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The effects of magma replenishment processes on 238U-230Th disequilibrium
Geochimica et Cosmochimica Acta, Vol. 63, No. 23/24, pp. 4101– 4110, 1999 Copyright © 1999 Elsevier Science Ltd Printed in the USA. All rights reserved 0016-7037/99 $20.00 ⫹ .00
Pergamon
PII S0016-7037(99)003117-7
The effects of magma replenishment processes on
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U-230Th disequilibrium
R. D. HUGHES*,† and C. J. HAWKESWORTH Department of Earth Sciences, The Open University, Walton Hall, Milton Keynes, UK, MK7 6AA (Received March 12, 1998; accepted in revised form June 14, 1999)
Abstract—Short lived isotope data are increasingly used to investigate magma chamber residence times. Arc lavas have excellent potential as tracers of magma evolution because their magmas are often out of U-series isotope equilibrium, and some arc magmas have yielded surprisingly old pre-eruption U-series ages from mineral separates. A model is presented to examine the behaviour of U-Th isotopes for a range of conditions between closed system and steady-state magmatic systems. Magmas can be maintained out of secular equilibrium for long periods of time by periodic mixing events with new magma batches. The latter results in oscillations in (230Th/232Th) consistent with the relatively constant values observed in lavas of different ages from some centres. The effects of periodic reinjection of magma and mixing of old and young crystals on U-series mineral isochrons are also considered. Mixtures of crystals produced by either replenished or closed system processes can readily result in linear arrays. In many cases it may be valid to interpret these as minimum average residence times for the crystals, whereas the liquid residence times calculated from U-series data for periodically replenished systems are maximum values. Copyright © 1999 Elsevier Science Ltd plex dynamic situations. In order to understand U-series data from complex magmatic systems, it is necessary to establish the causes of the variations in U/Th ratios and how Th isotope data are affected by periodic injections of new magma. Models of periodically refilled magma chambers have been developed for trace elements and longer lived isotopes (O’Hara, 1977; O’Hara and Mathews, 1981; Albare`de, 1985), and short lived isotope systematics have been modelled in steady-state systems (Pyle, 1992; Condomines, 1994; Pyle, 1994). A brief overview of some of the effects of general open system processes on U-series disequilibria is given by Condomines et al. (1982). A stepwise model of the behaviour of U-series systematics in magma chambers is developed here, which examines the effects of periodic refilling on the Th isotopic composition of the liquid and hence inferred timescales for magmatic processes. The model used in this work allows the effects of various intracrustal magmatic processes to be understood when they operate over timescales significant with respect to short lived isotope systems. Some of the implications of such processes are discussed with reference to the timescales inferred from short lived isotopes from both whole rock and mineral separate data.
1. INTRODUCTION
Uranium series isotope systematics have generated much attention in studies of the rates and timescales of magma genesis because these isotopes have considerable potential as tracers of geological processes which fractionate U and Th on the timescale of 10 –300 ka. A fuller discussion of the theory of short lived isotopes is given by Gill et al. (1992), and references therein. A considerable amount of high-precision U-Th isotope data now exists for a wide range of igneous environments, however, most efforts have concentrated in understanding these isotopes in relatively simple systems such as intra-oceanic arcs (e.g. Turner et al., 1996; Elliott et al., 1997; Turner et al., 1997; Chabaux et al., 1999), mid-ocean ridges (e.g., Goldstein et al., 1989; Goldstein et al., 1993; Volpe and Goldstein, 1993) and basic, relatively unevolved intraplate volcanoes (e.g., Cohen and O’Nions, 1993; He´mond et al. 1994). Some systems which erupt through relatively thin crust, often dominated by basaltic magmas, have U-Th data from which short crustal residence times have been inferred (Elliott et al., 1997; Turner and Hawkesworth, 1997; Turner et al. 1997). Where magma has to rise through thicker crust, whole rock and mineral separate U-Th results are more complex, often suggesting long magma residence times (Volpe and Hammond, 1991; Volpe, 1992; Turner et al., 1996; Heath et al., 1998). Whole rock geochemistry and petrography frequently provide evidence for intracrustal open system processes, such as periodic magma replenishment, crustal assimilation, crystallisation and mixing between primitive and evolved magmas from different sources. This contribution investigates how U-Th isotope data are affected by magma replenishment processes in crustal magma chambers, and the effect such processes have on the time information available from short lived isotopes in these com-
2. MODEL OUTLINE The model in this paper uses a stepwise approach to look at the effects of magma replenishment processes on U-series disequilibrium. The outline of the model given here mainly considers 230Th-238U disequilibrium, although the same ideas can equally be applied to other short lived isotope systems as will be discussed subsequently. The calculations used in this model can be broken down into a series of mixing cycles, each of which is further divided into two stages. In the first, magma chamber evolution stage, radioactive decay and crystallisation effects are calculated, and this is followed by a mixing stage, where fresh, primitive material is mixed with the existing magma. The initial magma is assumed to be out of 230Th-238U equilibrium, and all the examples used assume the parental magma lies to the right of the equiline, in U excess, which is characteristic of some island-arc lavas. However, the model could equally be applied to systems with Th excess, such as many MORB and OIB. The first, chamber evolution stage of the calculation is further broken down into a series of alternating steps which sequentially calculate the effects of radioactive
*Author to whom correspondence should be addressed (rhug99@esc. cam.ac.uk). † Current address: Department of Earth Sciences, University of Cambridge, Downing Street, Cambridge, UK. 4101
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decay and then fractional crystallisation, allowing simultaneous action of these processes to be approximated. For the examples discussed below, a simple system is assumed in which U and Th are both highly incompatible elements and have similar partition coefficients, such that DU ⫽ DTh ⫽ 0.05. The choice of partition coefficient is arbitrary as the examples used in this paper are not intended to reflect a particular crystallising assemblage, but the value chosen is consistent with published values for partition coefficients in minerals such as olivine, pyroxene and plagioclase (e.g., Dunn and Sen 1994; Hauri et al., 1994; Lundstrom et al., 1994; Halliday et al., 1995). The second, mixing stage is assumed to occur instantaneously, and mixes fresh, primitive magma which has the same elemental and isotopic composition as the initial magma in the chamber. In order to maintain a mass balance, the volume of the fresh magma is equal to the volume of magma removed from the system by crystallisation and eruption. Such a calculation assumes that the density of the system is approximately constant, and therefore volume and mass can be directly equated. 3. RESULTS
The model was run over a wide range of conditions by varying the time interval between the new inputs, the ratio of input volume to chamber volume, and the amount of crystallisation occurring during each iteration. Typical results are shown in Figure 1a (see figure caption for the running conditions). The overall effect of repeated injection and mixing is to cause the bulk magma in the chamber to evolve to an asymptotic (230Th/232Th) value which is out of secular equilibrium. For a non-replenished system the asymptote is at secular equilibrium where (230Th/232Th) ⫽ (238U/232Th), and it is reached after ⬃350 ka. In a periodically replenished system, magma may be maintained out of 230Th-238U equilibrium for periods of time which are long compared with the half life of 230Th. This is shown on a conventional equiline diagram (Fig. 1b), where the effect of new magma injections is to drag the (230Th/232Th) ratio of the magma in the chamber away from secular equilibrium and acts against the effects of radioactive decay which moves the liquid composition towards the equiline. Unless there is a constant rather than periodic influx (Wadge, 1982; Pyle, 1992), the magma in the chamber will not maintain a constant (230Th/232Th) composition, but it will oscillate around some mean value. This is shown in Figure 1a by the grey field, and is illustrated in Figure 1b by the difference in apparent isotopic age between the magma after a chamber evolution step and a replenishment step. The apparent isotopic age is calculated by rearranging Eqn. 1 (Appendix 1) to get a solution for time, and substituting the chamber and input Th isotopic compositions for (230Th/232Th) and (230Th/232Th) respectively (Eqn. 5, Appendix 1). Changing the parameters of the model changes the steady state (230Th/232Th) composition of the magma in the chamber, and the rate at which a steady state Th isotopic composition is reached. The effects of varying the model parameters are shown in Figure 2. Increasing the time between new magma influxes means the magma in the chamber has longer to evolve towards the equiline through radioactive decay in each closed system step and therefore the steady state (230Th/232Th) composition is closer to the equiline (Fig. 2a). As the time between replenishment events increases, the time required to approach a steady state Th isotopic value also increases. Knowing absolute volumes is not critical to the behaviour of the model, although it will affect the volume of crystals formed
Fig. 1. (a) The evolution of (230Th/232Th) through time in an replenished magma chamber. The shaded field outlines the compositions traversed by a replenished system through time, and the overlain sawtooth curve shows the variation in (230Th/232Th) before and after new injections of magma. A closed system radioactive decay curve is also shown for the same conditions but without replenishment. The model conditions were: (230Th/232Th)init ⫽ 0.75, (238U/ 232Th) ⫽ 0.9, [Th]init ⫽ 2 ppm, chamber volume ⫽ 50 km3, crystallisation ⫽ 10% per iteration, iteration period ⫽ 6 ka, eruption volume ⫽ 5 km3. (b) Equiline diagram for the same system modelled in figure 1a. The isochrons are drawn between the initial Th isotopic composition and the steady-state (230Th/232Th) values in the chamber before and after each replenishment step. For this set of results there is an oscillation in apparent isotopic ages of ⬃7 ka once a steady-state has been reached.
and the amount of magma erupted. The ratio of input volume to chamber volume is however important in controlling the Th isotopic evolution of the magma. This is shown in Fig. 2b, where the effect of increasing the amount of magma in each replenishment event relative to the volume of the magma chamber is to produce a steady-state Th isotopic value further out of secular equilibrium and closer to the composition of the input magma. Increasing the ratio of input volume to chamber volume also means that a steady state Th isotopic composition is approached more rapidly. The effects of changing the amount of crystallisation occurring in each closed system stage are less intuitive. Increasing the amount of crystallisation has a secondary effect on the input volume which has to increase in order to maintain the mass of magma in the chamber. Intuitively it might be expected that increasing the amount of crystallisation would move the steady state Th isotopic composition closer to secular equilibrium
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Fig. 2. (a) Model curves showing the influence of iteration length on (230Th/232Th) ratios. Longer chamber evolution steps result in a steady-state (230Th/232Th) ratio nearer to secular equilibrium and a longer time required to reach a steady-state. Conditions were: (230Th/232Th)init ⫽ 0.75, (238U/232Th) ⫽ 0.9, [Th]init ⫽ 2 ppm, chamber volume ⫽ 50 km3, erupted volume ⫽ 5 km3. Note that for these models, the system was assumed not to be crystallising. (b) Shows the effect of changing the ratio of input to chamber volume (volume ratio) on (230Th/232Th) ratios. Increasing the volume ratio means that the replenishment step has a greater effect on the composition of the magma and the system reaches a steady-state Th isotopic composition which is further out of secular equilibrium. Increasing the volume ratio also means that the time taken to reach a steady-state value decreases. Model conditions are as for (a) but with a chamber evolution step length of 6 ka. Note that the chamber volume was kept constant and the eruption volume varied to produce the different volume ratios. (c) Illustrates the effects of changing the amount of crystallisation occurring during each chamber evolution step. Increasing the amount of fractional crystallisation moves the steady-state Th isotopic composition of the system further out of secular equilibrium, which is explained in further detail in the text. The model conditions were the same as for (a) with a chamber evolution step length of 6 ka, chamber volume of 50 km3, and eruption volume of 5 km3. (d) Models showing the effect of changing the partition coefficients for U and Th used to calculate the effects of fractional crystallisation. If U and Th are highly incompatible, even order of magnitude differences in partition coefficient have very little effect on the steady-state Th isotopic composition of the system. If U and Th are more compatible the steady-state Th isotopic composition of the system is moved further out of secular equilibrium. The model conditions are as for (c) but using a fixed amount of crystallisation of 10% per iteration.
