is the mass fraction of crystals in the mafic magma. Note that we have neglected in Eq. 5 the changes of volume in the felsic magma due to variations in temperature. (ii) The final temperature of the mafic magma Tmf is related to the amount of crystallization. Following Huppert et al. [9] we consider the following relationship between temperature and crystal content: T D 1373
200x
which is derived from crystallization models for calc-alkaline magmas. (iii) The volume of the crystals is given by:
(7)
x²m 'Vfi ²c
(8)
where ²c is the mean density of the crystals. (iv) Assuming that the chamber walls are elastic, the chamber expansion is proportional to the pressure variation: D
∆P ¼
(9)
where ¼ is the rigidity of the surrounding rocks. (v) We also assume that the gas bubbles behave as a perfect gas in thermal equilibrium with its surrounding mafic magma [10]. At the final stage, after gas exsolution, we have: m g QTmf ¾ m g QTmf ∆P 1 (10) Vg D D Pi C ∆P Pi Pi
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where m g is the mass of gas, Q is a gas constant and Pi is the initial pressure. In Eq. 10 we have assumed ∆P − Pi . Note that Pi is the pressure just after the injection, before the exsolution of gas. Hence, Pi will equal the lithostatic pressure plus the overpressure already produced by the injection. (vi) We need also to relate the mass of gas exsolved m g to the mass fraction of crystals. We consider the following solubility law: D s.1
(11)
where is the solubility and s and n are constants which depend on the composition of the magmatic volatiles. In most natural cases, the mafic magma will initially be volatile undersaturated, so that it will require some time to cool and crystallize sufficiently to become volatile oversaturated. However, for simplicity we here consider that the mafic magma is initially volatile saturated, so that: i D s Pin D
m di m mi
(12)
where m di is the mass of volatiles initially dissolved within the mafic magma, and m mi is the initial mass of mafic magma. In our final stage, after some cooling and crystallization, we have: f D s.1 x/.Pi C ∆P/n m df m df ¾ m df D D D m mf m mi m c m mi .1 x/
(13)
where m df and m mf are respectively the mass of dissolved volatiles and the mass of mafic magma, after some time t. In Eq. 13 we have imposed the mass conservation m mi D m mf C m c C m g neglecting the contribution of the gas. Imposing an equality for the conservation of the volatile species, i.e. m di D m df C m g , using the identity m mi D ²m 'Vfi , and substracting Eq. 12 from Eq. 13 we get: mg D
s Pin
1
.1
Eq. 4 we obtain: ½ ∆P '.1 x/ 1 Þm .1373 200x Tmi / bm Q ∆P ²m C .1373 200x/ 1 s Pin C 'x ²c Pi Pi ½ ∆P n ²m ' ð 1 .1 x/2 1 C Pi ∆P ∆P .1 C '/ D 0 (15) bf ¼ which allows us to relate implicitly the overpressure ∆P to the volume fraction of injected mafic magma and the mass fraction of crystals formed during its cooling. Fig. 3 shows the overpressure produced by the exsolution of H2 O from the mafic layer for different values of ' as a function of the amount of crystallization and assuming that the chamber has rigid walls. As this overpressure must be added to the overpressure caused by the injection of new magma, values of ∆P below the tensile strength of the surrounding rocks could be able to fracture the chamber and trigger an eruption. Note also that we are in effect overestimating the effect of the gas because we have assumed that the injected magma is volatile saturated when the crystallization starts. If the injected magma were not saturated in volatiles, the amount of crystallization required to achieve a given overpressure would be greater. The greater the volume of injected magma, the less crystallization is required to achieve a given overpressure. The results predicted by Eq. 15 tend to converge on those predicted previously by Tait et al. [10] when the value of ' is progressively increased. The contractional effect of crystallization is also reflected in Fig. 3. As shown by Tait et al. [10], the crystallization contraction reduces the overpressure of the chamber and creates space for the gas. The greater the value of ' the more important is the effect of crystallization contraction. Fig. 4 shows the same results as Fig. 3, but reflects the effect of the elastic deformation of the chamber walls. Expansion of the chamber walls has an important effect because it relieves pressure creating more space for the exsolved gas. In consequence, more crystallization is required to obtain a given overpressure. Although both chamber expansion and the contraction due to crystallization tend to restrict the '
x/P n
x/
2
∆P 1C Pi
n ½
²m 'Vfi (14)
which relates the mass of gas to the amount of crystallization. Finally, substituting the above expressions into
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Fig. 3. Overpressure produced by the exsolution of H2 O in the mafic layer as a function of the mass fraction of crystals. Results for three values of ' compatible with the values of Blake [16]: (1) ' D 10 3 , (2) ' D 5 ð 10 4 , (3) ' D 10 4 . The overpressure ∆P produced by the injection, according to the model of Blake [16], is also shown. The expansion of the chamber walls is not considered .¼ ! 1/. The temperature in the mafic layer is given by Eq. 7. The three solid curves are for no crystal contraction, i.e. ²c D ²b D 2700 kg m 3 , while the three dashed curves are obtained considering crystal contraction with ²c D 3000 kg m 3 . The greater the volume of injected magma, the less crystallization is required to achieve a given overpressure. The crystallization contraction reduces the overpressure by creating more volume for the gas phase.
