Journal of Petrology | Volume 44 | Number 4 | Pages 733-756 | 2003
© Oxford University Press 2003
The Role of Chaotic Dynamics and Flow Fields in the Development of Disequilibrium Textures in Volcanic Rocks
1 DEPARTMENT OF EARTH SCIENCES, UNIVERSITY OF PERUGIA, PIAZZA UNIVERSITÀ, 06100 PERUGIA, ITALY
2 DEPARTMENT OF MINERALOGY AND PETROLOGY, UNIVERSITY OF PADOVA, C. SO GARIBALDI, 37, 35127 PADOVA, ITALY
Telephone: ++39 75 585 2652. Fax: ++39 75 585 2603. E-mail: diegop{at}unipg.it
RECEIVED MAY 13, 2002; ACCEPTED NOVEMBER 1, 2002
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONPETROGRAPHYDISEQUILIBRIUM TEXTURES IN...CAUSES OF VARIED DISEQUILIBRIUM...SIMULATION OF THE GROWTHOF...RESULTS AND DISCUSSIONCONCLUSIONSSUPPLEMENTARY DATAREFERENCES |
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Disequilibrium textures in minerals are often observed in igneous rocks. Their occurrence is commonly related to the variation of intensive variables (e.g. pressure, temperature, etc.) that perturbed a pre-existing state of equilibrium. However, if the variation of intensive variables provides a reliable explanation for the occurrence of disequilibrium textures in minerals, it does not explain why, over very short length scales (<1–2 cm), in the same rock, crystals of the same mineral phase often appear to have reacted very differently to the disequilibrium process. A good example of this puzzling phenomenon is given by clinopyroxene phenocrysts occurring in the Santa Venera alkali basalt (Mt. Etna, Italy), in which a great variety of disequilibrium textures, coexisting on very short length scales (<1–2 cm), are observed. Clinopyroxenes exhibit heterogeneously resorbed Cr–Al diopside cores around which a rim of Al–Fe3+ diopside, having a highly variable area, has grown. The area of the Al–Fe3+ diopside rim is used as a discriminant parameter for the studied pyroxenes as it displays a tri-modal statistical distribution. In addition, the chemical zoning from the core to the rim of pyroxenes exhibits both continuous and discontinuous patterns. These continuous and discontinuous patterns are associated with crystals having low and high values of the rim area, respectively. To explain these zoning patterns, a mixing process between magmas having different geochemical and thermodynamic properties, governed by chaotic dynamics, is proposed. In particular, the occurrence in the same system, and at short length scales, of regular and chaotic regions is suggested as the basic dynamic inducing a heterogeneous distribution of the magmas involved in the mixing process; this leads to a strong control on the propagation of the disequilibrium phenomena and on the crystallization of pyroxenes, even over short length scales. The occurrence of regular and chaotic regions within the same magmatic system can explain the entire spectrum of features observed in the studied pyroxenes, from the occurrence of the tri-modal distribution of rim areas to the presence of two distinct patterns of chemical zoning, continuous and discontinuous, from the core to the rim of pyroxenes.
KEY WORDS: chaotic dynamics; disequilibrium textures; heterogeneity; magma mixing; pyroxenes
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONPETROGRAPHYDISEQUILIBRIUM TEXTURES IN...CAUSES OF VARIED DISEQUILIBRIUM...SIMULATION OF THE GROWTHOF...RESULTS AND DISCUSSIONCONCLUSIONSSUPPLEMENTARY DATAREFERENCES |
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Disequilibrium textures in minerals have been widely observed and studied in igneous rocks (e.g. Hibbard, 1981
; Nixon & Pearce, 1987; Wallace & Carmichael, 1994; Umino & Horio, 1998; Kuscu & Floyd, 2001). Such textures are commonly related to different types of disequilibrium that occur during the evolution of magmatic systems and, in particular, are interpreted as the possible effects of variations in pressure, temperature, or composition that perturbed a pre-existing state of equilibrium of the magma body (e.g. Nixon, 1988; Ortoleva, 1990; Dobosi & Fodor, 1992; Rutherford & Hill, 1993; L'Heureux & Flower, 1994; Simonetti et al., 1996). Although the variation of intensive variables can be invoked as the basic process inducing disequilibrium phenomena, strong evidence exists that disequilibrium does not propagate homogeneously within the magma volume. Evidence of this is provided by the occurrence at very short length scales, of the order of a single thin section, of crystals belonging to the same phase showing very different disequilibrium textures. A good example of this phenomenon is given, for example, in the study by Anderson (1984), in which is described the coexistence of plagioclase crystals showing very dense zonation patterns that vary markedly from crystal to crystal. In this paper we study phenocrysts of clinopyroxene occurring in the alkali basaltic Santa Venera lava flow (Mt. Etna, Italy; Fig. 1), in which a great variety of disequilibrium textures coexisting at very short length scales (<1–2 cm) can be observed. These pyroxenes are analysed using microanalytical and statistical techniques, to study the variability in chemical composition from core to rim of the crystals and the area of the growth rim, with the aim of understanding the causes and the style of propagation of disequilibrium within the magma body. A numerical model, based on the theory of chaotic dynamical systems, is proposed to explain the observed disequilibrium in pyroxenes and the extreme variability of their textures.
