Increasing evidence supports the idea that stress changes play a fundamental role in triggering volcanic eruptions and in controlling their dynamics (Hill et al., 2002; Manga and Brodsky, 2006).

Stress changes in volcanic areas may vary in origin due to short- or long-term processes (Gudmundsson and Philipp, 2006; Andrew and Gudmundsson, 2007; Watt et al., 2008; Plateaux et al., 2014). The first includes earthquakes and landslides (Stein, 1999; Hill et al., 2002; Harris and Ripepe, 2007; Walter, 2007; Walter et al., 2007; Watt et al., 2008; De la Cruz-Reyna et al., 2010), while the second comprises unloading due to erosion and deglaciation (Davydov et al., 2005; Sigmundsson et al., 2010), tidal effects (Sohn, 2004; Cazaneve and Chen, 2010), or changes in the tectonic regime (Ventura and Vilardo, 1999; Waite and Smith, 2004; Diez et al., 2005; Miura and Wada, 2007; Lehto et al., 2010; Carbone et al., 2014). These processes superimpose to the possible local stress variations related to internal dynamics of a volcano, such as pressure increase in the magma chamber due to magma influx from depth or buoyancy induced by magma differentiation processes (Massol and Jaupart, 1999; Gudmundsson, 2006, 2016; Cañon-Tapia, 2014). Although usually claimed for explaining eruptive style transitions (i.e., from effusive to explosive, or from no-activity to eruption, Hasabe et al., 2001; Adams et al., 2006; Ida, 2007; Di Traglia et al., 2009; Schneider et al., 2012; Ripepe et al., 2013; Kereszturi et al., 2014), the magmatic processes internal to a volcano alone are sometimes not sufficient for equalling the elastic energy due to lithostatic loading (e.g., Gudmundsson, 2016; Sulpizio et al., 2016). In other cases the physical and chemical characteristics of the deposits do not support triggering mechanisms like magma mixing or bubble nucleation. For example, arrival of gas rich magma in a magmatic system or magma evolution within the chamber itself are usually claimed for explaining transitions from effusive to explosive eruptions, even in cases in which the geological evidences are lacking (i.e., the erupted material is poorly vesicular, as in the case of many basaltic eruptions; Fink et al., 1992; Wylie et al., 1999). In other cases, the arrival of fresh magma into a magma chamber is postulated as trigger magma chamber rupture and eventually fed an eruption, even in the absence of petrological evidences (i.e., mingling and mixing; e.g., Davì et al., 2011). All these considerations claim for discussion about the state of the art and perspectives about the interplay between volcanic activity and changes in the stress field. This review has not the presumption of being exhaustive of all the knowledge on stress changes and volcanic eruptions, but we will critically review the main mechanisms inducing short- and long-term stress changes at volcanoes, and their possible influence on eruption initiation and its dynamics. The review is intended to focus on the first order effects of stress change. In particular, the changing strength and strain energy due to not homogeneous lithosphere or different volcano edifice (e.g., Gudmundsson, 2012a, 2016) is not explicitly discussed, although they are implicitly contained in the equations describing the driving/resisting pressures. The review is organized in four main chapters: stress changes due to unloading, effects of seismic energy, changes in regional stress field (far field), and influence of stress change on eruption dynamics.

The unloading processes are the most common way to change the lithostatic load. This may induce fracture initiation/propagation, which changes the lithostatic component of the stress at any point in the lithosphere and, ultimately, may result in eruption initiation. The importance of unloading processes on volcanic activity is testified by the long-term eruptive histories of many volcanoes, which reveal that changes in eruption rate and/or magma composition follows partial destruction of the edifice (Presley et al., 1997; Hildenbrand et al., 2004; Hora et al., 2007; Longprè et al., 2009; Boulesteix et al., 2012).

The unloading can be a short- or long-term process, and the different mechanisms will be reviewed following the temporal scale of action.

Earthquakes can stress magmatic systems either through static stresses (the offset of the fault which generates a permanent deformation in the crust) or through dynamic stresses from the seismic waves (Manga and Brodsky, 2006). Both stresses increase with the seismic moment of the earthquake, but they decay in different way with distance r from the generation area. In particular, static stresses decreases as 1/r³, whereas dynamic stresses fall off more gradually (as 1/r^1.66) and are proportional to the seismic wave amplitude (e.g., Lay and Wallace, 1995).

The stress transfer due to regional earthquakes may be of great importance in reawakening a dormant system. Previous works suggested a statistical correlation among large earthquakes and eruptions in time and space (Linde and Sacks, 1998; Hill et al., 2002; Marzocchi, 2002; Walter and Amelung, 2007; Walter et al., 2007). However, not all the large earthquakes trigger eruptions, and this is compelling evidence that the magmatic system needs to be ready to erupt under a new energetic equilibrium. This implies that the eruption triggering depends on the initial state of the magmatic system prior to the earthquake (magma composition, volatiles, chamber overpressure, strength of the host rocks, and type, size, and distance of the foci; Hill et al., 2002). In this framework, an important event is the unclamping of previous faults, which is the reduction in normal stress due to earthquake energy.

