Numerical tests of parabolic equation algorithms for field computations over totally reflective three‐dimensional bottoms

Abstract

Computations with two‐ and three‐dimensional versions of the parabolic equation (PE) split‐step Fourier algorithm were compared with normal mode theory and diffraction theory to ascertain the adequacy of PE computations for propagation over a totally reflective bottom. All PE computations were for 10 Hz in a constant sound speed water column with discrete depth and range steps of 20 and 100 m, respectively. Totally reflective bottom boundaries were simulated by a discontinuous fluid sound speed at grazing angles less than critical. Transmission loss over a flat 13° critical angle fluid bottom reproduced essentially the same structure as given by normal mode theory for ranges less than 200 km. PE computations of the field near the edge of a perfect reflector provided a reasonable approximation of the general features exhibited in diffraction theory results. Swept beam three‐dimensional PE computations incorporating reflections from an arbitrarily inclined plane correctly displayed reflected beams at angles in agreement with geometrical considerations. Implications for computation of propagation effects over realistic bottoms composed of three‐dimensional sediment or rock facets are discussed.