Introduction

Eruptive style transitions are frequently observed at many volcanoes around the world (e.g. Hildreth and Fierstein 2000; Sigmundsson et al. 2010; Nicholson et al. 2011; Sulpizio et al. 2016). In particular, eruptions involving the formation of lava domes can show recurrent transitions to Vulcanian explosive eruptions, and occasionally to sub-Plinian and even Plinian events. Examples include Unzen (Nakada et al. 1999), Mount St. Helens (Swanson and Holocomb 1999), Santiaguito (Williams and Self 1983), Lascar (Melnik et al. 2008), Fuego de Colima (Saucedo et al. 2010) and Soufrière Hills (Sparks and Young 2002) volcanoes. Changes in eruptive style imply variations in magma flow dynamics, which may mirror modifications in the driving pressure or conduit geometry (Woods and Koyaguchi 1994; Melnik and Sparks 2002; Costa et al. 2009a; Massaro et al. 2018). Changes in magma composition (induced by magma mixing; Woods and Cowan 2009; Nicholson et al. 2011) and rheology (driven by volatile-dependent crystallization; Melnik and Sparks 1999; Wylie et al. 1999) may also account for possible changes in eruptive behaviour.

Satisfactory comprehension of the role played by these different processes has not yet been achieved, especially for the non-linear effects of their combinations that are of paramount importance for unravelling the physics of eruptive dynamics. Several studies have been focused on the processes acting within the magma chamber (i.e. magma mixing and fresh magma injection; Eichelberger and Izebkov 2000; Huppert and Woods 2002) and the conduit system (Jaupart and Allegre 1991; Gudmundsson and Philipp 2006; Martel and Poussineau 2007; Preece et al. 2016). Recently, attention has been paid to modifications of the conduit-feeding system geometry able to alter the eruptive (or pre-eruptive) equilibrium (Massaro et al. 2018). The conduit-feeding system connects magma chamber (or reservoir) to the Earth surface, allowing magma to rise. Its structure and dimensions are considered among the most relevant parameters influencing the eruptive behaviour (e.g. Scandone et al. 2007; Melnik et al. 2008; Costa et al. 2009a, 2011; Sulpizio et al. 2016; Massaro 2018).

Several models assumed a simple geometric configuration for the conduit-feeding system described by a cylindrical conduit connected to a deeper chamber (Dobran 1992; Varekamp 1993; Macedonio et al. 1994; Melnik 2000; Macedonio et al. 2005; Colucci et al. 2014). However, geological evidence indicates that volcanic eruptions are mainly fed through dykes (e.g. Eichelberger and Izebkov 2000; Gudmundsson and Brenner 2005; Costa et al. 2009a; Maccaferri et al. 2011; Zellmer and Annen 2014). Likewise, dykes are the only viable mechanism for developing a pathway through the brittle crust from a deep magma chamber to the surface during the initial stages of an eruption (Rubin 1995; Melnik et al. 2008; Rivalta et al. 2015). A cylindrical conduit may develop only at shallow levels, favoured by erosion of wall rock (Costa et al. 2007a; Melnik et al. 2008; Costa et al. 2009a; Melnik and Costa 2014). In many cases, the arrival of a dyke to the surface does not necessarily result into a continuous feeding of eruptive activity, but the coarse balance of driving and resisting forces may lead the eruptive system close to an equilibrium state (quasi-equilibrium) with formation of lava lakes and domes (Sulpizio et al. 2016). Effusive eruptions may shift to Strombolian and/or Vulcanian explosive phases depending on the interplay between the driving pressure and degassing-dependent viscous forces (Wylie et al. 1999; Ripepe et al. 2013).

The Fuego de Colima volcano (Mexico) exhibited quasi-equilibrium conditions (at least) in the last five centuries (Luhr 2002), developing a summit dome that is occasionally dismantled by Vulcanian and (rarely) sub-Plinian explosive eruptions (e.g. Bretòn-Gonzàlez et al. 2002; Gavilanes-Ruiz et al. 2009; Saucedo et al. 2010). The 1913 eruption was the last sub-Plinian event at Fuego de Colima and provides a well-documented example of the eruptive style transition from dome extrusion to a sub-Plinian explosive event (Saucedo et al. 2010). In this work, we present a first-order discussion of the physical processes that drove the transition of the 1913 eruption from a slow dome extrusion into an explosive eruption by means of numerical simulations carried out with the CPIUD code (Condotto PIU Dicco; Costa et al. 2009a, 2011), experimental petrology (Macìas et al. 2017) and data from finite element modelling, which provided assessment of the effect of gravitational loading on the volcano spreading (Norini et al. 2010). The CPIUD code is a numerical model that simulates a 2-D steady-state magma flow within conduits having elliptical cross sections, taking into account the wall-rock elasticity and local tectonic stress. Quasi-static elastic deformation of the dyke-shaped conduit is accounted for by an analytical solution (Muskhelishvili 1963), which couples cross-sectional area with the magma pressure. The viscosity of the magma is assumed constant, while dissolved and exsolved gas mass fraction is solved as function of solubility coefficient and exponent (Costa et al. 2009a). The model allows input into the conduit of either liquid magma or pyroclastic particulate, and solves the mass and momentum conservation equations. Input parameters include the depth of magma chamber top (i.e. conduit length), overpressure at the top of the magma chamber, rheological properties of magma (i.e. magma viscosity) and geometry of the conduit feeding system (pure dyke, pure cylinder or deeper dyke passing into a shallower cylinder).

