Igneous bodies are built incrementally by episodic magma injection events that vary in rate and duration. Such recharge events can either grow an upper crustal magma reservoir or trigger an eruption. This bifurcation in behavior remains poorly constrained but is essential to volcanic hazard assessment. Here we use a numerical model that couples the thermal and mechanical processes in a magma reservoir to study the evolution of the Santorini magmatic system (Greece) over the past 20 k.y. Our results constrain the recharge rate and duration that are necessary to trigger an eruption for the known long-term average inflow rate of 10−3 km3/yr. The size of the chamber and its exsolved volatile content are dominant controls on the critical recharge rate and duration that will trigger an eruption. Our model successfully reproduces the main features of the Minoan eruption and Nea Kameni activity, providing volume estimates for the active part of the current subvolcanic reservoir as well as information regarding the presence of exsolved volatiles. Thermomechanical models offer a new framework to integrate the historic eruption record with geodetic measurements and provide a context to understand the past, present, and future of active volcanic centers.
Magma reservoirs within the shallow crust (<10 km) underlie most active volcanic systems. Such reservoirs are built incrementally by injections of magma from below (recharge events) that vary in size and frequency (e.g., Schöpa and Annen, 2013). In this study, we distinguish between the magma chamber, which we define as the volume of magma that is mobile, and the magma reservoir, which accounts for the whole magmatic system. In many instances, volcanic eruptions are preceded by a recharge event, and petrological data typically show (1) evidence for a rapid inflow of less-evolved magma that promotes reheating prior to the eruption, and (2) that the recharge event contributes only a fraction to the total volume erupted (Wark et al., 2007; Martin et al., 2008; Druitt et al., 2012). These lines of evidence suggest an existing reservoir prior to magma intrusion. Many geodetic observations at active volcanic centers indicate that recharge events can also occur without triggering an eruption (Moran et al., 2011; Biggs et al., 2014). Therefore, it is paramount to assess when a recharge event will generate enough overpressure in the chamber to cause an eruption.
Observations at Santorini
The combination of a well-documented historical eruption record, geophysical data sets for episodes of unrest, and published petrological data from past eruptions make Santorini volcano (Greece) an ideal case to establish a relationship between recharge events and the triggering of eruptions over multiple recharge cycles. The 1600 B.C. Minoan eruption ejected a volume of 40–80 km3 dense-rock equivalent (DRE) (Sigurdsson et al., 2006; Johnston et al., 2014). The majority of this volume (∼85%–93%) was emplaced in the reservoir over the course of 18 k.y. and thus implies a long-term average inflow rate on the order of ∼10−3 km3/yr (Druitt et al., 2012). Diffusion time scales from trace element zoning in plagioclase suggest that a dacitic recharge event started 10–100 yr prior to the Minoan eruption, reheating the rhyolitic magma (Druitt et al., 2012). This recharge is inferred to have amounted to ∼7%–15% of the total erupted volume based on crystal and chemical mass balance, implying a recharge rate >5 × 10−2 km3/yr (Druitt et al., 2012).
Observations of the post-Minoan eruptions at Santorini suggest a similar long-term average inflow rate of ∼10−3 km3/yr over the last 3600 yr, with periods of quiescence interrupted by episodic recharge events that in some cases were followed by an eruption (Martin et al., 2008; Newman et al., 2012; Parks et al., 2012; Nomikou et al.; 2014; Johnston et al., 2015). Six eruptions occurred at the Nea Kameni island over the past 450 yr, i.e., roughly one per century. The erupted volumes are small, with estimates between 0.02 km3 and 0.1 km3. These products are dacitic in composition and contain <1% of mafic enclaves (Martin et al., 2006). Diffusion profiles in olivine crystals, found in the eruptive products of the A.D. 1925–1928 eruptive cycle, suggest that a hotter, more mafic magma intruded ∼1 month prior to eruption (Martin et al., 2008). Geodetic and gas geochemistry measurements during the unrest in A.D. 2011–2012 record the arrival of a magma with a volume of ∼0.01 km3 from below that stalled at a depth between 3 and 6 km (giving a recharge rate of ∼10−2 km3/yr; Newman et al., 2012; Parks et al., 2012; Rizzo et al., 2015). This recharge event was not followed by an eruption.
Thermal and Mechanical Models
Numerical modeling is a powerful approach to explore thermomechanical feedbacks in magma reservoirs (e.g., Annen, 2009; Karlstrom et al., 2010), but can produce contradictory results when thermal and mechanical processes are considered in isolation. Thermal models examine the competition between magma emplacement and heat loss in the crust. When the energy injected by magma recharge outpaces the loss of heat into the crust, a volume of mobile magma can form and potentially erupt. The long-term average rate of injection at which magma reservoirs can form depends on emplacement geometry, magma and crust composition, as well as tectonic environment. Recent modeling suggests that when magma injection rates of 10−4 km3/yr to 10−2 km3/yr are exceeded, pockets of mobile magma can form (Annen, 2009; Gelman et al., 2013; Karakas and Dufek, 2015).
