Data collection and treatment
Geochemical data of bulk volcanic rocks from 21 modern arcs (Supplementary Data File 1) were collected from the Georoc database (http://georoc.mpch-mainz.gwdg.de/georoc/) and treated according to the method described by ref. 7 and detailed in the Methods section. As in ref. 7, to reduce the bias induced by outliers and to extract information on general trends, median values of Zn, SiO2, and MgO for subpopulations corresponding to bins of 0.5 wt% MgO were calculated (Supplementary Data File 1). When less than 10 data were available for one of the investigated elements within the 0.5 wt.% MgO bin, the MgO interval was extended to a higher value (e.g., 1 or 1.5 wt.%) to incorporate more values of that element. For comparison with arc systematics, data were also collected for the mid-ocean ridge (MOR) environment (https://www.earthchem.org/), a typical oceanic island basalt magmatic sequence like Hawaii (http://georoc.mpch-mainz.gwdg.de/georoc/), and treated in the same way as for arcs.
Median values of zinc contents of magmas from different arcs follow distinct trends with geochemical differentiation (i.e., with decreasing MgO: Supplementary Figure S1). The averages of the median values of the 7 arcs (Bismark-New Britain, Kurile, Kermadec, Mariana, New Hebrides, South Sandwich, Tonga) emplaced in intraoceanic arcs with thin crust thickness (< 20 km) display a systematic increase of Zn contents with decreasing MgO from an initial value of ~ 70 ppm up to 90–100 ppm Zn at MgO values between 1 and 2 wt.%, after which Zn decreases to values of 40–50 ppm for the most evolved rocks (Figs. 1a and Supplementary Figure S1). However, several thin arcs do not show such a decrease because they do not evolve to rocks differentiated enough (Supplementary Figure S1).
Average values of zinc median contents of magmas emplaced in thick arcs (> 30 km: Mexico, Aleutians, Cascades, NVZ), in contrast, display an overall slight decline with decreasing MgO down to MgO values ~ 1.5 wt.%, after which Zn decreases along a steeper trend in the most differentiated rocks to an average value of ~ 40 ppm (Figs. 1a and Supplementary Figure S1). Zn trends in magmas of intermediate thickness arcs display an intermediate behavior (Supplementary Figure S1). The most differentiated magmas of the Lesser Antilles arc display an increase in Zn contents rather than a decrease like all other arcs (Supplementary Figure S1).
Table 1
Summary of the values of the regression slopes (MgO vs. SiO2 and Zn vs. MgO) and associated statistical values. Bold and italics indicate poor statistical correlations (see Supplementary Figure S1).
Arc | Crust thickness (a) | error (a) | Type according to crust thickness (b) | slope MgO-SiO2 | error (c) | r2 (c) | slope Zn-MgO | error (c) | r2 (c) | Average of median Fe2O3tot at MgO 4–6 wt.% (d) | error (d) | Average of median Sr/Y at MgO 4–6 wt.% (e) | error (e) |
S. Sandwich | 11.8 | 0.1 | < 20 km | -1.7719 | 0.2444 | 0.913 | -5.0157 | 0.7201 | 0.802 | 10.6 | 0.3 | 7.3 | 0.7 |
Mariana | 14.5 | 1 | < 20 km | -1.9778 | 0.2066 | 0.884 | -4.6166 | 0.52011 | 0.840 | 11 | 0.3 | 14.1 | 2.3 |
Kermadec | 15 | 3 | < 20 km | -1.3980 | 0.3308 | 0.749 | -3.9468 | 0.6076 | 0.710 | 11 | 0.5 | 10.5 | 2.9 |