Adopting an approach similar to Massaro et al. (2018), the model was here used to reconstruct the first-order geometry of the conduit-feeding system during the sub-Plinian phase of 1913 eruption, taking into account the volcanological data (Saucedo et al. 2010, 2011; Bonasia et al. 2011) as input and constraints for the numerical simulations. In particular, the mass discharge rate (MDR) estimated for the main explosive event recorded in the C1 fall bed, and the lithic-ejecta types within C1 (Saucedo et al. 2011) were used as target values of the numerical simulations and as constraints for the fragmentation depth, respectively. We assumed hybrid geometrical configuration composed of a deeper dyke connected to a shallower cylindrical conduit, as inferred from geophysical observations (Salzer et al. 2014). The results of numerical simulations were then compared with the available volcanological (Saucedo et al. 2010), geophysical (Spica et al. 2017) and experimental petrology (Macìas et al. 2017) data in order to evaluate the possible magmatic (magma chamber overpressure) or non-magmatic (lowering of lithostatic load) triggers of the observed eruptive style transition.

Geological framework

Fuego de Colima volcano is located in the western part of the Trans-Mexican Volcanic Belt, a calc-alkaline continental volcanic arc in the central part of Mexico (Fig. 1a). Together with Nevado de Colima, it constitutes a volcanic complex lying on a basement of Cretaceous limestones and intrusive rocks, covered by a graben-fill sequence including Quaternary alluvial, colluvial and lacustrine deposits, with andesitic volcanic rocks in the upper 2 km. Since the onset of the recorded eruptive activity, the behaviour of Fuego de Colima has been characterized by summit dome growth and intermittent explosive activity that sometimes culminated in large sub-Plinian (and Plinian) eruptions eventually leading to complete destruction of the dome (as in 1585, 1606, 1622, 1818, 1890 and 1913; De la Cruz-Reyna 1993; Luhr 2002). To date, Fuego de Colima is considered the most active volcano in Mexico (De la Cruz-Reyna 1993; Bretòn-Gonzàlez et al. 2002; Vargas-Bracamontès et al. 2009) with more than 43 eruptions since 1576 (Luhr and Carmichael 1981; Medina-Martinez 1983; De la Cruz-Rèyna 1993; Saucedo et al. 2005). The effusive-to-explosive cyclical nature of its long-term activity was extensively discussed in previous studies (Luhr and Carmichael 1980, 1990; Luhr 2002). The last eruptive cycle started in 1818 and ended with the 1913 sub-Plinian eruption, which is the object of the present study. A remarkable eruptive event occurred in July 2015 when the summit dome was completely dismantled producing pyroclastic density currents (PDCs) that filled the Montegrande and San Antonio ravines along the southern slopes of the volcano (Capra et al. 2016).

Fig. 1
figure 1

a Morphotectonic map of the Colima Volcanic Complex (NC = Nevado de Colima volcano; FC = Fuego de Colima volcano) and Colima Rift with the main tectonic and volcano-tectonic structures (modified from Norini et al. 2010). In the inset, the location of the Colima Volcanic Complex (CVC) within the Trans-Mexican Volcanic Belt (TMVB) is shown in the frame of the subduction-type geodynamic setting of Central America. b Schematic stratigraphy (and volcanological interpretation) of the products erupted during the 1913 eruption of Fuego de Colima (modified from Saucedo et al. (2010) and Sulpizio et al. (2015))

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The 1913 eruption

The 1913 sub-Plinan eruption occurred nearly a century later the 1818 eruption. This period was characterized by low to moderate intensity eruptive activity. Following historical accounts, the eruptive activity resumed in 1869, 51 years after the 1818 eruption. Between 1869 and 1909, only two lava effusions occurred, while thousands of low to moderate intensity Vulcanian eruptions punctuated the period (Díaz 1906), peaking in frequency and intensity between 1900 and 1903 (Navarro and Cortes 1993; Bretòn-Gonzàlez et al. 2002; Savov et al. 2008).

A series of low-intensity explosions on 17 January heralded the onset of 1913 eruption and partially destroyed the summit dome (Waitz 1915; Ortiz 1944; Bretòn-Gonzàlez et al. 2002; Saucedo et al. 2010). During the following 24 h, the eruption progressed through three eruptive phases (Saucedo et al. 2010). The opening Phase (1) was characterized by explosions that produced small Merapi-type block-and-ash flows (units F1, F2, F3; Fig. 1b) and a dilute PDC (unit S1). Phase (2) witnessed strong Vulcanian explosions that produced concentrated PDCs (unit F4) and a dilute PDC (unit S2). This phase cleared the vent and destroyed almost completely the summit dome decompressing the conduit system (Saucedo et al. 2010). The sub-Plinian (climactic) Phase (3) established a ca. 23 km high column that dispersed fallout deposits to the NE (unit C1; Fig. 1b). At the end of Phase (3), the sustained column collapsed, generating dilute PDCs (unit S3) and pumice-rich concentrated PDCs (unit F5) that dispersed radially from the vent up to a distance of 15 km (Saucedo et al. 2010). The 1913 eruption changed the volcano morphology, causing a loss of 100 m in height and developing a 400 m wide and 350 m deep summit crater (Waitz 1915; Bretòn-Gonzàlez et al. 2002).

