A - METHOD. GSA Data Repository

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1 GSA Data Repository Ganne et al., 2018, Deep into magma plumbing systems: Interrogating the crystal cargo of volcanic deposits: Geology, A - METHOD (1) Data Mining and statistical analysis Petrological and geochemical databases provide access to several tens of thousand rocks and minerals analyses covering most of the Earth s history. Data mining techniques allow the exploration of these datasets to uncover hidden patterns and trends short and long periods (up to tens to hundreds of Myr; e.g., Keller & Schoene, 2012; Tang et al., 2016 ; Ganne et al., 2016 ; Ganne et al., 2017 ; Ganne & Feng, 2017). However, these global trends are necessarily stained by statistical uncertainties, may suffer from sampling bias, and mask some of the natural variability in key parameters (e.g., T, P, H 2 O content, fo 2, ) that varies significantly in between different geological environments (e.g., different tectonic settings). We argue nonetheless that such statistical techniques can capture relevant insight into secular changes in rock/mineral compositions, although it should be coupled with more detailed studies that look at specific processes in specific localities. The pioneering work of Keller & Schoene (2012) inspired us to compile an extensive geochemical data set of continental and oceanic igneous rocks and minerals from the Phanerozoic to Archaean. Data from the GEOROC database (https// were filtered to exclude all samples whose summed oxides yield totals outside the % range. Geochronological data associated to these samples were reported as means with 1-standard-error uncertainty given by the method (e.g., U/Pb geochronology or biostratigraphy). Geo-referenced bulkrock chemistry and mineral analysis (3646 references) have been crossed to derive P and T estimates. The result was a data set including up to 130 variables for each of the >55,000 samples of rocks, and 80 variables for each of the >117,000 analyses of mineral for a total of more than 16 million data points. More than 88% of the minerals present in our database have been sampled in volcanic rock (88% for plagioclase, 83% for clinopyroxene, 90% for orthopyroxene, 92% for olivine and 85% for clinoamphibole). Results for global mean intensive (geochemical) and extensive (T, Tp) values with time are reported with associated 1-standard-error of the sample mean of the mean at different intervals. These intervals correspond to different variables of interest (e.g. one unit for the SiO 2 wt% of rocks). The standard error of the sample mean, which is the standard deviation divided by the square root of the sample size, gives us an estimate of how far away our sample error might be form the true population mean. Accordingly, the population mean is within 2 times the standard error from the sample mean about 95% of the time. These means were generated by Monte Carlo analysis with bootstrap resampling techniques to mitigate sampling bias (Fig. 1 SI). 36

2 Figure 1 SI. Distribution of minerals considered in this study plotted again the composition (SiO 2 wt% and Mg#) of their bulk rock. Statistical assessment of their equilibrium condition (%) through magma composition evolution is given by the colored drawbars (uncertainty bars correspond to ± 1 σ standard deviation for an compositional step of 1 wt%).the relative proportion of minerals analysed through magma composition evolution is given by the grey curve.

3 Our approach follows Keller & Schoene (2012) with information from the original source added where necessary. The following procedure was conducted: (1) a subset of data was randomly selected so that the probability of inclusion in the resampled subset is directly proportional to the sample weight; (2) a synthetic dataset for each sampled data point was drawn from a Gaussian distribution with a mean equal to the original value of the data point and the standard deviation equal to the estimated 1-standard uncertainty of the data point; (3) the resulting data were sorted into bins of composition (e.g. one unit for the SiO 2 wt% of rocks), with a mean and variance calculated for each variable; (4) steps 1 3 were repeated 1000 times. A minimum number of samples (threshold of 3) within each bin was fixed to perform or not the steps 1 3. (5) A total mean and standard error of the mean were calculated for each variable in each bin.

4 (2) Reliability of databases in statistical petrology Whilst it is increasingly accepted that statistical geochemistry can be established as a viable and powerful approach to understanding global issues in Earth Sciences, the robustness of geological interpretations derived from this approach remains in doubt when the statistical trends are not sufficiently supported by data. A robust bootstrap analysis requires high data density as well as a spatial and/or temporal continuity in the dataset to ensure data representativeness (Keller & Schoene, 2012). We assume that the robustness of our statistical approach is strengthened by the negligible occurrence of temporal sampling gaps for magma and mineral record in the database, more specifically in the Phanerozoic times (Ganne et al., 2016). We address and exclude the risk of spatial sampling gaps in Fig. 2 SI which shows a widely distribution of Phanerozoic samples covering much of the Earth surface with a dominant record of magmas formed at subduction zone plate margins. Plate margins are known to be subjected to transient switches in the style of overriding plate deformation (shortening or extension,), making them appropriate to explore correlations between crustal thickness and chemical and physical characteristics of magmatic columns Figure 1 SI (a) Distribution of magmatic rocks considered in this study (>55,000 samples) plotted again their age. The data illustrates a reasonable distribution of mafic and felsic magmas through the Earth history (source : Georoc). (b) Distribution of Phanerozoic magmas on the Earth s continental surface.

