Study On The 3D Acoustic Propagation Model Based On The Parabolic Equation

The acoustic propagation model is an important issue in underwater acoustic research.Precise acoustic propagation model is of great significance for ocean acoustic signal processing.The geometry of the seafloor and other acoustic parameters vary at different depth,range and bearing.In the 1D acoustic models,parameters vary at different depth.The 2D acoustic propagation models take the range dependence into consideration.The standard acoustic models can produce full 3D fields by assembling slices in the range-depth plane for different bearing angles,such models do not generally allow for refraction out of each range-depth plane,which is the 3D effects.The 3D effects can't be ignored in the long propagation when the geometry varies fast.The parabolic equation approximation models take far field and one direction approximation and march with environment parameters involved in the marching step.It's suitable for high dimensional acoustic propagation modeling.When the square-root Helmholtz operator is approximated within two-dimensional Laplace operator,it's a three-dimensional model.The precision and efficiency of current 3-D acoustic models remain to be improved.This article studies of 3-D acoustic propagation model based on the parabolic equation approximation.The work is organized as following.Firstly,a high order approximation of the square-root Helmholtz operator is proposed,which takes three order Taylor expansion with cross term into account.And the error limit of the approximation is analyzed in theory.Secondly,the model is implemented using the split-step Fourier transformation method.Finally,the model is tested by simulation in Pekeris waveguide,seamount environment and the wedge problem.The acoustic field computed by the proposed model matches the RAM results in the Pekeris waveguide,seamount environment,also agrees with the image method in the wedge problem.Specially,the proposed high-order parabolic equation model outperforms Lin's PE,which is illustrated in the simulation for the Pekeris waveguide.