Reconstruction of the Linear Distribution of the Squared Buoyancy Frequency According to the Known Dispersion Properties of the Field of Internal Waves

We propose a method for the solution of the inverse problem of reconstruction of the vertical stratification of density in the ocean according to the known dispersion curves for internal gravity waves. For the stratification of density modeled by a linear distribution, we determine the accuracy of its reconstruction for values of the frequency of oscillations and wave numbers given with different degrees of accuracy. The posed problem is studied in the Boussinesq approximation for two traditionally used types of boundary conditions on the surface of the fluid. We deduce dispersion equations and focus our attention on their asymptotic analysis. An asymptotic solution of the inverse problem is constructed and its sensitivity to the degree of accuracy of the input data is investigated.