5 Another risk of sampling bias we have to address concerns the choice of samples by authors. Though, our dataset is potentially weighted to analyses from certain rock or mineral types. As an example, the chemical distribution of magma in Fig. 4 SI is marked by two peaks in SiO 2, at respectively ~50 and 75 wt%, likely bracketing the Daly gap (Daly, 1925). The peak at 75% is smallest but, for some authors, it should really be comparable to the peak at 50 wt.% SiO 2. It is not, potentially because geochemists prefer basalts to rhyolites (i.e., they are more useful for answering questions about the mantle) and consequently, the database is weighted towards the analysis of basalts. If true, such potential bias of sampling is of important if we derive the average composition of magma on a timescale and reducing the weight of mafic samples rocks through bootstrap analysis appears necessary Figure 3 SI. (a) Distribution of magmatic rocks (>55,000 samples) considered in this study plotted again their composition (SiO 2 wt% ). (b) Distribution of magmatic minerals (>125,000 samples) considered in this study plotted again the composition (SiO 2 wt% ) of their bulk rock. 91 % of the minerals have been analyzed in volcanic rocks youngest than 5 Ma. It is also tempting to say that crystal richness of intermediate magma (andesites) can explain the peak in mineral analysis at around 60 wt% SiO 2, potentially because rocks with phenocrysts are preferably probed by petrologists compare to rocks with only microcrysts. Accordingly, the Georoc database reveals that small crystals (microcrysts) present in the groundmass of erupted magmas are teen (Opx) to twenty (feldspars) less sampled than larger ones (phenocryst, macrocryst, microphenocryst, xenocryst) and, within the population of large crystals, phenocrysts characterized by well identified

6 rims and core are sixteen (olivine, cpx, opx) to thirty eight (feldspars) more sampled than xenocrysts that often display partly resorbed cores and rims (Fig. 4 SI). Rim versus core analysis for phenocrysts can be identified in more than 25% of studies (16% for olivine to 32% for opx), revealing that core and rim are equally probed. As such, we can reasonably be confident that mineral data stored in Georoc provide a good statistical representation of the whole phenocryst population and chemistry that can exist in magma of different composition (Table 3 SI) Figure 4 SI. General information (if given) on magmatic clinopyroxene (cpx) stored in Georoc (grainsize, shape, other characteristics..). The proportion of core versus rim analysis is given (see also Table 3 SI). Bulk-rock chemistry and liquid composition We can further question (1) whether a phenocryst population and chemistry, corresponding to an early generation of minerals in a magma with often disequilibrium texture, is representative of the overall mineral population of a magma (which is not statistically measured chemically because we have not really access to the microcrysts of the matrix) and (2) how a bulk-rock composition can be used as a proxy for liquid compositions if some of the phenocrysts do not share equilibrium condition with the bulk rock. Here, we test our mineral-rock pairs for equilibrium and find that only half of the phenocrysts are in equilibrium with the host. Does it means that most of the phenocryst in the rocks are not primary to the magma? If this is the case, how can we trust the bulk-rock composition if most of the crystals that get crushed and incorporated into the analysis are entrained? In turn, how can we trust the bulk-rock Mg# when we are considering what is and is not in equilibrium? Finally, how can we then say that the bulk-rock composition approximates the liquid composition and thus can be used for mineral-liquid geothermometry or geobarometry?

7 In short, what is the maximum charge of phenocrysts in disequilibrium a bulk rock will contain beyond which it will deviate significantly from the whole rock data where crystals have been accumulated/recycled? One can posit that beyond this threshold (to be defined), the whole rock data will also reflect the entrainment of Mg-poor or Mg-rich minerals and one could get to a point where the whole rock Mg, if used as a proxy for melt composition, is lower or higher than that measured in the ferro-magnesian mineral chemistry. The above-stated problems can be addressed using a combination of statistics and a sense of judgment - and equilibrium tests, to help us out. In our database, > chemical analysis of cpx have been matched with a bulk-rock chemistry. The average (mean) composition of such rocks ranges around 53 wt% in SiO 2 and 48,28 for the Mg#. Mineral analysis obtained in this range of composition (basaltic andesites : ~50 to 55 wt% in SiO 2, Fig. 5 SI) correspond to plagioclase (35%), olivine (35%), cpx (25%) and opx (5%). It means that broadly half of the crystal cargo corresponds to ferro-magnesian minerals with composition in iron (FeOt) and magnesium (MgO) ranging from ~20 wt% for cpx to 60wt% for olivine.

