Source localization using matched-field processing in a range-depependent environment is evaluated with experimental data taken in the Gulf of Mexico. The bathymetry in this experiment is a moderately sloping flat bottom, resulting in mode coupling. The conventional adiabatic normal-mode method for the solution of the wave equation is not expected to be accurate here. A new range-dependent coupled-mode method for the evaluation of the replica fields is used. This is a one-way method in which the energy is propagated from one point in range to the next by a first-order differential equation. This approach allows for the relatively efficient calculation of replicas for many source positions. The ability to localize known sources at various ranges and frequencies with a fixed vertical array is quantified. Results from both the conventional adiabatic normal-mode method and the new range-dependent coupled-mode method are compared.