Dynamic and static deformation due to an earthquake may increase volcanic activity (Hill et al., 2002; Walter and Amelung, 2007). Seismic body and surface waves induce dynamic deformation, whereas displacement across a fault and subsequent viscoelastic relaxation of the crust account for permanent static deformation. A statistically significant response immediately after the earthquake (Linde and Sacks, 1998) has been observed for volcanoes at 750 km or more from the epicenters, suggesting they are triggered by dynamic deformation (Brodsky et al., 1998; Manga and Brodsky, 2006). The effect of static deformation in triggering eruptions remains poorly understood and it is unclear whether it is the most effective type of deformation in promoting eruptions (Marzocchi et al., 2002; Selva et al., 2004). The amplitude of static deformation decays more rapidly with distance than the seismic waves (Hill et al., 2002). Follows that to have eruption triggering from static deformation is most likely at volcanoes located in proximity to an earthquake rupture plane.

Classical examples of interaction between earthquakes and volcanic eruptions are the Kamchatka 1952 (M 9.0, followed by renewal of activity at Karpinsky and Maly Semiachik volcanoes, and at the Tao-Rusyr Caldera), Chile 1960 (M 9.5, followed by renewal of activity at Cordón-Caulle Planchón-Peteroa, Tupungatito and Calbuco volcanoes), Alaska 1964 (M 9.2, followed by renewal of activity at Trident and Redoubt volcanoes), Sumatra-Andaman 2004–2005 (M 9.3 and M 8.7, followed by renewal of activity at Talang and Barren Island volcanoes; Sepulveda et al., 2005; Walter and Amelung, 2007). All these examples are from subduction zones, which most of the time are partially locked and accumulate stress that is released during earthquakes (Figure 6A). Walter and Amelung (2007) related the triggering of the eruption listed above to the change in volumetric strain, which is the sum of the normal components of the strain tensor. Negative volumetric strain corresponds to volumetric contraction (compressing the rock), and positive volumetric strain corresponds to volumetric expansion (decompressing the rock). Earthquakes in subduction areas are associated with volumetric contraction in the near-trench portion of the forearc and volumetric expansion in the far-trench portion, which is where the volcanic arc is usually located (Figure 6B). The main observation is that all the erupted volcanoes underwent volumetric expansion induced by the earthquake. A direct mechanical effect of stress change due to volumetric expansion may be the unclamping of the fissure system. A pre-existing network of cracks may be connected, nucleate and thereby facilitate preferred paths for magma ascent. Unclamping of fracture system was claimed for the earthquake occurred on Kamchatka peninsula on January 1st, 1996 along a SW–NE trending fracture system, which triggered the twin-eruption at the volcanoes Karymsky and Akademia Nauk (Walter, 2007). The earthquake is hypothesized to have prompted dilatation of the magmatic system together with extensional normal stress at intruding N–S trending dykes, allowing magma to propagate to the surface.

Taking into account Equation (10) and adding the contribution of seismic stress, it can be written: (11)P0-ΔP0m=Pe+(ρr-ρm)gh+(ρrhr-ρihi)g[1-1ν-1]+σe+Rf

The change in tectonic stress has been claimed as trigger of large ignimbrite eruptions or for controlling the eruptive style of explosive eruptions (Korringa, 1973; Aguirre-Díaz and Labarthe-Hernandez, 2003; Miller and Wark, 2008; Costa et al., 2011).

The first order influence of far-field stress (σ_ff) on eruption triggering was investigated using numerical simulations, which demonstrated how the combined effect of crustal extension and magma chamber overpressure can sustain linear dyke-fed explosive eruptions with mass fluxes in excess of 10¹⁰ kg/s from shallow-seated (4–6 km depth) chambers affected by extensional stress regime (Costa et al., 2011). The model shows that for a far-field stress above the value able to counterbalance the lithostatic pressure at the fragmentation depth (Figure 7), a dyke of any length remains opened, and the Mass Eruption Rate (MER) is strongly controlled by the 3D geometry and extension of the system. It is worth noting that the requested value of σ_ff is as high as 40–60 MPa, which is not easily matched during normal geodynamic processes. As an example, a homogeneous horizontal tensile stress σ_tec = 5 MPa was used by Maccaferri et al. (2014) for modeling the dyke trajectories in rifting areas. In this model the dyke opens under assigned normal and shear stress given by the internal overpressure and by the shear component of the tectonic plus unloading stresses, respectively. The overpressure within the dyke is set as the difference between the magma pressure and the confining stress, which is the superposition of the lithostatic pressure, the normal component of the topographic unloading and the tectonic stress. When the unloading pressure P_u = ρ gD (ρ is crustal density, g acceleration due to gravity, and D is the effective depth accounting for the total deficit of mass from the topographic depression and low-density sediments with respect to before rifting) dominates over the tectonic tensile stress (D > πσ_tec/(2ρg), 250 m for ρ = 3,000 kgm⁻³), σ₃ becomes vertical beneath the rift in a volume centered at a depth z_c = ρgDW/(πσ_tec), where W is the graben width (Table 1; Figure 8). The upper limit of the volume is given by z₁ = (W/2K)(1−(1 − K²)^1/2) and the lower one by z₂ = (W/2K)(1 + (1 − K²)^1/2), where K = πσ_tec/(2P₀) (Table 1; Maccaferri et al., 2014).