overpressure that the exsolved gas is able to produce, the results obtained suggest that the exsolution of volatiles in the mafic magma during its cooling and crystallization is a plausible mechanism of generating overpressures of a few MPa. This overpressure could be responsible for triggering an eruption in those cases where the injection is not in itself immediately sufficient. The period of repose between the injection and the eruption would then depend on the amount of injected mafic magma and on its cooling history. For high values of ', close to the critical value, a short period of repose is expected because, as the initial overpressure due to the injection is high, less gas and therefore less crystallization is neces-
sary to create the overpressure required to trigger the eruption (Fig. 3). For low values of ', the eruption, if produced, would require a longer repose period. In this case, a large amount of exsolved gas is necessary to reach the critical overpressure, and most of the mafic magma would have to crystallize. Huppert and Sparks [24,25] showed that when a layer of ultrabasic melt is emplaced at the base of a basaltic magma chamber, the temperatures of the layers become identical over a period of a few months to a few years. The time required to cool the mafic layer is of the same order of magnitude as the repose periods observed, giving support to our conclusions.
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309
Fig. 4. Overpressure produced by the exsolution of H2 O in the mafic layer as a function of the mass fraction of crystals. Results for two values of ': solid curves using ' D 10 3 and dashed curves using ' D 5 ð 10 4 . In both cases the expansion of the surrounding rocks is analyzed considering rigid walls .¼ ! 1/ and an elastic deformation with ¼ D 15 GPa. The expansion of the chamber, due to the pressure increase ∆P, creates more space for the exsolved gas. In consequence, more crystallization is required to obtain a given overpressure.
In our calculations we have assumed that the felsic magma is volatile under-saturated when the mafic magma is intruded into the chamber. However, that the felsic magma is already volatile saturated before the replenishment of the chamber seems to be a common situation in shallow magma systems [10,30]. The presence of a gas phase in the felsic magma would imply greater compressibility for the resident magma so that a higher degree of crystallization would be required from the mafic magma to achieve the critical overpressure (Fig. 3). However, the presence of gas in the magma chamber prior to the injection of new magma would already imply an overpressure, so that the compressibility effect would to some extent be compensated for.
Although we have considered only the effect of H2 O in our calculations, other common volatile species in mafic magmas (CO2 , SO2 ) may be exsolved during crystallization and contribute to generating overpressures. Their effectiveness in overpressurizing the chamber will depend on their solubilities. Pallister et al. [2] suggest that exsolution of SO2 from a crystallizing basaltic magma which intruded a dacitic magma was responsible for the 1992 eruption of Pinatubo. A different situation occurs if we consider CO2 as the main volatile species. Fig. 5 shows the effect of CO2 , implying that due to its low solubility, this volatile species is not likely to be important in generating overpressures. Even when neither the contraction due to crystallization contraction nor
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Fig. 5. Overpressure produced by the exsolution of CO2 in the mafic layer for three values of ': (1) ' D 10 3 , (2) ' D 5 ð 10 4 , (3) ' D 10 4 . Neither the expansion of the chamber walls nor the crystallization contraction are considered here. The low solubility of CO2 in mafic melts prevents it from creating significant overpressures. When the amount of crystallization is lower than a critical value, the chamber may even become underpressured because the exsolved CO2 cannot dominate the thermal contraction of the mafic magma.