because the resulting increase in Th abundance in the magma chamber would make each replenishment event relatively less significant. However, the increase in input volume counters this
effect, and it can be seen from Figure 2c that there is very little effect from increasing the amount of crystallisation. In general, the value assumed for the partition coefficients of
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Fig. 3. The relationships between magma chamber turnover time and apparent isotopic age are shown for a range of conditions. If a steady-state has been reached, the isotopic age is always greater than the turnover time. Model conditions were: (230Th/232Th)init ⫽ 0.75, (238U/232Th) ⫽ 0.9, [Th]init ⫽ 2 ppm, chamber volume ⫽ 20 –200 km3 (data points at 20 km3 intervals), crystallisation ⫽ 10% per iteration, erupted volume ⫽ 5 km3.
U and Th makes little difference provided that both elements are highly incompatible (D ⱕ 0.1) (Fig. 2d). If U and Th become less incompatible (i.e. the field for DU ⫽ DTh ⫽ 0.5 in Fig. 2d), the Th concentration of the magma in the chamber increases to a much smaller degree through fractional crystallisation and therefore a given input of fresh magma has a greater effect on the Th isotopic composition of the resulting mixture. The apparent isotopic ages calculated from the evolved and input compositions as described above, may also be compared with the physical turnover time for magma within the chamber. This turnover time is defined in the same manner as used by Pyle (1992) and is simply the period required for the magma in the chamber to be completely replaced by new injections. Comparing the calculated U-Th isotopic age with the turnover time for a range of model parameters (Fig. 3), shows that the isotopic age is always in excess of the turnover time once the system has reached an asymptotic (230Th/232Th). The ratio of input to chamber volumes and the frequency of new injections are the main controlling factors for this relationship. The apparent isotopic age is simpler to estimate than the actual turn-
over time in many real systems, as it is generally easier to estimate initial (230Th/232Th) from measured U-Th data as discussed in detail later, than it is to make reasonable estimates for volumes and flux rates in crustal magma chambers. However, the apparent isotopic age will only be a true liquid residence time in a closed system, whereupon it does represents the time that an erupted liquid has spent in a chamber. 4. DISCUSSION
The modelling outlined above is simplistic because of the degrees of uncertainty surrounding many of the factors that contribute to the behaviour of short lived isotopes in periodically refilled magma chambers. Such simplicity is justified because the analytical uncertainty even in high precision TIMS data, makes it unrealistic to apply a more complex model to real data. Nonetheless, some of the assumptions are considered here in more detail. One of the assumptions of the model is maintaining a constant volume through time. This is unlikely in nature, however, the fixed input volume used in this simple
U-Th disequilibrium in replenished systems
model can be regarded as an approximation for an average input volume over a long period of time. Over the timescale of multiple replenishment events, it is the mean ratio of input to chamber volumes that is the controlling factor in determining the level of the sustained U-Th disequilibrium. It is also assumed that U and Th do not fractionate during crystallisation. Under normal conditions, both elements are highly incompatible during crystallisation of basic-intermediate magma, and they are only likely to be fractionated significantly once minor phases such as apatite and zircon start to crystallise. As the majority of studies which have found significant short lived isotope disequilibrium have centred on basic-intermediate systems, fractionation of U and Th during crystallisation is not considered here, although the model can be readily applied to model fractional crystallisation in systems where accessory phases form (Hughes, 1999). Variations in the degree of incompatibility of U and Th have been illustrated (see Fig. 2), but even order of magnitude differences in the value of the partition coefficients have little effect on the value at which (230Th/ 232 Th) becomes invariant, provided that U and Th remain significantly incompatible (D ⱕ 0.1). 4.1. Whole Rock Results The discussion this far has been concerned with bulk magma composition and in practice there is always the problem of calculating apparent magma ages from natural samples. This requires some estimate of the initial (230Th/232Th), which in practice could be achieved by looking for primitive material which may not have spent significant time in the crustal magma chambers, by estimating initial (230Th/232Th) from Th-Nd or Th-Sr isotope mixing relations for arc rocks (e.g., Turner et al., 1996; Hawkesworth et al., 1997a; Hawkesworth et al., 1997b), or in some cases from mineral-glass U-Th isochrons (Heath et al., 1998). The effects of crustal assimilation have not been considered above, and so this model is only applied to rock suites with Nd, Sr and Pb isotope systematics which have not been modified by intra-crustal contamination processes. Correctly accounting for the effects of small degree melts of local country rocks is problematic, since not only is the timing of assimilation critical to the calculations when considering U-Th systematics, but partial melting may also fractionate U from Th (particularly if a refractory accessory phase such as zircon is present) and thus lead to an assimilant that is also out of equilibrium. However, a crustal assimilant would tend to have lower U/Th and (230Th/ 232 Th) than most mantle derived magmas. For most systems, the amount of assimilation is likely to be greatest for rocks of dacitic and rhyolitic compositions (which are also most likely to be affected by crystallisation of accessory phases), but it may have had relatively little influence in less evolved compositions, producing subtle but systematic shifts in (238U/232Th) and (230Th/232Th) that can be evaluated by correlations with other chemical tracers. 4.2. Mineral Separates Data from real systems will be more complex than the simplified situation outlined here. Basaltic andesites and andesites commonly contain cumulate fragments, as well as
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showing zoning in phases such as plagioclase and pyroxene. An important thrust of this work is the consideration of U-series mineral isochrons and their interpretation for which such complexities are extremely relevant. In many cases crystal and liquid residence times will be different, since crystals from one phase of growth may be retained in the chamber and erupted later following fresh magma injections into the chamber. The situation might also be reversed with old liquids incorporating younger crystals during eruption. Apparently reasonable isochrons have been obtained from a number of evolved volcanic centres, where the mineral age is significantly in excess of the known eruption ages (e.g., Volpe and Hammond, 1991; Volpe, 1992; Heath et al., 1998). This has variably been interpreted as either some kind of average age of mixtures of crystals of different ages and younger liquids (Volpe and Hammond, 1991), or as recording long magma chamber residence times for crystals which have formed from a single batch of magma and have remained essentially unaffected by subsequent replenishment events (Turner et al., 1996; Heath et al., 1998). Two effects need to be considered in order to understand the significance of such internal U-series isochrons. First, the effects of magma replenishment processes maintaining a magma out of 230Th-238U equilibrium, and second, mixing of crystals and liquids of different ages. Both of these processes may operate in the same system resulting in additional complexity. Figures 4a and 4b demonstrate the effects of mixing old and young crystals in closed and periodically replenished systems respectively. The important detail to note is that the liquid composition of the system is extremely informative. Where periodic reinjection of magma has occurred the groundmass (if representative of the liquid composition at the time of eruption) will plot below an internal isochron. However in a closed system, not only does the groundmass lie on the isochron, but in principle mineral isochrons from rocks with different ages of crystal formation derived from the same magma batch, should have the same present day groundmass composition regardless of the eruption age, as all samples will have had the same time for (230Th/232Th) to evolve through radioactive decay. As a result of this, a closed system will demonstrate a systematic variation in initial (230Th/232Th) with eruption age. In contrast, in a replenished system, this initial Th isotopic ratio will be constant if the crystals all grow from magmas with the same Th isotopic composition, i.e., a steady-state has been achieved. In ideal systems, internal isochrons from a series of rocks with different crystallisation ages will rotate about the liquid composition in a closed system, whereas in a replenished steadystate system they will rotate about a point on the equiline with the (230Th/232Th) composition of the liquid. In considering the nature of U-Th mineral isochrons it is important to examine the diffusion of U and Th in basaltic minerals. Very little work has been done to investigate diffusion properties of U and Th in the systems described here, however, Heath et al. (1998) estimate through a series of extrapolations that at 1200°C over 50 ka, Th and U may move ⬃0.1 mm in plagioclase and ⬃0.04 mm in clinopyroxene. Whilst subject to large uncertainties, such estimates imply that diffusion constraints only become important in considering long-lived (ⱖ100 ka) closed systems in which small (⬍1 mm) crystals of plagioclase will be particularly susceptible to isotopic resetting towards liquid compositions. If magma injections
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Fig. 5. The effects of mixing of different crystal populations are shown for both closed and periodically refilled systems. The data points representing hypothetical mineral analyses were calculated as follows. Six periods of crystallisation were assumed, at 120 ka, 100 ka, 80 ka, 60 ka, 40 ka and 20 ka. Phase 1 (P1) crystallised in each of these periods. At 100 ka, 60 ka and 20 ka, phase 2 (P2) crystallised, and phase 3 (P3) only formed at 40 ka and 20 ka. It is assumed that there was no re-equilibration with the co-existing melt. In the closed system, the melt evolved through radioactive decay between each period of crystallisation. In the replenished model, crystallisation always occurred with the same initial (230Th/232Th). The various populations of each phase were assumed to be present in the rock in equal proportions, and the proportions of the different phases were; P1 20%, P2 20%, P3 5% with the remaining 55% assumed to be groundmass with a liquid composition. From these proportions a whole rock value was calculated. The isotopic conditions of the system were: (230Th/232Th)init ⫽ 0.75, (238U/232Th)liquid ⫽ 0.9, (238U/232Th)P1 ⫽ 0.8, (238U/232Th)P2 ⫽ 0.85 and (238U/232Th)P3 ⫽ 1.05. Fig. 4. (a) U-Th equiline diagram showing the effects of crystallisation in a closed system over long time periods where the crystals do not re-equilibrate with the evolving magma through time. Two isochrons are drawn, for crystals formed 50,000 years ago, and for crystals formed 5,000 years ago from the same body of magma immediately prior to eruption. In each case, the same hypothetical phases form with the same degree of U/Th fractionation. Any mixture of these crystals will form an isochron which lies somewhere between these limiting cases with an apparent (230Th/232Th)init lying on the equiline between the two isochrons. The initial (230Th/232Th) and (238U/232Th) ratios are the same as those used in Figures 1 and 2. (b) Equiline diagram showing the effects of crystallisation in a replenished magma chamber, which has reached a temporary equilibrium, over long time periods. As with figure 4a, there is no re-equilibration between crystals and melt. A liquid composition is labelled in preference to groundmass, although in a real system, the groundmass would more likely plot higher, as it would be a mixture of liquid and older material. The important difference between this and Figure 4a is that the apparent initial (230Th/ 232 Th) is invariant. The initial conditions were chosen to be consistent with the conditions used in Figures 1 and 2.
