High‐resolution methods based on simulated annealing and full‐wave sound propagation models are developed for nonlinear inversion for ocean‐bottom properties. Simulated annealing is used to search the high‐dimensional parameter space of ocean bottoms for the parameter set corresponding to the best replica field. The parabolic equation method is used to solve range‐dependent inversion problems. For data taken by Lynch et al. from a range‐dependent region of the Gulf of Mexico [J. Acoust. Soc. Am. 89, 648–665 (1991)], this approach achieves excellent agreement between the theoretical and measured acoustic pressures. The recovered sediment parameters suggest that a sound‐speed boundary layer exists in the upper part of the sediment and that the depth of an interface in the sediment is range dependent. For locally range‐independent problems, inversion is performed in wave‐number space. Large efficiency gains are possible with this approach because the number of wave‐number samples required for inversion is mu...