Magma recharge events are transient and impact the mass and energy balance within the reservoir. The dynamical processes that are caused by these recharge events span a wide range of time scales, from the near-instantaneous elastic response of the crust to the much slower cooling of the reservoir. In this context, thermal models operate as low-pass filters, in that they ignore processes with time scales shorter than the cooling time scale (see the GSA Data Repository1). As such, they do not capture several crucial aspects of the mechanical evolution of reservoirs following recharge events, which in turn influence the reservoirs’ stability and long-term thermal evolution (Jellinek and DePaolo, 2003; Karlstrom et al., 2010). In particular, recharge rates are much more rapid than the long-term average inflow rate (Schöpa and Annen, 2013) and can lead to pressurization of the magma chamber, ultimately triggering the nucleation and propagation of dikes, and possibly an eruption (Jellinek and DePaolo, 2003).
The growth of a magma body is promoted when viscous relaxation of the crust operates at a comparable time scale as the recharge rate, such that the production of dikes is suppressed (Jellinek and DePaolo, 2003). As a result, only chambers that already have a significant volume can support high recharge rates without erupting. Previous scaling arguments show that a chamber of initial volume, V0, can only support recharge rates, in, without erupting below approximately in ∼ V0 (ΔP)c/ηr, where ηr is the effective crustal viscosity and (ΔP)c is the critical overpressure necessary to nucleate a dike (Jellinek and DePaolo, 2003). For example, a chamber with 100 km3 of magma can only support a recharge rate below ∼10−2 km3/yr without erupting [using ηr = 1019 Pa·s and (ΔP)c = 40 MPa]. This argument demonstrates that large magma reservoirs cannot form on the time scale of a single recharge event (Schöpa and Annen, 2013) because these systems would erupt before building up any significant volume. Therefore, the thermal and mechanical evolution of magma reservoirs should be considered simultaneously.
We have adapted the numerical model of Degruyter and Huber (2014) that couples both thermal and mechanical processes related to the formation of a subvolcanic magma reservoir to explore the effects of episodic recharge events (see the Data Repository). We account for the evolution of pressure, temperature, chamber volume, phase volume fractions, densities, and water content by solving the conservation of mass, water, and energy in combination with closure equations for melting and exsolution. Our model assumes that the chamber sits in a viscoelastic crustal shell to which it loses heat. The crustal shell can be seen as a continuum between a mush zone near the chamber and the preexisting crust in the far field. Mass withdrawal from the chamber occurs when a critical overpressure of a few tens of megapascals is reached (here we use 40 MPa; Jellinek and DePaolo, 2003) and the average crystallinity of the magma remains below a critical value of 0.5 (Lejeune and Richet, 1995). We explore a range of recharge durations, τd, and recharge frequencies, fp, for a fixed long-term average inflow rate av = 10−3 km3/yr observed at Santorini and a typical value for silicic systems (White et al., 2006; Fig. DR3 in the Data Repository). We vary: (1) the recharge frequency fp between 10/τcool and 1000/τcool (τcool is the characteristic cooling time scale; see the Data Repository); (2) the recharge duration, by varying the product τdfp between 0.01 and 1; (3) the initial volume, V0, of the magma chamber between 10 km3 and 100 km3; and (4) conditions where the magma either does or does not contain exsolved volatiles.
Our modeling results show that an eruption will occur if the following conditions are met. First, the magma must remain mobile, i.e., the frequency of injections needs to outpace the rate of cooling (1/fp < τcool). Note that this is the only condition tested with purely thermal models (Annen, 2009; Gelman et al., 2013), and thus these are likely to provide an incomplete description of the behavior of the system. A second critical condition is that the overpressure cannot be dissipated by viscous relaxation, i.e., the inflow rate of the magma is faster than the accommodation of stresses by creep in the surrounding crust (Jellinek and DePaolo, 2003; τrelax > τinflow; see the Data Repository). The third condition is that a sufficient volume of magma is added to the chamber such that the overpressure can reach a critical value and dikes can nucleate out of the chamber [inτd/V0 > (ΔP)c, with the effective bulk modulus of the magma]. As a consequence, for a similar long-term average inflow rate, recharge events with slow inflow rate or short durations will lead to growth of the magma chamber (Figs. 1A and 2), while rapid, voluminous recharges will favor dike propagation and associated cooling of the remaining magma body (Figs. 1A and 2). Additionally, when the dike is created, it needs to reach the surface in order to produce an eruption. To do so, a dike must not freeze, must be voluminous enough, and must not encounter a thick low-density layer in the crust (Rubin, 1995, Taisne et al., 2011). We assume that all of these conditions are met when the critical overpressure of ∼40 MPa is reached.