occur more frequently than 50 ka, the homogenisation effects of diffusion will be minimal. Rather narrow, oscillatory compositional bands (⬍0.1 mm) will be produced whose width depends on the frequency of new injections, and the diffusion will be further complicated by the evolution of (230Th/232Th) through radioactive decay for different compositions at differ-
ent rates, dependant on the U/Th ratio and the degree of U-230Th disequilibrium. The effects of mixing crystals which have grown at different times in both closed and replenished systems are illustrated in Figure 5. The example uses an arbitrary mixture of crystals and order of formation to accentuate the effects of different crystal populations. In reality the crystallisation sequence is likely to be less complex, particularly in a steady-state system where the magma might be close to a cotectic. If mixtures of crystals ranging from 5–120 ka (see caption to Fig. 5) are mixed together, reasonable apparent isochrons may be generated given typical errors of ⬃1% (2 on U-Th analyses. Even in the simplest systems, the amount of scatter about the apparent isochrons will increase with increasing difference in age between the oldest and youngest crystals. The amount of variation is also greater where injection of fresh magma occurs, principally as a result of the lower (230Th/232Th) of the liquid composition, although the scatter introduced in this way is less if the system has not reached a steady-state. As the only information available for most systems on the liquid composition comes from measurements of the groundmass, which will also contain other non-liquid components, the groundmass values calculated here are probably lower than would be observed in most real data. However, an apparent isochron which includes groundmass with relatively low (230Th/232Th), still 238
U-Th disequilibrium in replenished systems
yields useful information, even though the groundmass needs to be treated with caution. Even if the older crystals come from cumulate masses, they primarily represent material on or near the surface of the magma chamber boundaries, and so any age obtained from an apparent mineral isochron including such crystals can still be treated as an average crystal residence time. A residence time obtained in this way will not be just a simple measure of the average time a crystal spends in a magma chamber, but it will be weighted by the timing and volumes of crystallisation, and by the likelihood that an eruption may preferentially remove younger crystals from chamber surfaces. If a mineral aliquot contains crystals from two different populations of a given phase, the (230Th/232Th) of the mixture will reflect the percentage of each population present, and the mixing line will have a linear scale assuming that the Th concentration is approximately the same in both. However, the difference in (230Th/232Th) between these populations reflects an exponential time scale, and so the age given by a mixture of two different populations is younger than their true average residence time. For example, a mixture in equal proportions of 5 ka and 55 ka crystals with the same Th concentration should have an arithmetical mean of 30 ka, but the (230Th/232Th) value halfway between the points for each of the populations is closer in time to the younger population, and the actual calculated age is 27.2 ka (assuming (230Th/232Th) ⫽ 0.75 and (238U/232Th) ⫽ 0.9 in line with the other modelling). This relationship is also sensitive to the distance from the equiline, and becomes more pronounced as a system evolves towards equilibrium. Consequently, the residence time inferred from U-series mineral data will usually reflect a minimum average residence time for the crystals where mixing of different populations of crystals has occurred. In contrast, the relationship demonstrated between turnover time and apparent isotopic age of the liquid (Fig. 3) suggests that, where magma replenishment processes are common, the actual residence time of a particular batch of liquid may be considerably less than any maximum age indicated by the liquid composition that plots on an internal isochron. The implications of this work for estimating realistic liquid and crystal residence times from U-Th data highlight the need to understand the degree to which magma replenishment processes may have influenced measured compositions. If replenishment is having a significant effect on (230Th/232Th), then one way in which it might be manifest is by eruption of lavas with near constant whole rock (230Th/232Th), or constant initial (230Th/232Th) values from mineral isochrons that produce different ages, over significant periods of time. Invariant (230Th/ 232 Th) values could also reflect constant transport and residence time in a closed system. However, that requires that each batch of magma evolving in a closed system erupts once, or over a short time period relative to the temporal resolution of U-Th data, which is perhaps unrealistic. 4.3. Combined U-Th and Ra-Th Systematics In addition to the use of 230Th-238U systematics, there is increasing use of 226Ra-230Th data in attempts to interpret the timescales of magmatic processes. These processes operate over different timescales as the half-life of 226Ra is ⬃1.6 ka compared with 75 ka for 230Th. Replenishment processes will
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Fig. 6. Combined U-Th-Ra systematics demonstrating the effects of different replenishment timescales. The difference in half-life between 226 Ra and 230Th is sufficiently large that if the timescale is short enough to produce significant effects on (226Ra/230Th) then (230Th/238U) reaches a steady-state close to that of the parental magma. The model conditions used were: (230Th/232Th)init ⫽ 0.75, (238U/232Th) ⫽ 0.9, [Th]init ⫽ 2 ppm, [226Ra]init ⫽ 300 fg g⫺1, [Ba]init ⫽ 200 ppm, DU ⫽ DTh ⫽ 0.05, DRa ⫽ DBa ⫽ 0.25, Chamber volume ⫽ 50 km3, Eruption volume ⫽ 5 km3, Crystallisation ⫽ 10% per iteration.
have markedly different effects on these systems depending on the frequency and volume of inputs of fresh magma. This is illustrated in Fig. 6, where the effects of varying the frequency of replenishment events on the combined U-Th-Ra systematics are shown. The example illustrated assumes that the system has an initial 226Ra excess, although as mentioned previously, the results would apply equally to a Th excess. When injections of new magma occur frequently with respect to the half-life of 226 Ra, the Th isotopic ratio (and therefore (230Th/238U) ratio) of the magma is maintained close to its starting composition, whereas radioactive decay has a more significant effect on (226Ra/230Th) between each new input. As the time between new inputs increases, the steady-state (226Ra/230Th) ratio approaches secular equilibrium, and the Th isotopic ratio deviates further from the initial composition. In real systems if replenishment events were only occurring on one timescale, it would be difficult to identify these in both of the systems. If the replenishment timescale is quite long (⬎500 –1000 years), the system will rapidly approach Ra-Th equilibrium (whilst maintaining a U-Th disequilibrium). If the replenishment timescale is short (⬍500 years) the Th isotopic composition of the system will be very close to that of the parental magma, and the Ra-Th systematics will reach a steadystate between the parental composition and secular equilibrium. However, if replenishment events occur on different timescales, perhaps reflecting processes operating at different crustal levels or in different magma storage systems, combined U-Th-Ra systematics offer the possibility of examining these processes in further detail.
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4.4. Natural Systems The time required to reach a steady-state in a periodically replenished system and the duration for which it may be maintained have been discussed above. Demonstrating the existence of such a steady-state from natural samples is still difficult despite the quantity of published U-Th data for various arcs e.g. (Elliott et al., 1997; Regelous et al., 1997; Turner et al., 1997). Condomines et al. (1982) use a limited series of data for Mount Etna to identify several possible chamber refilling events, and mixing trends between evolved and primitive magmas are reported for Mount Shasta (Newman et al., 1986), but there is no recently published data with sufficient sample density, and which has good stratigraphic coverage over a sufficiently long time period to look directly at whether the steady-state U-Th chemistry described occurs in practice. It is possible however, to look for evidence of magma replenishment processes, and to assess their relative importance in controlling the U-Th systematics of the system. One line of evidence that might point towards such magma replenishment processes is the eruption over long time periods of lavas with similar ranges in initial Th isotope ratios. The absence of good stratigraphic coverage from individual centres makes this hard to assess, but there is evidence from Mount Ruapehu that andesitic magmas have been erupted with similar U-Th systematics for ⬃100 ka (Hughes, 1999). In detail, however, subtle variations in U-Th data from Ruapehu suggest that there may in fact be considerable differences in the pre-eruption histories of different magma batches. Regardless of the degree to which mixing of different crystal populations has occurred, if fresh injections of parental magma have taken place, the liquid composition will plot below an isochron for co-existing older mineral phases. Mineral isochrons from Soufriere, St. Vincent (Heath et al., 1998) and Mt. Shasta (Volpe, 1992), have groundmass compositions that plot outside error, below the data points for separated mineral phases, consistent with a reduction in (230Th/232Th) on the injection of fresh magma. Other published U-Th isochrons either have groundmass data which falls on the equiline, e.g., (Volpe and Hammond, 1991), or there are no groundmass analyses available. In the case of Soufriere (Heath et al., 1998), four mineral isochrons from material erupted within the last 4 ka have isochron ages ranging from 46 –77 ka with very similar initial (230Th/ 232 Th). In addition to the groundmass data plotting below the mineral separate analyses, the degree of scatter about the isochrons as shown by MSWD values of 2.6 –19.3 is too great to be explained by analytical error given an upper limit of ⬃2.5 (for a 95% confidence limit) for MSWD values with no geological scatter (Wendt and Carl, 1991). The fact that there appears to be significant geological scatter about the isochrons, implies that the mineral separates may well represent a mixture of crystals of various ages. Thus, the interpretation of these data favoured here is that the apparent isochrons are produced by mixing of crystals formed at different times in a system that has seen at least occasional injections of new magma, although the frequency of these events is difficult to assess. Whilst the groundmass data plots below the isochrons, they are still closer than would be expected in a steady-state system, which suggests that any periodic refilling either occurred relatively infrequently or that the ability of the stored magma to mix with the