The main fallout deposit of Phase (3) (Fig. 1b) covered an area of ca. 191,000 km2, with an estimated volume of ca. 0.56 km3 (ca. 0.23 km3 dense rock equivalent, DRE; Saucedo et al. 2011), representing ca. 80% of the total erupted volume of the eruption. Bonasia et al. (2011) reported a total mass of ca. 2.36 × 1011 kg, a column height of 25 km and a DRE volume of fallout deposits of ca. 0.22 km3, in good agreement with Saucedo et al. (2011), who calculated ca. 2–6 × 1011 kg. Connor et al. (2016) provided a range of the erupted mass between ca. 5.5 × 1010 kg (volume of 0.04–0.06 km3, column height of ca. 14 km) based on field data and ca. 1.4 × 1011 kg (volume of 0.1–0.5 km3) by taking into account the thickness derived from historical accounts. Considering typical uncertainties in tephra volume estimations (Bonadonna and Costa 2012; Bonadonna et al. 2015), the latter values of the erupted mass and volume are in agreement with those of Saucedo et al. (2011) and Bonasia et al. (2011), and will hereafter be used for the purposes of this paper.

Methodology

Numerical modelling

The numerical simulations were carried out using the CPIUD code (Costa et al. 2009a, 2011) in order to obtain a first-order reconstruction of the conduit-feeding system during the sub-Plinian fallout phase of the 1913 eruption of Fuego de Colima. This is assumed as a “snapshot” of the climactic phase of the eruption, being the model based on a steady-state solution. The CPIUD code solves a set of cross section averaged equations derived from the generalization of Macedonio et al. (2005) model as proposed by Costa et al. (2009a). We tested a range of hybrid geometrical configurations of the conduit-feeding system, obtained varying the respective lengths of the lower dyke and the shallower cylinder. In CPIUD code, the magma flow in the conduit is governed by mass and momentum balance equations under quasi-steady-state conditions:

$$ \frac{\partial }{\mathrm{\partial z}}\left(\rho AV\right)=0 $$
(1)
$$ V\frac{\partial V}{\partial z}=-\frac{1}{\rho }\ \frac{dP}{dz}-g- fft $$
(2)

where ρ is the magma density, A is the cross-sectional area, V is the mixture velocity, and g is the gravity acceleration. The fft friction term is expressed below the fragmentation level as (Costa et al. 2007a, 2009a)

$$ fft=4\ \frac{\mu }{\rho }\ \frac{a^2+{b}^2\ }{a^2{b}^2}V $$
(3)

where a and b are the major and minor axes of the elliptical cross section, and μ is the effective magma viscosity, here assumed constant. Above fragmentation level, fft = 0. The magma density ρ is defined considering a homogeneous mixture as in Macedonio et al. (2005):

$$ \frac{1}{\rho }=\kern0.5em \frac{xe}{\rho g}+\frac{1- xe- xc\ }{\rho l}+\frac{xc}{\rho c} $$
(4)

where ρg is the gas density, ρl is the density of the melt phase, ρg is the crystal density, xe is the exsolved gas mass fraction, and xc is the crystal mass fraction. The exsolved and the dissolved gas mass fraction can be expressed as

$$ xe=\kern0.5em \frac{xtot- xd\ }{1- xd}\left(1- xc\right);\kern0.5em xd=\kern0.5em s\ {P}^n $$
(5)

where xtot is the initial total gas mass fraction, xd is the dissolved gas mass fraction, and the solubility exponent n and the constant solubility coefficient s in the solubility law (Battino and Clever 1966) depend on magma composition only. The gas phase (perfect gas) and the condensed phases are compressible.

This model contains some important assumptions, summarized as follows:

  1. 1.

    Cross section averaged variables are used to describe magma flow in the conduit in which vertical deformations are much smaller than horizontal ones.

  2. 2.

    Quasi-static elastic deformation of the conduit is accounted by an analytical solution (Muskhelishvili 1963) that couples the cross-sectional area with the magma pressure.

  3. 3.

    Magma flow in the conduit is approximated as steady state, assuming that the time-scale of pressure variations at the conduit base (hours) is much longer than the travel time of the magma in the conduit (few minutes).

  4. 4.

    Both the gas and the condensed phase (liquid and crystals) are assumed to have the same velocity.

  5. 5.

    As a first-order approach, isothermal assumption is justified by the heat capacity of the magmatic mixture and effective heat transfer between the condensed phase and rapidly expanding gas (Wilson et al. 1980).

  6. 6.

    Following points 3 and 4, magma can enter the conduit in either homogeneous or the bubbly flow regime, and exits in the particulate flow regime, after fragmentation is assumed to occur when the gas volumetric fraction α reaches a critical value αc (Costa et al. 2009a; Macedonio et al. 2005), corresponding to the bubble maximum packing (typically αc ≈ 0.75; Sparks 1978).

  7. 7.

    Magma behaves as a compressible liquid even when the pressure is greater than the bubble nucleation pressure. If the pressure is lower than the nucleation pressure, the gas exsolves and a liquid–gas mixture becomes much more compressible. It is assumed that no supersaturation is required for bubble nucleation.

A fixed pressure is assumed as boundary condition at the base of the dyke because the pressure change is much longer than magma ascent time through the conduit. Pressure at the conduit bottom is fixed, defined as Pch (at magma chamber top), and choked flow conditions are assumed at the conduit exit.

To integrate the governing equations avoiding singularity at the outlet (exit condition) in Eqs. (1) and (2), Costa et al. (2009a) introduced two characteristic velocities, “isothermal” sound velocity in the erupting magma s (Macedonio et al. 2005) and wave velocity in a deformable tube c (Young 1808; Shapiro 1977; Paıdoussis 2006):

$$ \frac{1}{s^2}\equiv {\left(\frac{d\rho}{d P}\right)}_T\mathrm{and}\frac{1}{c^2}\equiv {\left(\frac{\rho dA}{AdP}\right)}_T $$
(6)

where T is the temperature of the gas phase. Considering these velocities in mathematical manipulations, the governing Eqs. (1) and (2) can be rewritten using the Mach number M = V/s as independent variable. Consequently, the new equations are integrated between the initial Mach number at the conduit inlet, Mi, and the Mach number at the conduit exit, Mo, which is set equal to Mo = 1/(1 + γ2)1/2 (with γ = s/c), defining the choked flow condition. For simplicity, we fix the conduit length L (instead of the Mach number) at the conduit entrance; therefore, the value of Mi is searched using the standard shooting methods, until the mathematical integration gives z = L at the conduit exit, where M = Mo (Costa et al. 2009a).

