Parabolic approximation of nonlocal boundary conditions in ocean acoustics

Abstract

A method for constructing parabolic approximations of the nonlocal

boundary condition which model the seabed of an oceanic acoustic waveguideis presented. The analysis departs from the exact impedance boundary conditon derived from the primitive elliptic model. The main tool is an appropriate asymptotic decomposition of the kernel of the integral operator in the nonlocal boundary condition, which reveals the forward and backward componentof the wavefield at the interface. This decomposition, in combination with the standard parabolic approximation of the field inside the waveguide, leads to a Volterra-type impedance boundary condition for the parabolic equation.It appears that this condition is almost, but not exactly, the same withthat derived when someone uses from the beginning the parabolic approximation of the wave field in the bottom

Keywords:

• acoustic waves
• asymptotic expansions
• transform methods
• nonlocal boundary conditions