fresh material was limited. The high eruption frequency of Soufrie´re, possibly ⬎140 eruptions in 5000 years (Heath et al., 1998), might imply frequent injections of new magma if such injections act as eruption triggers (e.g., Sparks et al., 1977). Although all four isochrons have very similar initial (230Th/ 232 Th), this does not necessarily require growth of all the crystals at the same time. As the samples were all erupted in the last 4000 years, they may well have all picked up similar mixtures of crystals and therefore would have the same apparent initial ratio. The implications of the modelling presented here is that such ages probably reflect an average crystal residence time (although not necessarily a liquid residence time) for mixtures of minerals formed at different times. The period of time over which a steady-state may be maintained is dependant on the magma chamber not completely solidifying. Studies of large rhyolitic systems have often suggested that it is possible to keep such magmas above their solidus temperatures for several hundred thousand years, by repeated injections of fresh, hot basalt, (e.g., Christensen and DePaolo, 1993), and the possibility of keeping less evolved systems hot for long periods of time have also been discussed with reference to U-Th data (Heath et al., 1998). This suggests that maintaining a steady-state for 50 –100 ka or even for considerably longer presents no major thermal problem, and it is more likely that limits on the timescales of magma chamber evolution will result from changes in magma supply, perhaps due to local tectonic controls. 5. CONCLUSIONS
Frequent mixing of evolved magma in a crustal chamber with new injections of a similar but more primitive magma will sustain 230Th-238U disequilibria, and can lead to an asymptotic steady-state (230Th/232Th) value which is out of secular equilibrium. The timescales required to generate such disequilibria are strongly dependant on conditions, but they can be achieved in 10 –30 ka and then persist for much longer than the half-life of 230Th (75 ka). Magma replenishment processes are likely to result in apparent mineral isochrons which have groundmass glass compositions that plot away from the line defined by other phases, closer to the composition of the parental magma. By mixing crystals of different ages, reasonable apparent isochrons can be produced. Whilst such data do not directly refer to a specific crystallisation age, they will in many systems reflect the minimum average residence time for crystals in a crustal magma chamber. Where magma replenishment and crystal mixing are common, crystal residence times indicated by U-series data are minimum ages, whilst the calculated liquid residence times are maximum values. No long-lived steady-state magma system has yet been identified due to a paucity of high quality data on magmatic rocks erupted over sufficiently long periods of time. However, some systems do show evidence for replenishment processes and mixing of crystal populations. Acknowledgments—We thank Steve Blake, Dave Peate and Simon Turner for helpful discussions about residence times, magma chamber dynamics and U-Th systematics. Steve Blake and Simon Turner are thanked for careful and helpful informal reviews. Two anonymous
U-Th disequilibrium in replenished systems reviewers are thanked for useful thoughts which greatly improved the paper. RH was supported by a NERC studentship (ref: GT4/95/240/E). REFERENCES Albare`de F. (1985) Regime and trace-element evolution of open magma chambers. Nature 318, 356 –358. Chabaux F., He´mond C., and Alle`gre C. J. (1999) 238U-230Th-226Ra disequilibria in the Lesser Antilles arc: Implications for mantle metasomatism. Chem. Geol. 153, 171–185. Christensen J. N. and DePaolo D. J. (1993) Time scales of large volume silicic magma systems: Sr isotopic systematics of phenocrysts and glass from the Bishop Tuff, Long Valley, California. Contrib. Mineral. Petrol. 113, 100 –114. Cohen A. S. and O’Nions R. K. (1993) Melting rates beneath Hawaii: Evidence from uranium series isotopes in recent lavas. Earth Planet. Sci. Lett. 120, 169 –175. Condomines M. (1994) Comment on: “The volume and residence time of magma beneath active volcanoes determined by decay series disequilibria methods”. Earth Planet. Sci. Lett. 122, 251–255. Condomines M., Tanguy J. C., Kieffer G., and Alle`gre C. J. (1982) Magmatic evolution of a volcano studied by 230Th-238U disequilibrium and trace elements systematics: The Etna case. Geochim. Cosmochim. Acta 46, 1397–1416. Dunn T. and Sen C. (1994) Mineral/matrix partition coefficients for orthopyroxene, plagioclase, and olivine in basaltic to andesitic systems; a combined analytical and experimental study. Geochim. Cosmochim. Acta 58, 717–733. Elliott T., Plank T., Zindler A., White W., and Bourdon B. (1997) Element transport from slab to volcanic front at the Marianas arc. J. Geophys. Res. 102, 14991–15019. Gill J. B., Pyle D. M., and Williams R. W. (1992) Igneous rocks. In Uranium series disequilibrium, applications to environmental problems (ed. M. Ivanovich and R. S. Harmon). pp. 207–258. Oxford University Press. Goldstein S. J., Murrell M. T., and Janecky D. R. (1989) Th and U systematics of basalts from the Juan de Fuca and Gorda Ridges by mass spectrometry. Earth Planet. Sci. Lett. 96, 134 –146. Goldstein S. J., Murrell M. T., and Williams R. W. (1993) 231Pa and 230 Th chronology of mid-ocean ridge basalts. Earth Planet. Sci. Lett. 115, 151–159. Halliday A. N., Lee D.-C., Tommasini S., Davies G. R., Paslick C. R., Fitton J. G., and James D. E. (1995) Incompatible trace element enrichment in OIB and MORB and source enrichment in the suboceanic mantle. Earth Planet. Sci. Lett. 133, 379 –395. Hauri E. H., Wagner T. P., Grove T. L., Foley S. F., and van der Laan S. R. (1994) Experimental and natural partitioning of U, Th, Pb and other trace elements between garnet, clinopyroxene and basaltic melts: Trace-element partitioning with application to magmatic processes. Chem. Geol. 117, 149 –166. Hawkesworth C. J., Turner S. P., McDermott F., Peate D. W., and van Calsteren P. (1997a) U-Th isotopes in arc magmas: Implications for element transfer from the subducted crust. Science 276, 551–55. Hawkesworth C., Turner S., Peate D., McDermott F., and van Calsteren P. (1997b) Elemental U and Th variations in island arc rocks: Implications for U-series isotopes. Chem. Geol. 139, 207–221. Heath E., Turner S. P., Macdonald R., Hawkesworth C. J., and van Calsteren P. (1998) Long magma chamber residence times at an island arc volcano (Soufriere, St. Vincent) in the Lesser Antilles:
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Evidence from 238U-230Th isochron dating. Earth Planet. Sci. Lett. 160, 49 – 63. He´mond Ch., Hofmann A. W., Heusser G., Condomines M., Raczek I., and Rhodes M. (1994) U-Th-Ra systematics in Kilauea and Mauna Loa basalts, Hawaii. Chem. Geol. 116, 163–180. Hughes R. D. (1999) The timescales of andesite generation at Mount Ruapehu, New Zealand. PhD Dissertation, The Open Univ. Lundstrom C. C., Shaw H. F., Ryerson F. J., Phinney D. L., Gill J. B., and Williams Q. (1994) Compositional controls on the partitioning of U, Th, Ba, Pb, Sr and Zr between clinopyroxene and haplobasaltic melts: Implications for uranium series disequilibria in basalts. Earth Planet. Sci. Lett. 128, 407– 423. Newman S., Macdougall J. D., and Finkel R. C. (1986) Petrogenesis and 230Th-238U disequilibrium at Mt. Shasta, California, and in the Cascades. Contrib. Mineral. Petrol. 93, 195–206. O’Hara M. J. (1977) Geochemical evolution during fractional crystallisation of a periodically refilled magma chamber. Nature 266, 503–507. O’Hara M. J. and Mathews R. E. (1981) Geochemical evolution in an advancing, periodically replenished, periodically tapped, continuously fractionated magma chamber. J. Geol. Soc. Lon. 138, 237–277. Pyle D. M. (1994) Reply to comment by M. Condomines on “The volume and residence time of magma beneath active volcanoes determined by decay-series disequilibria methods”. Earth Planet. Sci. Lett. 122, 257–258. Pyle D. M. (1992) The volume and residence time of magma beneath active volcanoes determined by decay-series disequilibria methods. Earth Planet. Sci. Lett. 112, 61–73. Regelous M., Collerson K. D., Ewart A., and Wendt J. I. (1997) Trace element transport rates in subduction zones: Evidence from Th, Sr and Pb isotope data for Tonga-Kermadec arc lavas. Earth Planet. Sci. Lett. 150, 291–302. Sparks R. S. J., Sigurdsson H., and Wilson L. (1977) Magma mixing: A mechanism for trigerring acid explosive eruptions. Nature 267, 315–318. Turner S. and Hawkesworth C. (1997) Constraints on flux rates and mantle dynamics beneath island arcs from Tonga-Kermadec lava geochemistry. Nature 389, 568 –573. Turner S., Hawkesworth C., Rogers N., Bartlett J., Worthington T., Hergt J., Pearce J., and Smith I. (1997) 238U-230Th disequilibria, magma petrogenesis, and flux rates beneath the depleted TongaKermadec island arc. Geochim. Cosmochim. Acta 61, 4855– 4884. Turner S., Hawkesworth C., van Calsteren P., Heath E., Macdonald R., and Black S. (1996) U-series isotopes and destructive plate margin magma genesis in the Lesser Antilles. Earth Planet. Sci. Lett. 142, 191–207. Volpe A. M. (1992) 238U-230Th-226Ra disequilibrium in young Mt. Shasta andesites and dacites. J. Volcanol. Geotherm. Res. 53, 227– 238. Volpe A. M. and Goldstein S. J. (1993) 226Ra-230Th disequilibrium in axial and off-axis mid-ocean ridge basalts. Geochim. Cosmochim. Acta 57, 1233–1241. Volpe A. M. and Hammond P. E. (1991) 238U-230Th-226Ra disequilibria in young Mount St. Helens rocks: Time constraint for magma formation and crystallisation. Earth Planet. Sci. Lett. 107, 475– 486. Wadge G. (1982) Steady state volcanism: Evidence from eruption histories of polygenetic volcanoes. J. Geophys. Res. 87, 4035– 4049. Wendt I. and Carl C. (1991) The statistical distribution of the mean squared weighted deviation. Chem. Geol. 86, 275–285.
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R. D. Hughes and C. J. Hawkesworth APPENDIX 1: EQUATIONS
In the chamber evolution stage, the following equations are used to calculate Th isotopic evolution through radioactive decay and the change in concentrations of U, 232Th and 230Th during crystallisation respectively, 230
(232
Th )⫽ Th
冉 冊 230
232
Th Th
冉 冊 238
e⫺t ⫹ 0
232
U {1 ⫺ e⫺t} Th
X ⫽ Xi (1 ⫺ f)(D⫺1)
(1)
where parentheses denote activity ratios, square brackets denote concentrations, V represents volume, subscript i denotes values for the fresh input of magma and subscript c represents values for the magma chamber. Mixing in terms of elemental abundance follwed by conversion to an activity ratio has been used in preference to a direct calculation involving isotopic ratios because it allows greater flexibility for expansion of the model to consider problems such as crustal assimilation. Turnover time and apparent isotopic age are calculated as follows,
冉 冊 230
Th is the Th Th 0 isotopic ratio of the magma prior to radioactive decay, is the decay constant of 230Th, X is the new concentration of element X, Xo is the concentration of element X prior to crystallisation, f is the fraction of the magma crystallised and Dx is the partition coefficient of element X. In the mixing stage the following equation is used to calculate the Th isotopic composition of the mixture, where in Eqn. 1 parentheses denote activity ratios,
冉 冊 230
Th 232 Th
232
[230Th]c Vc ⫹ [230Th]i Vi ⫽ 232 ⫻ 185885 [ Th]c Vc ⫹ [232Th]i Vi mix
(3)
再 冎 冉 冊 冉 冊 冉 冊 冉 冊
Tt ⫽
(2)
冦
1n Tiso ⫽
230
232
Vc Vi
Th Th
230
232
Th Th
t
238
⫺
232
⫺
232
c
U Th
238
i
⫺
U Th
(4)
冧
(5)
where parentheses denote activity ratios, is the decay constant of 230 Th, t is the length of the iteration, Tt ⫽ turnover time, Tiso⫽ apparent isotopic age, subscript i and subscript c represent input and chamber values respectively.
