Introduction

The last decades have seen a continuous increase in the understanding of how porphyry copper deposits form. Several studies have unveiled the different processes that control the formation of porphyry copper deposits, including geodynamic setting, tectonics, magma genesis, magma evolution, and fluid chemistry1,2,3,4,5,6,7,8,9,10,11,12,13,14. Recent work13 has shown that Cu-rich porphyry copper deposits occur in association with syn-subduction calc-alkaline magmas in thick continental arcs. In contrast, Au-rich porphyry copper deposits preferentially occur in association with variably alkaline rocks in complex settings, such as post-subduction in continental and thinner island arcs. In this study we focus exclusively on the syn-subduction Cu-rich porphyry copper deposit type (hereafter referred to as porphyry copper deposits), occurring in thick continental arcs.

Recent efforts have been directed towards a physical understanding of the processes leading to the formation of porphyry copper deposits through thermodynamic and petrologic modelling15,16,17,18. Simple mass balance constraints are useful to set quantitative boundaries within which various processes interact to form porphyry copper deposits. Arc magmas are characterized by a narrow range of Cu contents19,20 and fluid-melt partition coefficients for Cu are also limited to a relatively restricted range21. Thus, purely from mass balance considerations, the main parameter determining the size of a porphyry copper deposit (considering similar precipitation efficiencies from the hydrothermal fluid22) is the mass of fluid, which, in turn, is closely associated with the mass of degassing magma16,17. The model17 uses the Cu concentrations of magmas in thick (>30 km) arcs as constrained by several thousands of analyses on recent arcs20. Magmas in thick arcs undergo a continuous depletion during crustal differentiation, and intermediate to felsic magmas, typically associated with porphyry copper deposits, contain 20–50 ppm Cu17. Therefore, in order to form supergiant porphyry copper deposits the relatively low Cu contents of thick arc magmas need to be compensated by large volumes of magma accumulated in the mid- to lower crust17 (depths >15 km; Fig. 1). The resulting model17 is consistent with trace element geochemistry (e.g., Sr/Y), timescales of magmatic processes associated with porphyry copper deposits (long precursor magmatic activity in the mid- to lower crust), and volumes of magma associated with mineralization inferred from fluid inclusion chemistry and geophysical constraints23. Other models advocate the need of Cu-rich magmas24, but the lack of a systematic record of Cu enrichment in thick arc magmas20, while not excluding it, make this process less likely. Recycling of Cu-sulphides9 is also possible, but sulfide pre-concentrations would require extraction of Cu from large amounts of low-Cu thick arc magma, falling back in the model of17.

Fig. 1: Transcrustal magmatic systems associated with porphyry copper deposits and with large eruptions.
figure 1

a Transcrustal magmatic systems associated with porphyry copper deposits. b Transcrustal magmatic systems associated with large eruptions. The sketch highlights the similarities between the two systems and is inspired from sketches of previous works17,33,35,64,69. The ~40 km depth is indicative and used for consistency with the model which is run for a maximum pressure of 1.2 GPa.

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However, the accumulation of large magma volumes at mid- to lower crust depths (Fig. 1) does not guarantee the formation of a porphyry copper deposit. This is confirmed by the absence of a relationship between the duration of magma accumulation at mid- to lower crustal levels25,26,27,28 and the Cu endowments of porphyry copper deposits (Fig. 2).

Fig. 2: Cu endowments (Mt) versus duration of magma injection into the crust.
figure 2

Plot showing Cu endowments (Mt) versus duration of magma injection into the crust (Myr). Colored dots are 50% precipitation efficiency simulations from17 and different colors indicate the volumes of the magma accumulated as specified in the legend. The black dots are porphyry copper deposits for which data are available for Cu endowments and duration of magmatic activity13,17 (Supplementary Data 1). Ay Antapaccay, Ch Chaucha, Chu Chuquicamata, Cc Coroccohuayco, Es Escondida, EA El Abra, ES El Salvador, ET El Teniente, Ju Junin, LP Los Pelambres, Qv Quellaveco, RB Rio Blanco, Tk Tampakan.

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Magmas in the mid- to lower crust are mostly H2O-undersaturated, because of the strong pressure dependency of H2O solubility in silicate melts29. The exsolution of mineralising fluids requires magma ascent to upper crustal levels, in the so-called parental magma reservoir22,30 (~5–15 km depth; Fig. 1), which feeds the porphyry apophyses around which mineralization commonly occurs at depths < ~6 km (Fig. 1).