The dimensions of the major and minor semi-axes (a and b) of the dyke depend on the magmatic overpressure ΔP (Muskhelishvili 1963; Mériaux and Jaupart 1995; Costa et al. 2007a), which is in turn considered as the difference between the local magmatic pressure and lithostatic pressure:

$$ a(z)={a}_0(z)+\frac{\Delta P}{2G}\left[2\left(1-\nu \right){b}_0(z)-\left(1-2\nu \right){a}_0(z)\right] $$
(7)
$$ b(z)={b}_0(z)+\frac{\Delta P}{2G}\left[2\left(1-\nu \right){a}_0(z)-\left(1-2\nu \right){b}_0(z)\right] $$
(8)

where G is the rigidity of wall-rock and ν is the Poisson ratio. The a0 and b0 are the initial unpressurized values of the dyke semi-axes. Equations (7) and (8) are based on the assumption that elastic deformation can be locally described as plain strain approximation (Muskhelishvili 1963). This implies that these relationships can be applied only if the local length-scales characterizing vertical changes in the conduit geometry and fluid pressure are much larger than the transversal dimensions of the conduit (i.e. the conduit diameter D or the dyke thickness H). Moreover, Eqs. (7) and (8) are not valid near the free surface where both boundary and topographic effects can be important. Purely elastic rock properties are assumed, and no rock failure is allowed. This latter assumption can be assessed a posteriori if solutions are likely to exceed the wall-rock strength. The transition from dyke to cylinder is a parameterised value (Costa et al. 2009a); LT and wT define the position and the vertical extent of the transition zone, approximating the behaviour of a dyke in the limit a > > b and recover the case of a cylinder when a = b = R. It is worth noting that in this model, the magma properties are treated in an approximate way. This includes equilibrium water exsolution, absence of gas overpressure with respect to magma pressure and constant viscosity assumption.

Input data and constraints

Input values for the model are obtained from geophysical, petrological, rock property, and stratigraphic data of the 1913 eruption collected from the literature (Touloukian et al. 1989; Atlas et al. 2006; Savov et al. 2008; Costa et al. 2009a; Saucedo et al. 2010; Bonasia et al. 2011; Alvarez and Yutzis 2015; Connor et al. 2016; Macìas et al. 2017), and are summarized in Table 1. Seismic tomography data indicate that the feeding system of Fuego de Colima is composed of two magma chambers at different depths (Spica et al. 2017). The shallow reservoir has its top at depth of ca. 6 km within Cretaceous limestones (Norini et al. 2010) and has an estimated volume of ca. 40 km3 (Cabrera-Gutiérrez and Espíndola 2010). The deep reservoir has its top at depth of ca. 15 km, and a volume > 650 km3 (Spica et al. 2017). The deep reservoir supplies magma into the shallow magma chamber, as demonstrated by petrological studies indicating periodical arrival of magma batches triggering mixing and mingling processes with the resident magma (Macìas et al. 2017). Due to the small erupted volume during the 1913 eruption, we assume that the eruptive dynamics of the climactic phase was controlled by the shallower part of the feeding system. This is because the erupted magma volume (ca. 0.22 km3; Bonasia et al. 2011) is significantly lower than the estimated volume of the shallower magma chamber (ca. 40 km3; Cabrera-Gutiérrez and Espíndola 2010). The total length of the conduit connecting the shallow magma chamber to the surface was set at ca. 6 km, as suggested by the mineral phase equilibria (presence of fresh amphibole crystals, which are stable at 170–210 MPa; Luhr 2002; Macìas et al. 2017), melt inclusions (Reubi and Blundy 2008) and tomographic data (Nùnez-Cornù et al. 1994; Medina-Martinez 1983; Zobin et al. 2002; Zamora-Camacho et al. 2007; Alvarez and Yutsis, 2015).

Table 1 Parameters used in the CPIUD simulations
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The CPIUD simulations were carried out considering a reference value of magma overpressure (i.e. the pressure driving the eruption) of 20 MPa at the top of the magma chamber, although other values were also tested. Such a reference value is sufficient for driving explosive eruptions from a magma chamber at 6 km of depth (Costa et al. 2011) and is also in the range of overpressure assessed for Colima magmas through rapid decompression experiments (Lavallè et al. 2012). It is important to note that changing the overpressure in a reasonable range of values (10–60 MPa) does not influence the model outputs significantly and, in particular, the calculated MDRs are of the same order of magnitude (Massaro 2018).

Magma temperature was set at 950 °C, as suggested by petrological experiments of Savov et al. (2008) carried out using the andesitic melt composition of the 1913 eruption and the presence of amphibole crystals. The pre-eruptive concentration of dissolved water in the melt was assessed based on ion-probe studies of melt inclusions trapped in pyroxenes of the 1913 eruption magmas. Luhr et al. (2006) reported H2O contents between 5.7 and 6.2 wt%, while Atlas et al. (2006) provided a lower value of 3.4 wt%. Because the 1913 products contain stable hornblende crystals (stable in silicate melts containing 3–4% of H2O; Rutherford and Hill 1993; Moore and Carmichael 1998; Carmichael 2002; Savov et al. 2008), we considered the value of Atlas et al. (2006) for calculating the effective melt viscosity of the 1913 eruption.

