On the method of wave propagation in local angle domain

On the basis of the Helmoholtz equation for inhomogeneous media, we have deduced wave propagation formula using beamlet decomposition of wave field in general frame and employing the pseudo-differential operator, and obtain the marching algorithm of wave propagation in phase space (local angle domain). And also we have more freedom when choosing the frame of beamlet decomposition in one-way wave marching algorithm. Taking the scale-variable Gabor-Daubechies tight frame as an example, the specific expression of oneway wave propagator and corresponding marching algorithm are derived. And the high-frequency asymptotic problem of propagator based on Gabor-Daubechies tight frame is discussed in detail and its validity conditions are investigated, which could be used to increase the computation efficiency. The wave propagation results respectively by integrated propagator and high-frequency asymptotic one are compared by numerical examples, which demonstrates that the error of wave fields is quite small in certain high-frequency asymptotic conditions and the computation cost is averagely reduced by 30%.