New Hebrid. | 15.6 | 0.2 | < 20 km | -1.6128 | 0.4708 | 0.516 | -2.1136 | 0.8971 | 0.270 | 11.2 | 0.9 | 29.6 | 3.8 |
Kuriles | 18.3 | 0.9 | < 20 km | -1.5281 | 0.2560 | 0.798 | -2.0405 | 0.7744 | 0.332 | 9.2 | 0.2 | 15.3 | 0.9 |
Tonga | 20 | 0 | < 20 km | -1.4867 | 0.2237 | 0.786 | -2.6703 | 0.6144 | 0.486 | 11.1 | 0.3 | 11.9 | 1.8 |
Bismark-NB | 22.5 | 6.5 | < 20 km | -1.7614 | 0.2099 | 0.865 | -0.7489 | 0.4575 | 0.124 | 9.8 | 0.3 | 27.9 | 7.9 |
Ryukyu | 24.5 | 3.4 | 20–30 km | -1.2420 | 0.3479 | 0.614 | 3.2332 | 1.4993 | 0.215 | 9.6 | 1 | 14.6 | 1.4 |
Kamchatka | 24.6 | 5.4 | 20–30 km | -1.1359 | 0.3028 | 0.501 | -0.7217 | 0.5025 | 0.108 | 9.2 | 0.3 | 19.3 | 1.7 |
Lesser Antilles | 24.7 | 0.7 | 20–30 km | -1.0392 | 0.2039 | 0.743 | 1.4182 | 0.4301 | 0.420 | 9.3 | 0.2 | 16.3 | 4.8 |
Aeolian | 24.9 | 1 | 20–30 km | -0.9813 | 0.1454 | 0.820 | 2.2710 | 0.5283 | 0.627 | 8.5 | 0.1 | 30.8 | 2 |
Sulawesi | 27.4 | 2.2 | 20–30 km | -0.9439 | 0.4256 | 0.451 | -1.1683 | 0.5830 | 0.334 | 10.3 | 0.5 | 20.2 | 1.8 |
Luzon | 27.8 | 4.5 | 20–30 km | -1.0296 | 0.0941 | 0.916 | -1.0374 | 1.5086 | 0.044 | 9 | 0.5 | 25.9 | 3.4 |
Central America | 28 | 7 | 20–30 km | -0.8691 | 0.0470 | 0.961 | -0.8611 | 0.4467 | 0.179 | 9.6 | 0.3 | 31 | 2.8 |
Aegean | 28.2 | 0.6 | 20–30 km | -0.7484 | 0.1090 | 0.825 | -2.1850 | 0.5792 | 0.587 | 7.5 | 0.8 | 24 | 3.9 |
New Zealand | 28.6 | 3.2 | 20–30 km | -0.7093 | 0.1482 | 0.638 | 2.8065 | 0.5898 | 0.618 | 7.8 | 0.3 | na | na |
Honshu | 29.2 | 2.6 | > 30 km | -1.4021 | 0.1133 | 0.922 | -0.2739 | 0.3475 | 0.029 | 9.7 | 0.3 | na | na |
Mexico | 30.3 | 5.5 | > 30 km | -0.6281 | 0.0410 | 0.933 | 1.2997 | 0.3705 | 0.370 | 7.6 | 0.5 | 27.4 | 2 |
Aleutians | 37.5 | 2.5 | > 30 km | -0.8012 | 0.0885 | 0.911 | 2.6022 | 0.5834 | 0.434 | 9.4 | 0.2 | 18.3 | 3.9 |
Cascades | 38.8 | 1.9 | > 30 km | -0.9349 | 0.0950 | 0.898 | 0.2498 | 0.4216 | 0.019 | 8.4 | 0.5 | 30.3 | 1.6 |
NVZ | 42 | 9.8 | > 30 km | -0.4906 | 0.0236 | 0.971 | 3.7100 | 0.6348 | 0.698 | 7.6 | 0.2 | 40.1 | 0.9 |
MOR | 6.5 | 0.5 | < 20 km | -2.3322 | 0.3155 | 0.785 | -10.076 | 0.6704 | 0.922 | 14.3 | 1.7 | 4.1 | 1.5 |
(a) From 60, except Tonga thickness, which is from 61, Kermadec thickness, which is from 62, Aleutians thickness which is from 63, and Northern Andes thickness which is from 64. The Tonga crustal thickness here taken corresponds to the maximum crustal thickness of 61 because arc magmatism occurs in coincidence with the thickest part of the Tonga arc (Fig. 9 in 61). Crustal thicknesses have been calculated by 60 using the global crustal model at 2x2 degrees, CRUST 2.0, administered by the US Geological Survey and the Institute for Geophysics and Planetary Physics at the University of California 65, which is an updated version of CRUST 5.1, a global crustal model at 5x5 degrees 66.The model is based on seismic refraction data published up to 1995 and a detailed compilation of sediment thickness. The crustal thicknesses of 60 are within the ranges of crustal thicknesses reported in previous studies 67,68 with which they show good linear correlations (r = 0.70 with respect to crustal thicknesses of 67, and r = 0.74 with respect to crustal thicknesses of 68). Oceanic crust thickness is from . |
