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KZK equation is used as the base of calculation. When the grazing angle of the source is smaller than the critical angle, the Snell’s law can not be used to determine the progressive direction of the evanescent wave in the sediment that is necessary for solving the KZK equation by using the finite difference method. In this paper, a phase-lag method is used to solve this problem. Numerical results are compared with the experimental results published by Muir et al. [J.Sound.Vib. 64, 539-551(1979)] and are shown in good agreement. Keywords—parametric array; bottom penetration; KZK equation

Numerical Calculation of the Penetration of Parametric Beams into Sediment