This volume forms a stress barrier zone, which deflects the ascending dykes to the rift sides.

Sideways from the rift center, σ₃ becomes first inward dipping and then horizontal (Figure 8). Three scenarios for dyke propagation and for the final surface distribution of magmatism can occur, depending on where the dykes nucleate relatively to the stress barrier zone. When z_in < z₁ in-rift volcanism occurs, while off-rift volcanism occurs for z₁ < z_in < z₂ and z_in > z₂ (Table 1; Figure 8).

Incorporating the far-field tectonic stress in Equation (11) we have: (12)P0-ΔP0m=Pe+(ρr-ρm)gh+(ρrhr-ρihi)g[1-1ν-1]+σe+σtec+Rf which is the final formulation of driving vs. resisting forces that drives the transition from no eruption to full on eruption.

With the only exception of unloading due to ice cap retreat, the above discussed changes in stress field may play a role also in short term variation of eruption style. Complex transitions between effusive and explosive eruptive styles are frequently described in volcanic activity (e.g., Jaupart and Allegre, 1991; Villemant and Boudon, 1998; Adams et al., 2006; Platz et al., 2007) and the alternation of pyroclastic deposits and lavas is common in almost all stratovolcanoes. Shifts in eruptive style have been related to many complex sub-surface processes such as decompression-induced crystallization (Hammer et al., 2000; Blundy and Cashman, 2005), increase in magma viscosity due to groundmass crystallization caused by volatile loss and temperature gradients (Stevenson et al., 1996; Manga, 1998; Melnik and Sparks, 2002; Cashman and Sparks, 2013), and time-dependent release of overpressure due to the contrasting effects of magma viscosity and elastic energy released from country rocks deformation (Wylie et al., 1999).

All these processes can for sure participate to changes in eruptive style, but sharp changes in local or far-field stress may sometimes play a similar role in driving eruptive activity. This is especially true when dealing with changing eruptive style in eruptions or eruptive cycles with similar magmatic composition, which do not account for any petrologic or textural trigger of the changing eruptive behavior. For instance, the interplay between magma overpressure and stress acting on the volcanic system was claimed for explaining the eruptive style transitions of Monte dei Porri (Salina Island, Italy; Sulpizio et al., 2016), and effusive eruptions following local stress decrease due to spreading of the volcanic edifice were repeatedly observed at Mount Etna volcano (Borgia et al., 1992; Froger et al., 2001; Lundgren et al., 2004; Neri et al., 2004).

The contribution of stress lowering to the change of eruptive style can be easily explained using the Equation (12) in the ΔP vs. σ_tot space (Figure 9; Sulpizio et al., 2016). It shows how a transition from no-eruption to eruption or from a given eruptive style to another is allowed through the superimposition of internal magmatic pressure (increase of ΔP) and changing in the total stress field (σ_t), defined by the sum of all the defined partial stresses defined early.

Understanding the interplay between crustal stress and volcanic activity and its dynamics is essential for comprehension of a number of natural phenomena and for mitigating the related hazards and risk. Significant evidence of coupling between stress change and volcanic events emerges from investigation of tectonic earthquakes, flank collapses, and also long-term processes such as erosion and landslides. The effect of these processes superimposes on changes in magma overpressure, including the growth of gas bubbles and input of new magma in the chamber. This is because, although dyke initiation and propagation to the surface is usually governed by the depth-dependent magma parameters, the source location is also subject to the stress field conditions that vary from one point to another in the crust and that can promote or prevent brittle failures.

During last decades many authors provided precious contributions to this topic, and this review presented the state of the art of the knowledge about some of the main mechanisms inducing stress change and able to influence eruption initiation and dynamics. In particular, we reviewed three main pivotal issues correlated to stress: the unloading and its long- and short-term effects, the seismic energy, and the regional (or far-field) stress changes. Their occurrence alone was used as a preliminary guide in this study.

The contribution of each mechanism has been analyzed, and an equilibrium equation for magma chamber rupture and dyke opening to the surface has been presented. The equation was also used for interpreting the possible changes in eruptive style of single eruptions or eruptive cycles. The three mechanisms can have different impact on magmatic systems, and can influence or not the triggering of volcanic eruptions. However, it emerges clearly from this review how a single mechanism is hardly responsible for eruption initiation, but the concur of internal processes is usually necessary. It emerges how internal (magmatic processes) end external (stress field variations) processes concur in modulating eruptive activity.

All authors listed, have made substantial, direct and intellectual contribution to the work, and approved it for publication.