The melt viscosity of the 1913 magma was calculated using the Giordano et al. (2008) model. For estimating magma viscosity (Costa et al. 2009b; Cimarelli et al. 2011), we accounted for a crystal mass fraction of about 10%, as assessed from the petrography of 1913 erupted products (Savov et al. 2008; Massaro 2018). The effect due to the presence of bubbles on magma rheology was neglected. An effective mean viscosity value of the order of 105 Pa s−1 was estimated. The choice of using an effective mean viscosity value rather than more sophisticated viscosity models is adequate as CPIUD considers cross section averaged variables. Moreover, the model does not account for magma temperature variations, and gas overpressure with respect to magma pressure (Costa et al. 2009a). A more realistic description of the magma viscosity should account for the coupling with dissolved water, magma cooling with country rocks, viscous dissipation, crystal resorption and intrinsically two-dimensional effects (e.g. Costa and Macedonio 2005; Costa et al. 2007c; Cimarelli et al. 2011). All these effects can change the local magma viscosity of an order of magnitude (Costa et al. 2007b, c; Cimarelli et al. 2011).

The static rigidity of Cretaceous limestones hosting the shallow magma chamber was assessed at 13 GPa (Touloukian et al. 1989; Table 1). The adopted geometric configuration for the conduit-feeding system of the 1913 eruption is a dyke connected to the uppermost magma chamber that evolves into a cylindrical conduit at shallow depths, which is suggested as the most stable geometry configuration for volcanic conduits reaching the surface (Costa et al. 2009a; Rivalta et al. 2015). The constraints and target values for the CPIUD simulations derive from volcanological and subsurface data for the 1913 erupted products (Norini et al. 2010; Saucedo et al. 2010, 2011; Bonasia et al. 2011; Table 2), to reduce the uncertainty of the model inversion as much as possible.

Table 2 Constraints used for the CPIUD simulations. Volume (V, from Bonasia et al. 2011), mass discharge rate (MDR, calculated with Mastin et al. 2009 equation, using the value reported in Bonasia et al. 2011), and fragmentation level (FL, from Norini et al. 2010)
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The exclusive occurrence of lava lithic fragments in the main C1 fallout deposit (Saucedo et al. 2010) indicates that the fragmentation level was shallower than ca. 2 km during the climactic Phase 3, in agreement with the reconstructed subsurface stratigraphy (Norini et al. 2010). Thus, we assume that lithic erosion mainly occurred at or above the fragmentation depth (Barberi et al. 1989; Macedonio et al. 1994; Costa et al. 2009a; Campbell et al. 2013). The mass discharge rate (MDR) represents the main target value of the CPIUD model outputs. A peak MDR of 8.9 × 107 kg s−1 was obtained using the Mastin et al. (2009) empirical relationship considering a maximum column height of 25 km (as estimated by Bonasia et al. 2011). A mean MDR equal to 2 × 107 kg s−1 was calculated by taking into account the total erupted mass of ca. 2.36 × 1011 kg from Bonasia et al. (2011) and a time duration of ca. 3.5 h for the sustained column phase of the 1913 eruption (from 11:30 a.m. to ca. 15:00 p.m. local time; Saucedo et al. 2010).

Results

The CPIUD results are shown in Fig. 2, by plotting MDRs versus fragmentation levels. The simulations were carried out using the (initial) width (W) and thickness (H) of the dyke and transition level (TL) between the dyke and the cylindrical conduit as independent input variables, while MDR and fragmentation level are the outputs. It is important to stress that the solutions of the conduit-feeding system geometry are non-unique (e.g. Anderson and Segall 2011, 2013; Costa et al. 2009a; Massaro et al. 2018) but represent the best compromise between the volcanological data and the controlling physical parameters of the model (Costa et al. 2009a). The best match solutions were chosen by comparing the CPIUD outputs versus the target range of MDR and the maximum depth of lithic provenance (ca. 2 km). The target value of the peak MDR is 8.9 × 107 kg s−1 (Bonasia et al. 2011), which is similar to that reported by Saucedo et al. (2011) and to the maximum estimate provided by Connor et al. (2016) taking into account historical data. The mean MDR value obtained from the erupted mass (from Bonasia et al. 2011) and time duration (from Saucedo et al. 2010) were used as a lower limit of the acceptable output values (Fig. 2). Dyke width W between 200 and 5000 m and dyke thickness H from 10 to 80 m were explored (Table 1). For simplicity, the diameter of the cylindrical conduit (D) was fixed equal to the dyke thickness H.

Fig. 2
figure 2

Outputs of the CPIUD simulations for the sustained explosive phase of 1913 eruption. The diagrams show the variation of MDR versus fragmentation level for a conduit/feeding system composed of an elongated dyke passing into a cylinder conduit near the surface. The simulations are carried out with dyke width W from 200 to 5000 m and dyke thickness H from 10 to 100 m, considering three dyke-to-conduit transition levels at 500 (a), 1000 (b), and 1500 m (c). The whole set of simulations is shown only for TL = 500 m. The blue area corresponds to the acceptable range of MDRs between the mean and maximum values obtained from Bonasia et al. (2011) and Saucedo et al. (2010), respectively

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Different model runs were performed considering a transition level (TL) between the dyke and the cylinder conduit at depths of 500, 1000 and 1500 m. Results show that the depth variation does not influence significantly the model outputs (Fig. 2). We assumed TL equal to 500 m on the basis of InSAR data indicating the present-day pressure source around that depth (Salzer et al. 2014).