The effect of a transient recharge event will also be highly sensitive to properties of the magma chamber, mainly the presence of exsolved volatiles and the preexisting volume of magma. If volatiles are exsolved, the bulk compressibility increases by almost an order of magnitude (Huppert and Woods, 2002). Therefore, a magma body with exsolved volatiles will build up less pressure at a given injection rate than a magma body free of vapor bubbles (Fig. 1B). Finally, larger magma bodies require larger recharge events to reach the critical overpressure (Fig. 1C).
RESERVOIR EVOLUTION AT SANTORINI
When applied to the Minoan eruption at Santorini, our model shows that a chamber with an initial volume of 50 km3 at 200 MPa, a temperature just prior to recharge of ∼815 °C, and initial dissolved water content of 5.8 wt% (Cadoux et al., 2014; Cottrell et al., 1999), exposed to a recharge of magma at ∼900 °C, lasting <100 yr and with a recharge rate >5 × 10−2 km3/yr, will experience a temperature increase of ∼40 °C and grow by ∼6% in mass prior to reaching the critical overpressure of 40 MPa that drives the eruption (Figs. 1A and 2; Fig. DR4). The model calculations of the fraction of magma injected by the recharge that triggered the eruption and the associated thermal signal agree very well with petrological constraints inferred from the erupted products (Druitt et al., 2012).
In contrast with the Minoan event, the post-Minoan eruptions involve magmas with sparse mafic enclaves (<1% of the erupted volume, while dacite is inferred to make up >7% in the Minoan products) and the erupted volumes are much smaller. Our calculations can explain all of these observations if the current chamber at Santorini is much smaller than the pre-Minoan chamber, on the order of 10 km3, and does not contain exsolved volatiles (Figs. 1B and 1C). Under these conditions, we find that the critical overpressure is reached even with recharges that add <1% to the mass of the chamber. Our model also predicts that the mass of magma withdrawn by these eruptions is ∼0.08 km3 DRE, in excellent agreement with the estimated erupted volumes ranging from 0.01 km3 to 0.1 km3 (Parks et al., 2012; Fig. DR4). A smaller active magma body devoid of exsolved volatiles further explains the elevated eruption frequency over the past 450 yr and is compatible with the recharge scenarios inferred for the A.D. 1925–1928 eruptive cycle and the A.D. 2011–2012 unrest (Fig. 2B). The lack of exsolved volatiles is supported by low water contents of 3–4 wt% measured in the post-caldera dacites (Barton and Huijsmans, 1986) in combination with chamber depth estimates between 3 and 6 km (Newman et al., 2012; Parks et al., 2012).
The activity of Santorini is cyclic, with a period on the order of ∼104 yr. A cycle is defined by a large number of small but relatively frequent eruptions, culminating into a large silicic caldera-forming eruption (Druitt and Francaviglia, 1992). We propose that this behavior can be explained by a long-lived magma chamber that is gradually built by episodic replenishment of new magma and is largely evacuated by the caldera-forming eruption at the end of each cycle, the Minoan event being the end of the last one (Fig. 3). Today, the injection of new material in the upper crust is growing a new chamber through episodic recharges separated by periods of quiescence. Small but relatively frequent eruptions are currently building the island of Nea Kameni and are evidence for a magma chamber with a volume ∼10 km3 that contains little to no exsolved volatiles. If the recharge events continue in the future at a similar rate, the current magma chamber can grow further (with periodic smaller eruptions), accumulate exsolved volatiles, differentiate (induced by melt extraction from the surrounding mush), and potentially reach a size comparable to that just prior to the Minoan eruption (Fig. 3). The strong coupling between the thermal and mechanical evolution of a chamber offers a bridge between geophysical, geochronological, and petrological observations of volcanic systems, and models that couple both aspects are well positioned to assist volcano monitoring efforts in the future.
Funding for this project was provided by U.S. National Science Foundation (NSF) grant EAR-1426887 to Degruyter and Huber, Swiss Federal Institute of Technology in Zurich (ETHZ) funds to Degruyter and Bachmann, NSF grant EAR-1426858 to Cooper, and NSF grant EAR-1425491 to Kent. We thank B. Murphy for editorial handling and acknowledge the reviews of S. Barker, T. Druitt, and D. Pyle that significantly improved our manuscript.