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PETROGRAPHY |
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The pyroxenes studied here occur in the alkali basaltic Santa Venera lava flow (Table 1; Le Maitre et al., 1989
), Mt. Etna, Sicily (Fig. 1). The Santa Venera lava, dated at 
0·12 Ma (Condomines et al., 1982), lies directly over a Quaternary sedimentary substratum (Spadea, 1972), and belongs to the low-phosphorus group of Etna basaltic rocks as defined by Busà et al. (1999).
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The Santa Venera basalt has a porphyritic seriate texture (Porphyritic Index, PI
30), with a microcrystalline intergranular groundmass. The main mineral phases present are, in order of decreasing abundance, clinopyroxene (18·0 vol. %), olivine (7·0 vol. %), plagioclase (5·0 vol. %) and Ti-magnetite (<1·0 vol. %). Rare spinel, enclosed in Mg-rich olivine (Fo87–86), is also present.
Clinopyroxene, occurring as phenocrysts from 0·2 to 1·0 mm in diameter and as microlites in the groundmass, is the most abundant phase. It is present as: (1) unzoned Cr–Al diopside [classification after Morimoto (1988); Cr–Al Di; Table 1, Px A]; (2) variously resorbed anhedral cores of Cr–Al Di around which a rim of variable area of Al–Fe3+ diopside (Al–Fe3+ Di; Fe3+ is stoichiometric) composition has grown (Table 1, Px B and C); (3) Al–Fe3+ Di microlites (Table 1, Px D). Al–Fe3+ Di rims are in equilibrium with Al–Fe3+ Di microlites, as they have the same chemical composition (Table 1). In general, the smaller and more resorbed the Cr–Al Di core, the larger is the area of the Al–Fe3+ Di rim. Cr–Al Di is colourless, optically homogeneous, and free of inclusions with respect to the Al–Fe3+ Di rims, which are pale brown, show optically a colour gradation toward the periphery of crystals, and have abundant inclusions of Ti-magnetite, acicular apatite and rare plagioclase (Fig. 2a–c). Ti-magnetite and acicular apatite inclusions are abundant (50 crystals/mm2, on average) in pyroxenes having the largest Al–Fe3+ Di rims, whereas they are scarce (5 crystals/mm2, on average) in crystals with the thinnest rims.
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Olivine, varying from euhedral to subhedral in crystal form, is up to 2 mm in diameter; its Fo content varies from 87 to 74 mol %.
Plagioclase phenocrysts (from 0·05 to 0·8 mm in diameter) are typically zoned and show boxy-cellular and sieve textures (Fig. 2d and e; e.g. Hibbard, 1981, 1991), although unzoned plagioclase is also common. Boxy-cellular and sieve-textured plagioclase phenocrysts have a core with a more calcic composition (An75–80) than the surrounding clear mantle (An55–65). At the contact between the core and the mantle, microphenocrysts of Ti-magnetite (Fig. 2f) and acicular apatite are commonly observed. Unzoned plagioclase has a composition similar to the inner core of both the boxy-cellular and the sieve-textured plagioclase, and is free of inclusions.
Spinel in Mg-rich olivines shows a continuous range of Al2O3 (21–29 wt %), low and constant TiO2 content (0·84–1·07 wt %) and Cr-number [Cr/(Cr + Al)] from 42 to 55.
Ti-magnetite is present as microphenocrysts enclosed in the rim of clinopyroxene, in the sieve texture of plagioclase and in the groundmass. The same pattern holds for acicular crystals of apatite.
Because pyroxene can retain disequilibrium textures for long time periods, given its very slow ability to re-equilibrate by internal diffusion (e.g. Thompson, 1974; Shimizu, 1990), it can be considered a suitable dynamic marker to understand the style and the propagation of disequilibrium processes within a magma body (e.g. Simonetti et al., 1996). Therefore, our attention will be mainly focused on this mineral phase.
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DISEQUILIBRIUM TEXTURES IN PYROXENES |
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Pyroxenes show a continuous range of textures varying from unzoned euhedral Cr–Al Di to anhedral resorbed cores of Cr–Al Di having a rim of variable area of Al–Fe3+ Di composition (Fig. 3). This feature is evidence that Cr–Al Di suffered variable disequilibrium conditions at some time during crystallization, causing resorption and allowing Al–Fe3+ Di to crystallize as pyroxene rims (Fig. 3). That disequilibrium conditions occurred is also confirmed by the occurrence of boxy-cellular and sieve textures in plagioclase crystals (Fig. 2d and e). The most striking feature exhibited by the Santa Venera basalt is the coexistence of pyroxene crystals having these extremely variable textures over a very short length scale, of the order of a single thin section (i.e. a few centimetres).
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To study the pattern of chemical zoning exhibited by the Santa Venera pyroxenes, electron probe microanalysis has been performed along transects extending from the rim to the core of zoned crystals. Geochemical transverses across two representative pyroxenes (Fig. 4) are reported in Table 2 (more geochemical transverses are reported in the Electronic Appendix A, which may be downloaded from the Journal of Petrology web site at http://www.petrology.oupjournals.org). The two pyro- xenes have different areas of the Al–Fe3+ Di rim (Fig. 4) and represent the range of pyroxene zoning that can be observed in the Santa Venera basalt. Figure 5 shows the variation of SiO2, MgO and FeO from the core to the rim of the two crystals shown in Fig. 4. On the basis of the pattern of zoning, pyroxenes can be grouped into two main types: (1) pyroxenes in which element abundances vary irregularly (Fig. 5a–c); (2) pyroxenes in which there are relatively smooth, continuous zoning trends (Fig. 4d–f). Continuous trends are characteristic of pyroxene crystals with the smallest areas of the Al–Fe3+ Di rim, whereas irregular patterns are typical for crystals having the largest rim areas. It is noteworthy that zoning occurs in the rims only, and cores are compositionally homogeneous.
