Time-reversal is addressed for imaging elastic targets situated in an acoustic waveguide. It is assumed that the target-sensor range is large relative to the channel depth. We investigate the theory of wideband time-reversal imaging of an extended elastic target, for which the target dimensions are large relative to the principal wavelengths. When performing time-reversal imaging one requires a forward model for propagation through the channel, and the quality of the resulting image may be used as a measure of the match between the modeled and actual (measured) channel parameters. It is demonstrated that the channel parameters associated with a given measurement may be determined via a genetic-algorithm (GA) search in parameter space, employing a cost function based on the time-reversal image quality. Example GA channel-parameter-inversion results and imagery are presented for measured at-sea data.