Dynamics of Sonic Wave under Reflection and Transmission at the Interface of Water and Sand Saturated with Water or Gas Hydrate

The problem of reflection and refraction of acoustic wave at oblique fall on the interface of water and sand saturated with water or gas hydrate is considered. It is assumed that the sound source is located away from the interface. The water is assumed to be compressible in acoustic approximation, and the sand is assumed to be an elastic isotropic body. The mathematical model includes equations for velocity potentials of incident and reflected waves, as well as longitudinal and transverse waves passing into sand. The components of the displacement vector of medium particles, wave numbers of waves are recorded. Boundary conditions express the equality of the displacement vector components normal to the interface, and the equality of normal stresses. In addition, there are no tangential stresses in the sand during the passage of an acoustic wave. The coefficients of reflection of the incident wave from the interface, as well as the coefficients of propagation of the longitudinal and transverse waves through the sand, are analytically obtained. An analysis of the influence of the angles of incidence of the sound wave on the modules of reflection and propagation coefficients at different saturation of sand with water or gas hydrate was carried out. The dynamics of the signal near the interface was built using the fast Fourier transform algorithm.