Despite more high-precision and accurate geochronological data are needed, a broad correlation13,16,17,31 suggests that a longer period of the overall ore-forming process will result in a larger Cu endowment of the deposit (Fig. 3). In particular, it is recognized that the largest porphyry copper deposits (>~40 Mt Cu) are formed by superposition of repeated magmatic-hydrothermal events over time spans of up to >1 Myr13 (Fig. 3). Therefore, ultimately the endowments of porphyry copper deposits depend on the efficiency of transfer of the largest possible magma volumes from the mid- to lower crust into the shallow parental magma reservoir feeding the porphyry apophyses around which ore deposition occurs (Fig. 1).

Fig. 3: Relationship between the overall duration of ore period and Cu endowments.
figure 3

Plot showing the relationship between the overall duration of the ore period (Myr) and Cu endowments (Mt) of porphyry copper deposits. The data from porphyry copper deposits (Cu Mt, ore durations and associated 1 SD uncertainty bars) are from Supplementary Data 1. Overall durations of the ore periods are the calculated differences between the oldest and youngest ages of recorded magmatic-hydrothermal mineralizing events with their propagated uncertainties where uncertainties on the above ages are available. The equation reported is the best-fit linear regression between the two variables with associated uncertainties for the slope and intercept.

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Here, we show that Cu endowments of porphyry copper deposits increase with volumes and rates of magma transfer from the mid- to lower-crust into the shallow parental magma reservoir. The largest porphyry copper deposits require magma volumes (from several hundreds to a few thousands km3) and injection rates into the upper crustal parental magma reservoir (>0.001 km3 yr−1) that are similar to those leading to large eruptions in rift-, hot-spot, and subduction-related settings15,32,33,34,35 (Fig. 1). Because volcanic eruptions are detrimental for magmatic-hydrothermal systems, as they would either destroy them or prevent their formation36,37,38, the largest porphyry copper deposits can be considered failed large eruptions.

Results and discussion

Model rationale and constraints

We used two simple constraints to obtain average magma injection rates from the mid- to lower crust accumulation zone into the upper crustal magma reservoir above which mineralization takes place (Fig. 1): (i) the volume of magma required to precipitate a specific Cu mass, with a conservative precipitation efficiency of 50%22; (ii) the time interval within which such magma volume is transferred from the mid- to lower crust accumulation zone (i.e., >~15 km depth) into the upper crust (i.e., 5–15 km depth) where Cu is precipitated. The ratio between these two parameters gives the average magma injection rate corresponding to a specific Cu endowment.

Magma volume and Cu endowments

Point (i) above is constrained by the relationship between potential Cu endowments of transcrustal magmatic systems and the volume (mass) of magma accumulated in the mid- to lower crust13,17 (Methods and Table 1). Modelling17 indicates that the largest potential Cu endowments are associated with magma accumulations occurring at pressures greater than 0.4 GPa (>~14 km depth) and for injection periods longer than 2.5–3.0 Myr.

Table 1 Constraints on the parameters used in the Monte Carlo modelling of magma injection rates.
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The magmas accumulated at pressures greater than 0.4 GPa and up to 1.2 GPa (the maximum pressure modelled: Table 1) are characterized by relatively high H2O contents (mostly in the range 6–12 wt.%), yet they are mostly H2O-undersaturated at depths >0.4 GPa because of the strong pressure dependence of H2O solubility in silicate melts29. These magmas can release fluids and potentially lead to the formation of porphyry copper deposits only if they ascend to depths at which they become H2O-saturated, i.e., between ~8 and 17 km17, which overlaps with the depth (5–15 km) of the parental magma reservoir22,30. Fluid saturation would be achieved at greater depths if magma also contained CO229; however, early exsolved fluids would be CO2-rich39 and represent a small contribution to the total mass of fluid released29. For these reasons, in our calculations we simplistically consider that magmas contain exclusively H2O and that the volumes of magma generated in the mid- to lower crust (0.4–1.2 GPa), which determine the maximum potential Cu endowment of the porphyry deposits17, are transferred up to their H2O saturation depth interval, corresponding to the parental magma reservoir (Fig. 1). There, we consider that magmas release the entire amount of H2O (and associated Cu through the random range, 2–100, of KD values used in the model: Table 1), i.e., we consider that all H2O is exsolved because of decompression and isobaric crystallization. This results in a slight overestimation of the exsolved H2O since intermediate-felsic plutonic rocks may retain some H2O in the form of hydrated minerals like amphibole and biotite. Such overestimation is largely compensated by the conservative 50% precipitation efficiency of Cu used in the model.

