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The slant-stack or T-P domain offers an alternative representation for seismic data. lts theoretical advantages over the conventional time-offset domain have been studied extensively and are well known. In practice, however, the numerical artefacts of the T-P transform, produced by spatial aliasing and aperture limitations, quite often overpower the expected theoretical advantages. Moreover, the presence of random and coherent noise in the data further deteriorates the performance of the transform. Thus, subsequent processing in the T-P domain becomes less effective. In this paper, we present some applications of slant-stack processing for seismic reflection data. The cornerstone is a new improved T-P transform which incorporates a time- and offset-variant velocity filter. The resulting T-P gathers are free of most transform artefacts and exhibit improved signal-to-noise ratios. First, the performance of the transform is shown with applications both to noise-free synthetic data and to field data contaminated with coherent noise. The forward/inverse T-P transform pair is then applied to the common-shot gathers and the results are compared with those obtained from conventional frequency-wavenumber (f-k) filtering. FinaIly, we combine the forward transform with elliptical moveout (EMO) and stacking and obtain stacked sections in the slant-stack domain. This processing sequence avoids the need for an inverse transform and has several advantages over conventional norm al moveout (NMO) and stacking in the time-offset domain.