Surface displacement field induced by an ascending Weertman crack: numerical modeling versus analogue experiments.

Magma intrusions ascending through the upper crust induce a displacement of the Earth’s surface, the amplitude of which  increases as the magma approaches the surface. Most geodetic observations of ground displacements induced by magma transport are interpreted using static elastic models of open dislocations or pressurized surfaces without any a priori knowledge on the surface shape of the magma intrusion. Furthermore, the numerical models currently developed for the propagation of fluid-filled cracks, which are also elastic, do not generally resolve the 3D displacement field induced at the free surface. Our aim is to bridge these two distinct approaches by using fluid-filled crack propagation models to derive the evolution of the surface displacement over time, thus providing a useful tool for the assimilation of geodetic data based on dynamic models.

In a first step, we use Weertman crack theory, which provides the shape of a non-viscous fluid-filled crack to derive the surface displacement field from a finite element model. This solution is then compared to the classical dislocation model (OKADA formulation) and to 2D displacement field inferred from the simulation of the propagation of the fluid filled using a 2D boundary element model. Eventually, the results are validated using analogue experiments injecting a finite volume of air inside a transparent gelatin characterised by elastic behaviour. In the experiments, the position and shape of the crack are monitored by cameras while the surface displacement field is recovered by photogrammetry (3D components) and by scanner measurements (only the vertical component).