Abstract: A method of prestack time migration based on the principles of prestack Kirchhoff time migration that can be applied to both 2-D and 3-D data. Common scatter point (CSP) gathers are created as an intermediate step for each output migrated trace. Normal moveout (NMO) and stacking of CSP gathers is performed to complete the prestack migration process. The method of the present invention allows the CSP gathers to be formed at any arbitrary location for velocity analysis, or to prestack migrate a 2-D line from a 3-D volume. The CSP gather is similar to a CMP gather as both contain offset traces, and both represent a vertical array of scatter points or reflectors. The CSP gather is formed from all the input traces within the migration aperture. Samples in the input traces are assigned an equivalent offset for each CSP location, then copied into the appropriate offset bin of the CSP gather in an efficient manner. The input time samples remains at the same time when copied to the CSP gather.