Spatiotemporal dynamics of the sound field in a shallow-water waveguide: Space-time horizontal rays and Klein–Gordon equation for mode amplitudes in the time domain

The paper considers spatiotemporal evolution of a pulse in a horizontally inhomogeneous waveguide (coastal wedge). The acoustical field is simulated using two different approaches. The first approach consists in numerical computation for mode amplitudes in the time domain. It is shown that these amplitudes as functions of time and horizontal spatial coordinates satisfy the Klein–Gordon equation. This equation can be efficiently solved numerically using finite-difference method and transparent boundary conditions. The second method is based on the theory of space-time rays applied to “vertical modes and horizontal rays” approach in marine acoustics case. Such a method allows us to efficiently compute amplitude and phase distributions in dynamics (in time) with addition of other more detailed characteristics like amplitude and phase fronts, pulse deformations in time and space, etc. at the given area in space without construction of the global solution in some sufficiently large area. Within the framework of both methods, the evolution of amplitude and phase fronts of a pulse signal propagating in a coastal wedge with perfectly reflecting boundaries are studied. The position of caustics and the spectra of observed signals for the receivers deployed at different distances from the source along the wedge apex are considered. The applicability of the spatiotemporal ray method is discussed.