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The use of focused acoustic fields for the mechanical destruction of fluid-borne targets is applied zn. the medical field for the comminution of kidney stones by lithotripsy. Inhomogeneities in the propagation medzum are of practical concern to both the medical and the ocean acoustics communities. The use of phase conjugation to compensate for medium inhomogeneities and multipath efjects has been demonstrated for linear acoustics in both medical and ~nderwater contexts. The feasibility of focusing an intense acoustic field onto ~aterborne targets has implications for mine countermeasures because of the possibilitu of remotely neutralizing mines. The demonstration of the concept in actual mine countermeasure applications has yet to be realized. We present the results of a numerical study which investigates the performance of linear arrays using time .reversal as a means of focusing acoustic fields onto targets in an arbitrary medium modeled after a shallow water channel. The simulation investigates the cases where jitter exists in the initial phase of the time signals. The existence of tight focal wzdths, narrower than the free-space diffraction limit prediction, sometimes called "super-focusing", was observed for simulations containing small-scale inhomogeneitaes.