(b) Attribution to a crust thickness type takes into account the 1σ uncertainty and the geochemical systematics: for instance, Bismark/New Britain has average crust thickness slightly above 20 km, but taking into account the 1σ uncertainty minimum values are largely < 20 km and geochemical trends are more typical of arcs < 20 km thick. This subdivision is purely semantic and does not change the mathematical correlations. |
(c) errors and correlation coefficients r2 of the regressions were calculated using the "LINEST" function in Excel. |
(d) From 7 |
(e) From 8 |
The trend of MOR magmatic rocks is characterized by a steeper negative slope than the average trend of the thin arcs in the Zn-MgO space (Fig. 1a). The most primitive MOR basalts have similar median Zn contents as the most primitive thin and thick arc basalts (~ 75 ppm) and grow to a median Zn content of ~ 170 ppm at ~ 2 wt.% MgO, that is significantly higher than the average value of thin arcs (Fig. 1a), after which Zn contents drop to a median value of ~ 100 ppm with further differentiation.
In order to quantify the differences of the Zn-MgO trends in different arcs, slopes of the linear regressions between Zn and MgO were calculated for the early differentiation segments, i.e., excluding the median values corresponding to the strong Zn decreases (or increase for the Lesser Antilles) in the most differentiated rocks of all arcs (Table 1 and Supplementary Figure S1). Thicker arcs are characterized by positive Zn-MgO slopes, whereas thin arcs are characterized by negative Zn-MgO slopes and intermediate thickness arcs have intermediate slope values (Fig. 1b). The slopes so calculated display a statistically significant correlation with the thickness of the corresponding arc crust (Fig. 1b). Several arcs, however, do not display statistically significant correlations between Zn and MgO (e.g., Bismark-New Britain, Ryukyu, Cascades, Luzon, Honshu, Central America: Table 1) and are represented by a shaded symbol in Fig. 1b.
Also MgO-SiO2 trends of the early evolutionary paths of arc magmas (i.e., before a break in the slope of the trend to a significantly shallower slope for MgO contents below a variable arc-dependent threshold of 2–5 wt.%; Supplementary Figure S2) display different slopes, steeper in thin arcs and shallower in thick arcs (Fig. 2a, Supplementary Figure S2, and Table 1). MOR magmatic rocks display an overall steeper slope than thin arcs during early evolution in the MgO-SiO2 space (Fig. 2a). The values of the slopes defined by the early to intermediate differentiation trend of arc and MOR magmas in the MgO-SiO2 space display again significant correlations with the crust thickness of the corresponding arc and of MOR (Fig. 2b). Although there might be some degree of arbitrariness in the choice of the point at which the slope breaks in the MgO-SiO2 space (especially for some arcs: Supplementary Figure S2), changing the break point to higher MgO values does not significantly change the slope of arcs in such a way to affect the correlation of Fig. 2b. In fact, inter-arc changes of such slopes are much larger than the small changes that arise from a different choice of the break point within a specific arc.
