Modelling volcanic eruptions from the volcano to the atmosphere

Volcanic eruptions are complex processes involving multiple interacting phases, such as ascending magma, exsolved gases, deformation of the host rock and atmospheric dynamics. Typically, numerical models treat the sub-aerial eruptive column and the subsurface rock deformation as distinct domains due to the different timescales and material properties involved. This study presents a 2D numerical framework that couples the propagation of atmospheric waves with the elastic deformation of the host rock via a unified formulation. Using a finite volume method to solve the conservative form of the mass and momentum equations on a staggered grid, we demonstrate that this formulation can correctly predict the localisation of shock waves in the atmosphere, as well as the propagation of elastic waves in the host rock. Furthermore, we show that a single discretisation can capture both the conversion of acoustic waves into elastic waves from the atmosphere to the host rock, and the reverse process. This provides a foundation for fully coupled models of explosive volcanic events to potentially offers new insights into the interaction between the subsurface and the atmosphere during these processes.