8 Figure 5 SI. Cumulative histograms for the occurrence of selected magmatic minerals (ol, cpx, opx, pl) as phenocrysts in the continental record (from Ganne et al., 2016). Figure 5a SI concerns mineral in equilibrium and disequilibrium (residual) with the hosting rock. In (b), only minerals in equilibrium with the magmatic rocks have been considered. Olivine proportion is dominant in Si-poor composition of magma whereas the couple orthopyroxene-plagioclase is dominant in the Si-rich component of magmas. Note that clinopyroxene appears within a wide range of composition in nearly similar proportion. Our study reveals that ~50% of minerals in the crystal cargo grew in disequilibrium with the basalt andesitic magma that erupted (Fig. 4c in the main text) and that ~50% of those minerals in disequilibrium are represented by olivine (25%) and cpx (25%). More exceptionally, it increases to 80% in the more dacitic composition (> 65 wt% in SiO 2 ). For security, we will consider that ~70% of minerals in the crystal cargo grew in disequilibrium with the basalt andesitic magma (1th assumption **)

9 Now, let s consider that olivine and cpx in disequilibrium with the basalt andesitic magma (35% of the crystal cargo) have a ferro-magnesian composition (FeO / MgO = 1). A crystal cargo of 18% in volume will (roughly) propagated to a mass increase of 2.5 wt% in MgO and 2.5 wt% FeO in the magma (Fig. 6b SI), acknowledging that one fifth of the bulk composition of cpx and three fifth of the olivine chemistry are given by such elements (18% of 35% = 6.3% of cpx + olivine in disequilibrium with the bulk rock composition => 6.3% x [20% of FeO-MgO wt% in Cpx + 60% of FeO-MgO wt% in olivine] => wt% (2 nd assumption****) Figure 6 SI. (a) The relative proportion of crystals (e.g. the ratio between sampled crystals and sampled rocks, by step of 5 wt % for SiO 2 ) in the magma increases with increasing silice content until SiO 2 ~60-65 wt% (andesite) ; beyond this threshold, it progressively decreases. (b) Mg# evolution of a chemical system (bulk rock) with increasing recycling of ferro-magnesian minerals. (c) Tests for equilibrium (red points) and disequilibrium (grey points) between clinopyroxene (cpx) and their hosting magma. Statistical assessment of their equilibrium condition through magma composition evolution (Mg#) is given by the red drawbars (uncertainty bars correspond to ± 1 σ standard deviation for compositional step of 1). The range of magma composition (Mg#, white boxes) for which equilibrium conditions are satisfied with a population of cpx (characterized by a specified Mg#) is

10 large (±7.5% in Mg# around a mean given by the red drawbars). (d) The relative proportion of iron or magnesium in minerals strongly impacts the shape of the curves (in color). In turn, an increase of 2.5 w% in MgO and 2.5 wt% in FeO will increase the Mg# of the erupted magma of 7.5 %. If we consider that olivine and cpx in disequilibrium are close to their Mg-rich endmember (forsterite, diopside) or Fe-rich endmember (fayalite, hedenbergite), an increase or decrease of and % is expected for the Mg# of the magma, respectively. It means that recycling Fe-rich (more evolved) crystal has less impact on the bulk rock chemistry than recycling their Mg-rich endmembers. Such a tendency was modelled in the Fig. 6d SI. In the Rhode s diagrams, the range of composition (Mg#) in which a bulk rock of basalt andesitic composition appears in equilibrium with a population of cpx or olivine (characterized by a specified Mg#) is large (±7.5% in Mg#, Fig. 6c SI). It means that recycling less than 6.3% (in volume) of Fe- Mg olivine and Cpx in this chemical system (total phenocrysts mode < 18%) will not significantly change its Mg#. However, in the Rhode s diagram, we note that the range of composition (Mg#) for cpx and olivine, growing in disequilibrium with the basalt andesitic magma, is large (± 10% in Mg#) and dominantly magnesian, with a mean positioned at ~ 70 (Fig. 6c SI). Accounting for this chemical parameters, we estimate that recycling 6.8% of Mg (70) -Fe (30) olivine and Cpx in a basalt andesitic magma will increase its Mg# of 13.12%,.which will lead to a wrong application of the Kd equilibrium rules. To meet the rules, the iron and magnesium elements carried to the system must not exceed 2 wt % (Fig. 6d SI). Accordingly, crystal recycling of Mg (70) -Fe (30) olivine and Cpx must not excess 2.52% in volume of the crystal cargo (see relationships **** described above : 6.3% x 2 wt%] / 5 wt% => 2.52% ) which implies than less than 7.2% of phenocryst [see assumption ** described above : 50% of ferromagnesian and 50% of feldspars] must be expressed in the bulk rock system or thin section analysed. As a whole, we can reasonably be confident in our use of the Rhode s diagram if we assume that most of the basalt andesitic magma erupted with less than 7 % of phenocrysts (Fig. 6a SI), 30% of them being in equilibrium and 70% in disequilibrium. It means that the charge of unequilibrated mineral phases must not exceed 5% in volume of the rock. Beyond this threshold, the Kd equilibrium rules are violated and a bulk rock composition cannot be considered as a liquid. Thus, there is room for doubt in our following statement (main text) that (1) in mafic units, most minerals crystallized from melts that are more evolved than what their bulk-rock suggest and (2) in silicic units, most minerals crystallized from melts that are less evolved that what their bulk-rock suggest.