Figure 4 shows the expected broad positive correlation between potential Cu endowments and calculated magma volumes accumulated at mid- to lower crustal levels (i.e., at pressures between 0.4 and 1.2 GPa). The range of variable Cu endowments associated with a specific magma volume depends on: (1) the different depths at which magmas can accumulate in the model (0.4–1.2 GPa), which in turn controls the fluid content of the residual melt; (2) the different durations of magma injections (0–5 Myr), and, to a lesser extent, the range of KD fluid-melt values for Cu used in the model (2–100). Since more than 95% of the simulations fall within the two exponential curves of Fig. 4, we have modelled the magma injection rates for the transfer of the magma volumes to the shallow crust comprised within these two curves (Table 1 and Methods). Figure 4 shows that the largest potential Cu endowments (>~20 and up to a maximum of 150 Mt Cu in the model, for a 50% precipitation efficiency) are associated with volumes of magma accumulated in the mid- to lower crust of >500 and up to ~2500  km3. These magma volumes are of the same order of magnitude as those explosively ejected by supereruptions35.

Fig. 4: Plot of magma volumes versus potential Cu endowments.
figure 4

Plot of magma volumes versus potential Cu endowments at 50% precipitation efficiency for magmatic systems accumulated at depths corresponding to pressures of 0.4–1.2 GPa. Over 10000 simulations are reported from the algorithm of13,17. Density distribution is shown on top of the data as different color shades. More than 95% of the simulations fall within the two exponential curves, as discussed in the Methods and Table 1.

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Duration of ore deposition events

The second constraint of the model (ii) is provided by available geochronological data on the overall duration of ore deposition. Geochronological data indicate that the overall ore deposition durations in the largest porphyry deposits are < ~2 Myr (e.g., Chuquicamata 106 Mt Cu, 1.3 ± 0.36 Myr40,41; El Teniente, 130 Mt Cu, 1.88 ± 0.04 Myr42,43; Rio Blanco, 100.4 Mt Cu, 1.4 ± 0.04 Myr44; Fig. 3). This translates into average Cu deposition rates at these deposits of 74 ± 7 Cu tonnes yr−1. Taking into account all major porphyry copper deposits with available geochronological estimation of ore deposition duration13, the average rate of Cu deposition for all these deposits is 65 ± 7 Cu tonnes yr−1 (Fig. 3). We reasonably assume that the overall duration of the mineralizing events constrains the duration of the magma injection from the mid- to lower crust into the upper crust (Methods). In order to comply with the above figures, in our model we have taken as a maximum temporal limit a duration of 2.0 Myr for the transfer into the upper crust of the magma volumes associated with deposition of up to 150 Mt Cu at 50% efficiency.

Magma injection rates

Models based on geological cross-cutting relationships45,46, geochronology47,48,49,50, geospeedometry based on element diffusion31, and thermodynamic51 as well as numerical modelling52 suggest that porphyry copper deposits are formed by multi-step magmatic-hydrothermal pulses, reflecting a variable number of magmatic intrusions and fluid release cycles. High-precision dating of both hydrothermal (e.g., molybdenite Re-Os dating) and magmatic activity (U-Pb dating of zircons) suggests that the duration of each pulse may be as short as a few tens of thousands or even a few thousands of years47,48,49,50,53. These results are corroborated also by Ti diffusion in hydrothermal quartz, which indicates timescales of single pulses of magmatic-hydrothermal activity as short as a few thousands of years or even less31. Recent studies on Ti-in-quartz diffusivity54,55 suggest slower Ti diffusion rates in quartz (up to two orders of magnitude less than those taken into account by31). These would result in longer durations of single hydrothermal pulses, which, nonetheless, remain on the order of tens to hundreds of thousand years. Thermodynamic and numerical modelling agrees with timescales determined for individual magmatic-hydrothermal pulses as well51,52.