Pergamon
PII S0016-7037(99)003117-7
The effects of magma replenishment processes on
238
U-230Th disequilibrium
R. D. HUGHES*,† and C. J. HAWKESWORTH Department of Earth Sciences, The Open University, Walton Hall, Milton Keynes, UK, MK7 6AA (Received March 12, 1998; accepted in revised form June 14, 1999)
Abstract—Short lived isotope data are increasingly used to investigate magma chamber residence times. Arc lavas have excellent potential as tracers of magma evolution because their magmas are often out of U-series isotope equilibrium, and some arc magmas have yielded surprisingly old pre-eruption U-series ages from mineral separates. A model is presented to examine the behaviour of U-Th isotopes for a range of conditions between closed system and steady-state magmatic systems. Magmas can be maintained out of secular equilibrium for long periods of time by periodic mixing events with new magma batches. The latter results in oscillations in (230Th/232Th) consistent with the relatively constant values observed in lavas of different ages from some centres. The effects of periodic reinjection of magma and mixing of old and young crystals on U-series mineral isochrons are also considered. Mixtures of crystals produced by either replenished or closed system processes can readily result in linear arrays. In many cases it may be valid to interpret these as minimum average residence times for the crystals, whereas the liquid residence times calculated from U-series data for periodically replenished systems are maximum values. Copyright © 1999 Elsevier Science Ltd plex dynamic situations. In order to understand U-series data from complex magmatic systems, it is necessary to establish the causes of the variations in U/Th ratios and how Th isotope data are affected by periodic injections of new magma. Models of periodically refilled magma chambers have been developed for trace elements and longer lived isotopes (O’Hara, 1977; O’Hara and Mathews, 1981; Albare`de, 1985), and short lived isotope systematics have been modelled in steady-state systems (Pyle, 1992; Condomines, 1994; Pyle, 1994). A brief overview of some of the effects of general open system processes on U-series disequilibria is given by Condomines et al. (1982). A stepwise model of the behaviour of U-series systematics in magma chambers is developed here, which examines the effects of periodic refilling on the Th isotopic composition of the liquid and hence inferred timescales for magmatic processes. The model used in this work allows the effects of various intracrustal magmatic processes to be understood when they operate over timescales significant with respect to short lived isotope systems. Some of the implications of such processes are discussed with reference to the timescales inferred from short lived isotopes from both whole rock and mineral separate data.
1. INTRODUCTION
Uranium series isotope systematics have generated much attention in studies of the rates and timescales of magma genesis because these isotopes have considerable potential as tracers of geological processes which fractionate U and Th on the timescale of 10 –300 ka. A fuller discussion of the theory of short lived isotopes is given by Gill et al. (1992), and references therein. A considerable amount of high-precision U-Th isotope data now exists for a wide range of igneous environments, however, most efforts have concentrated in understanding these isotopes in relatively simple systems such as intra-oceanic arcs (e.g. Turner et al., 1996; Elliott et al., 1997; Turner et al., 1997; Chabaux et al., 1999), mid-ocean ridges (e.g., Goldstein et al., 1989; Goldstein et al., 1993; Volpe and Goldstein, 1993) and basic, relatively unevolved intraplate volcanoes (e.g., Cohen and O’Nions, 1993; He´mond et al. 1994). Some systems which erupt through relatively thin crust, often dominated by basaltic magmas, have U-Th data from which short crustal residence times have been inferred (Elliott et al., 1997; Turner and Hawkesworth, 1997; Turner et al. 1997). Where magma has to rise through thicker crust, whole rock and mineral separate U-Th results are more complex, often suggesting long magma residence times (Volpe and Hammond, 1991; Volpe, 1992; Turner et al., 1996; Heath et al., 1998). Whole rock geochemistry and petrography frequently provide evidence for intracrustal open system processes, such as periodic magma replenishment, crustal assimilation, crystallisation and mixing between primitive and evolved magmas from different sources. This contribution investigates how U-Th isotope data are affected by magma replenishment processes in crustal magma chambers, and the effect such processes have on the time information available from short lived isotopes in these com-
2. MODEL OUTLINE The model in this paper uses a stepwise approach to look at the effects of magma replenishment processes on U-series disequilibrium. The outline of the model given here mainly considers 230Th-238U disequilibrium, although the same ideas can equally be applied to other short lived isotope systems as will be discussed subsequently. The calculations used in this model can be broken down into a series of mixing cycles, each of which is further divided into two stages. In the first, magma chamber evolution stage, radioactive decay and crystallisation effects are calculated, and this is followed by a mixing stage, where fresh, primitive material is mixed with the existing magma. The initial magma is assumed to be out of 230Th-238U equilibrium, and all the examples used assume the parental magma lies to the right of the equiline, in U excess, which is characteristic of some island-arc lavas. However, the model could equally be applied to systems with Th excess, such as many MORB and OIB. The first, chamber evolution stage of the calculation is further broken down into a series of alternating steps which sequentially calculate the effects of radioactive
*Author to whom correspondence should be addressed (rhug99@esc. cam.ac.uk). † Current address: Department of Earth Sciences, University of Cambridge, Downing Street, Cambridge, UK. 4101
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decay and then fractional crystallisation, allowing simultaneous action of these processes to be approximated. For the examples discussed below, a simple system is assumed in which U and Th are both highly incompatible elements and have similar partition coefficients, such that DU ⫽ DTh ⫽ 0.05. The choice of partition coefficient is arbitrary as the examples used in this paper are not intended to reflect a particular crystallising assemblage, but the value chosen is consistent with published values for partition coefficients in minerals such as olivine, pyroxene and plagioclase (e.g., Dunn and Sen 1994; Hauri et al., 1994; Lundstrom et al., 1994; Halliday et al., 1995). The second, mixing stage is assumed to occur instantaneously, and mixes fresh, primitive magma which has the same elemental and isotopic composition as the initial magma in the chamber. In order to maintain a mass balance, the volume of the fresh magma is equal to the volume of magma removed from the system by crystallisation and eruption. Such a calculation assumes that the density of the system is approximately constant, and therefore volume and mass can be directly equated. 3. RESULTS
The model was run over a wide range of conditions by varying the time interval between the new inputs, the ratio of input volume to chamber volume, and the amount of crystallisation occurring during each iteration. Typical results are shown in Figure 1a (see figure caption for the running conditions). The overall effect of repeated injection and mixing is to cause the bulk magma in the chamber to evolve to an asymptotic (230Th/232Th) value which is out of secular equilibrium. For a non-replenished system the asymptote is at secular equilibrium where (230Th/232Th) ⫽ (238U/232Th), and it is reached after ⬃350 ka. In a periodically replenished system, magma may be maintained out of 230Th-238U equilibrium for periods of time which are long compared with the half life of 230Th. This is shown on a conventional equiline diagram (Fig. 1b), where the effect of new magma injections is to drag the (230Th/232Th) ratio of the magma in the chamber away from secular equilibrium and acts against the effects of radioactive decay which moves the liquid composition towards the equiline. Unless there is a constant rather than periodic influx (Wadge, 1982; Pyle, 1992), the magma in the chamber will not maintain a constant (230Th/232Th) composition, but it will oscillate around some mean value. This is shown in Figure 1a by the grey field, and is illustrated in Figure 1b by the difference in apparent isotopic age between the magma after a chamber evolution step and a replenishment step. The apparent isotopic age is calculated by rearranging Eqn. 1 (Appendix 1) to get a solution for time, and substituting the chamber and input Th isotopic compositions for (230Th/232Th) and (230Th/232Th) respectively (Eqn. 5, Appendix 1). Changing the parameters of the model changes the steady state (230Th/232Th) composition of the magma in the chamber, and the rate at which a steady state Th isotopic composition is reached. The effects of varying the model parameters are shown in Figure 2. Increasing the time between new magma influxes means the magma in the chamber has longer to evolve towards the equiline through radioactive decay in each closed system step and therefore the steady state (230Th/232Th) composition is closer to the equiline (Fig. 2a). As the time between replenishment events increases, the time required to approach a steady state Th isotopic value also increases. Knowing absolute volumes is not critical to the behaviour of the model, although it will affect the volume of crystals formed
Fig. 1. (a) The evolution of (230Th/232Th) through time in an replenished magma chamber. The shaded field outlines the compositions traversed by a replenished system through time, and the overlain sawtooth curve shows the variation in (230Th/232Th) before and after new injections of magma. A closed system radioactive decay curve is also shown for the same conditions but without replenishment. The model conditions were: (230Th/232Th)init ⫽ 0.75, (238U/ 232Th) ⫽ 0.9, [Th]init ⫽ 2 ppm, chamber volume ⫽ 50 km3, crystallisation ⫽ 10% per iteration, iteration period ⫽ 6 ka, eruption volume ⫽ 5 km3. (b) Equiline diagram for the same system modelled in figure 1a. The isochrons are drawn between the initial Th isotopic composition and the steady-state (230Th/232Th) values in the chamber before and after each replenishment step. For this set of results there is an oscillation in apparent isotopic ages of ⬃7 ka once a steady-state has been reached.
and the amount of magma erupted. The ratio of input volume to chamber volume is however important in controlling the Th isotopic evolution of the magma. This is shown in Fig. 2b, where the effect of increasing the amount of magma in each replenishment event relative to the volume of the magma chamber is to produce a steady-state Th isotopic value further out of secular equilibrium and closer to the composition of the input magma. Increasing the ratio of input volume to chamber volume also means that a steady state Th isotopic composition is approached more rapidly. The effects of changing the amount of crystallisation occurring in each closed system stage are less intuitive. Increasing the amount of crystallisation has a secondary effect on the input volume which has to increase in order to maintain the mass of magma in the chamber. Intuitively it might be expected that increasing the amount of crystallisation would move the steady state Th isotopic composition closer to secular equilibrium
U-Th disequilibrium in replenished systems
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Fig. 2. (a) Model curves showing the influence of iteration length on (230Th/232Th) ratios. Longer chamber evolution steps result in a steady-state (230Th/232Th) ratio nearer to secular equilibrium and a longer time required to reach a steady-state. Conditions were: (230Th/232Th)init ⫽ 0.75, (238U/232Th) ⫽ 0.9, [Th]init ⫽ 2 ppm, chamber volume ⫽ 50 km3, erupted volume ⫽ 5 km3. Note that for these models, the system was assumed not to be crystallising. (b) Shows the effect of changing the ratio of input to chamber volume (volume ratio) on (230Th/232Th) ratios. Increasing the volume ratio means that the replenishment step has a greater effect on the composition of the magma and the system reaches a steady-state Th isotopic composition which is further out of secular equilibrium. Increasing the volume ratio also means that the time taken to reach a steady-state value decreases. Model conditions are as for (a) but with a chamber evolution step length of 6 ka. Note that the chamber volume was kept constant and the eruption volume varied to produce the different volume ratios. (c) Illustrates the effects of changing the amount of crystallisation occurring during each chamber evolution step. Increasing the amount of fractional crystallisation moves the steady-state Th isotopic composition of the system further out of secular equilibrium, which is explained in further detail in the text. The model conditions were the same as for (a) with a chamber evolution step length of 6 ka, chamber volume of 50 km3, and eruption volume of 5 km3. (d) Models showing the effect of changing the partition coefficients for U and Th used to calculate the effects of fractional crystallisation. If U and Th are highly incompatible, even order of magnitude differences in partition coefficient have very little effect on the steady-state Th isotopic composition of the system. If U and Th are more compatible the steady-state Th isotopic composition of the system is moved further out of secular equilibrium. The model conditions are as for (c) but using a fixed amount of crystallisation of 10% per iteration.
because the resulting increase in Th abundance in the magma chamber would make each replenishment event relatively less significant. However, the increase in input volume counters this
effect, and it can be seen from Figure 2c that there is very little effect from increasing the amount of crystallisation. In general, the value assumed for the partition coefficients of
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Fig. 3. The relationships between magma chamber turnover time and apparent isotopic age are shown for a range of conditions. If a steady-state has been reached, the isotopic age is always greater than the turnover time. Model conditions were: (230Th/232Th)init ⫽ 0.75, (238U/232Th) ⫽ 0.9, [Th]init ⫽ 2 ppm, chamber volume ⫽ 20 –200 km3 (data points at 20 km3 intervals), crystallisation ⫽ 10% per iteration, erupted volume ⫽ 5 km3.