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Back-scattered electron (BSE) images of pyroxenes were collected from six adjacent thin sections cut from the same rock sample. Care has been taken to collect images from non-overlapping thin sections. For statistical significance 280 images of different crystals were obtained. The BSE images are useful because the rims of the pyroxene crystals have different compositions from the cores and this allows identification of the boundary between the resorbed core and the rim (Fig. 6a). To avoid errors caused by sectioning of crystals along different crystallographic directions, measurements were performed only on crystals sectioned orthogonal to the crystallographic axes. The crystallographic orientation of crystals has been verified by optical microscopy on thin sections considering the classical birefringence scheme for clinopyroxene. For the same reason, measurements were performed only on crystals of the same total size (in the range of 770–830 µm across).
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The Al–Fe3+ Di rim area was measured by applying to each image a threshold filter to produce a binary (black and white) image in which the rim appeared black whereas all other parts of the image were white (Fig. 6b). The rim area was calculated by counting the number of black pixels constituting the rim and then rescaling to real dimensions. The rim area of crystals thus measured is a parameter quantifying the growth of pyroxenes after the Cr–Al Di core underwent disequilibrium resorption. Black and white images have been used also to measure the perimeter of the resorbed Cr–Al Di cores as reported in Fig. 6b.
It is worth noting that, given the strong chromatic contrast between the cores and rims of crystals (Figs 3 and 6a), the reduction of images from grey levels to black and white allows us to distinguish and hence to measure the rim area with great precision, as evidenced by the low errors (better than 0·05%) calculated by applying different threshold settings to the images.
Figure 7 is a histogram showing the statistical distribution of the rim area for the 280 pyroxene grains studied. The histogram shows three main peaks, labelled A, B and C, that correspond to three crystal populations with progressively increasing rim area. In particular, peak A corresponds to a population of crystals with no growth rim (i.e. euhedral Cr–Al Di), whereas peaks B and C represent populations of crystals with increasing rim areas on average about 0·03 and 0·08 mm2, respectively.
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Figure 8 shows the variation of the perimeter of resorbed Cr–Al Di cores against the area of the Al–Fe3+ Di rims. The graph shows that as the perimeter of cores increases, the rim area decreases, defining a negative exponential trend. Such a trend is further evidence of the strongly heterogeneous conditions of disequilibrium and crystallization of pyroxenes from the Santa Venera basalt.
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CAUSES OF VARIED DISEQUILIBRIUM TEXTURES IN PYROXENES |
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Various hypotheses can be considered to explain the occurrence of disequilibrium textures in the studied pyroxenes (Fig. 9).
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A possible hypothesis is that Cr–Al Di cores and Al–Fe3+ Di rims crystallized at different pressures (hypothesis a, Fig. 9), as a pressure variation can induce disequilibrium in mineral phases and successive crystallization (e.g. Kushiro, 1968
; Wass, 1979). Figure 10 shows a graph of IVAl vs VIAl for cores and rims of 28 analysed crystals. As suggested by several workers (e.g. Aoki & Kushiro, 1968; Simonetti et al., 1996) this graph provides information on the crystallization pressure of pyroxenes. For comparison, pyroxenes that are known to have crystallized in both high- and low-pressure environments are plotted (Thompson, 1974; Thy, 1991; Métrich & Rutherford, 1998; Shaw & Eyzaguirre, 2000). The graph shows that no appreciable difference exists in the crystallization pressure of the core and rim of the studied pyroxenes. In addition, all the analysed pyroxenes straddle the field of low-pressure crystallization. These results can be corroborated using an independent method applied to the same pyroxenes (cores and rims), based on a crystallographic method in which the variation of crystal cell and M1 octahedral volumes are related to the crystallization pressures of the pyroxenes (Dal Negro et al., 1982; Nimis, 1995). No significant change in pressure conditions is revealed by this analysis, which, in turn, suggests pressure conditions of 4·0–5·0 kbar for both the core and the rim of crystals (Nazzareni et al., 2003). These results lead to the conclusion that (1) there is no significant variation in crystallization pressure between the cores and rims of pyroxenes and (2) the cores and rims of crystals are likely to have crystallized in a low-pressure environment (P < 4–5 kbar).
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data from Shaw & Eyzaguirre (2000)
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, 
, 
, clinopyroxenes crystallized from olivine-rich alkali basalt, transitional basalt, tholeiite andesite, and olivine tholeiite starting melt composition, respectively; data from Thompson (1974)In addition, given the occurrence over very short length scales (several centimetres) of the extreme textural variants of the zoned pyroxene crystals, it seems unlikely that pressure variation played a key role in determining the observed variability.
An alternative hypothesis is that the Cr–Al Di crystals are xenocrysts that represent phenocrysts either of mantle origin or derived from a compositionally different rock (hypothesis b, Fig. 9), caught up in the host basaltic magma during ascent. Cr–Al Di xenocrysts reacted and resorbed within the melt, and successively acted as nuclei for the crystallization of Al–Fe3+ Di rims.
