The adjoint model method of control theory is known to give accurate and efficient data assimilation processes in oceanography and meteorology. However, it has rarely been applied in underwater acoustics for inversion purposes. Based on the back-propagation of the mismatch between observations and their predictions, the adjoint model can produce the corrections to the associated direct forward model input parameters. In this paper, the adjoint of a parabolic equation propagation model with non local impedance boundary conditions at the water sediment interface is used in order to determine an acoustically equivalent representation of the seabed. The bottom is represented by these boundary conditions that play the role of the control parameter.