U and Th makes little difference provided that both elements are highly incompatible (D ⱕ 0.1) (Fig. 2d). If U and Th become less incompatible (i.e. the field for DU ⫽ DTh ⫽ 0.5 in Fig. 2d), the Th concentration of the magma in the chamber increases to a much smaller degree through fractional crystallisation and therefore a given input of fresh magma has a greater effect on the Th isotopic composition of the resulting mixture. The apparent isotopic ages calculated from the evolved and input compositions as described above, may also be compared with the physical turnover time for magma within the chamber. This turnover time is defined in the same manner as used by Pyle (1992) and is simply the period required for the magma in the chamber to be completely replaced by new injections. Comparing the calculated U-Th isotopic age with the turnover time for a range of model parameters (Fig. 3), shows that the isotopic age is always in excess of the turnover time once the system has reached an asymptotic (230Th/232Th). The ratio of input to chamber volumes and the frequency of new injections are the main controlling factors for this relationship. The apparent isotopic age is simpler to estimate than the actual turn-
over time in many real systems, as it is generally easier to estimate initial (230Th/232Th) from measured U-Th data as discussed in detail later, than it is to make reasonable estimates for volumes and flux rates in crustal magma chambers. However, the apparent isotopic age will only be a true liquid residence time in a closed system, whereupon it does represents the time that an erupted liquid has spent in a chamber. 4. DISCUSSION
The modelling outlined above is simplistic because of the degrees of uncertainty surrounding many of the factors that contribute to the behaviour of short lived isotopes in periodically refilled magma chambers. Such simplicity is justified because the analytical uncertainty even in high precision TIMS data, makes it unrealistic to apply a more complex model to real data. Nonetheless, some of the assumptions are considered here in more detail. One of the assumptions of the model is maintaining a constant volume through time. This is unlikely in nature, however, the fixed input volume used in this simple
U-Th disequilibrium in replenished systems
model can be regarded as an approximation for an average input volume over a long period of time. Over the timescale of multiple replenishment events, it is the mean ratio of input to chamber volumes that is the controlling factor in determining the level of the sustained U-Th disequilibrium. It is also assumed that U and Th do not fractionate during crystallisation. Under normal conditions, both elements are highly incompatible during crystallisation of basic-intermediate magma, and they are only likely to be fractionated significantly once minor phases such as apatite and zircon start to crystallise. As the majority of studies which have found significant short lived isotope disequilibrium have centred on basic-intermediate systems, fractionation of U and Th during crystallisation is not considered here, although the model can be readily applied to model fractional crystallisation in systems where accessory phases form (Hughes, 1999). Variations in the degree of incompatibility of U and Th have been illustrated (see Fig. 2), but even order of magnitude differences in the value of the partition coefficients have little effect on the value at which (230Th/ 232 Th) becomes invariant, provided that U and Th remain significantly incompatible (D ⱕ 0.1). 4.1. Whole Rock Results The discussion this far has been concerned with bulk magma composition and in practice there is always the problem of calculating apparent magma ages from natural samples. This requires some estimate of the initial (230Th/232Th), which in practice could be achieved by looking for primitive material which may not have spent significant time in the crustal magma chambers, by estimating initial (230Th/232Th) from Th-Nd or Th-Sr isotope mixing relations for arc rocks (e.g., Turner et al., 1996; Hawkesworth et al., 1997a; Hawkesworth et al., 1997b), or in some cases from mineral-glass U-Th isochrons (Heath et al., 1998). The effects of crustal assimilation have not been considered above, and so this model is only applied to rock suites with Nd, Sr and Pb isotope systematics which have not been modified by intra-crustal contamination processes. Correctly accounting for the effects of small degree melts of local country rocks is problematic, since not only is the timing of assimilation critical to the calculations when considering U-Th systematics, but partial melting may also fractionate U from Th (particularly if a refractory accessory phase such as zircon is present) and thus lead to an assimilant that is also out of equilibrium. However, a crustal assimilant would tend to have lower U/Th and (230Th/ 232 Th) than most mantle derived magmas. For most systems, the amount of assimilation is likely to be greatest for rocks of dacitic and rhyolitic compositions (which are also most likely to be affected by crystallisation of accessory phases), but it may have had relatively little influence in less evolved compositions, producing subtle but systematic shifts in (238U/232Th) and (230Th/232Th) that can be evaluated by correlations with other chemical tracers. 4.2. Mineral Separates Data from real systems will be more complex than the simplified situation outlined here. Basaltic andesites and andesites commonly contain cumulate fragments, as well as
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showing zoning in phases such as plagioclase and pyroxene. An important thrust of this work is the consideration of U-series mineral isochrons and their interpretation for which such complexities are extremely relevant. In many cases crystal and liquid residence times will be different, since crystals from one phase of growth may be retained in the chamber and erupted later following fresh magma injections into the chamber. The situation might also be reversed with old liquids incorporating younger crystals during eruption. Apparently reasonable isochrons have been obtained from a number of evolved volcanic centres, where the mineral age is significantly in excess of the known eruption ages (e.g., Volpe and Hammond, 1991; Volpe, 1992; Heath et al., 1998). This has variably been interpreted as either some kind of average age of mixtures of crystals of different ages and younger liquids (Volpe and Hammond, 1991), or as recording long magma chamber residence times for crystals which have formed from a single batch of magma and have remained essentially unaffected by subsequent replenishment events (Turner et al., 1996; Heath et al., 1998). Two effects need to be considered in order to understand the significance of such internal U-series isochrons. First, the effects of magma replenishment processes maintaining a magma out of 230Th-238U equilibrium, and second, mixing of crystals and liquids of different ages. Both of these processes may operate in the same system resulting in additional complexity. Figures 4a and 4b demonstrate the effects of mixing old and young crystals in closed and periodically replenished systems respectively. The important detail to note is that the liquid composition of the system is extremely informative. Where periodic reinjection of magma has occurred the groundmass (if representative of the liquid composition at the time of eruption) will plot below an internal isochron. However in a closed system, not only does the groundmass lie on the isochron, but in principle mineral isochrons from rocks with different ages of crystal formation derived from the same magma batch, should have the same present day groundmass composition regardless of the eruption age, as all samples will have had the same time for (230Th/232Th) to evolve through radioactive decay. As a result of this, a closed system will demonstrate a systematic variation in initial (230Th/232Th) with eruption age. In contrast, in a replenished system, this initial Th isotopic ratio will be constant if the crystals all grow from magmas with the same Th isotopic composition, i.e., a steady-state has been achieved. In ideal systems, internal isochrons from a series of rocks with different crystallisation ages will rotate about the liquid composition in a closed system, whereas in a replenished steadystate system they will rotate about a point on the equiline with the (230Th/232Th) composition of the liquid. In considering the nature of U-Th mineral isochrons it is important to examine the diffusion of U and Th in basaltic minerals. Very little work has been done to investigate diffusion properties of U and Th in the systems described here, however, Heath et al. (1998) estimate through a series of extrapolations that at 1200°C over 50 ka, Th and U may move ⬃0.1 mm in plagioclase and ⬃0.04 mm in clinopyroxene. Whilst subject to large uncertainties, such estimates imply that diffusion constraints only become important in considering long-lived (ⱖ100 ka) closed systems in which small (⬍1 mm) crystals of plagioclase will be particularly susceptible to isotopic resetting towards liquid compositions. If magma injections
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R. D. Hughes and C. J. Hawkesworth
Fig. 5. The effects of mixing of different crystal populations are shown for both closed and periodically refilled systems. The data points representing hypothetical mineral analyses were calculated as follows. Six periods of crystallisation were assumed, at 120 ka, 100 ka, 80 ka, 60 ka, 40 ka and 20 ka. Phase 1 (P1) crystallised in each of these periods. At 100 ka, 60 ka and 20 ka, phase 2 (P2) crystallised, and phase 3 (P3) only formed at 40 ka and 20 ka. It is assumed that there was no re-equilibration with the co-existing melt. In the closed system, the melt evolved through radioactive decay between each period of crystallisation. In the replenished model, crystallisation always occurred with the same initial (230Th/232Th). The various populations of each phase were assumed to be present in the rock in equal proportions, and the proportions of the different phases were; P1 20%, P2 20%, P3 5% with the remaining 55% assumed to be groundmass with a liquid composition. From these proportions a whole rock value was calculated. The isotopic conditions of the system were: (230Th/232Th)init ⫽ 0.75, (238U/232Th)liquid ⫽ 0.9, (238U/232Th)P1 ⫽ 0.8, (238U/232Th)P2 ⫽ 0.85 and (238U/232Th)P3 ⫽ 1.05. Fig. 4. (a) U-Th equiline diagram showing the effects of crystallisation in a closed system over long time periods where the crystals do not re-equilibrate with the evolving magma through time. Two isochrons are drawn, for crystals formed 50,000 years ago, and for crystals formed 5,000 years ago from the same body of magma immediately prior to eruption. In each case, the same hypothetical phases form with the same degree of U/Th fractionation. Any mixture of these crystals will form an isochron which lies somewhere between these limiting cases with an apparent (230Th/232Th)init lying on the equiline between the two isochrons. The initial (230Th/232Th) and (238U/232Th) ratios are the same as those used in Figures 1 and 2. (b) Equiline diagram showing the effects of crystallisation in a replenished magma chamber, which has reached a temporary equilibrium, over long time periods. As with figure 4a, there is no re-equilibration between crystals and melt. A liquid composition is labelled in preference to groundmass, although in a real system, the groundmass would more likely plot higher, as it would be a mixture of liquid and older material. The important difference between this and Figure 4a is that the apparent initial (230Th/ 232 Th) is invariant. The initial conditions were chosen to be consistent with the conditions used in Figures 1 and 2.
