A high-frequency asymptotic expansion of a time-harmonic wavefield given on a curved initial surface into Gaussian beams is determined. The time-harmonic wavefield is assumed to be specified on the initial surface in terms of a complex-valued amplitude and a phase. The asymptotic expansion has the form of a two-parametric integral superposition of Gaussian beams. The expansion corresponds to the relevant ray approximation in all regions, where the ray solution is sufficiently regular (smooth) in effective regions of the beams under consideration.
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