Non-Newtonian magma flow in a growing laccolith and stress induced by dyke formation in a tectonically active region: two examples of advanced multiphysics models.

Understanding the formation and development of magmatic plumbing systems is fundamental to comprehend the dynamics of volcanic processes. Magmatic plumbing systems form the primary path to transport magma through the Earth’s crust and can comprise diverse structures like dykes, sills, and magma reservoirs. The geometry of these interconnected channels or conduits influences the volume of magma carried through the plumbing system and thus affects the way magma erupts and interacts with the surrounding rock. However, the mechanisms which control their formation are difficult to assess, as they result from a combination of complex and intertwined processes and factors, including the properties of the magma, the host rock rheology and the tectonic forces at play in the area.   

The development of multi-purpose Finite-Element (FE) softwares during the last two decades has offered geoscientists a wide range of tools to solve problems that include multiple types of physics. Here, we present two examples of advanced, fully coupled multiphysics problems in which magmatic intrusions are modelled considering i) a temperature field, the velocity field of flowing magma and its interaction with the surrounding rock and ii) a temperature field and external tectonic forces in a heterogeneous crust. Both models are implemented using the FE software COMSOL Multiphysics.

In the first example, we model the evolution of an inflating laccolith embedded in an elastoplastic host-rock. The initial set-up of the model is defined by a feeding dyke connected to a sill at 500 m depth. The magma, here defined as a non-Newtonian flow, is injected at the base of the dyke at a rate of 127 Kg/s over ~50 years, and accumulates in the interconnected sill that inflates with the pressure build up. Following the injection phase, the magma cools down until it reaches its solidus temperature after which the laccolith is essentially solidified. We show that during the injection phase, strain localizes along the edges of the inflating laccolith forming 10 to 15 m-wide bands of high shear strain that develop parallel to the interface with the surrounding rock.

The second example uses the dyke feeding the eruption at Fagradalsfjall, Iceland, in 2021 as a case study. Fagradalsfjall is located on the obliquely spreading Reykjanes peninsula in SW-Iceland, where volcanically active periods alternate with periods of quiescence, which last for ca. 800-1000 years.
 In a first step, tectonic stresses accumulating between volcanically active periods are simulated considering crustal heterogeneity and a thermal structure. Following this, a dyke is opened in the previously simulated, heterogeneous tectonic stress field using the same crustal and thermal structures. Although the surface deformation of such a model is comparable to that of a dyke opening driven by magmatic overpressure alone, the stress fields at depth can differ. Understanding the evolution of the stress field at depth can help to assess the risk of successive dyke intrusions.

We show with these two models that multi-purpose modelling software such as COMSOL has rendered the implementation of coupled multiphysics problems more accessible, opening up new lines of inquiry in various geological fields, including volcanology.