occur more frequently than 50 ka, the homogenisation effects of diffusion will be minimal. Rather narrow, oscillatory compositional bands (⬍0.1 mm) will be produced whose width depends on the frequency of new injections, and the diffusion will be further complicated by the evolution of (230Th/232Th) through radioactive decay for different compositions at differ-
ent rates, dependant on the U/Th ratio and the degree of U-230Th disequilibrium. The effects of mixing crystals which have grown at different times in both closed and replenished systems are illustrated in Figure 5. The example uses an arbitrary mixture of crystals and order of formation to accentuate the effects of different crystal populations. In reality the crystallisation sequence is likely to be less complex, particularly in a steady-state system where the magma might be close to a cotectic. If mixtures of crystals ranging from 5–120 ka (see caption to Fig. 5) are mixed together, reasonable apparent isochrons may be generated given typical errors of ⬃1% (2 on U-Th analyses. Even in the simplest systems, the amount of scatter about the apparent isochrons will increase with increasing difference in age between the oldest and youngest crystals. The amount of variation is also greater where injection of fresh magma occurs, principally as a result of the lower (230Th/232Th) of the liquid composition, although the scatter introduced in this way is less if the system has not reached a steady-state. As the only information available for most systems on the liquid composition comes from measurements of the groundmass, which will also contain other non-liquid components, the groundmass values calculated here are probably lower than would be observed in most real data. However, an apparent isochron which includes groundmass with relatively low (230Th/232Th), still 238
U-Th disequilibrium in replenished systems
yields useful information, even though the groundmass needs to be treated with caution. Even if the older crystals come from cumulate masses, they primarily represent material on or near the surface of the magma chamber boundaries, and so any age obtained from an apparent mineral isochron including such crystals can still be treated as an average crystal residence time. A residence time obtained in this way will not be just a simple measure of the average time a crystal spends in a magma chamber, but it will be weighted by the timing and volumes of crystallisation, and by the likelihood that an eruption may preferentially remove younger crystals from chamber surfaces. If a mineral aliquot contains crystals from two different populations of a given phase, the (230Th/232Th) of the mixture will reflect the percentage of each population present, and the mixing line will have a linear scale assuming that the Th concentration is approximately the same in both. However, the difference in (230Th/232Th) between these populations reflects an exponential time scale, and so the age given by a mixture of two different populations is younger than their true average residence time. For example, a mixture in equal proportions of 5 ka and 55 ka crystals with the same Th concentration should have an arithmetical mean of 30 ka, but the (230Th/232Th) value halfway between the points for each of the populations is closer in time to the younger population, and the actual calculated age is 27.2 ka (assuming (230Th/232Th) ⫽ 0.75 and (238U/232Th) ⫽ 0.9 in line with the other modelling). This relationship is also sensitive to the distance from the equiline, and becomes more pronounced as a system evolves towards equilibrium. Consequently, the residence time inferred from U-series mineral data will usually reflect a minimum average residence time for the crystals where mixing of different populations of crystals has occurred. In contrast, the relationship demonstrated between turnover time and apparent isotopic age of the liquid (Fig. 3) suggests that, where magma replenishment processes are common, the actual residence time of a particular batch of liquid may be considerably less than any maximum age indicated by the liquid composition that plots on an internal isochron. The implications of this work for estimating realistic liquid and crystal residence times from U-Th data highlight the need to understand the degree to which magma replenishment processes may have influenced measured compositions. If replenishment is having a significant effect on (230Th/232Th), then one way in which it might be manifest is by eruption of lavas with near constant whole rock (230Th/232Th), or constant initial (230Th/232Th) values from mineral isochrons that produce different ages, over significant periods of time. Invariant (230Th/ 232 Th) values could also reflect constant transport and residence time in a closed system. However, that requires that each batch of magma evolving in a closed system erupts once, or over a short time period relative to the temporal resolution of U-Th data, which is perhaps unrealistic. 4.3. Combined U-Th and Ra-Th Systematics In addition to the use of 230Th-238U systematics, there is increasing use of 226Ra-230Th data in attempts to interpret the timescales of magmatic processes. These processes operate over different timescales as the half-life of 226Ra is ⬃1.6 ka compared with 75 ka for 230Th. Replenishment processes will
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Fig. 6. Combined U-Th-Ra systematics demonstrating the effects of different replenishment timescales. The difference in half-life between 226 Ra and 230Th is sufficiently large that if the timescale is short enough to produce significant effects on (226Ra/230Th) then (230Th/238U) reaches a steady-state close to that of the parental magma. The model conditions used were: (230Th/232Th)init ⫽ 0.75, (238U/232Th) ⫽ 0.9, [Th]init ⫽ 2 ppm, [226Ra]init ⫽ 300 fg g⫺1, [Ba]init ⫽ 200 ppm, DU ⫽ DTh ⫽ 0.05, DRa ⫽ DBa ⫽ 0.25, Chamber volume ⫽ 50 km3, Eruption volume ⫽ 5 km3, Crystallisation ⫽ 10% per iteration.
have markedly different effects on these systems depending on the frequency and volume of inputs of fresh magma. This is illustrated in Fig. 6, where the effects of varying the frequency of replenishment events on the combined U-Th-Ra systematics are shown. The example illustrated assumes that the system has an initial 226Ra excess, although as mentioned previously, the results would apply equally to a Th excess. When injections of new magma occur frequently with respect to the half-life of 226 Ra, the Th isotopic ratio (and therefore (230Th/238U) ratio) of the magma is maintained close to its starting composition, whereas radioactive decay has a more significant effect on (226Ra/230Th) between each new input. As the time between new inputs increases, the steady-state (226Ra/230Th) ratio approaches secular equilibrium, and the Th isotopic ratio deviates further from the initial composition. In real systems if replenishment events were only occurring on one timescale, it would be difficult to identify these in both of the systems. If the replenishment timescale is quite long (⬎500 –1000 years), the system will rapidly approach Ra-Th equilibrium (whilst maintaining a U-Th disequilibrium). If the replenishment timescale is short (⬍500 years) the Th isotopic composition of the system will be very close to that of the parental magma, and the Ra-Th systematics will reach a steadystate between the parental composition and secular equilibrium. However, if replenishment events occur on different timescales, perhaps reflecting processes operating at different crustal levels or in different magma storage systems, combined U-Th-Ra systematics offer the possibility of examining these processes in further detail.
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4.4. Natural Systems The time required to reach a steady-state in a periodically replenished system and the duration for which it may be maintained have been discussed above. Demonstrating the existence of such a steady-state from natural samples is still difficult despite the quantity of published U-Th data for various arcs e.g. (Elliott et al., 1997; Regelous et al., 1997; Turner et al., 1997). Condomines et al. (1982) use a limited series of data for Mount Etna to identify several possible chamber refilling events, and mixing trends between evolved and primitive magmas are reported for Mount Shasta (Newman et al., 1986), but there is no recently published data with sufficient sample density, and which has good stratigraphic coverage over a sufficiently long time period to look directly at whether the steady-state U-Th chemistry described occurs in practice. It is possible however, to look for evidence of magma replenishment processes, and to assess their relative importance in controlling the U-Th systematics of the system. One line of evidence that might point towards such magma replenishment processes is the eruption over long time periods of lavas with similar ranges in initial Th isotope ratios. The absence of good stratigraphic coverage from individual centres makes this hard to assess, but there is evidence from Mount Ruapehu that andesitic magmas have been erupted with similar U-Th systematics for ⬃100 ka (Hughes, 1999). In detail, however, subtle variations in U-Th data from Ruapehu suggest that there may in fact be considerable differences in the pre-eruption histories of different magma batches. Regardless of the degree to which mixing of different crystal populations has occurred, if fresh injections of parental magma have taken place, the liquid composition will plot below an isochron for co-existing older mineral phases. Mineral isochrons from Soufriere, St. Vincent (Heath et al., 1998) and Mt. Shasta (Volpe, 1992), have groundmass compositions that plot outside error, below the data points for separated mineral phases, consistent with a reduction in (230Th/232Th) on the injection of fresh magma. Other published U-Th isochrons either have groundmass data which falls on the equiline, e.g., (Volpe and Hammond, 1991), or there are no groundmass analyses available. In the case of Soufriere (Heath et al., 1998), four mineral isochrons from material erupted within the last 4 ka have isochron ages ranging from 46 –77 ka with very similar initial (230Th/ 232 Th). In addition to the groundmass data plotting below the mineral separate analyses, the degree of scatter about the isochrons as shown by MSWD values of 2.6 –19.3 is too great to be explained by analytical error given an upper limit of ⬃2.5 (for a 95% confidence limit) for MSWD values with no geological scatter (Wendt and Carl, 1991). The fact that there appears to be significant geological scatter about the isochrons, implies that the mineral separates may well represent a mixture of crystals of various ages. Thus, the interpretation of these data favoured here is that the apparent isochrons are produced by mixing of crystals formed at different times in a system that has seen at least occasional injections of new magma, although the frequency of these events is difficult to assess. Whilst the groundmass data plots below the isochrons, they are still closer than would be expected in a steady-state system, which suggests that any periodic refilling either occurred relatively infrequently or that the ability of the stored magma to mix with the