Crustal thickness control on fractionating mineral assemblages
The data reduction of the large dataset used in this study leads to results (median values) that statistically represent the most common values within a population with a normal distribution like that for the elements here considered within the ~ 0.5 wt.% MgO bins. This means that the interpretation of these results is forcedly a simplification of the processes occurring in arcs, as indicated by the large distribution clouds of single rock analyses compared to the median values calculated from them for the MgO bins within each arc (Supplementary Figures S1-S2). Therefore, the processes interpreted on such a basis are first-order processes and do not exclude, within each specific arc, the occurrence of additional second or lower order processes (e.g., ref. 23). Such processes might be important in some arcs, where correlations of median values of elements are not statistically significant (e.g., Fig. 1b and Table 1).
The different trends displayed by magmas of distinct arcs (and MOR) in the Zn-MgO and MgO-SiO2 spaces (Figs. 1–2 and Supplementary Figures S1-S2) must be, to their greatest extent, the result of differentiation processes occurring within the crust because of the large SiO2 and MgO ranges that they encompass (Supplementary Figures S1-S2). A variety of studies agree in considering differentiation of arc magmas as the complex result of various processes, including fractional crystallization24,25, recharge/mixing13,26,27, partial melting 28 and assimilation of host rocks 29. Arguably, fractional crystallization (and to some extent partial melting, which is the opposite process of fractional crystallization) can be considered as the main process responsible for the large SiO2 and MgO variability observed in arc magmas 25. Superimposed on this, mixing/recharge are also universal processes occurring in arcs that tend to homogenize the signals of fractional crystallization 27.
Figure 1 shows that Zn displays different degrees of increase or decrease during magmatic differentiation that depend on the thickness of the arc crust. Because primitive basalts have very similar values (70–80 ppm) both in arcs of different thickness and in MOR (Fig. 1a) and because the continental (72 ppm: ref. 30) and oceanic crust (~ 75 ppm: Fig. 1a) Zn contents also fall within this range, wholesale assimilation of crustal lithologies (either oceanic or continental) concomitant or not with fractional crystallization cannot explain the Zn systematics observed in arcs and MOR magmas. Partial melting of crustal lithologies producing SiO2-rich melts could be a significant process in arcs, especially at higher depths (and therefore in thicker arcs) because of thermal constraints 31. Mixing of basalt with such SiO2-rich and either Zn-poor or Zn-rich partial melts would be needed to explain the decreasing and increasing trends of Zn with MgO in thick and thin arcs, respectively.
However, almost all arcs show a kink in both the Zn-MgO and MgO-SiO2 trends suggesting that mixing with a SiO2-rich and Zn-poor or Zn-rich crustal melts is not a viable explanation either. Mixing certainly occurs in arcs (there is ample petrographic and mineral chemistry evidence for that) and is probably also a cause of the scatter of single rock analyses around the kinked trends in the Zn-MgO and MgO-SiO2 spaces (Supplementary Figures S1-S2). However, mixing in the crust must involve end-member magmas whose Zn-MgO-SiO2 systematics are controlled by fractionating or restitic minerals. Therefore, although treating the different trends observed in arcs in the Zn-MgO-SiO2 space as the result of fractional crystallization is an approximation, these trends ultimately tell us what are the mineral phases that are involved in producing their different slopes through combined fractional crystallization, partial melting and mixing processes.
