Interaction between deformation sources and implications for numerical modelling of magma storage

Volcano ground deformation due to magma movement in the subsurface is commonly modelled using simple point (Mogi) or dislocation (Okada) sources, embedded in a homogeneous,
isotropic, elastic half-space, and representing respectively a magma chamber and a dike. When datasets are too complex to be explained by a single deformation
source, the magmatic system is often represented by a combination of these sources and their displacements �elds are simply summed. By doing so, the assumption of homogeneity in the half space is violated and the resulting interaction between sources is neglected.
This thesis seeks to determine the limits in which the combination of analytical sources is justi�ed, by testing the analytical surface displacements against the solutions of corresponding 3D �nite element models, which account for the interaction between sources. For models with dike and magma chamber aligned vertically or along the dike-strike
direction, the calculated discrepancies, and therefore the source interaction, are insignificant (< 5%), independently of the source separation. Although the discrepancies
depend on the physical model parameters and can not be generalized, for models with a magma chamber next to a dike (in the direction perpendicular to the dike-strike), or
for horizontally or vertically aligned pressurized magma chambers, care must be taken for source separation of less than 4 times the radius of the magma chamber as the
discrepancies can reach 20% at a wall-to-wall distance of 0.5 source radii. Furthermore, a statistical study of the retrieved source parameters employing an inversion scheme
(based on analytical solutions, hence neglecting the source interaction), demonstrates the di�culty of solving the structure of vertically layered magmatic system without
additional, e.g. petrological, constraints. Finally, modelling the dike employing various FE methods has pointed out the fact that the rheology of the magma needs to be
integrated in future numerical modelling approaches.