Regarding the possibility of mantle provenance, one might expect different crystallization pressures for Cr–Al Di cores and the Al–Fe3+ Di rims. As discussed above, the cores and rims crystallized at similar and low pressures, arguing against a mantle origin for the Cr–Al Di cores. Further evidence against the Cr–Al Di being mantle xenocrysts is the total lack of crystal deformation.
The hypothesis that Cr–Al Di may represent mantle or magmatic xenocrysts (hypothesis b, Fig. 9) is also unlikely because some Cr–Al Di cores would have not retained a euhedral habit as observed in the studied samples. The host magma was not saturated in clinopyroxene before entrapment of Cr–Al Di, as evidenced by the absence of Al–Fe3+ Di phenocrysts in the Santa Venera basalt. Under these conditions, it seems reasonable to suppose that Cr–Al Di pyroxene xenocrysts would not have survived resorption once entrained in the magma. In addition, along with pyroxene xenocrysts, the basaltic magma would also have incorporated Cr–Al Di-bearing xenoliths. No evidence of xenocrysts of other mineral phases or remnants of xenoliths is present in the Santa Venera basalt, excluding the possibility that the Cr–Al Di pyroxenes are xenocrysts.
The occurrence of Cr–Al Di pyroxenes in the studied samples could be related to a simple fractional crystallization process from a single parental magma at low pressure (hypothesis c, Fig. 9). Such a process is likely to lead to compositional zoning in the pyroxenes with a more ‘mafic’ composition at the core that progressively shifts towards a more ‘evolved’ composition at the rim (normal zoning). The analysed pyroxenes show this kind of zoning, indicating that a fractional crystallization process from a parental magma could be a suitable hypothesis to explain the changing composition of the pyroxenes. However, there is evidence of strong resorption of the Cr–Al Di cores before crystallization of the Al–Fe3+ Di rims and this is difficult to reconcile with a simple closed-system fractional crystallization process. In addition, the presence of titaniferous magnetite, occurring as crystals up to 50 µm across, as inclusions only in the rims of pyroxenes and in the sieve-textured plagioclase, suggests disequilibrium conditions of crystallization. The fact that oxide inclusions are almost exclusively confined to the rims of crystals suggests that conditions of crystallization, such as temperature or oxygen fugacity, differed from those that existed during precipitation of their cores (e.g. Santacroce et al., 1993; Simonetti et al., 1996). These features suggest that pure fractional crystallization was not the main process generating the observed disequilibrium textures.
A further hypothesis to explain the observed textures (hypothesis d, Fig. 9) is that Cr–Al Di represents early cumulates crystallized from a parental magma leading to a zoned magma chamber. Back-mixing of such cumulates with the evolved residual liquid induced disequilibrium resorption of Cr–Al Di and crystallization of Al–Fe3+ Di rims (Fig. 9). To test this hypothesis, we utilized the MELTS software (Ghiorso & Sack, 1995; Asimov & Ghiorso, 1998) to model the crystallization of a basaltic composition in equilibrium with Cr–Al Di. The starting basaltic composition (see Fig. 9 caption) is that of a melt inclusion occurring in olivine crystals belonging to the Santa Venera basalt having the same Mg-number as Cr–Al Di and, thus, being in equilibrium with the Cr–Al Di. We started the crystallization of the melt using the liquidus temperature calculated by the software (1270°C), the Ni–NiO oxygen buffer, and a pressure of 5·0 kbar, as suggested by barometric analysis on Cr–Al Di (Nazzareni et al., 2003). As expected, the first crystallizing pyroxene is a Cr–Al Di and, as the crystallization proceeds, the pyroxene composition shifts progressively toward more evolved pyroxene compositions reaching Al–Fe3+ Di, without interruptions in the crystallization of pyroxene. The back-mixing process should produce the Santa Venera basalt by mixing between the parental magma and the evolved residual melt. The calculated residual melt is too evolved (i.e. MgO 2·5%) to be an end-member of the back-mixing process, as the parental magma and the Santa Venera basalt have similar degree of evolution (i.e. MgO 9·0%); hence the back-mixing process can be discarded. This is corroborated by the absence of Al–Fe3+ Di phenocrysts in the Santa Venera basalt, indicating that the hypothetical residual liquid was not saturated in clinopyroxene; this is in contrast to the MELTS modelling, where the residual liquid is always saturated in clinopyroxene.
A further possible process that may account for the textural features exhibited by the mineral phases of the Santa Venera basalt is an interaction between two (or more) compositionally distinct magmas (hypothesis e, Fig. 9). Such a process is known to be able to generate strong heterogeneities within magma bodies also on very short length scales (e.g. Oldenburg et al., 1989; Perugini et al., 2002). Magma mixing has been recognized as one of the main processes that can induce disequilibrium phenomena such as those observed in the studied samples (e.g. Hibbard, 1981, 1991; Simonetti et al., 1996). The occurrence of inclusions of acicular apatite within the rims of Al–Fe3+ Di and the sieve and boxy-cellular textures of plagioclase is evidence that undercooling of a more mafic magma occurred in contact with a cooler more evolved magma (e.g. Hibbard, 1981, 1991). In addition, the occurrence of Ti-magnetite as microphenocrysts and as inclusions in the rims of pyroxene and in the sieve and boxy-cellular textured plagioclase suggests that intensive variables such as temperature and fO2, and composition, drastically changed, and this can be related to the mixing of magmas (e.g. Simonetti et al., 1996). Also, the presence of sieve textures in plagioclase argues in favour of a magmatic interaction process to explain the observed disequilibrium textures (e.g. Hibbard, 1981, 1991).
