Deformation above a producing reservoir provides a valuable source of information concerning fluid flow and flow properties. Quasi-static deformation occurs when the displacements are so slow that we may neglect inertial terms in the equations of motion. We present a method for inferring reservoir volume change and flow properties, such as permeability, from observations of quasi-static deformation. Such displacements may represent surface deformation such as tilt, leveling, interferometric synthetic aperture radar (InSAR), or bathymetry observations or subsurface deformation, as inferred from time-lapse seismic surveys. In our approach, the equation for fluid flow in a deforming reservoir provides a mapping from estimated fractional volume changes to reservoir permeability variations. If the reservoir behaves poroelastically over the interval of interest, all the steps in this approach are linear. Thus, the inference of reservoir permeability from deformation data becomes a linear inverse problem. In an application to the Wilmington oil field in California, we find that observed surface displacements, obtained by leveling and InSAR, are indeed compatible with measured reservoir volume fluxes. We find that the permeability variations in certain layers coincide with fault-block boundaries suggesting that, in some cases, faults are controlling fluid flow at depth.