Thus, for simplicity I will model the distinct Zn-MgO-SiO2 trends of arcs as the dominant result of fractional crystallization during which Zn behavior shifts from incompatible to compatible for magma differentiation occurring within an increasing crustal thickness (Fig. 1a). Such a behavior should be discussed considering the partition coefficients of Zn between melt and the main minerals fractionating in arc (and MOR) magmas (i.e., olivine, plagioclase, amphibole, clinopyroxene, garnet and magnetite). A compilation of KD values from the literature (Supplementary Table S1 and Fig. 3) suggests that, among the potential fractionating phases during the early and intermediate stages of arc magma differentiation, magnetite is the one for which Zn has the highest affinity, compared to pyroxenes and particularly to plagioclase, which has very low KD values for Zn. Zn is slightly incompatible in olivine in equilibrium with basalt but becomes compatible in this mineral when the latter crystallizes from basaltic andesite and andesite melt (Fig. 3). In contrast Zn is compatible in magnetite already crystallizing from basalt and its compatibility strongly increases with magmatic differentiation (Fig. 3). Zn has KD values slightly < 1 for garnet in equilibrium with basaltic to andesitic melts 32 (Fig. 3 and Supplementary Table S1). At intermediate stages of magmatic evolution (andesite, dacite) Zn becomes increasingly compatible in amphibole, clinopyroxene (Fig. 3) and biotite (KD ~18 in dacitic melts: Supplementary Table S1). The onset, in the most evolved stages of arc magmas, of crystallization of biotite and magnetite, plus other accessory mineral phases (e.g., ilmenite) for which Zn has a strong affinity, is likely responsible for the strong Zn decreases in most arcs below 2–4 wt.% MgO. Only some thin arcs do not display such a decrease (South Sandwich, Kermadec, New Hebrides, Kurile), perhaps because not enough differentiated rocks occur in the databases of these arcs. Zn contents display a strong increase in the most differentiated rocks of the Lesser Antilles arc. Although these trends in the most differentiated rocks may be of interest for those specific arcs, their discussion is beyond the scope of this work which considers the Zn-MgO trends of the early to intermediate differentiating magmas, excluding the most differentiated rocks.
Modelling trends in the MgO-SiO2 and MgO-Zn spaces
In order to quantify the relationship of Zn-MgO-SiO2 systematics with fractionating mineral assemblage of arcs with different thickness, mass balance calculations using a Monte Carlo approach (see Methods and Supplementary Tables S2-S3) have been used to model simultaneously the Zn-MgO and MgO-SiO2 trends of the different arcs (and of MOR magmas) through fractionation of the main phenocrystic minerals occurring in mafic to intermediate arc and MOR magmas (olivine, amphibole, clinopyroxene, plagioclase, magnetite, garnet). This corresponds to reproducing the trends through fractionation of mineral assemblages in the tridimensional SiO2-MgO-Zn space. This approach provides stringent constraints to the combination of mineral proportions and residual melt fractions that satisfy simultaneously the Zn-MgO and MgO-SiO2 trends.
The model was run using a home-made RStudio script (see Methods and the examples of Supplementary Data File 1). The solutions of the simulations returned the combinations of bulk fractionating mineral assemblages and residual melt fractions able to reproduce the end point in the tridimensional SiO2-MgO-Zn space of the trends of each arc starting from an appropriate parental composition in the same tridimensional space (Supplementary Figures S1-S2).
Overall, results of the Monte Carlo simulations of fractionation processes applied to Zn-MgO-SiO2 systematics (Supplementary Table S4) show that the fractionating mineral assemblages gradually shift from plagioclase-dominated in thin arcs to amphibole-, magnetite-, and garnet-dominated in increasingly thicker arcs (Fig. 4). Clinopyroxene and olivine do not significantly correlate with crustal thickness, suggesting that these minerals act as buffers in the fractionating assemblages. High proportions of both olivine and plagioclase in fractionating magmas of thin arcs are needed to explain on one hand the steep decrease of MgO at low SiO2 values (olivine effect, because of SiO2/MgO < 1 in olivine: Supplementary Table S5) and on the other the broadly incompatible behavior of Zn (plagioclase effect, due to the very low KD values of Zn in plagioclase: Fig. 3). In contrast the high proportions of clinopyroxene, amphibole and garnet and the low proportions of plagioclase in fractionating magmas in thick arcs are consistent with both the shallower decrease of MgO with SiO2 (due to the high SiO2/MgO values in all these minerals, between 3 and 4: Supplementary Table S5) and with the slightly compatible behavior of Zn (due to the KD values of Zn in these minerals around or slightly > 1: Fig. 3).
These results agree with petrographic observations that phenocrysts in relatively primitive thin arc rocks (e.g., Mariana, South Sandwich: refs. 23,33,34) consist of olivine, plagioclase and pyroxenes (with virtually no amphibole), whereas relatively primitive rocks and cumulates of thick arcs (e.g., Ecuador, Mexico, Cascades, Central Andes: refs. 35–38) contain variable amounts of amphibole. They also support and quantify the suggestion that extensive cryptic amphibole (and garnet) fractionation may occur in arcs 39, especially in increasingly thicker ones.