the expansion of the surrounding elastic rocks is considered, the chamber remains slightly underpressured until the amount of crystals reaches a critical value. When the mass fraction of crystals is lower than this critical value, the amount of exsolved CO2 is not sufficient to counteract the underpressure produced by the thermal contraction of the mafic magma and, in consequence, the chamber remains underpressured. As crystallization proceeds, the amount of exsolved gas is progressively increased and its overpressure finally dominates the underpressure produced by the thermal contraction. However, even in this extreme case, the overpressure produced by the exsolution of CO2 is small. Kress [31] has recently suggested that the 1991 Pinatubo eruption was triggered by the exsolution of SO2 from redox reactions accompanying the injection of a reduced sulphide-saturated basaltic magma
into an oxidized sulphate-saturated dacitic melt. This idea is presented as an alternative explanation to that of Pallister et al. [2] and implies the exsolution of significant amount of volatiles from both the felsic and the mafic magmas. Kress [31] presents his model as a mechanism to achieve rapid exsolution of volatiles in the absence of the extended period of time assumed necessary to generate enough gas from the crystallization of a mafic magma. However, petrological and geophysical data [32] indicate that the 15 June Pinatubo eruption occurred several months after the dacitic magma chamber was invaded by basaltic magma. This indicates that the critical overpressure was not achieved immediately after the intrusion and that exsolution of volatiles after the intrusion event triggered the eruption. Our calculations suggest that sufficient gas can be obtained in a few months after the intrusion from the
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cooling and crystallization of the mafic magma, as was suggested initially by Huppert et al. [9]. Therefore, we suggest that both mechanisms [2,31], could together have accounted for the paroxysmal Pinatubo eruption.
5. Summary and conclusions We have investigated the consequences of the injection of mafic magma into a felsic magma chamber. Previous authors [1] have proposed that this process triggers exsolution of volatiles from the felsic magma because it heats up and convects vigorously. This implies that parcels of heated felsic magma will rise to zones of lower pressure where magma will become volatile-oversaturated and start to exsolve gas. Our calculations indicate, however, that the effect of temperature on the solubility of volatiles in magmas is relatively small compared with the effect of pressure and magma composition, so that for a homogeneous felsic magma, significant changes in volatile solubility must be related to variations in pressure. In the lower parts of the felsic magma layer, where the increase in temperature due to the transfer of heat from the mafic magma will be highest, the exsolution of volatiles will still be prevented by the higher pressure exerted on the deeper parts of the chamber. In addition, our calculations indicate that the net temperature increase of the felsic magma is only of the order of a few degrees, so that any significant changes in the volatile solubility of the felsic magma will necessarily be associated with variations in pressure. Convection induced by the intrusion of mafic magma can, in fact, account for these pressure changes, as deep parts of the felsic magma will be transported to shallower levels in the chamber. However, mass conservation implies that, at the same time, shallower parts of the felsic magma will be transported to deeper zones of the chamber thus compensating for the decompression effect. Overpressures could be created only if the gas bubbles formed when a rising parcel of felsic magma crosses the saturation limit could separate and accumulate at the top of the chamber. However, this has also been shown to be unlikely, due to the high viscosity of the felsic magma and the small size of the bubbles. Therefore, we suggest that exsolution
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of volatiles from the felsic magma is not an effective mechanism to create overpressure at the time scale of a few days to a few months after the intrusion. Exsolution of volatiles from the mafic magma due to its cooling and crystallization [9] is revealed to be a more effective mechanism for generating the additional overpressure required to trigger the eruption. Figs. 3 and 4 show the calculated overpressures produced by the exsolution of H2 O from the mafic magma for different volumes of injected magma as a function of the amount of crystallization for a rigid and an elastic magma chamber, respectively. The results confirm that the overpressure necessary to cause the rupture of the chamber can be achieved by the injection of new magma and the