Many geophysical processes -- such as the development of magma bodies or the sequestration of CO2 in saline reservoirs -- involve changes in pressure at depth that lead to small, but measurable, deformation at the surface. It is often difficult to study these processes directly, so this surface deformation offers valuable information about what is occurring below.

In this talk I will discuss three models of such sub-surface systems, each based around a simplified model of the overlying earth. I will begin with a purely elastic model of a constant-pressure region surrounded by a deformable Winkler material, and then move on to two models involving fluid flow – one for a layer of Newtonian fluid, and another for two-phase fluid flow through a deformable porous medium. I will discuss the behaviours of each of these systems as different physical processes dominate, the limitations of what can be observed at the surface, and applications to real-world examples of magma bodies and CO2 sequestration.