Crust thickness control on fractionating assemblages
The systematic correlations of the changing proportions of fractionating amphibole, garnet, magnetite, olivine and plagioclase with changing crustal thickness are consistent with experimental petrology results carried out on hydrous basaltic to andesitic melts fractionating at different pressures40–47. These results show that plagioclase, clinopyroxene and olivine are the main minerals crystallizing at the liquidus of hydrous mafic melts at low pressures (e.g., < 0.1–0.3 GPa depending on H2O content) whereas amphibole, garnet, clinopyroxene, garnet, magnetite crystallize at or near the liquidus of hydrous mafic melts at high pressures (> 0.8 GPa). The data presented and discussed here suggest that there is a gradual and continuous crustal thickness-controlled change in the proportions of fractionating minerals between the above two end-member assemblages that results in the systematic changes of SiO2-MgO-Zn trends of arc magmas.
The preferential fractionation of amphibole and garnet in thicker arcs is unlikely to result only from higher H2O contents in the primitive basalts of thicker arcs10,11,14, considering that the H2O contents of primitive arc basalts are broadly similar for all arcs independent of their thickness 48. In addition, the occurrence of variable amounts of garnet required for the thicker arcs by the modelling here presented indicates pressures of crystallization of at least 0.8 GPa even in H2O-rich magmas 42. A thicker crust will result, as suggested by the data above discussed, in an average magma evolution at deeper levels 8 which will increase H2O contents in the residual magma more significantly than magma evolution at shallower levels already in the early fractionation stages (Supplementary Note 2 in Supplementary Information), because of the strong pressure dependency of H2O solubility in silicate melts49. This will, in turn, further stabilize the fractionation of amphibole and garnet from relatively unevolved basaltic andesite and andesite magmas at mid- to lower crustal levels41,42. If a systematic H2O enrichment in primary basalts of thick arcs does occur11,14, this would further enhance amphibole and garnet fractionation in thick arcs.
The variable crustal thickness-controlled proportions of the fractionating mineral assemblages obtained by modelling Zn-MgO-SiO2 arc systematics also correlate with the median Fe2O3tot values at 4–6 wt.% MgO of arcs (Fig. 5), which are a measure of the tholeiitic versus calc-alkaline character of arc magmas7,50. Overall, these data suggest that first order processes of differentiation observed in arc magmas and the generation of a continuous transition from tholeiitic to calc-alkaline character are the result of pressure-dependent stability of different fractionating mineral phases (see also ref. 25), which is ultimately controlled by crustal thickness. A thicker crust results in an average evolution of arc magmas at deeper crustal levels and, therefore, is characterized by fractionation of higher-pressure assemblages (olivine, clinopyroxene, amphibole, garnet, magnetite) from the hydrous basalts typical of the arc environment. This leads to the development of a typical calc-alkaline trend in associated arc magmas (Fig. 5). In contrast, a thinner crust results in an average shallower crustal evolution of arc magmas characterized by the fractionation of the assemblage olivine, plagioclase, pyroxenes from such hydrous basalts. This leads to the development of tholeiitic trends in associated arc magmas (Fig. 5). Nonetheless, it is important to highlight that the results presented here suggest that there is a continuum between these two extremes without a neat subdivision between calc-alkaline and tholeiitic trends, but rather a gradual transition, that is controlled by the role that crustal thickness of the arc has on the proportions of fractionating minerals.
It is significant that MOR magmas, which are almost anhydrous 51, fall on the continuation of the trends of Figs. 1b and 2b suggesting that Zn-MgO and MgO-SiO2 systematics seem to be insensitive to the largely different H2O contents of primitive basalts in MOR (~ 0.1–0.2 wt.%: ref. 51) and thin arcs (~ 4 wt.%: Plank et al., 2013) and that crustal thickness seems to be the main controlling factor on the different Zn-MgO-SiO2 systematics of magmas in these distinct settings.