We allow a random range of 5–20 pulses to inject, from the mid- to lower-crust into the upper crust parental reservoir, the magma volume required for the deposition of a specific amount of Cu (Fig. 4). We vary randomly the duration of the single magma pulse transfer events between 2000 and 100000 years to comply with the available geochronological data discussed above.

The transfer of the magma volume corresponding to a specific Cu endowment from the mid- to lower crust to the parental magma reservoir is accomplished through random combinations of fixed magma volume pulses and fixed durations of the magma pulse within the combination of 2000–100000 years pulse duration and 5–20 number of pulses, corresponding to a maximum possible duration of 2.0 Myr and a minimum of 10000 years. It follows that each simulation represents an average magma injection rate that results in the transfer of a specific magma volume and associated Cu endowment from the deep accumulation zone to the shallow crustal reservoir (Fig. 1). Five hundred thousand simulations were performed (Table 1) using the RStudio script56 provided in the Supplementary Note 1.

Magma injection rates in supergiant porphyry copper deposits

The average rate of magma injection into the upper crust controls whether magma will rapidly cool and form plutonic intrusions or whether it will accumulate and form variably large reservoirs that eventually may erupt catastrophically15,32,57,58. Recent studies have started to include magma injection rates in the formation models of porphyry deposits15,16,38. Intuitively, high magma injection rates favor explosive volcanic eruptions15,32,57,58 and are detrimental for the formation of porphyry deposits36,37,38. This is supported by the occurrence of porphyry-type deposits at the end of variably long periods of precursor volcanic activity and coinciding with periods characterized by the lack of or by very low volcanic activity (e.g., Yanacocha59). In contrast, magma injection rates that allow the accumulation of magma at shallow levels without its eruption may eventually result in a magmatic system exsolving fluids and generating a mineralized magmatic-hydrothermal system38. However, there are no studies that have addressed, quantitatively and on a global scale, how and if different rates of magma injection, encompassing the broad range below the threshold of those leading to eruption, control the formation and size of porphyry deposits.

Figure 5 shows simulations of magma volume versus magma injection rate. Also shown are the fields corresponding to large porphyry copper deposits based on zircon age distribution modelling15, those corresponding to various individual porphyry copper deposits based on combination of hydrothermal and magmatic activity durations16, and the field for the Bingham Canyon porphyry deposit, as inferred from geochemical and thermal modelling of zircons60. Our constrained magma injection rates overlap with the variably broad ranges defined by these previous studies (~0.0001–0.04 km3 yr−1), but further constrain the magma injection rates associated with specific porphyry copper deposits, excluding lower magma injection rates (Fig. 5). Figure 5 further shows that larger Cu endowments require larger minimum magma injection rates to transfer increasingly larger amounts of magmas and Cu from the mid- to lower crust accumulation zone to the shallow parental reservoir within the timescales constrained by geochronology. All simulations for the largest possible Cu endowments (>100 Mt Cu) require magma injection rates higher than ~0.001 km3 yr−1 (Fig. 5). Additionally, the broadly normal density distributions of the simulations for various Cu endowment intervals (<10, 10–30, 30–50, 50–70, 70–100, >100 Mt; Supplementary Fig. 1) show that all the Cu endowment intervals >10 Mt Cu (supergiant porphyry copper deposits according to the nomenclature of61) require mode values of magma injection rates, i.e., the statistically most recurrent value in our simulations, higher than 0.001 km3 yr−1. For instance, the mode value of magma injection rates for porphyry copper deposits with >100 Mt Cu is >0.003 km3 yr−1 (Supplementary Fig. 1).

Fig. 5: Monte Carlo simulations of magma volumes versus injection rates.
figure 5

Monte Carlo simulations of magma volumes versus injection rates subdivided by color codes indicating different intervals of potential Cu endowments. The blue fields and associated blue labels correspond to individual porphyry copper deposits from combination of hydrothermal and magmatic activity ages of the deposits16, the field enclosed by the blue dashed line is the field of large porphyry copper deposits (PCD) based on zircon age distribution modelling15, and the Bingham Canyon (Bh) value is inferred from geochemical and thermal modelling of zircons60. The black bars (and associated black labels) correspond to the magma volumes and magma injection rate intervals constrained by the present study on the basis of Monte Carlo simulations for the same individual deposits of16,60. Es Escondida, ET El Teniente, Gr Grasberg, LP Los Pelambres, RB Rio Blanco, RD Reko Diq.

