Migration of deep seismic data is often hindered by a narrow recording aperture (line length by record length) and a low signal-to-noise ratio. The severity of typical migration artifacts (e.g., lateral smearing of discontinuous reflections into synforms, smiles) increases with travel time such that interpreters of deep seismic data have often substituted migrated line drawings for the actual sections. As part of Project INDEPTH (International Deep Profiling of Tibet and the Himalaya), a new migration method was developed to address both the noise and migration issues. The method works in the time-space domain and uses the simple, constant velocity, straight ray path to perform the migration. First, only amplitudes within a given range are retained for migration, thus avoiding high-amplitude noise bursts and low-amplitude background noise. Then, the local dip of a reflection is found by automatically fitting a straight line to the highest amplitudes within a small window (several time samples by several traces) and calculating the dip of the line using a constant velocity. Finally, using this dip, the method migrates a selected amplitude value. The dips, lateral positions, and depths of the migrated events compare very well with output from more conventional algorithms (e.g., fk-Stolt, finite difference, etc.). The advantages of the new method include fewer artifacts, fast computer run times, low memory use and the ability to migrate long profiles and travel times (e.g., 50 s). The output of the method is a grid of migrated amplitudes (not wavelets) or dip values which is particularly effective for making small figures, such as those needed for publication. The principal disadvantage is the use of a constant migration velocity.¿ 1997 American Geophysical Union