11 Mineral distribution in volcanic rocks The primary problem is thus to arrive at an estimate of the volume of phenocrysts present in the rocks analyzed by authors. Such information is virtually never reported, except for IODP and few studies (~15%) collected in Georoc where samples are named on the basis of groundmass texture and abundance of primary minerals, following a standard (IODP) or less standard (literature) nomenclature. In cryptocrystalline to microcrystalline rocks, there is a clear distinction between phenocrysts and groundmass crystals. These were described based on the identification of phenocrysts in hand sample following the criteria listed below : aphyric (<1% phenocrysts), sparsely phyric (1% 5% phenocrysts), moderately phyric (5% 10% phenocrysts), highly phyric (>10% phenocrysts) Bulk rocks from Georoc matched with their hosting minerals (mostly phenocrysts) indicate that cumulative textures (including the reference to abundant phenocrysts ) account for less than 10% of the eruptive rocks analyzed (Fig. 7 SI). Our database reveal that amphibole-bearing rocks have been preferentially selected for cumulative texture (>25%) whereas Cpx-bearing are less (<5%). These values fall below 4% for feldspars- and olivine-bearing rock, decreasing to 1% for rocks containing opx Figure 7 SI. General information (if given) on magmatic rocks stored in Georoc.

12 Figure 8 SI. Modal abundance of phenocrysts in MORB-type basalt from the all of Site 1256 (East Pacific Rise) and from the Mid-Atlantic Ridge (MAR). (source IODP at Data from the IODP global survey of MORBs along the East Pacific Rise (Holes 1256) and Mid- Atlantic Ridge indicate that moderately phyric (>5% phenocrysts) rocks and cumulates are less than 50 % (Fig. 8 SI), that is consistent with Georoc information. Fig. 6a SI suggest that andesite can contain, in average, one and half times more phenocrysts than MORBs (e.g. ratio between sampling crystals and sampling rocks in our database ; see also Fig. 3 SI) but such crystal cargo is not likely to excess 7.5% in volume because MORBs with aphyric (<1% phenocrysts) to sparsely phyric (1% 5% phenocrysts) textures are largely dominant (50 to 75%), with a peak positioned at 3% (Fig. 8 SI). And it was suggested in Fig. 6a that 7 % of phenocrysts in a rock was the critical threshold beyond which the Kd equilibrium rules are violated and a bulk rock composition cannot be considered as a liquid. As such, less than 50% of the bulk rock compositions remain potentially problematic for our estimation of equilibrium conditions because they contain an important charge of phenocrysts, likely more than 5% in volume (threshold beyond which the term moderately phyric is used for IODP MORBs). How far this observation will impact our conclusions?

13 Reasons for optimism (Putirka, 2017) Our statistical petrology results suggest that roughly half of the erupted crystals are in equilibrium with the erupted magma, over a large range of temperature and composition (Fig. 3 C in the main text). What such a ratio is likely reflecting? in essence, that ~50% of crystals extracted from a chemical horizon of a magmatic column are not in equilibrium with the erupted rock containing them, whereas ~50% of crystals erupted from this chemical horizon share equilibrium conditions with their hosting rock. However, does this mean that 50% of the crystal cargo in disequilibrium is equally distributed through crystal-rich (>7% phenocrysts), then suspect samples, and crystal-poor (<7% phenocrysts), then reliable samples? clearly not. A statistical analysis of our database reveals a more complex distribution, with 27% of rocks in total disequilibrium with the minerals they host whereas other ones (<7%) contains more than 90% of crystal in equilibrium. A similar distribution is observed through a large range of bulk rock composition with nevertheless a significant decrease of the population of fully equilibrated rocks for 70 > SiO 2 > 60 wt% (Fig. 9SI). We note also that the more disequilibrium conditions for samples, the higher the range of composition for minerals in samples (Fig. 10SI) and the more crystal-rich magma is. Among other geological examples, note the good consistency between the crystallinity of volcanic rocks (Carpenter Ridge Tuffs) erupted from the mushy reservoirs of San Juan Mountains Volcanic Field systems and the (Table 4 SI) and their equilibrium condition Figure 9 SI. (a) Schematic illustration of a mushy magma reservoir having reached a medium crystallinity stage (~30-70 vol% crystals): the absence of convection and the high-permeability provide a favorable window for crystal-melt separation (Bachmann & Bergantz, 2008). (b) Distribution of rocks erupted from mushy reservoirs of a magmatic column (Fig. 11 SI) and plotted again the fraction (%) of un-equilibrated mineral they contain. The minimum number of mineral analyses within each sample of rock (threshold) was fixed to 3. (c) The ratio between rocks hosting less than 10% and more than 90% of un-equilibrated mineral is calculated for different ranges of rock composition (grey curve). The ratio is ploted on the Y-axis. The red curve corresponds to the ratio between rocks hosting less and more than half of un-equilibrated mineral, respectively (see also Fig. 11 to 13 SI).

