We consider the problem of determining information about underground fluid flows by means of low-frequency electromagnetic measurements taken at the surface. Such methods yield information about the electrical conductivity of the soil, from which flow information can be inferred. Spatial resolution is generally poor and in particular yields little depth information. We propose a simple linearized method which, rather than attempting to recover depth information, recovers the vertically averaged conductivity, thus yielding data on lateral extent of plumes. The method is computationally efficient and we show through numerical experiments that horizontal resolution is relatively good compared to a full linear inversion scheme.