Efficient one-pass 3-D time migration

An efficient one-pass 3-D time migration algorithm is introduced as an alternative to Ristow's splitting approach. This algorithm extends Black and Leong's k(y)-separation approach with a time-dependent Stolt stretch operation called dilation. Migration using k(y) dilation consists of a single pass over the 3-D data volume after k(y) slices are formed with each k(y) slice downward continued independently. A number of downward continuation algorithms based upon the 3-D wave equation may be used. Dilation accommodates any lateral variations in velocity before the 3-D data volume is decomposed into k(y) slices via a Fourier transform. An inverse dilation operation is performed after the downward-continuation operation and after the data volume have been inverse Fourier transformed subsequently along the k(y) direction. Migration using the k(y)-dilation approach yields a one-pass 3-D time migration algorithm that is practical and efficient where the medium velocity is smoothly varying.