Three-dimensional parabolic equation model for seismo-acoustic propagation: Theoretical development and preliminary numerical implementation

Tang Jun^{1, 2}, Piao Sheng-Chun^{1, 2}, Zhang Hai-Gang^{1, 2, †}

(color online) Plots of phase error ε versus azimuth φ for Padé approximations for n = 4, 6, and 8. The quantity n_s denotes the number of stability constraints. Intersections between the curves and the horizontal line of ε = 0.0002, which represents the error tolerance, shows the limitation angle in each case.