Methods for geophysical-model assessment — in particular, the computation of model-parameter resolution — indicate the value and the limitations of time-lapse data in estimating reservoir flow properties. A trajectory-based method for computing sensitivities provides an effective means to compute model-parameter resolution. We examine the common situation in which water encroaches into a reservoir from below, as caused by the upward movement of an oil-water contact. Though the techniques described are not limited to this case, we treat the situation in which the time-lapse response is primarily caused by changes in saturation. Using straightforward techniques, we find that, by including reflections off the top and bottom of a reservoir tens of meters thick, we can infer reservoir permeability based upon time-lapse data. We find that, for the case of water influx from below, using multiple time-lapse snapshots does not necessarily improve the resolution of reservoir permeability. An application to time-lapse data from the Norne field in the North Sea illustrates that we can resolve the permeability near a producing well using reflections from three interfaces associated with the reservoir.