additional overpressure produced by exsolution of volatiles from the mafic magma on the required time scale of a few days to a few months. The study of the products of mixing-related eruptions reveals that in most cases magma mixing apparently does not occur on a large scale. In cases similar to that we have described here, where a felsic magma chamber is invaded by mafic magma, evidence of mixing is provided by the presence of small inclusions of quenched mafic magma within the felsic pumice clasts, with the total erupted volume of felsic magmas being much greater than that of mafic magma [1,11]. Moreover, the compositions of the two components are generally relatively unmodified, suggesting that the duration of the injection-mixing event has not been long enough to allow large scale chemical diffusion within the chamber. When the presence of hybrid compositions intermediate between the two end-members is observed, they represent only a small amount of the total erupted volume [2,3,33–35]. However, estimates of the volume of mafic magma involved in the mixing process, based on petrological and geophysical data, suggest much larger volumes (e.g. [2]). Therefore, over the time scale of a few days to a few months between the intrusion of mafic magma and the eruption, large scale magma mixing affecting the whole chamber seems unlikely. However, once the eruption has started, physical co-mingling of mafic and felsic magmas may occur depending on the eruption dynamics [21– 23]. Huppert et al. [5,9] proposed that overturning of the mafic magma, and consequent large-scale magma
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Fig. 6. Bulk density of the mafic layer as a function of its mass fraction of crystals. Overturn can occur when the bulk density of the mafic magma equals that of the felsic layer, here assumed to be ²s D 2300 kg m 3 . Results obtained using the Eq. A.4 for different values of ': (1) ² D 10 3 , (2) ² D 5 ð 10 4 and (3) ² D 10 4 . We have assumed that neither the crystals nor the gas are removed from the mafic layer and that the mafic magma is saturated in volatiles when the crystallization starts. Under these circumstances, the additional overpressure required to trigger the eruption will be reached before significant crystallization has occurred in the mafic magma allowing it to overturn and mix with the felsic magma (see Fig. 3).
mixing, can occur when its density and viscosity approach those of the overlying felsic magma, after some cooling and crystallization. In our case, where volatile exsolution is driven by crystallization, the additional overpressure required to trigger the eruption will be reached before the mafic magma has crystallized sufficiently to cause it to overturn and mix with the felsic magma (Fig. 6). Therefore, most of the mixing eruption products will correspond to parts of the upper part of the mafic magma layer entrained in the felsic magma layer during convection while most of the mafic magma remains at the bottom of the chamber (see [1,11]). Evidence of large scale mixing in the eruption products probably indicates that the time period between the injection of mafic magma and the eruption is much longer than the time scale considered here, suggesting that neither the intrusion, nor the exsolution of volatiles
from the mafic magma, were sufficient to cause the overpressure necessary to trigger the eruption. In this case, if new injections or further exsolution of volatiles due to fractional crystallization in the felsic magma are able to trigger an eruption, the observed mixed products may correspond to previous replenishment events. Such could be the case for very dry basic magmas.
Acknowledgements This research has been founded by the EC contract ENV4-CT96-0259 and the CICYT Project AMB96-0498-C04. A. Folch is grateful for a CIRIT research fellowship. We also thank L. Wilson and D.L. Sahagian for their constructive reviews. [RV]
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Appendix A In this appendix we derive an expression to obtain the mean bulk density of the mafic layer as a function of its crystal content, in order to envisage the possibility of having an overturning during the cooling process. At some time t, the mafic layer contains crystals, exsolved gas bubbles and the residual liquid phase, so that the mean bulk density is: ²N D
²c Vc C ²mf Vmf C ²g Vg VT
(A.1)
where VT is the total volume occupied by the mafic layer, i.e., VT D 'Vfi C
∆P ∆P Vfi .1 C '/ C Vfi ¼ bf
Using the fact that ∆P ²mf D ²mi 1 C bm
Þm ∆Tm
(A.2)
(A.3)
and the expressions Eqs. 6 and 14 we finally get: ( " ( 2 # ∆P Þm ∆Tm .1 x/ ²N D ²mi ' x C 1 bm " #)) ∆P 2 C s Pin 1 .1 x/2 1 C Pi ² ¦ ∆P ∆P ð 'C .1 C '/ C bf ¼
1
(A.4)
which gives the bulk density ²N as a function of the mass fraction of crystals. The relation between the overpressure ∆P and the mass fraction of crystals x is implicitly given by Eq. 15.