Building on this hypothesis, it is possible to conceive the mixing system as a magma chamber at low pressure containing a magma (X1) from which Cr–Al Di is crystallizing (Fig. 11a, Stage 1). At some time, a more evolved magma (X2) enters the magma chamber and mixing occurs (Fig. 11b, Stage 2). Cr–Al Di experiences disequilibrium caused by the mixing event and becomes resorbed to varying degrees, acting as nuclei for the successive crystallization of the Al–Fe3+ Di (Fig. 11c, Stage 3). During the mixing process the bulk composition and thermodynamic conditions of the magmatic system change and this phenomenon favours nucleation of Ti-magnetite and apatite, and crystallization of Al–Fe3+ Di pyroxenes either as rims around Cr–Al Di (Fig. 11c) or as microlites during eruption (Fig. 11d).
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Such a magma mixing process may be, therefore, a suitable explanation for the origin of the disequilibrium textures observed in the Santa Venera basalt. However, although this hypothesis may explain the basic process (resorption and regrowth) for the origin of the observed textures in the studied pyroxenes, it does not explain why, on short length scales, such different textures coexist (Fig. 11e). The main question that arises is how mixing dynamics can induce such differential growth in crystals occurring on so short a length scale (<1–2 cm), within the same magmatic system.
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SIMULATION OF THE GROWTHOF PYROXENES IN A MIXING SYSTEM GOVERNED BYCHAOTIC DYNAMICS |
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The occurrence of substantial textural variability of the pyroxenes in the Santa Venera basalt and the tri-modal distribution of rim area (Fig. 7) suggest that different dynamical regions, coexisting on short length scales, prevented the disequilibrium phenomena, and the successive growth of pyroxenes, from being homogeneously distributed within the magma volume. Moreover, exponential trends, such as that observed between the rim area and the perimeter of cores (Fig. 8), are inherent to chaotic dynamical systems whose evolution is related to the presence of fractal domains (e.g. Mandelbrot, 1982
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It has been proposed that chaotic dynamics inside magma mixing systems can produce extremely heterogeneous flow fields that can propagate within the magma volume over a large number of scale lengths (from several metres to a few microns) generating fractal structures (e.g. Metcalfe et al., 1995; Flinders & Clemens, 1996; Perugini & Poli, 2000; Perugini et al., 2002; Poli & Perugini, 2002). In particular, two main dynamical regions have been recognized to coexist on very short length scales (i.e. a few microns) within the same magma: (1) coherent regions (CR) that act as barriers to chemical and thermal exchange, in which the magma maintains, almost unaltered, its original properties; (2) active mixing regions (AMR) in which magmas mix intimately, favouring chemical and thermal exchange and leading over short time scales to portions of the magma body having high degrees of hybridization (Bresler et al., 1997; Ottino et al., 2000; Perugini et al., 2002). The fact that on very short length scales and inside the same magma body these two types of dynamical regions can coexist implies that scalar quantities such as chemical composition, temperature or fO2 are advected by the flow fields of the magmatic system, leading to a heterogeneous distribution of these quantities inside the magma chamber. Given that mineral phases record the geochemical and thermodynamics histories of the magmas from which they crystallize, the above considerations suggest that a heterogeneous distribution of composition, temperature or fO2 inside the magma body may be responsible for the genesis of the textural variability observed in the studied pyroxenes.
To test this possibility we simulated the process of growth of crystals within a magma mixing system in which a host magma (X1 magma) mixes with a more evolved magma (X2 magma) using a chaotic dynamical system in which both AMR and CR exist. The numerical system that we use is a typical discrete time advection–diffusion system in which the advection term (physical dispersion, ‘mingling’) is simulated considering the following iterated map:
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The map is known as the ‘sine-flow map’ and is a typical two-dimensional conservative chaotic dynamical system widely used to study chaotic fluid mixing (e.g. Liu et al., 1994; Clifford et al., 1998, 1999). The [mod 1] statement means that the domain of the system is periodic between zero and one [i.e. 0 
(x, y) 1]. (xn, yn) and (xn+1, yn+1) are the coordinates of each fluid particle at time t = n and t = n + 1, respectively, and k is the parameter of the map that regulates the intensity of mixing. More details on the theory of chaotic mixing and on the procedures used in the simulation are reported in the Electronic Appendix B, which may be downloaded from the Journal of Petrology web site at http://www.petrology.oupjournals.org.
Figure 12 shows the Poincaré sections of the mixing system (see Electronic Appendix B; e.g. Ottino et al., 1988; McCauley, 1993), that correspond to the flow fields in the mixing system for different values of k. The images show that CR, consisting of closed trajectories, coexist with AMR, where precise trajectories cannot be defined and where the points are iterated in a more irregular way. Bearing in mind that the efficiency of mixing lies in the ability of the components involved to spread across the system, possibly in an irregular way (e.g. Ottino et al., 1988; Liu et al., 1994), it follows that CR and AMR are regions where fluids are poorly mixed and well mixed, respectively. Figure 12 provides insights on the effects of k on AMR and CR. In fact, CR are found to shrink as k increases (from Fig. 12a–c), and, at higher k values, they are reduced considerably in size, leaving most of the space to AMR. Bresler et al. (1997) showed that the genesis of CR is closely related to the efficiency of mixing. In particular, CR form in those portions of the mixing system where the mixing dynamics are weak [in correspondence to elliptic points; see Bresler et al. (1997) and Electronic Appendix B for details], whereas AMR form in portions of the mixing system where the mixing dynamics are very efficient [in correspondence to hyperbolic points; see Bresler et al. (1997) and Electronic Appendix B for details]. k is hence a parameter regulating the efficiency of the mixing process, which depends, in turn, on many physical factors such as viscosity, density, thermal and chemical gradients. The possibility to explore different mixing intensities varying a single parameter (k) makes such models very useful prototypical systems to study the complexity inherent to mixing processes.