fresh material was limited. The high eruption frequency of Soufrie´re, possibly ⬎140 eruptions in 5000 years (Heath et al., 1998), might imply frequent injections of new magma if such injections act as eruption triggers (e.g., Sparks et al., 1977). Although all four isochrons have very similar initial (230Th/ 232 Th), this does not necessarily require growth of all the crystals at the same time. As the samples were all erupted in the last 4000 years, they may well have all picked up similar mixtures of crystals and therefore would have the same apparent initial ratio. The implications of the modelling presented here is that such ages probably reflect an average crystal residence time (although not necessarily a liquid residence time) for mixtures of minerals formed at different times. The period of time over which a steady-state may be maintained is dependant on the magma chamber not completely solidifying. Studies of large rhyolitic systems have often suggested that it is possible to keep such magmas above their solidus temperatures for several hundred thousand years, by repeated injections of fresh, hot basalt, (e.g., Christensen and DePaolo, 1993), and the possibility of keeping less evolved systems hot for long periods of time have also been discussed with reference to U-Th data (Heath et al., 1998). This suggests that maintaining a steady-state for 50 –100 ka or even for considerably longer presents no major thermal problem, and it is more likely that limits on the timescales of magma chamber evolution will result from changes in magma supply, perhaps due to local tectonic controls. 5. CONCLUSIONS
Frequent mixing of evolved magma in a crustal chamber with new injections of a similar but more primitive magma will sustain 230Th-238U disequilibria, and can lead to an asymptotic steady-state (230Th/232Th) value which is out of secular equilibrium. The timescales required to generate such disequilibria are strongly dependant on conditions, but they can be achieved in 10 –30 ka and then persist for much longer than the half-life of 230Th (75 ka). Magma replenishment processes are likely to result in apparent mineral isochrons which have groundmass glass compositions that plot away from the line defined by other phases, closer to the composition of the parental magma. By mixing crystals of different ages, reasonable apparent isochrons can be produced. Whilst such data do not directly refer to a specific crystallisation age, they will in many systems reflect the minimum average residence time for crystals in a crustal magma chamber. Where magma replenishment and crystal mixing are common, crystal residence times indicated by U-series data are minimum ages, whilst the calculated liquid residence times are maximum values. No long-lived steady-state magma system has yet been identified due to a paucity of high quality data on magmatic rocks erupted over sufficiently long periods of time. However, some systems do show evidence for replenishment processes and mixing of crystal populations. Acknowledgments—We thank Steve Blake, Dave Peate and Simon Turner for helpful discussions about residence times, magma chamber dynamics and U-Th systematics. Steve Blake and Simon Turner are thanked for careful and helpful informal reviews. Two anonymous
U-Th disequilibrium in replenished systems reviewers are thanked for useful thoughts which greatly improved the paper. RH was supported by a NERC studentship (ref: GT4/95/240/E). REFERENCES Albare`de F. (1985) Regime and trace-element evolution of open magma chambers. Nature 318, 356 –358. Chabaux F., He´mond C., and Alle`gre C. J. (1999) 238U-230Th-226Ra disequilibria in the Lesser Antilles arc: Implications for mantle metasomatism. Chem. Geol. 153, 171–185. Christensen J. N. and DePaolo D. J. (1993) Time scales of large volume silicic magma systems: Sr isotopic systematics of phenocrysts and glass from the Bishop Tuff, Long Valley, California. Contrib. Mineral. Petrol. 113, 100 –114. Cohen A. S. and O’Nions R. K. (1993) Melting rates beneath Hawaii: Evidence from uranium series isotopes in recent lavas. Earth Planet. Sci. Lett. 120, 169 –175. Condomines M. (1994) Comment on: “The volume and residence time of magma beneath active volcanoes determined by decay series disequilibria methods”. Earth Planet. Sci. Lett. 122, 251–255. Condomines M., Tanguy J. C., Kieffer G., and Alle`gre C. J. (1982) Magmatic evolution of a volcano studied by 230Th-238U disequilibrium and trace elements systematics: The Etna case. Geochim. Cosmochim. Acta 46, 1397–1416. Dunn T. and Sen C. (1994) Mineral/matrix partition coefficients for orthopyroxene, plagioclase, and olivine in basaltic to andesitic systems; a combined analytical and experimental study. Geochim. Cosmochim. Acta 58, 717–733. Elliott T., Plank T., Zindler A., White W., and Bourdon B. (1997) Element transport from slab to volcanic front at the Marianas arc. J. Geophys. Res. 102, 14991–15019. Gill J. B., Pyle D. M., and Williams R. W. (1992) Igneous rocks. In Uranium series disequilibrium, applications to environmental problems (ed. M. Ivanovich and R. S. Harmon). pp. 207–258. Oxford University Press. Goldstein S. J., Murrell M. T., and Janecky D. R. (1989) Th and U systematics of basalts from the Juan de Fuca and Gorda Ridges by mass spectrometry. Earth Planet. Sci. Lett. 96, 134 –146. Goldstein S. J., Murrell M. T., and Williams R. W. (1993) 231Pa and 230 Th chronology of mid-ocean ridge basalts. Earth Planet. Sci. Lett. 115, 151–159. Halliday A. N., Lee D.-C., Tommasini S., Davies G. R., Paslick C. R., Fitton J. G., and James D. E. (1995) Incompatible trace element enrichment in OIB and MORB and source enrichment in the suboceanic mantle. Earth Planet. Sci. Lett. 133, 379 –395. Hauri E. H., Wagner T. P., Grove T. L., Foley S. F., and van der Laan S. R. (1994) Experimental and natural partitioning of U, Th, Pb and other trace elements between garnet, clinopyroxene and basaltic melts: Trace-element partitioning with application to magmatic processes. Chem. Geol. 117, 149 –166. Hawkesworth C. J., Turner S. P., McDermott F., Peate D. W., and van Calsteren P. (1997a) U-Th isotopes in arc magmas: Implications for element transfer from the subducted crust. Science 276, 551–55. Hawkesworth C., Turner S., Peate D., McDermott F., and van Calsteren P. (1997b) Elemental U and Th variations in island arc rocks: Implications for U-series isotopes. Chem. Geol. 139, 207–221. Heath E., Turner S. P., Macdonald R., Hawkesworth C. J., and van Calsteren P. (1998) Long magma chamber residence times at an island arc volcano (Soufriere, St. Vincent) in the Lesser Antilles:
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Evidence from 238U-230Th isochron dating. Earth Planet. Sci. Lett. 160, 49 – 63. He´mond Ch., Hofmann A. W., Heusser G., Condomines M., Raczek I., and Rhodes M. (1994) U-Th-Ra systematics in Kilauea and Mauna Loa basalts, Hawaii. Chem. Geol. 116, 163–180. Hughes R. D. (1999) The timescales of andesite generation at Mount Ruapehu, New Zealand. PhD Dissertation, The Open Univ. Lundstrom C. C., Shaw H. F., Ryerson F. J., Phinney D. L., Gill J. B., and Williams Q. (1994) Compositional controls on the partitioning of U, Th, Ba, Pb, Sr and Zr between clinopyroxene and haplobasaltic melts: Implications for uranium series disequilibria in basalts. Earth Planet. Sci. Lett. 128, 407– 423. Newman S., Macdougall J. D., and Finkel R. C. (1986) Petrogenesis and 230Th-238U disequilibrium at Mt. Shasta, California, and in the Cascades. Contrib. Mineral. Petrol. 93, 195–206. O’Hara M. J. (1977) Geochemical evolution during fractional crystallisation of a periodically refilled magma chamber. Nature 266, 503–507. O’Hara M. J. and Mathews R. E. (1981) Geochemical evolution in an advancing, periodically replenished, periodically tapped, continuously fractionated magma chamber. J. Geol. Soc. Lon. 138, 237–277. Pyle D. M. (1994) Reply to comment by M. Condomines on “The volume and residence time of magma beneath active volcanoes determined by decay-series disequilibria methods”. Earth Planet. Sci. Lett. 122, 257–258. Pyle D. M. (1992) The volume and residence time of magma beneath active volcanoes determined by decay-series disequilibria methods. Earth Planet. Sci. Lett. 112, 61–73. Regelous M., Collerson K. D., Ewart A., and Wendt J. I. (1997) Trace element transport rates in subduction zones: Evidence from Th, Sr and Pb isotope data for Tonga-Kermadec arc lavas. Earth Planet. Sci. Lett. 150, 291–302. Sparks R. S. J., Sigurdsson H., and Wilson L. (1977) Magma mixing: A mechanism for trigerring acid explosive eruptions. Nature 267, 315–318. Turner S. and Hawkesworth C. (1997) Constraints on flux rates and mantle dynamics beneath island arcs from Tonga-Kermadec lava geochemistry. Nature 389, 568 –573. Turner S., Hawkesworth C., Rogers N., Bartlett J., Worthington T., Hergt J., Pearce J., and Smith I. (1997) 238U-230Th disequilibria, magma petrogenesis, and flux rates beneath the depleted TongaKermadec island arc. Geochim. Cosmochim. Acta 61, 4855– 4884. Turner S., Hawkesworth C., van Calsteren P., Heath E., Macdonald R., and Black S. (1996) U-series isotopes and destructive plate margin magma genesis in the Lesser Antilles. Earth Planet. Sci. Lett. 142, 191–207. Volpe A. M. (1992) 238U-230Th-226Ra disequilibrium in young Mt. Shasta andesites and dacites. J. Volcanol. Geotherm. Res. 53, 227– 238. Volpe A. M. and Goldstein S. J. (1993) 226Ra-230Th disequilibrium in axial and off-axis mid-ocean ridge basalts. Geochim. Cosmochim. Acta 57, 1233–1241. Volpe A. M. and Hammond P. E. (1991) 238U-230Th-226Ra disequilibria in young Mount St. Helens rocks: Time constraint for magma formation and crystallisation. Earth Planet. Sci. Lett. 107, 475– 486. Wadge G. (1982) Steady state volcanism: Evidence from eruption histories of polygenetic volcanoes. J. Geophys. Res. 87, 4035– 4049. Wendt I. and Carl C. (1991) The statistical distribution of the mean squared weighted deviation. Chem. Geol. 86, 275–285.
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R. D. Hughes and C. J. Hawkesworth APPENDIX 1: EQUATIONS
In the chamber evolution stage, the following equations are used to calculate Th isotopic evolution through radioactive decay and the change in concentrations of U, 232Th and 230Th during crystallisation respectively, 230
(232
Th )⫽ Th
冉 冊 230
232
Th Th
冉 冊 238
e⫺t ⫹ 0
232
U {1 ⫺ e⫺t} Th
X ⫽ Xi (1 ⫺ f)(D⫺1)
(1)
where parentheses denote activity ratios, square brackets denote concentrations, V represents volume, subscript i denotes values for the fresh input of magma and subscript c represents values for the magma chamber. Mixing in terms of elemental abundance follwed by conversion to an activity ratio has been used in preference to a direct calculation involving isotopic ratios because it allows greater flexibility for expansion of the model to consider problems such as crustal assimilation. Turnover time and apparent isotopic age are calculated as follows,
冉 冊 230
Th is the Th Th 0 isotopic ratio of the magma prior to radioactive decay, is the decay constant of 230Th, X is the new concentration of element X, Xo is the concentration of element X prior to crystallisation, f is the fraction of the magma crystallised and Dx is the partition coefficient of element X. In the mixing stage the following equation is used to calculate the Th isotopic composition of the mixture, where in Eqn. 1 parentheses denote activity ratios,
冉 冊 230
Th 232 Th
232
[230Th]c Vc ⫹ [230Th]i Vi ⫽ 232 ⫻ 185885 [ Th]c Vc ⫹ [232Th]i Vi mix
(3)
再 冎 冉 冊 冉 冊 冉 冊 冉 冊
Tt ⫽
(2)
冦
1n Tiso ⫽
230
232
Vc Vi
Th Th
230
232
Th Th
t
238
⫺
232
⫺
232
c
U Th
238
i
⫺
U Th
(4)
冧
(5)
where parentheses denote activity ratios, is the decay constant of 230 Th, t is the length of the iteration, Tt ⫽ turnover time, Tiso⫽ apparent isotopic age, subscript i and subscript c represent input and chamber values respectively.