A slight deepening of the fragmentation level is observed increasing dyke width W and decreasing thickness H. At the same time, a sharp decrease of MDR occurs decreasing dyke thickness H. Figure 2 shows that the best fit solutions of the model are for dyke having thickness H of about 40 m and a width W ranging from 200 to 5000 m. Possible solutions are also obtained for thickness H of 30 m and a width W ranging from 2000 to 5000 m. These results give a first-order geometrical configuration of the conduit/feeding system of Fuego de Colima volcano during the 1913 eruption. The best-fit geometric configurations correspond to dyke volumes in the range of 3.45 × 107 to 3.45 × 108 m3, as reported in Table 3.

Table 3 Volumes of hybrid geometries obtained with CPIUD simulations, for a fixed dyke thickness H = 40 m and transition level TL = 500 m. The total erupted volume DRE is equal to 2.2 × 108 m3 (from Bonasia et al. 2011)
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Discussion

Geometry of the conduit-feeding system before the sub-Plinian explosive phase

Massaro (2018) reconstructed the geometric configuration of the conduit-feeding system of Fuego de Colima during the 1998–2015 period of (mainly) dome extrusion and lava flows using the magma flow model of Costa et al. (2007a) and Melnik and Costa (2014), who generalized the model proposed by Melnik and Sparks (2005) for a shallow dyke to cylinder conduit and a dual magma chamber system. The model accounts for rheological changes due to volatile loss and temperature-driven crystallization. The best fit geometry for lava dome eruptions is described by a deep dyke having width W of 200 m and thickness H of 40 m passing into a 500-m long cylindrical conduit at shallow depths (Fig. 3a). We assume a similar geometry also for the conduit-feeding system during the time period preceding the 1913 eruption, considering similar conditions of dome extrusion and magma compositions. This assumption is also supported by the combination of estimated magma volumes of the 1913 sub-Plinian explosive phase combined with petrography of the erupted products. The products erupted after 1913 or in the period between 1818 and 1913 not contain hornblende, or, when present, it shows reaction borders indicating prolonged ascent times at pressures below 170–210 MPa (6–7 km of depth, Macìas et al. 2017). In other words, these products underwent long transit times in the conduit system of Fuego de Colima before eruption, as typical of dome or low effusion rate lava flow eruptions (e.g. Luhr and Carmichael 1980; Mora et al. 2002; Macìas et al. 2017). The presence of fresh hornblende in the 1913 magma indicates the rapid withdrawal of magma from the shallow magma chamber, located at 6 km of depth and therefore within the stability field of amphibole. The volume stored in the conduit system of 1913 was less than the total erupted of ca. 220 × 106 m3 estimated by Bonasia et al. (2011). This allows us to constraint the possible geometrical configurations obtained by CPIUD simulations, excluding volumes of the conduit-feeding system greater or comparable to the erupted volumes (see Table 3). As such, geometrical configurations with dyke width W equal to 1600 m (corresponding to volume of 276 × 106 m3) can be excluded, and the solutions with W equal to 1000 m (volume of 173 × 106 m3) are less probable. Consequently, dyke widths equal to 200 and 400 m are considered more likely. This leads to a refinement of the geometrical configuration of the conduit-feeding system before the sustained phase of 1913 eruption with an elongated dyke, having width W of 200–400 m and thickness H of 40 m, which evolves at shallow depths into a cylindrical conduit with a diameter D of 40 m and a length of 500 m.

Fig. 3
figure 3

Cartoon showing the main geometrical changes of the conduit-feeding system of Fuego de Colima during the effusive-to-explosive transition of the 1913 eruption (not to scale). NC Nevado de Colima, FC Fuego de Colima, GF Graben filling deposits; SMC shallow magma chamber. a Geometrical configuration of the conduit/feeding system prior to the 1913 eruption. The deep reservoir has its top at depth of ca. 15 km of depth and is weakly connected to the shallower magma chamber with its top at depth of ca. 6 km. This latter is connected to the surface by a dyke (width W = 200 m, thickness H = 40 m) that evolves into an upper cylindrical conduit at depth of 500 m (transition level TL). The diameter of the cylinder D is equal to the dyke thickness H. b Diagram of the variation of magma overpressure (ΔP) as function of the volume of magma injected into a magma chamber (ΔV) immersed in a perfect elastic medium for different magma chamber volumes. The red dashed line indicates a ΔP = 25 MPa. c Geometrical configuration of the volcanic system of Fuego de Colima showing the possible effects of a lowering of the lithostatic load in the upper part of the conduit induced by a sector collapse of sudden lateral spreading. The location and magnitude of the maximum strain rate affecting the summit volcano are shown as derived from numerical simulations of Norini et al. (2010)

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What triggered the sub-Plinian explosive phase?

We consider Fuego de Colima during dome extrusion before the 1913 eruption as an open conduit system close to equilibrium, and the driving pressure, given by the magma chamber overpressure (P0) minus the pressure required for maintaining open the dyke (ΔP0m), is balanced by the weight of magma column (i.e. magmastatic loading, ρgh), the lithostatic stress (σl) and the resisting forces per unit area (Rp; Jaupart and Allegre 1991; Gudmundsson 2012; Sulpizio and Massaro 2017):

$$ {P}_0-\Delta {P}_{0 m}=\rho gh+{\sigma}_l+{R}_p $$
(9)

Being the conduit open and dome extrusion in process, the main variables that can abruptly change to alter the equilibrium and trigger a transition to the explosive phase of 1913 eruption are P0 (magma overpressure) and σl (component of the lithostatic stress). An effusive-to-explosive transition in eruptive style can be triggered by an increase in magma overpressure (magmatic triggering), a decrease of lithostatic pressure (non-magmatic trigger), a decrease of the resisting forces due to non-linear effects (e.g. Woods and Koyaguchi 1994; Melnik and Sparks 1999; Voight et al. 2006), or a combination of them.