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The rates of magma transfer to the upper crust obtained here are minimum values, because the overall ore deposit durations considered are maximum values, bracketing the beginning and end of the mineralizing process. If, within these temporal intervals, most of the copper is precipitated within shorter timescales, the magma injection rates would be higher than those obtained here. Conversely, the rates of magma transfer would decrease, at equal overall duration of the mineralization, for deposits with a higher Cu precipitation efficiency than the one used here (50%)22. Nonetheless, the broadly linear correlation between Cu endowments and duration of ore deposition for porphyry copper deposits (Fig. 3) suggests that precipitation efficiencies are probably similar for most porphyry copper deposits.

Also in the ore duration versus Cu endowment space (Fig. 6) our results show that all porphyry copper deposits require magma injection rates >0.0010 and up to at least ~0.0022 km3 yr−1 (i.e., 10−3.0 and 10−2.65 km3 yr−1, respectively, in Fig. 6). This is in agreement with recent work38, suggesting that magma injection rates higher than 0.0013 km3 yr−1 are necessary to form porphyry copper deposits. The minimum upper limit of the magma injection rate interval (~0.0022, i.e., 10−2.65 km3 yr−1), appropriate for the formation of most porphyry copper deposits according to our simulations, falls in the range of magma injection rates into the upper crust that lead to large eruptions15,32,33,34. The lower limit (~0.001 km3 yr−1) corresponds to the highest possible magma injection rates that may result in the build-up of non-eruptible (i.e., plutonic) magma bodies at upper crustal levels15. However, an important aspect to consider is that there is no fixed threshold of magma injection rate known for large eruptions58. Protracted magmatic activity results in the long-term modification of the physical properties of the crust and of the magma within the plumbing system58. For instance, the viscosity of the crust decreases with increasing temperature, and the magma within the plumbing system becomes progressively richer in excess fluids. Both these phenomena contribute to dampen the pressure developed by magma injection into the shallow portion of the plumbing system58,60,62 thus decreasing the probability of volcanic eruptions58. This process could generate conditions that are suitable for the formation of porphyry copper deposits even under high magma injection rates into the upper crust that have been commonly associated with large eruptions.

Fig. 6: Monte Carlo simulations of duration of ore deposition versus Cu endowments.
figure 6

Monte Carlo simulations of duration of ore deposition (which also correspond to duration of magma injection into the upper crust) versus Cu endowments subdivided by color codes indicating different intervals of magma injection rates. The plot shows that all deposits fall within the interval of magma injection rates (~−3 < log10[magma injection rate] <~−2.65) potentially corresponding to large eruptions. The data from porphyry copper deposits (Cu Mt, ore durations and associated 1 SD uncertainty bars) are available in Supplementary Data 1. Overall durations of the ore periods are the calculated differences between the oldest and youngest ages of recorded magmatic-hydrothermal mineralizing events with their propagated uncertainties where uncertainties on the above ages are available.

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Our data imply that all supergiant porphyry copper deposits (>10 Mt Cu) are formed by the efficient transfer to upper crustal depths of large magma volumes from the mid- to lower crust33 with average magma injection rates (i.e, >0.001 km3 yr−1)15,32 that overlap those typically leading to large eruptions15,32,33,34. Our data support similar conclusions on the formation of the Bingham Canyon deposit, for which magma injection rates of ≥0.0065 km3 yr−1, based on thermal and geochemical modelling of zircons60, have been proposed (Fig. 5). Since eruption is obviously detrimental to the formation of porphyry copper deposits, our results suggest that supergiant porphyry copper deposits can be considered as failed large eruptions.

