The feasibility of inverting acoustic field statistics to obtain the parameters of a stochastic internal wave model is demonstrated using numerical simulations. For weak scattering satisfying the Rytov approximation, the parameters of a generalized form of the Garrett–Munk internal wave model can be obtained. A hierarchy of experiment scenarios has been studied. Scenarios range from a densely populated vertical receiving array to single-point measurements. In each case, the intrinsic range-averaging of acoustic measurements provides integral constraints on the environmental model. The success of the inversion improves with increasing experimental complexity. With a vertical array, up to four parameters of the internal wave model can be recovered. For the simplest situation, two parameters can be fit with reasonable accuracy. The implications of these results for understanding oceanographic processes are discussed.