Treatment of an elastic bottom in the parabolic approximation

Abstract

The use of impedance boundary conditions in the solution of the parabolic equation in underwater acoustics enables the treatment of bottoms of various types provided that appropriate boundary conditions can be expressed. The conditions are incorporated in an implicit finite difference (IFD) scheme for the parabolic equation. The integrals appearing in the computing scheme are evaluated either analytically, if possible, or numerically. For a sea bottom considered as an elastic homogeneous half-space, an impedance boundary condition can be evaluated relating the acoustic field in the sea at the water-bottom interface with that of the elastic bottom. The condition is inserted in the IFD scheme and the pertinent integrals are evaluated numerically by means of a fast Fourier transform algorithm. Results demonstrating the satisfactory behavior of the scheme are presented for range-independent environments. However, the method is also directly applicable to range-dependent environments.