This chapter is devoted to a brief presentation of the theoretical principles of spectral and non-spectral algorithms for analyzing in-situ measurements of wave packets in the ocean, which make it possible to determine the characteristics of the wave tsunamis constituting the measured hydrophysical fields: velocities and propagation directions, shapes, as well as ocean parameters along the propagation path of these wave tsunamis. Non-spectral algorithms for processing natural data based on mathematical modeling of the dynamics of linear and especially non-linear packets of internal gravity waves in the ocean make it possible to identify wave trains with certain characteristics, for example from non-local sources of disturbances, among other wave trains and random noise, which makes it possible to check the adequacy of the mathematical models used based on natural experiment data.