14 Figure 10 SI. Composition of plagioclases and clinopyroxenes erupted from a mushy andesitic to dacitic reservoir (SiO 2 : 60 to >70 wt%) with [40-50%] and [90-100%] of disequilibrium, respectively. A minimum number of mineral analyses within each sample of rock was fixed to 3. Note that the more disequilibrium conditions for samples, the higher the range of composition for minerals in samples.tests for equilibrium between mineral (min.) and nominal coexisting liquid (liq.) have been made by comparing observed and predicted values for Fe-Mg exchange. Analyses that are not within one standard deviation of the equilibrium lines (red points) based on the partition coefficient [K D (Fe- Mg) min-liq. ] of 0.27±0.03 for clinopyroxene and 0.1 ± 0.05 / 0.27 ± 0.11 for plagioclases were not included in the thermo-barometry calculations (grey points). See details below, in Method, section 5. Importantly, we observe that the crystal-cargo in fully equilibrium (Fig. 11a SI) or fully disequilibrium (Fig. 11c SI) are not homogeneously distributed. More than half of rock samples in the

15 [0-10%] range contain less than 2 mineral analysis per sample. For consistency with the bootstrap analysis (see Method section 1), only samples with more than 3 mineral analysis (threshold), have been report in the previous (Fig. 9 and 10 SI) and following diagrams (Fig. 12 to 14 SI) Figure 11 SI. The absolute number of mineral analysis (Y-axis) within each sample (X-axis) is given in (a) (b) and (c), for different range of equilibrium condition (i.e. 0-10, and %). (d) Average proportion of minerals within samples of rock. The relative proportion is given by the ratio : number of minerals versus number of rocks. The ratios are plotted again different ranges of equilibrium condition (%). Here, a minimum number of mineral analyses within each sample of rock was fixed before to produce this histogram (threshold of 3). Now, if we compare Fig. 12 to 13 SI and Fig. 8 SI, there is an obvious relation between the ~29% of mafic samples (SiO wt%) in nearly total disequilibrium (90-100%) with their crystal cargo ( crystal-rich endmember ) and the ~37% of samples having a crystal cargo > 10 % in phenocrysts (Fig. 8 SI). In general, these samples do not provide P or T estimates for the minerals they host and thus are not likely to modify the general P and T trends proposed in the study.

16 Figure 12 SI. Distribution of rocks erupted from the mushy reservoirs of a magmatic column and plotted again the fraction (%) of un-equilibrated mineral they contain. (ER) and (UR) refer to the drained, liquid-rich or crystal-rich material in the mushy reservoirs, respectively. Here, a minimum number of mineral analyses within each sample of rock was fixed before to produce histograms (threshold of 3) Figure 13 SI. Percentage of rocks erupted from the mushy reservoirs of a magmatic column, with more (>50%) or less (<50%) equilibrium conditions, and plotted again their range of composition (SiO 2 wt%). Note that the more samples erupting with >50% of disequilibrium (blue curve, nearly dominant record)), the less material erupting with intermediary equilibrium conditions (green curve). Such correlation is particularly clear in the range of andesitic to dacitic magma compositions(sio 2 :

17 to 70 wt%). Here, a minimum number of mineral analyses within each sample of rock was fixed before to produce histograms (threshold of 3) Figure 14 SI. Percentage of rocks erupted from the mushy reservoirs of a magmatic column with more or less equilibrium conditions. (a) The ratio between rocks hosting less than 10% and more than 90% of un-equilibrated mineral is calculated for different ranges of rock composition (SiO 2 wt%). (b, c) The blue and red curve corresponds to the percentage of rocks hosting less and more than 90% of equilibrated mineral, respectively (see also Fig. 9 SI). Note that, in general, the more samples erupting with >90% of disequilibrium (nearly dominant record)), the less material erupting with 90% of equilibrium. The minimum number of mineral analyses within each sample of rock (threshold) was fixed to 3.