Implications for the exploration of supergiant porphyry copper deposits

The above conclusion may have implications on exploration strategies for supergiant (>10 Mt Cu) porphyry copper deposits, both at the field mapping level and concerning the use of rock and mineral fertility tracers. From a field mapping perspective, it has long been recognized that recent caldera structures and associated large ignimbrite deposits are unfavorable to the formation of porphyry copper deposits36, albeit post-caldera magmatic activity may still lead to relatively small mineralization63. Conversely, volcanic centers (even old calderas) that, in conjunction with geochronology, are demonstrably characterized by protracted magma input during several Myr may be suitable target areas. In fact, they could correspond to the build-up of a large magma reservoir in the upper crust that, under the high magma injection rates discussed above and if accompanied by only small erupted magma volumes, could become the parental reservoir of a supergiant deposit. For instance, the >50 Moz Au high-sulfidation epithermal deposit of Yanacocha and the deeper Kupfertal Cu-Au porphyry are associated with eruption of only ~88 km3 of volcanic material over a ~6 Myr period59, which corresponds to a very low average 0.000014 km3 yr−1 eruption rate, almost 2 orders of magnitude less than long-term average magma fluxes in arcs64. On the basis of what discussed above, we speculate that old calderas, which inherently witness high magma injection rates, with superimposed long-lived stratovolcanoes characterized by average to low eruption rates could be a potential target for supergiant porphyry copper exploration.

Our results may have implications also on the use of rock and mineral geochemical fertility indicators. In fact, we have shown that both large eruptions and supergiant porphyry copper deposits require the accumulation of similar large magma volumes (from several hundreds to >1000 km3) in the upper crust under high magma injection rates (see above and Fig. 1). Recent work suggests that, similarly to porphyry copper deposits, silicic melt segregation from a mid- to lower crustal zone is a pre-requisite for large eruptions65 (Fig. 1). All the above points imply broadly similar conditions of magma evolution and storage in the transcrustal magmatic systems leading either to supergiant porphyry copper deposits or to large eruptions, as highlighted in Fig. 1. These magma storage and evolution conditions can be captured by geochemical bulk rock and mineral tracers. Zircon is a particularly powerful tool to decipher physical and chemical magma storage and evolution conditions (e.g., fractionation of pressure-, temperature-, and composition-sensitive minerals, oxygen fugacity) in transcrustal systems and is extensively used as an exploration tool to recognize fertile magmatic systems associated with porphyry copper deposits66. Without entering into the details of the meaning of zircon fertility tracers, which is beyond the scope of this study, it is noteworthy that geochemical fertility indices of zircons from subduction-related large eruptions overlap with those of zircons from mineralized porphyry copper deposits (Fig. 7). This supports similar magmatic storage and evolution conditions for porphyry copper deposits and large eruptions (Fig. 1). In contrast, zircons from large eruptions in subduction-unrelated settings display distinct trace element signatures (e.g., Bishop Tuff, rift-related Fig. 7), probably as the result of a range of different magma storage and evolution conditions leading to large eruptions33. We suggest that improved understanding and further development of petrochronological tracers, able to trace the physico-chemical evolution of transcrustal magmatic systems, may be the key to an improved strategy for the exploration of supergiant porphyry copper deposits.

Fig. 7: Trace element plots of zircons from eruptive centers and porphyry copper deposits.
figure 7

Trace element plots of zircons (a Eu/Eu*-Log10(Ce/Nd); b Eu/Eu*-Log10[(Ce/Nd)/Y]; c 10000*Log10[(Eu/Eu*)/Y]-Log10(Ce/Nd)) from eruptive centers of different geodynamic settings (rift: Bishop Tuff; subduction-related: Lassen Peak, Fish Canyon Tuff, FCT, Kneeling Nun Tuff) compared to the field of zircons associated with porphyry copper deposits and the high-sulfidation epithermal deposit of Yanacocha. The division lines within the plots are from66. The porphyry copper deposit field includes zircons from mineralized porphyry intrusions at Butte, Chuquicamata, Escondida, Esperanza, El Salvador, El Teniente, Mirador, Oyu Tolgoi, Yanacocha, and Yerington. Data used in the plot are reported in the Supplementary Data 2.

