Transient pressure variations within a reservoir can be treated as a propagating front and analyzed using an asymptotic formulation. From this perspective, one can define a pressure “arrival time” and formulate solutions along trajectories, in the manner of ray theory. We combine this methodology and a technique for mapping overburden deformation into reservoir volume change as a means to estimate reservoir flow properties, such as permeability. Given the entire “travel time” or phase field obtained from the deformation data, we can construct the trajectories directly, thereby linearizing the inverse problem. A numerical study indicates that, using this approach, we can infer large-scale variations in flow properties. In an application to Interferometric Synthetic Aperture Radar (InSAR) observations associated with a injection at the Krechba field, Algeria, we image pressure propagation to the northwest. An inversion for flow properties indicates a linear trend of high permeability. The high permeability correlates with a northwest trending fault on the flank of the anticline that defines the field.