18 (3) Thermometry calculations - A large set of T values is included in the database (Table 5 SI). These values (Fig. 13 and 14 SI) were calculated using different equations proposed in different excel files (at the accuracy and range of applicability of which is discussed in Putirka (2008). Keeping in mind that T estimates for samples with significant volatile contents, typical of arc-setting magma, are less accurate, the reported standard error of the estimate (SEE) for hydrous samples are larger. For instance, SEE for the clinopyroxene calibration of Putirka (Equation 32a) increase from ±58 C for anhydrous samples using to ±87 C for hydrous samples. Olivine-liquid calculations were performed at 1.5 Gpa, following Equation (19) and (22) providing the best estimates for anhydrous and hydrous conditions, respectively. Putirka (2008) suggests that differences of temperature between the two equations reflect calibration errors and that there is no disadvantage to using both equations and averaging the results. The accuracy of the averaged calculated temperatures is ±48 C. Plagioclase and alkali feldspar-liquid calculations were performed at 1.5 Gpa, following Equation (24a) and (24b), respectively. They provide the best estimates for anhydrous and hydrous condition. The plagioclase-liquid thermometer is calibrated at T < 1450 C, with a calibration error of ±36 C. The alkali felsdpar-liquid thermometer is calibrated at T >1050 C, with a calibration error of ±23 C. Clinopyroxene-liquid calculations use Equation (33) calibrated against experiments at temperatures less than 2400 C to produce SEE of 45 C. For orthopyroxene-liquid thermometry, Equation (28a) rectifies past overestimates for the temperature of hydrous samples and is applicable for samples with temperatures from C, pressures below 11 GPa, SiO 2 weight percent from 33 to 77%, and H 2 O less than 14.2 weight percent. Based on petrography, major element compositions and the calculated temperatures, these assumptions are valid for our set of data. Clinoamphibole-liquid calculations use Equation (4a) calibrated against experiments at temperature less than 1200 C to produce SEE of 23 C.

19 Figure 15 SI. (a, b) Averaged temperature of mineral crystallization (Putirka, 2008) plotted against their Mg# or the Mg# of the rock. The grey drawbars correspond to their averaged (all minerals integrated) temperature record through magma evolution (step of 10 C). The steepest curve is for olivine, which means (as we know) that of all the minerals plotted, the Mg# in olivine is the most sensitive to temperature. Thermometers for Cpx are based on Jd-Di exchange, or Di-En exchange, because there are other T-sensitive exchanges that mute a simple Mg# sensitivity. For Plag and Amph, Mg# does not change much with respect to T (or even to liquid Mg#) and indeed for Amph, in some experimental data sets, Mg# actually increases with decreasing T. But if we plot An content for Plag and Si-in-Amph, we might see much larger fractional changes in mineral composition. Both minerals are very sensitive to T - no less so than Opx, Cpx and olivine, but that T sensitivity is a function of Ca/(Na + Ca) for Plag and Si/(Ai + Al) in Amph.

20 Figure 16 SI. Comparative evolution of averaged temperature of mineral crystallization (Putirka, 2008) plotted against the Mg# or the SiO 2 wt% of the rock. In (a), all magmatic settings (arc, continent, ocean) have been considered; in (b) only the circum-pacific orogenic belts (arc setting) have been considered. The grey drawbars correspond to their averaged (all minerals integrated) temperature record through magma evolution (step of 10 C). The different minerals behave in slightly variable ways; opx indicate crystallization from melts with higher SiO 2 content, mostly at low temperature (<1050 ºC), while cpx and olivine become rapidly rich in iron below ~1050 C, in contrasts to the more monotonous chemical trend of crystallization for opx and amph. These trends appear independent from the tectonic setting considered.

21 (4) Barometry calculations - Experimentally derived equations to obtain pressure from magmatic mineral are associated with by an elevated standard error of the estimate (SEE). The reported SEE is ±3.6 kbars for the clinopyroxene-liquid barometer of Putirka (2008) (Equation 31) that used a global regression of water-saturated clinopyroxene experiments for calibration at pressures less than 70 kbars. The orthopyroxene-liquid barometer in Equation (29a) provides more accurate pressures for hydrous data but it does tend to underestimate low pressures. Clinoamphibole-liquid calculations use Equation (7a) calibrated against experiments at pressures less than 10 kbars to produce SEE of 1 kbar. The maximum inaccuracy is given by the plagioclase-liquid barometer (Equation 25a) that yields SEE of ± 4 kbars. One aim of this work is to examine how or whether the thickness of continental crust (Mooney et al., 1998) might affect the depths and temperatures at which newly emplaced magmas partially crystallize. We thus desire to compare total crust thickness to our estimates of crystallization P-T conditions (Fig. 17 and 18 SI). To do this we must avoid the problem of a region being significantly tectonically thickened or thinned after crystallization, and so we focus on geologically young igneous systems (< 5 Ma). Note for Fig. 18a SI the good consistency with Figure 1 E given in Putirka (2017), showing that cpx mostly crystallized at mid-crustal level in recent arc magmatic systems (e.g. Cascades or Central Andes, for comparison) Figure 17 SI. (a) Pressure and (b) Temperature of clinopyroxene and plagioclase crystallization (all minerals integrated) plotted against crustal thickness (Mooney et al., 1998) where young magmas (ca. <5 Ma), hosting these minerals, were emplaced. The black line is an estimated projection of the MOHO position along the y-axe of the graph, assuming a ratio 1:3 between pressure (kb) and depth (km). (c) Statistical assessment of their equilibrium condition (with orthopyroxene + olivine + plagioclase) through crustal thickness evolution is given by the black drawbars. The averaged