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We argue that the unique association of porphyry copper deposits with the arc environment is the result of a self-constrained process, whereby the arc environment reunites all the geodynamic (subduction-related changes in the overriding plate stress regime1,67), crustal architecture (crust thickness, transcrustal tectonic structures), and geochemical requirements (high H2O, Cl, S contents of the parental basalts) that favor mineralization. In addition, we also argue that the combination of high magma injection rates, required to form supergiant porphyry copper deposits (this study), thermal pre-conditioning of the crust58, and high compressibility of hydrous magmas in the upper crust (all factors contributing to decrease the likelihood of large eruptions to occur even with high magma injection rates) are optimized in the arc environment. This is due to the hydrous nature of arc magmas and to the peculiar occurrence of long periods of compression in the overriding plate in the syn-subduction setting, different from other settings (e.g., rifting, hot-spot) where the largest eruptions occur33. Secular changes of the compressive stress field in the thick crust of the overriding plate1,67, associated with large geodynamic processes5, could modulate thermal pre-conditioning of the crust, magma volume transfer and injection rates into the upper crust, that ultimately lead either to the formation of supergiant porphyry copper deposits or to large eruptions.

Methods

Monte Carlo modelling (500000 simulations) was carried out using previous conceptual frameworks13,17.

The starting point of the model is the covariation between potential Cu endowments of magmatic systems (at 50% precipitation efficiency) and magma volumes for the potentially most productive magmatic systems13,17, i.e., those accumulated in the mid- to lower crust (Fig. 1), at pressures of 0.4–1.2 GPa (Fig. 4). Compared to previous works13,17, where the maximum pressure of magma accumulation was 0.9 GPa, we extended the upper pressure limit to 1.2 GPa. Figure 4 shows >10000 simulations and their density distribution. More than 95% of the simulations fall within the two curves of Fig. 4, which are reproduced mathematically by exponential equations of the type

$${{{{{\rm{MLC}}}}}}\_{{{{{\rm{magmaVol}}}}}}=a\ast {{{{{{\rm{MtCu}}}}}}}^{b}$$
(1)

where parameter “a” ranges randomly between 60 and 700, parameter “b” is defined by the equation

$$b=-0.187767\ast \,{{{{\mathrm{ln}}}}}(a)+1.507068$$
(2)

MLC_magmaVol is the mid- to lower crust magma volume corresponding to a specific Cu endowment (within the random range above 0–150 Mt Cu), and “MtCu” is the Cu endowment (at 50% precipitation efficiency) that is allowed to vary randomly between 0 and 150 Mt Cu (Table 1).

Because the longest durations of ore precipitations associated with the largest porphyry copper deposits (i.e., El Teniente 130 Mt Cu, Chuquicamata 106 Mt Cu, Rio Blanco 101 Mt Cu: data from USGS at https://mrdata.usgs.gov/porcu/) are <2.0 Myr13,17, we have allowed a maximum time of 2 Myr for the transfer of all magma volumes (including those associated with the maximum potential Cu endowments of 150 Mt Cu) from the mid- to lower crust into the shallow reservoir where fluids exsolve and precipitate Cu with a 50% efficiency (Fig. 1).

Additionally, because geological and geochronological evidences indicate that porphyry copper deposits are formed by repeated magmatic-hydrothermal pulses with durations of few to several tens of kyr, we have allowed magma volume transfer from the mid- to lower crust into the upper crust to occur within any random combination of 5–20 magmatic pulses, each one varying randomly between 2000 and 100000 years. This means that in our model the transfer of any magma volume from the mid- to lower crust into the upper crust can occur from a minimum of 10000 years (5 pulses with a 2000 years duration of each pulse) to a maximum of 2 Myr (20 pulses with a 100000 years duration of each pulse). This random temporal variability for the transfer of any magma volume defined by Eq. (1) above translates into broadly different average magma injection rates that are plotted in Figs. 5, 6.

The volume of each magma pulse is calculated as the ratio between the accumulated magma volume in the mid- to lower crust, that corresponds to a specific Cu endowment and must be transferred to the upper crust to exsolve fluids and Cu, and the random number of pulses (5–20) through which the deep accumulated volume is transferred. Average magma injection rates from the mid- to lower crust into the upper crust are then calculated as the ratios between the volume of the magma pulses and the random durations of each pulse in the interval 2000–100000 years that, incrementally (through the random number of pulses), results in the transfer of the overall magma volume associated with a certain Cu endowment (for 50% precipitation efficiency).

The duration of the injection of magma from the mid- to lower crust into the upper crust (which corresponds to the duration of the ore deposition event, since we assume that each pulse results in an “instantaneous” hydrothermal event) is given by the product of the random number of pulses (5–20) and the random duration of pulses (2000–100000 years).

The full RStudio56 script of the Monte Carlo modelling is provided in the Supplementary Note 1.