The historical activity at Fuego de Colima indicates that sustained (sub-Plinian) explosive eruptions as 1913 are rare (one about every 100–200 years), and the eruptive behaviour is dominated by long periods of dome extrusion occasionally interrupted by small Vulcanian explosive eruptions (Luhr and Carmichael 1980; De la Cruz-Reyna 1993; Luhr 2002; Gavilanes-Ruiz et al. 2009; Lavallè et al. 2012). This means that either magmatic or non-magmatic processes able to alter the usual eruptive dynamics and trigger a sustained explosive eruption occur occasionally.

The most common way to increase magma overpressure and trigger an explosive eruption is the arrival of fresh magma into a shallow magma chamber (e.g. Eichelberger and Izebkov 2000; Smith et al. 2004; Sigmarsson et al. 2011). Mineralogical and geochemical data of the 1913 juvenile products (banded scoriae, plagioclase and pyroxene phenocrysts with reaction rims) show evidence of magma mixing well before the sustained (sub-Plinian) explosive phase (Luhr and Carmichael 1980; Savov et al. 2008; Saucedo et al. 2010; Macìas et al. 2017), suggesting that the injection of fresh magma into the shallow magma chamber occurred frequently. Crummy et al. (2014) found that pulses of phlogopite-rich mafic magmas periodically enter the Colima plumbing system on timescales of a few thousand years. This is in agreement with the results of Macìas et al. (2017), who highlighted how the 1818 and 1913 magmas are the products of mixing of andesitic resident magma with mafic pargasite-rich batches at a pressure of 170–210 MPa. The repeated injection of fresh magma into the shallow chamber accounts for observed disequilibrium textures in 1913 phenocrysts and compositional variability in minerals and groundmass (Macìas et al. 2017) or pattern in trace elements (Savov et al. 2008). This also suggests homogeneous (andesitic) bulk composition of the magma in the shallow magma chamber, with limited difference in temperature between the residing and injected magma (Macìas et al. 2017).

Considering a perfectly elastic medium, we can calculate the overpressure induced by injection of fresh magma into the shallower magma chamber (Rivalta et al. 2015). Supposing that magma is supplied in the shallow magma chamber at a rate greater than the effusion rate, magma accumulates in the chamber with time, and this increases the chamber overpressure as

$$ \Delta P=\frac{\Delta V}{V}\frac{1}{\left({\beta}_c+{\beta}_m\right)} $$
(10)

where ΔV is the volume of injected magma, V is the original volume of the magma chamber, βc is the magma chamber compressibility and βm is the magma compressibility controlled mainly by bubbles. Both parameters can vary by an order of magnitude, depending on chamber size and depth (Melnik and Sparks 2005). In particular, the magma chamber compressibility depends on the shape of the chamber and on the rigidity of the host medium μ (e.g. Melnik and Sparks 2005; Amoruso and Crescentini 2009; Rivalta 2010). For spherical chambers and μ = 3–25 GPa, βc = 0.3–3 GPa−1. Magma compressibility βm is very small for a bubble-free magma (0.04–0.2 GPa−1, Spera 2000) but relatively large if volatiles exsolve (for basaltic magma up to 10 GPa−1 depending on depth; Rivalta and Segall 2008; Rivalta 2010). If we use the minimum value of βc (0.3 GPa−1) and considering injection of gas-free magma (βm = 0.04–0.2 GPa−1), an injection of ca. 200–250 × 106 m3 of magma induces an overpressure of ca. 25 MPa. It is worth note that the volume of injected magma to induce 25 MPa of overpressure may lower of one order of magnitude (to ca. 10 × 106 m3) if the upper values of βc (3 GPa−1) and βm (10 GPa−1) are used (i.e. the magma has high volatile content). An increase in magma chamber overpressure would result into growing dyke dimensions (Fig. 3b), because of the partition of overpressure into vertical driving pressure (allowing magma ascent) and horizontal driving pressure (producing rock fracture and enlargement of the dyke). Considering an initial dyke width W of 200 m, the best solutions of CPIUD simulations allow the possibility of dyke enlargement to 2000 m (Fig. 2).

Another argued possibility for triggering the effusive-to-explosive transition during the 1913 eruption is a rapid decompression of the conduit-feeding system (or part of it). Lowering of the lithostatic stress was long claimed as play a fundamental role in triggering volcanic eruptions and in controlling their dynamics (Gudmundsson and Phillip 2006; Andrew and Gudmundsson 2007; Watt et al. 2009; Plateaux et al. 2014; Sulpizio and Massaro 2017). Changes of stress acting on both edifices and magma chambers can be usually related to processes with different characteristic time-scales. In particular, the occurrence of tectonic earthquakes (Walter and Amelung 2007) and sector or flank collapses (Pinel and Jaupart 2005) are short-term processes that can affect eruptive style transition (Sulpizio and Massaro 2017). Concerning earthquakes, no large seismic activity has been reported in the Fuego de Colima area prior to the onset of the eruption in January 1913. There was an earthquake 2 months before (on November 1912) in the region of Acambay graben (Urbina and Camacho 1913), about 400 km from Fuego de Colima. This was the most severe historical earthquake recorded in the area, with a surface magnitude (Ms) of 6.9 (Abe 1981; Suter et al. 1995), but it is hard to infer if it could have had an influence in triggering the 1913 explosive eruption. For example, larger earthquakes struck the area near the town of Manzanillo (moment magnitude Mw = 7.6) in 1995 (García-Pérez and Urrutia-Fucugauchi 1997) or in Tecoman (moment magnitude Mw = 7.8) in 2003 (Yagi et al. 2004). In particular, the Manzanillo earthquake occurred at about 90 km from Fuego de Colima, without conditioning volcanic activity, characterized by open conduit system conditions similar to those of 1913.