References [1] S.R.J. Sparks, H. Sigurdsson, L. Wilson, Magma mixing: a mechanism for triggering acid explosive eruptions, Nature 267 (1977) 315–318. [2] J.S. Pallister, R.P. Hoblitt, A.G. Reyes, A basalt trigger for the 1991 eruptions of Pinatubo volcano, Nature 356 (1992) 426–428. [3] D.Y. Venezky, M.J. Rutherford, Preeruption conditions and timing of dacite–andesite magma mixing in the 2.2 ka eruption at Mount Rainer, J. Geophys. Res. 102 (1997) 20069–20086. [4] K.J. Wolf, J.C. Eichelberger, Syneruptive mixing, degassing, and crystallisation at Redoubt Volcano, eruption of December, 1989 to May 1990, J. Volcanol. Geotherm. Res. 75 (1997) 19–37. [5] H.E. Huppert, J.S. Turner, R.S.J. Sparks, Replenished magma chambers: effects of compositional zonation and input rates, Earth Planet. Sci. Lett. 57 (1982) 345–357. [6] R.S.J. Sparks, L.A. Marshall, Thermal and mechanical constraints on mixing between mafic and silicic magmas, J. Volcanol. Geotherm. Res. 29 (1986) 99–124.
313
[7] J.S. Turner, I.H. Campbell, Convection and mixing in magma chambers, Earth Sci. Rev. 23 (1986) 255–352. [8] D. Snyder, S. Tait, Replenishment of magma chambers: comparison of fluid-mechanic experiments with field relations, Contrib. Mineral. Petrol. 122 (1995) 230–240. [9] H.E. Huppert, R.S.J. Sparks, J.S. Turner, Effects of volatiles on mixing in calc-alkaline magma systems, Nature 297 (1982) 554–557. [10] S. Tait, C. Jaupart, S. Vergniolle, Pressure, gas content and eruption periodicity of a shallow, crystallising magma chamber, Earth Planet. Sci. Lett. 92 (1989) 107–123. [11] D. Snyder, S. Tait, Magma mixing by convective entrainment, Nature 379 (1996) 529–531. [12] J.C. Eichelberger, Vesiculation of mafic magmas during replenishment of silicic magma reservoirs, Nature 288 (1980) 446–450. [13] S. Self, Krakatau revisited: The course of events and interpretation of the 1883 eruption, Geol. J. 28 (1992) 109– 121. [14] N. Thomas, S. Tait, T. Koyaguchi, Mixing of stratified liquids by the motion of gas bubbles: application to magma mixing, Earth Planet. Sci. Lett. 115 (1993) 161–175. [15] C. Mandeville, S. Carey, H. Sigurdsson, Magma mixing, fractional crystallization and volatile degasing during the 1883 eruption of Krakatau volcano, Indonesia„ J. Volcanol. Geotherm. Res. 74 (1996) 243–274. [16] S. Blake, Volcanism and dynamics of open magma chambers, Nature 289 (1981) 783–785. [17] S. Bower, A. Woods, Control of magma volatile content and chamber depth on the mass erupted during explosive volcanic eruptions, J. Geophys. Res. 102 (1997) 10273– 10290. [18] I.H. Campbell, J.S. Turner, Turbulent mixing between fluids with different viscosities, Nature 313 (1985) 39–42. [19] A. Kouchi, I. Sunagawa, A model for mixing basaltic and dacitic magmas as deduced from experimental data, Contrib. Mineral. Petrol. 