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Together with the advection of the two magmas using the sine-flow map discussed above, a diffusion term is introduced. On the plane of the iterated map, constituted by a 350 x 350 square cell grid, a concentration field of a chemical element cij, where i, j represent the coordinates of each cell, is defined. At the beginning of the simulation the X2 magma has a concentration equal to zero (corresponding to black in terms of grey-scale shades), whereas the host X1 magma has a concentration equal to 255 (corresponding to white in terms of grey-scale shades).
The diffusion term is introduced as follows (e.g. Pierrehumbert, 1995):
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), and corresponds to the discretization of the diffusion Laplace equation (e.g. Jain, 1989). cij is updated to new shades ranging from zero to 255 according to the amount of diffusion in each cell calculated using the above equation. After several iterations of the map coupled with the diffusion step, the concentration will have changed. Bearing in mind that the simulation is carried out using grey values, the concentration of each pixel will range from zero to 255.
To simulate the growth of pyroxenes inside the magma mixing system defined by the above formulation, a number of crystal nuclei (15 000) were distributed randomly inside the space of the system. This number of crystal nuclei is equal to the measured percentage of Cr–Al Di cores occurring in the Santa Venera basalt (12%). The random positioning of nuclei was performed using a random number generator with a Gaussian probability density function (e.g. James, 1990; Leva, 1992). This procedure ensures a homogeneous distribution of crystal nuclei inside the X1 magma; the latter was considered to be completely homogeneous before the arrival of the X2 magma. Each nucleus occupies a single cell and grows according to the concentration of the element present in its neighbourhood, as shown in Fig. 13a. The crystals move together with the flow fields and, if two crystals are adjacent, their growth will occur only on the free crystal faces. Growth of crystals occurs until the total amount of pyroxenes (nuclei plus growth rims) reaches the percentage of pyroxenes (Cr–Al Di cores plus Al–Fe3+ Di rims) observed in the Santa Venera basalt (18%). To calculate the growth rate of the pyroxene nuclei within the mixing system, we define a parameter named the growth potential (GP; 
tot) as follows. Let n, the partial GP of each nucleus at each iteration of the magma mixing system, be defined as
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tot) is defined as
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tot is a measure of the growth rate of pyroxene nuclei after a number of iterations (n) of the magma mixing process.
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As the magma mixing simulation is performed using a white host magma (X1 magma; colour code 255) and a black intruded magma (X2 magma; colour code 0),
n ranges from 0 (i.e. 0 x 8; Fig. 13c) to 2040 (i.e. 255 x 8; Fig. 13c). It should be noted that the minimum and maximum values expressed as colour codes of n correspond to the maximum and minimum values of growth of pyroxenes, respectively (Fig. 13c).
To illustrate this concept in detail, Fig. 14 shows a typical simulation performed using A = 0·4, k = 0·5, and percentages of the X1 and X2 magmas equal to 75% and 25%, respectively. Figure 14a–c shows the magma X1 in which crystal nuclei are randomly positioned, the introduction of the magma X2 as rounded black blobs, and the second iteration of the mixing process. It should be noted that changing the shape of magma X2 and the statistical distribution of crystal nuclei does not change the results. Figure 14d shows the sixth iteration of the process; magnifications are shown in Fig. 14e–g to graphically illustrate the procedure used to calculate n. In particular, Fig. 14g shows the computation of n as the sum of the grey values constituting the neighbourhood of a pyroxene nucleus. In the case reported in the figure, n is equal to 1144.
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In the simulation, A is needed to create a compositional gradient of the simulated chemical element within the mixing system. As the focus here is the investigation of the general behaviour of the magma mixing system and not about absolute values of chemical exchanges between magmas, A is kept constant at 0·4. However, varying A only reduces (A > 0·4) or increases (A < 0·4) the relative number of iterations of the simulation and does not influence the reported results. Simulations were performed using different values of k (i.e. mixing intensities), and variable percentages of the X1 and X2 magmas as indicated in Fig. 15.
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As the growth potential (GP;
tot) is an estimate of the growth rate of pyroxenes, its values are analogous to measuring the rim area of crystals as we have done for the pyroxenes occurring in the Santa Venera basalt. For this reason, analogous to the natural case, frequency histograms of tot have been constructed for the various simulations (Fig. 15). |
RESULTS AND DISCUSSION |
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TOPABSTRACTINTRODUCTIONPETROGRAPHYDISEQUILIBRIUM TEXTURES IN...CAUSES OF VARIED DISEQUILIBRIUM...SIMULATION OF THE GROWTHOF...RESULTS AND DISCUSSIONCONCLUSIONSSUPPLEMENTARY DATAREFERENCES |
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For the sake of clarity the results of the mixing simulations are discussed in terms of the different amounts of the X2 magma participating in the mixing process and different values of k. For low quantities of the X2 magma (5%) and low values of k (Fig. 15a), histograms are composed of two peaks (P1 and P2) corresponding to two population of crystals having different statistical means of
tot. In particular, the peak P1 corresponds to crystals showing no growth, whereas the peak P2 is related to a population of crystals having higher growth and a higher mean value of tot. As k increases (Fig. 15b and c), i.e. the intensity of the mixing process increases, the frequency of the peak P1 decreases whereas peak P2 increases. Remembering that with the increase of k the CR inside the mixing system decrease in size and that contemporaneously the AMR increase, the decrease of the frequency of the peak P1 and the respective increase of the peak P2 are due to the effect of k (mixing intensity). The peak P1 is, therefore, due to the growth of crystals inside CR whereas the peak P2 is related to crystals growing inside AMR.
