大步长单程波算子相位积分实现方式初探

大步长单程波算子是穿过厚层的单程波算子的积分,在理论上它可以通过频率波数域表达式和波数域到空间域变换来实现,目前,通过李代数积分和指数映射的研究,已经导出频率波数域表达式,需要研究波数域到空间域变换的实现方式,波数域到空间域的变换可以通过鞍点法和相位积分来实现,本文研究了相位积分的三种实现途径:分裂方法、相移加插值方法和佳格点方法,在相移加插值方法中提出一种波场"角度域插值"的插值方法.

Preliminary study on the phase integral method with a Large step one-way wave operator

The large step one-way operator is the integral of one-way operators which go through the thick layer. In theory, it can be realized by frequency-wavenumber domain expression and transform from wavenumber domain to space domain. At present, frequency-wavenumber domain expression has been derived by Lie algebra integral and exponential mapping, and we need to research the method of transform from wavenumber domain to space domain. Transform from wavenumber domain to space domain can be realized through the saddle point method and phase integral. This paper presents a preliminary study on three methods about phase integral: split method, PSPI method and Good Grid Point method. In the PSPI method, we syggest a wave field angle domain interpolation method.