A representation of the solution of the initial-boundary value problem for the wave equation in a half-plane is given as an integral superposition of parameter-dependent packets (localized solutions). The parameters of each packet have the meaning of a coordinate on the boundary from which the packet is emitted, the direction in which it is emitted, the time of its emission, and its characteristic frequency. The excitation coefficient of an individual packet is a wavelet transform of the boundary data, which depends on the parameters and processes the boundary data. The resulting representation is applied to seismic migration.