Deformation in the material overlying an active reservoir is used to monitor pressure change at depth. A sequence of 11 field estimates allows us to construct a measure of diffusive traveltime throughout a reservoir. The dense distribution of traveltime values means that we can construct an exactly linear inverse problem for reservoir flow properties. Application to interferometric synthetic-aperture radar (InSAR) data gathered over a carbon dioxide injection site in Algeria reveals pressure propagation along two northwest-trending corridors. An inversion of the traveltimes indicates the existence of two northwest-trending high-permeability zones. The high-permeability features trend in the same direction as the regional fault and fracture zones. Model-parameter-resolution estimates indicate the features are well resolved.