Three dimensional acoustic parabolic equation based on Chisholm approximation with the splitting denominator

Abstract

We propose the generalized form of three dimensional acoustic parabolic equation (3DPE) based on Chisholm approximation [Chisholm, Math. Comp. 27, 841-848 (1973)] of a rational approximant for two variables, and the splitting denominator assumption. The proposed form has wider angle accuracy to the inclination angle of ±620 from the range axis of 3DPE at the bearing angle of 450. Moreover, the splitting denominator makes the split-step algorithm with finite-difference depth solver more efficient in that the 3DPE can be easily transformed into the tridiagonal matrices system. One drawback of this method is the increase of the phase error in the evanescent region, but should be practically remedied by several skills. In this study, the comparative study of other PE approximations will be conducted based on the phase error analysis. Also, numerical examples with three dimensional problems will be given for the performance and benchmark test.