Asymptotic methods provide an efficient means by which to infer reservoir flow properties, such as permeability, from time-lapse seismic data. A trajectory-based methodology, similar to ray-based methods for medical and seismic imaging, is the basis for an iterative inversion of time-lapse amplitude changes. In this approach, a single reservoir simulation is required for each iteration of the algorithm. A comparison between purely numerical and the trajectory-based sensitivities demonstrates their accuracy. Analysis of a set of synthetic amplitude changes indicates that we are able to recover large-scale reservoir permeability variations from time-lapse amplitude data. In an application to actual time-lapse amplitude changes from the Bay Marchand field in the Gulf of Mexico, we are able to reduce the misfit by 81% in 12 iterations. The time-lapse observations indicate lower permeabilities are required in the central portion of the reservoir.