For higher quantities of the X2 magma (25–50%) and low values of k (Fig. 15d and g), a variation in the statistical distribution of tot is observed. In particular, a third peak (P3) appears on the graph, having a mean value of tot intermediate between the peak related to crystals having no growth (P1) and that associated with crystals of higher tot (P2). In this case, however, the peak P2 is shifted towards higher tot values with respect to the case in which the percentage of X2 magma was lower (5%; Fig. 15a). This is explained by considering that higher quantities of the X2 magma introduced into the system higher concentrations of the chemical element responsible for the growth of crystals. As k increases, the peaks P1 and P3 decrease and P2 increases. This changing of the statistical distribution of tot with the increase in k is analogous to that observed for lower quantities of the X2 magma with the difference that, in this case, the increase of the peak P2 is accompanied by the decrease of the two peaks, P1 and P3 (Fig. 15e and h). As pointed out above, with the increase of k, CR decrease in size and AMR increase. The decrease of the frequency of the peaks P1 and P3 and the contemporaneous increase of the P2 peak, as k increases, indicates, therefore, that P1 and P3 are due to the growth of crystals inside CR, whereas the peak P2 is related to crystals growing inside AMR. The fact that both peaks P1 and P3 belong to CR can be explained considering the relative position of crystals within CR. In fact, the peak P1 represents crystals that are placed close to the centre of CR and, in this position, their growth is strongly inhibited because the arrival of nutrients is very scarce. The peak P3 represents, on the other hand, crystals that are placed progressively far away from the centre of CR where they can grow more easily because the arrival of nutrients is more enhanced.
For quantities of the X2 magma above 50% (Fig. 15j–l) the histograms are composed of a single peak P1 spanning a range of tot values similar to those associated with the peak P2 in the simulation performed using quantities of X2 magma equal to 25% and 50%. In this case the effect of k on the simulation is less obvious than in the other cases, as evidenced by the fact that, as k increases, only the relative frequencies of the peak P1 are slightly increased, leaving the structure of the histogram unaltered (Fig. 15k and l). This is explained by considering that large quantities of the X2 magma occupy a large part of the system, and therefore the chemical nutrient is homogeneously distributed, even if CR and AMR still exist; pyroxene nuclei grow, hence, in a more homogeneous manner with respect to the cases in which the quantity of the X2 magma was lower.
It is notable that, considering that quantities of the X2 magma are continuously variable, a continuous change in the structure of the histograms is observed. In particular, for quantities of the X2 magma below 20% only two peaks, having the same structure as those reported in Fig. 15a and b, are observed. As the percentage of the X2 magma approaches 20% a third peak appears in the histogram, generating structures similar to those reported in Fig. 15d and e. This behaviour is observed up to 50% of X2 magma. Higher percentages of the X2 magma generate histograms characterized by a single peak similar to those shown in Fig. 15j–l.
Comparing the histogram constructed using the data from natural pyroxenes (Fig. 7) with the histograms obtained from the simulation (Fig. 15), there is a striking similarity to the simulations. In fact, in the natural case, three peaks are present, one associated with pyroxenes showing no Al–Fe3+ Di growth rim and the other two related to two population of crystals having increasing area of the growth rim, exactly as in the simulated systems in which the percentage of the X2 magma is between 20% and 50% (Fig. 15d, e, g and h).
From this analysis it seems reasonable to hypothesize that the peaks A and B associated with the growth of the rim of natural pyroxenes (Fig. 7) are the result of crystallization inside CR in which chemical exchange between the interacting magmas is limited by the closed structure of the flow fields precluding extensive growth of the rims of crystals. It follows that the peak C (Fig. 7) is related to pyroxenes residing in AMR, where the growth of their rims is high because of the chaotic structure of the flow fields, which allows chemical exchange to be very efficient. The fact that three populations of crystals are observable only when the percentage of the X2 magma is between 20% and 50% suggests that similar quantities of the more evolved magma can be invoked for the natural magma mixing process.
Simulations can also be used to investigate the variability in concentration of a chemical element from the core to the rim of the simulated pyroxenes as their growth proceeds. This is analogous to performing microanalysis along a transect passing from the core to the rim of the simulated pyroxenes, as we have done for the natural pyroxenes (Fig. 5). Figure 16 shows the variation of the chemical element along a line connecting the core and rim of two simulated pyroxenes, one grown inside a CR (Fig. 16a) and the other inside the AMR (Fig. 16b). In the first case, the concentration of the chemical element decreases continuously from the core to the rim of the crystal; this is explained by considering that the CR act as a barrier to chemical exchange and, in this kinematic regime, the growth of pyroxenes inside CR depletes progressively all the available chemical element as crystallization continues, leading to smooth concentration patterns of the chemical element from the core to the rim of pyroxenes.
