Efficient prediction of acoustic pulses accounting for fractional travel time

Predicting a full waveform of an acoustic broadband signal propagating over different impedance surfaces is a stringent test of both the method used in the modeling of propagation and the surface impedance models. It has been shown that predicted waveforms might be sensitive to the fractional travel time, when the propagation time of the pulse does not equal an integer number of computational time steps. A method overcoming this issue is developed and demonstrated for different propagation conditions: a pulse propagating over a snow layer, frozen ground, and their combinations along the propagating path with homogeneous and vertically stratified atmosphere for a range of 60 m. For the numerical simulations, a conventional one-way parabolic equation with the Crank-Nicholson numerical algorithm is modified to improve computational efficiency and insure that the experimental time of arrival and spatial location of the receiver are matched exactly to the digital grids used in the simulations. The results are in a good agreement with experimental measurements and prior knowledge, and confirm that physical properties of a snow layer, sublayer ground, atmospheric conditions, and the order of range dependent ground properties affect the pulse waveforms.