Sudden explosive eruptions are frequently triggered by a sector or flank collapse unloading the conduit-feeding system (i.e. Mt. St. Helens in 1980, Belousov et al. 2007; Reid et al. 2010; Walter 2011). This most likely occurred in the past at Fuego de Colima (Cortes et al. 2010; Roverato et al. 2011). Particularly, the unloading induced by a collapse was responsible for the explosive eruption of 10–11 July 2015, in which the failure of part of the summit crater produced PDCs with a total volume of 4.5 × 106 m3 (Capra et al. 2016). However, no major sector/flank collapses or summit crater failures have been reported prior to the 1913 eruption at Fuego de Colima.

Another mechanism accounting for reduction in the lithostatic load acting on a volcano is the lateral spreading, defined as the lateral deformation of a volcanic edifice along a basal ductile layer that deforms under the volcano weight (e.g. Lundgren et al. 2004; Norini and Acocella 2011; Acocella et al. 2016). This process was assumed as a trigger for eruptions at different volcanoes around the world (e.g. Etna, Kīlauea, and Piton de la Fournaise; Acocella et al. 2003; Neri et al. 2004; Poland et al. 2017). In our case study, geological/structural data and numerical modelling (Norini et al. 2010; Alvarez and Yutsis 2015) reported a southward (lateral) gravitational spreading of the whole Colima volcanic complex (comprising the Fuego de Colima and Nevado de Colima volcanoes) over the sedimentary fill of the Colima Rift. In particular, published time independent finite element modelling (Norini et al. 2010) highlighted that, beside a general spreading of the volcanic complex, the Fuego de Colima shows shear strain in the order of 8–10 kPa and a vertical displacement up to 16 m in the upper part of the cone (Fig. 3c). These results indicate the susceptibility of Fuego de Colima to southward lateral movement. Being the shear strain and vertical displacement located in the upper part of the Fuego del Colima cone (Fig. 3c), it can be argued that the southward lateral movement occurs as sudden and stepwise rock faulting and brittle deformation (Norini et al. 2010; Alvarez and Yutsis 2015). This mechanism has the same effect that producing a small overpressure in the system, which can alter the MDR. If the value of MDR exceeds a threshold limit, it triggers a transition to an explosive eruption (Woods and Koyaguchi 1994). The explosive activity is maintained as long as the overpressure is balanced and the value of MDR falls below the threshold, restoring effusive eruption conditions (Woods and Koyaguchi 1994).

The eruption of magma contained in the upper part of the conduit could have also a feedback reducing the static load on the magma chamber. Assuming a magma density of 2100–2500 kg m−3 (compatible with the andesitic rock compositions; Luhr 2002), it is necessary to empty 1000–1200 m of the upper conduit in order to have a decompression of 25 MPa, which is in the range hypothesized for the magma chamber overpressure from magma influx. This hypothesis is compatible with the CPIUD results (W = 200 m, H = 40 m, D = 40 m, TL = 500 m), and the geometric configuration of the conduit/feeding system might remain unaltered passing from dome extrusion to the sub-Plinian explosive phase.

Distinguishing between an internal (magma overpressure) or external (sector/flank collapse and spreading) trigger for the onset of the sub-Plinian explosive phase of 1913 eruption is not straightforward due to the lack of compelling petrological and geophysical evidence. Considering that sub-Plinian (to Plinian) explosive phases are rare compared with effusive activity (dome extrusion and lava flows), it can be argued that the triggers of these sustained explosive eruptions are exceptional events, and the concurrence of more than one has also to be taken into account. Further research and high-quality petrological and geophysical (i.e. deformation) data are thus required to shed light on processes responsible for abrupt changes in eruptive style at Fuego de Colima.

Conclusions

The mechanisms triggering the effusive-to-explosive style transition at the onset of the 1913 eruption of Fuego de Colima were investigated by coupling CPIUD numerical simulations with geophysical, petrological and volcanological data from the literature and hystorical accounts. The best-fit geometry of the conduit-feeding system is that with a dyke width W of ca. 200–400 m and H thickness of ca. 40 m, evolving into a shallower cylindrical conduit with a diameter D of 40 m at depth of 500 m. This geometrical configuration was inferred considering the peak and mean mass discharge rates, with a fragmentation level shallower than 2 km. The results of the numerical simulations do not allow discrimination between a magmatic (magma chamber overpressure) or non-magmatic (lowering of the lithostatic load) trigger for the transition to the explosive phase of the 1913 eruption. A trigger due to magma overpressure would imply enlargement of the dyke during the sustained explosive phase, which is reasonable considering the best-fit results of dyke width W up to 2000 m. On the other hand, an external trigger, such as a lateral spreading of the volcano, would decompress the magma stored in the conduit-feeding system (or the shallow magma reservoir) without requiring a change in dyke dimensions. The calculations show that a lowering of magmastatic pressure of 25 MPa is necessary to induce the eruption of ca. 1000 m of the magma stored in the conduit, which is not so different from the 700–800-m column of magma assumed to have erupted during the July 2015 eruption. We highlight here that a sudden jerk of volcanic (lateral) spreading of the volcano could trigger cascading processes with non-linear effects on the quasi-equilibrium eruptive state at Fuego de Colima, eventually triggering large explosive eruptions.