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The pattern of variation of the chemical element from core to rim of pyroxenes that grew inside the AMR (Fig. 16b) is completely different, evidenced by an irregular variation. This is explained by considering that within AMR the chemical element is transported in an irregular way inside the magma, given the chaotic behaviour of these regions. It follows that the growth of pyroxenes inside AMR occurs in an unpredictable and irregular way, leading to the irregular variation in the concentration of the chemical element from the core to the rim of crystals.
Comparing the patterns of variation of the chemical element from core to rim of the simulated pyroxenes (Fig. 16) with those found in the Santa Venera flow (Fig. 5) a striking similarity can be observed. In fact, in both cases, two main kinds of patterns of variation of chemical elements can be observed, regular and irregular, leading to the conclusion that the regular patterns are due to crystallization of pyroxenes inside CR whereas the irregular ones are associated with pyroxenes that crystallized within AMR.
The apparent dichotomy of the association of regular patterns of variation of chemical elements in pyroxenes with thin growth rims but irregular patterns of variation in crystals with a larger rim area needs further consideration. This feature can be explained by considering that the growth of pyroxenes inside CR, although inhibited by the closed structure of the flow field inside these regions (thin growth rims), proceeds by consuming regularly the chemical elements trapped inside the CR and this produces smooth patterns of chemical variation. On the contrary, pyroxenes growing inside AMR develop thicker rims because chemical exchange is strongly favoured, but the patterns of variation are irregular because of the chaotic structure of the flow fields inside the AMR that change quickly and drastically the amount of nutrients in the crystal neighbourhoods. These considerations can also explain the observation that pyroxenes with the thinnest Al–Fe3+ Di rims are those with more euhedral Cr–Al Di cores, whereas thicker rims are associated with strongly resorbed cores.
All scalar quantities, such as temperature or oxygen fugacity, in addition to concentration, are strongly controlled by the structure of the flow fields. This implies that the entire thermodynamics of the magmatic system is strongly modulated because of the presence of the different dynamical regions. Thus, CR are coherent for all thermodynamic properties of the magma volumes that are trapped inside them, as also evidenced by the occurrence of unzoned plagioclases and primitive olivines and included spinels in the Santa Venera basalt. Analogously, AMR are chaotic for all thermodynamic properties. It follows that inside CR pyroxenes travel within small regions of the magmatic system (Fig. 17c), suffering the minimum effects of disequilibrium, and, hence, their resorption is much lower than that of pyroxenes travelling inside AMR (Fig. 17d) where they can encounter unpredictable and abrupt changes in intensive variables and concentration suffering the largest effects of disequilibrium, leading to strong resorption. Therefore, the process controlling the resorption of crystals has to be linked to the structure of the flow fields inside the magma body. These considerations are also corroborated by the fact that pyroxenes with the largest Al–Fe3+ Di rim areas include higher quantities of acicular apatite and Ti-magnetite relative to pyroxenes displaying the lowest rim areas. As discussed above, acicular apatite and Ti-magnetite nucleation occurred in response to variation of the intensive variables and/or concentration; therefore, pyroxenes that include high quantities of these two minerals can be thought to represent crystals that suffered large disequilibrium with respect to crystals including lower quantities.
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CONCLUSIONS |
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TOPABSTRACTINTRODUCTIONPETROGRAPHYDISEQUILIBRIUM TEXTURES IN...CAUSES OF VARIED DISEQUILIBRIUM...SIMULATION OF THE GROWTHOF...RESULTS AND DISCUSSIONCONCLUSIONSSUPPLEMENTARY DATAREFERENCES |
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Disequilibrium textures in pyroxene crystals occurring in the Santa Venera lava flow (Mt. Etna) have been studied with the aim of providing a possible explanation for the puzzling phenomenon of the coexistence of mineral phases having extremely variable textures over very short length scales (<1–2 cm) in magmatic rocks.
The textures and mineral chemistry of the studied pyroxenes, along with the occurrence of disequilibrium textures in plagioclase, argue in favour of a mixing process between magmas having different geochemical and thermal properties as the basic process contributing to the production of the observed disequilibrium textures.
Following this idea a chaotic advection–diffusion model, in which active mixing regions and coherent regions coexist over short length scales, is proposed to simulate the growth of pyroxenes inside a magma mixing system. Results show that it is possible to reproduce, with good approximation, natural occurrences, allowing us to give a physical explanation for both the textural and geochemical features observed in natural pyroxenes.
We have shown that chaos theory provides powerful techniques that may be of great help in understanding the petrogenesis of igneous rocks. Chaos theory allows us to simulate magmatic systems incorporating in the models the typical long-term unpredictability inherent in natural systems, and thus provides the opportunity to explain phenomena and processes that at first sight may appear very complex.
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SUPPLEMENTARY DATA |
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TOPABSTRACTINTRODUCTIONPETROGRAPHYDISEQUILIBRIUM TEXTURES IN...CAUSES OF VARIED DISEQUILIBRIUM...SIMULATION OF THE GROWTHOF...RESULTS AND DISCUSSIONCONCLUSIONSSUPPLEMENTARY DATAREFERENCES |
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Supplementary data for this paper are available on Journal of Petrology online.
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ACKNOWLEDGEMENTS |
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We are grateful to D. A. Jerram, L. Coogan, P. Hoskin and M. Wilson for helpful suggestions and criticisms in reviewing the manuscript. The excellent editorial handling of M. Wilson is gratefully acknowledged. This work was funded by CNR and MURST grants.
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