22 composition of magma is given by the mauve drawbars (compositional step of 10 km). The maximum record of mineral stability (~50%) occurs in the thickest (continent-like) crustal sections (> 40 km). The distribution of mineral is given by the grey histogram. The large range of pressure that is observed is consistent with (1) polybaric differentiation (i.e., different crystals recording different depths of crystallization) and (2) crystallization in cases happening below the MOHO, suggesting that some magmatic systems are not restricted to the crust, but can have roots in the lithospheric mantle (Macpherson et al., 2006). It also appears that pressure plays a role on the amount of equilibrium between minerals and their host rocks; there is a slight increase in mineral-melt equilibrium(~30 to 40 %) for increasing crustal thickness (Fig. 18c SI) Figure 18 SI. Comparative distribution (histograms) of young (< 5 Ma) magma chemistry (SiO 2 wt%) through different section of crust. Statistical assessment of their equilibrium condition with minerals (olivine, plagioclase, cpx, opx) is given by the black drawbars. The maximum record of mineral stability (~40-50%), in the ~40-60 (wt%) range of SiO 2, concerns the thickest (continent-like) crustal sections (> 20 km).

23 (5) Reliability of P and T calculations - Tests for equilibrium between mineral (min) and a nominal coexisting liquid (liq) can be made by comparing observed and predicted values for Fe-Mg exchange, or K D (Fe-Mg) min-liq. Analyses that are not within one standard deviation of the equilibrium lines (red points in Fig. 19 SI), based on the partition coefficient of 0.28 ± 0.11 for clinoamphibole, 0.27 ± 0.03 for clinopyroxene, 0.29 ± 0.06 for orthopyroxene and 0.30 ± 0.03 for olivine were not included in the thermo-barometry calculations (grey points in Fig. 19 SI). Additional tests accounting for the Ca-Fe- Mg exchanges in pyroxenes have been performed (Fig. 20 SI). For plagioclase feldspars, we used a test for equilibrium by comparing An-Ab exchange. The equilibrium constant is sensitive to T; At T < 1050 C, the value should be about 0.1 ± 0.05, otherwise, it should be 0.27 ± An additional utility for these diagrams is that deviations from equilibrium can be used to explain disequilibrium, as shown by arrows in Fig. 19a SI. For example, if the maximum Mg content (Mg# min ) of a suite of mineral from a given erupted rock were in equilibrium with the whole rock (Mg# liq ), the vertical trend would (as indicated) be consistent with (though not uniquely attributable to) close system differentiation with mineral crystallization (C). Conversely, the horizontal trends would be consistent with open system differentiation, involving either (1) in mafic rocks, an entrainment (E) of more evolved crystals (e,g, Mg and Ca-depleted), likely from previously crystallized deep mush zones, and (2) in silicic rocks, the presence of less evolved crystals (e.g., enriched in Mg and/or Ca), likely derived from mafic magma recharge/mingling (M), into the mid to upper crustal mush zones (Fig. 21 SI)..

24 Figure 19 SI. Tests for equilibrium between mineral (min.) and nominal coexisting liquid (liq.) can be made by comparing observed and predicted values for Fe-Mg exchange. Analyses that are not within one standard deviation of the equilibrium lines (red points) based on the partition coefficient [K D (Fe-Mg) min-liq. ] of 0.27±0.03 for clinopyroxene and 0.29±0.06 for orthopyroxene, 0.28±0.11 for clinoamphibole and 0.30±0.03 for olivine were not included in the thermo-barometry calculations (grey points).

