The average rate of magma injection into the upper crust controls whether magma will freeze and form plutonic intrusions or whether it will accumulate and form variably large reservoirs that eventually may erupt catastrophically15,48,49. Recent studies have started to include magma injection rates in the formation models of porphyry deposits15,16,42. Intuitively, high magma injection rates favor explosive volcanic eruptions15,48,49 and are detrimental for the formation of porphyry deposits40–42. 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., Yanacocha50). 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 system42. 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.
Zircon age distribution modelling15 and zircon thermometry51 as well as inversion of hydrothermal and magmatic activity ages16 suggest a broad range of > 2 orders of magnitude of average magma injection rates (~ 0.0001-~0.04 km3/yr) potentially associated with the formation of porphyry deposits. Ref. 42 suggests that magma injection rates higher than 1.3x10− 3 km3/yr are necessary to form porphyry deposits. Our results allow us to narrow down the ranges of average upper crust magma injection rates associated with porphyry deposits towards the high value side, and to unveil a relationship between magma injection rates and Cu endowments of porphyry deposits.
Figure 4 shows simulations in magma volume versus magma injection rate space. Also shown are the fields corresponding to large porphyry Cu deposits based on zircon age distribution modelling15, those corresponding to various individual porphyry Cu deposits based on inversion of hydrothermal and magmatic activity ages16, and the field for Bingham inferred from geochemical and thermal modelling of zircons51. Our constrained magma injection rates overlap with the variably broad ranges defined by these previous studies, but further constrain the magma injection rates associated with specific porphyry Cu deposits to narrower ranges, especially trimming out the low magma injection rate side (Fig. 4). Figure 4 further shows that increasing Cu endowments require increasing minimum magma injection rates to transfer increasingly larger amounts of magmas and Cu from the deep accumulation zone to shallower levels within the timescales constrained by geochronology. All simulations for the largest possible Cu endowments (> 100 Mt Cu) require magma injection rates > ~ 0.001 km3/yr (Fig. 4). Additionally, the broadly normal density distributions of the simulations for potential Cu endowment intervals (< 10, 10–30, 30–50, 50–70, 70–100, > 100 Mt; Fig. 5) show that all the Cu endowment intervals > 10 Mt Cu (supergiant porphyry Cu deposits according to the nomenclature of ref. 52) require mode values of magma injection rates larger than 0.001 km3/yr.
It should be further emphasized that, if the 50% precipitation efficiency of Cu is a realistic one43, 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 metals are precipitated within shorter timescales, the transfer rates would be higher than those obtained here. Conversely, for deposits in which there is a higher Cu precipitation efficiency (> 50%), the rates of magma transfer would decrease at equal overall duration of the mineralization. Nonetheless, the broadly linear correlation between Cu endowments and duration of ore deposition for porphyry Cu deposits (Fig. 2) suggests that precipitation efficiencies are probably similar for most porphyry Cu deposits.
Our results show that all deposits fall within magma injection rates between 10− 2.65 and 10− 3.0 km3/yr (i.e., ~ 0.0022 − 0.001 km3/yr; Fig. 6). Interestingly, the higher limit of the magma injection rate interval (~ 10− 2.65 km3/yr) appropriate for the formation of most porphyry Cu deposits, broadly coincides with magma injection rates into the upper crust that may lead to large eruptions15. The lower limit (~ 10− 3 km3/yr) is the same estimated for the highest possible magma injection rates that may result in the build-up of non-eruptible large magma bodies at shallow crustal levels15. However, an important aspect to consider is that there is no fixed threshold of magma injection rate for large eruptions. Protracted magmatic activity results in the long-term modification of the physical properties of the crust and the magma within the plumbing system. For instance, the viscosity of the crust decreases with increasing temperature, and the magma within the plumbing system becomes progressively richer in fluids. Both these phenomena contribute to dampen the pressure developed by magma injection into the shallow portion of the plumbing system49,51,53 thus decreasing the probability of volcanic eruptions to occur and generating conditions that are suitable for the formation of porphyry Cu deposits. Such a scenario is consistent with the long-lived precursor magmatic activity recorded for porphyry Cu deposits for which geochronological data are available (Fig. 1).
We suggest that the efficient transfer to upper crustal depths of large volumes of fluid-rich magma that fractionated in the middle-middle-crust is key for the formation of the largest porphyry Cu deposits. Changing stress conditions in the crust1,54 could be a likely cause of the modulation of magma volume transfer and injection rates into the upper crust, and control the size of porphyry Cu deposits (Figs. 4–6).
The data here presented and discussed imply that all supergiant porphyry Cu deposits (> 10 Mt Cu) are formed by magma volumes31 and average magma injection rates (i.e, > 0.001 km3/yr)15,30 into the upper crust that largely overlap those typically leading to large eruptions, supporting similar conclusions on the formation of the Bingham deposit, for which magma injection rates of ≥ 0.0065 km3/yr, based on thermal and geochemical modelling of zircons51, have been proposed (Fig. 4). Since eruption is obviously detrimental to the formation of porphyry deposits, our results suggest that supergiant porphyry Cu deposits can be considered as failed large eruptions. Our conclusion that high magma injection rates into the upper crust are associated with all supergiant porphyry Cu deposits finds its ultimate explanation in the prolonged magma accumulation occurring at deep crustal levels during long-lived compression, which is an essential condition for the formation of porphyry Cu deposits17. Such accumulation not only builds up enormous amounts of magma, volatile and metal in the deep crust, but is also responsible for the thermal pre-conditioning of the upper crust that prevents eruption of magmas even when magma injection rates at shallow depth are high49.