A two‐step model for dynamical dike propagation in two dimensions: Application to the July 2001 Etna eruption

Abstract

We developed a hybrid numerical model of dike propagation in two dimensions solving both for the magma trajectory and velocity as a function of the source overpressure, the magma physical properties (density and viscosity), and the crustal density and stress field. This model is used to characterize the influence of surface load changes on magma migration toward the surface. We confirm that surface loading induced by volcanic edifice construction tends both to attract the magma and to reduce its velocity. In contrast, surface unloading, for instance, due to caldera formation, tends to divert the magma to the periphery‐retarding eruption. In both cases the deflected magma may remain trapped at depth. Amplitudes of dike deflection and magma velocity variation depend on the ratio between the magma driving pressure (source overpressure as well as buoyancy) and the stress field perturbation. Our model is then applied to the July 2001 eruption of Etna, where the final dike deflection had been previously interpreted as due to the topographic load. We show that the velocity decrease observed during the last stage of the propagation can also be attributed to the local stress field. We use the dike propagation duration to estimate the magma overpressure at the dike bottom to be less than 4 MPa. This approach can be potentially used to forecast if, where, and when propagating magma might reach the surface when having knowledge on the local stress field, magma physical properties, and reservoir overpressure.

On the Propagation Path of Magma‐Filled Dikes and Hydrofractures: The Competition Between External Stress, Internal Pressure, and Crack Length

“…For laterally propagating dikes over long distance, as often observed in rifting area, the influence of the external stress field on the propagation path will depend on the balance between the increasing dike length and the pressure drop due to magma withdraw from the magma chamber, so that a progressively larger effect of the background stress (which would be expected by neglecting the effect of the dike length and accounting for the magma pressure drop solely) would not necessarily occur and should be examined in each circumstance. Last, for research intended to address the propagation path and the rising velocity of magmatic intrusions (e.g., Pinel et al, ), our results show that the length of the intrusion should be taken into account in order to evaluate whether the direction of maximum compressive stress defines the propagation path of the intrusion.…”

“…From a numerical modeling perspective, the problem of calculating magmatic dike trajectories has been addressed by different authors (e.g., Dahm, ; Meriaux & Lister, ; Maccaferri et al, ; Heimisson et al, ; Pinel et al, ). Particularly, Dahm () and Maccaferri et al () reproduced similar results as obtained by Watanabe et al () for surface loading and by Menand et al () in the presence of horizontal compression.…”

“…Also, given a background stress model, the critical ratio for deflection represents an important reference value to validate forecast trajectories of magmatic intrusions (Corbi et al, ). Practically, the critical ratio for deflection has been used to identify two end member scenarios for the propagation paths of the intrusions (Pinel et al, ): (i) The total stress field is dominated by the background stress (the effect of the stress change due to the intrusion on its propagation path is negligible). In this case the trajectory of the intrusion is expected to follow closely the direction perpendicular to the least compressive background‐stress axis; (ii) the total stress field is dominated by the stress change induced by the fluid‐filled crack (the effect of the background stress on the propagation path of the intrusion is negligible); in this case the fluid‐filled crack would tend to propagate straight along the crack plane.…”

What Drives the Lateral Versus Vertical Propagation of Dikes? Insights From Analogue Models

“…Moreover, stiffer layers overlying more compliant ones may provide barriers to magma ascent (A. Gudmundsson, ; Kavanagh et al, ; Maccaferri et al, ; Rivalta et al, ). Topographic reliefs provide a driving pressure for propagation by inducing lateral stress gradients (Acocella & Neri, ; Fialko & Rubin, ; Fiske & Jackson, ; Kervyn et al, ; Maccaferri et al, ; Muller et al, ; Pinel et al, ; Pinel & Jaupart, ; Rubin & Pollard, ), also inducing an increasingly intense compression at the tips of ascending dikes or approaching a relief, favoring dike arrest (Kervyn et al, ; Maccaferri et al, , ; Urbani et al, ; Watanabe et al, ). Additionally, reliefs modify dike trajectories by inducing rotations of the principal stress axes that may lead a dike to change propagation direction, for example, from vertical to horizontal or vice versa (Bagnardi et al, ; Corbi et al, , ; Dahm, ; Maccaferri et al, ; Watanabe et al, ).…”

The Roles of Elastic Properties, Magmatic Pressure, and Tectonic Stress in Saucer‐Shaped Sill Growth

“…The growth of the sill is strongly coupled to the magma pressure and host rock elasticity (cf. Pinel et al, 2017) through the dependence of the channel width w ( ϵ 3 ) on the elastic opening of the channel; ϵ 3 is the maximum (elongation) principal strain in the damaged (sill) region. The magma flows to accommodate this strain and fill the enlarged channel (note then that the strain refers to the expansion of the channel opening and not a strain of the magma).…”