Wavelet transforms allow efficient analysis of signals in one or more dimensions. The signals may be expressed at different scales of resolution. This provides schemes for compression of informations in image and speech processing. The mathematical framework of wavelet analysis is novel and well grounded in theoretical works and the computation of wavelet transforms is based on an efficient iterative algorithm. This work deals with the use of wavelet transform in the downward continuation problem for acoustic propagation. The operator for a constant velocity layer is expressed using a one-level wavelet transform. The wavelet representation of this operator is sparser than its standard space representation. The different parts of the impulse response wavefield, corresponding to four submatrices of the wavelet space operator are separated and illustrate the dominance of the slowly varying (‘low frequency’) part of the wavefield. Seismic data is often slowly varying as a function of horizontal spatial variables. This suggests that very efficient downward continuation may be obtained by separating seismic wavefields using wavelet analysis.