A time domain geoacoustic inversion method using ship noise received on a towed horizontal array is presented. The received signal, containing ship noise as a source of opportunity, is time-reversed and then back-propagated to the vicinity of the ship. The back-propagated signal is correlated with the modeled signal which is expected to peak at the ship's location in case of a good match for the environment. This match is utilized for the geoacoustic parameter inversion. The objective function for this optimization problem is thus defined as the normalized power focused in an area around the source position, using a matched impulse response filter. A hybrid use of global and local search algorithms, i.e., GA and Powell's method is applied to the optimization problem. Applications of the proposed inversion method to MAPEX 2000 noise experiment conducted north of the island of Elba show promising results, and it is shown that the time domain inversion takes advantage of dominant frequencies of the source signature automatically.