89 (1985) 17–23. [20] S. Blake, G.N. Ivey, Density and viscosity gradients in zoned magma chambers and their influence on withdrawal dynamics, J. Volcanol. Geotherm. Res. 30 (1986) 210–230. [21] F. Spera, D. Yuen, J. Greer, G. Sewell, Dynamics of magma withdrawal from stratified magma chambers, Geology 14 (1986) 723–726. [22] F. Spera, Some numerical experiments on the withdrawal of magma from crustal reservoirs, J. Geophys. Res. 89 (1984) 8222–8238. [23] A. Trial, F. Spera, J. Greer, D. Yuen, Simulations of magma withdrawal from compositionally zoned bodies, J. Geophys. Res. 97 (1992) 6713–6733. [24] H.E. Huppert, R.S.J. Sparks, The fluid dynamics of a basaltic magma chamber replenished by influx of hot, dense ultrabasic magma, Contrib. Mineral. Petrol. 75 (1980) 279– 289. [25] H.E. Huppert, R.S.J. Sparks, Double-diffusive convection due to crystallization in magmas, Annu. Rev. Earth Planet. Sci. 12 (1984) 11–37. [26] A.A. Proussevitch, D.L. Sahagian, A.T. Anderson, Dynam-
314
[27]
[28]
[29]
[30]
[31] [32]
[33]
A. Folch, J. Martı´ / Earth and Planetary Science Letters 163 (1998) 301–314 ics of diffusive bubble growth in magmas, Isothermal case, J. Geophys. Res. 98 (1993) 22283–22308. A. Toramaru, Measurement of bubble size distributions in vesiculated rocks with implications for quantitative estimation of eruption processes, J. Volcanol. Geotherm. Res. 43 (1990) 71–90. S. Hurwitz, O. Navon, Bubble nucleation in rhyolitic melts: Experiments at high pressure, temperature, and water content, Earth Planet. Sci. Lett. 122 (1994) 267–280. N. Thomas, S. Tait, The dimensions of magmatic inclusions as a constraint on the physical mechanism of mixing, J. Volcanol. Geotherm. Res. 75 (1997) 167–178. S. Blake, Volatile oversaturation during the evolution of silicic magma chambers as an eruption trigger, J. Geophys. Res. 89 (1984) 8237–8244. V. Kress, Magma mixing as a source for the Pinatubo sulphur, Nature 389 (1997) 591–593. Ch.G. Newhall, R.S. Punongbayan (Eds.), Fire and Mud: Eruptions and Lahars of Mount Pinatubo, Philippines, University of Washington Press, Seattle, 1996, 1126 pp. J.A. Wolff, Zonation, mixing and eruption of silica-undersaturated alkaline magma: a case study from Tenerife, Ca-
nary Islands, Geol. Mag. 122 (1985) 623–640. [34] V. Arana, Q J. Martı´, A. Aparicio, L. Garcı´a-Cacho, R. Carcı´a-Garcı´a, Magma mixing in alkaline magmas: An example from Tenerife, Canary Islands, Lithos 32 (1994) 1– 19. [35] G.J. Ablay, G.G.J. Ernst, J. Martı´, R.S.J. Sparks, The 2020 ybp subplinian eruption of Montan˜a Blanca, Tenerife (Canary Islands), Bull. Volcanol. 57 (1995) 337–355. [36] A. Toramaru, Numerical study of nucleation and growth of bubbles in viscous magmas, J. Geophys. Res. 100 (1995) 1913–1931. [37] T. Murase, A. McBirney, Properties of some common igneous rocks and their melts at high temperatures, Geol. Soc. Am. Bull. 84 (1973) 3563–3592. [38] E. Stolper, J.R. Holloway, Experimental determination of the solubility of carbon dioxide in molten basalt at low pressure, Earth Planet. Sci. Lett. 87 (1988) 397–408. [39] D.L. Hamilton, C.W. Burnham, E.F. Osborn, The solubility of water and effects of oxygen fugacity and water content on crystallization of mafic magmas, J. Petrol. 4 (1964) 21– 39.