Deformation in the overburden proves useful in deducing spatial and temporal changes in the volume of a producing reservoir. Based on these changes, we have estimated diffusive traveltimes associated with the transient flow due to production, and then, as the solution of a linear inverse problem, the effective permeability of the reservoir. An advantage of the approach based on traveltimes, as opposed to one based on the amplitude of surface deformation, is that it is much less sensitive to the exact geomechanical properties of the reservoir and overburden. Inequalities constrain the inversion, under the assumption that the fluid production only results in pore volume decreases within the reservoir. The formulation has been applied to satellite-based estimates of deformation in the material overlying a thin gas production zone at the Krechba field in Algeria. The peak displacement after three years of gas production is found to be approximately 0.5 cm, overlying the eastern margin of the anticlinal structure defining the gas field. Using data from 15 irregularly spaced images of range change, we have calculated the diffusive traveltimes associated with the startup of a gas production well. The inequality constraints were incorporated into the estimates of model parameter resolution and covariance, improving the resolution by roughly 30% to 40%.