25 Figure 20 SI. (a) Supplementary equilibrium tests for cpx having passed the Kd test (Fig. 6b SI) but yielding negative values (10% of the dataset). Such new tests compare predicted vs. measured DiHd and EnFs values for cpx. Cpx successfully plot in the EnFs discriminant diagram (caption e) but slightly diverge through the DiHd diagram (caption a and b) that accounts for both the Ca, Fe and Mg elements. The most divergent cpx (~5% of the dataset) have been discarded. It mostly concerns the low temperature cpx, stabilized with low Ca content (caption c), whereas their bulk rocks plot in a (comparatively) higher Ca field (caption d). The remaining data (~5% of the dataset) yield negative

26 pressures that do not exceed 2 to -3 kbar. As a rule of thumb (Putirka, pers. com.), any results in this range of negative pressure are possibly OK, and may simply indicate near-1 atm pressures Figure 21 SI. (b) Percentage of crystalline phases (olivine, clinopyroxene, orthopyroxene, plagioclase, amphibole) that are less evolved than their hosts, suggesting recharge. Here, phenocrysts in equilibrium are not considered and data are plotted again the range of magma composition (SiO2 wt%) hosting the crystal cargo

27 532 B - SUPPLEMENTARY TABLES Sup. Table 1 Table 1 SI. Averaged (chemical integrated) composition of equilibrated magma between 700 and 1600 C.

28 Sup. Table 2 Table 2 SI. Physical characteristics (density, viscosity) of equilibrated magma trapped in the mush column, using Bottinga & Weill (1970) and Giordano et al (2008 excel spreadsheet, respectively. Different possibilities have been tested (e.g. dry and hot basalts, wet and hot basalts, cool and wet

29 basalts, cool and dry basalts), depending of the thermal state (hot/cold) of the mush columns and the possibility to evacuate the fluid (H 2 O) trapped in the magma (wet/dry). For active magmatic columns, a temperature of 1200 C at 40 km depth was chosen (Kelemen et al., 2003). For remnant ( dead ) and fully crystallized magmatic columns, a temperature of 400 and 600 C was fixed at 25 and 50 km depth, respectively (McKenzie et al., 2005).

30

31 Sup. Table 3 Table 3 SI. General information (if given) on magmatic minerals stored in Georoc (grainsize, shape, other characteristics). The proportion of core versus rim analysis for each group of mineral (olivine, cpx ) is given.

32 Table 4 SI. (a) Example of rocks erupted from the mushy reservoirs of San Juan Mountains Volcanic Field systems and plotted again the fraction (%) of un-equilibrated mineral they contain. The crystalpoor rhyolites (CRT08-8) are in nearly total equilibrium with their crystal cargo of plagioclase ( An20-30) whereas the intermediate to crystal-rich trachydacites (fiamme and mafic enclaves) are less. Data come from Dorais et al (1991) and Bachmann et al (2014). (b) Other geological examples, showing that the more crystal-rich is a volcanic rock, the less equilibrium conditions are reached between rock and minerals. Such a correlation appears independent of the bulk rock composition (SiO 2 wt%).

33 C - SUPPLEMENTARY REFERENCES Bachmann, O., and Bergantz, G.W., 2004, On the origin of crystal-poor rhyolites: Extracted from batholitic crystal mushes: Journal of Petrology, v. 45, p , doi: /petrology/egh019. Connolly, J. A. D. Computation of phase equilibria by linear programming : A tool for geodynamic modeling and its application to subduction zone decarbonation. Earth Planet. Sci. Lett. 236, (2005). Daly, R.A., 1925, The geology of Ascension Island: American Academy of Arts and Sciences Proceedings, 60, Dorais, M.J., Whitney, J.A. & Stormer, J.C., Mineralogical constraints on thepetrogenesis of trachytic inclusions, Carpenter Ridge Tuff, Central San Juan volcanic field, Colorado. Contrib. Mineral. Petrol, 107, Ganne, J., Feng, X., Rey, P., de Andrade, V., Statistical Petrology Reveals a Link Between Supercontinents Cycle and Mantle Global Climate. American Mineralogist, 101, p Ganne, J., Schellart, W., Rosenbaum, G., Feng, X., de Andrade, V., Probing crustal thickness evolution and geodynamic processes in the past from magma records: An integrated approach. GSA Special Paper, 526 ; doi: / (01) Ganne, J., Feng, X., Primary magmas and mantle temperatures through time. Geochemistry, Geophysics, Geosystems. doi: /2016GC Holland, T. J. B. and Powell, R. An internally consistent thermodynamic data set for phases of petrological interest. Journal of Metamorphic Geology, 16, (1998). Kelemen, P.B. and Behn, M.D.. Formation of lower continental crust by relamination of buoyant arc lavas and plutons. Nat. Geosci., 9, (2016). Keller, C.B. & Schoene, B. Statistical geochemistry reveals disruption in secular lithospheric evolution about 2.5 Gyr ago. Nature 485, (2012).

34 McKenzie, D., Jackson, J., Priestley, K. Thermal structure of oceanic and continental lithosphere. Earth Planet. Sci. Lett. 233, (2005). Mooney, W. D., Laske, G. & Masters, T. G., 1998, CRUST 5.1: A global crustal model at 5 5. Journal of Geophysical Research, v. 103, p Tang, M., Chen, K., Rudnick, R.L. Archean upper crust transition from mafic to felsic marks the onset of plate tectonics. Science, 351, (2016).