Efficient one‐pass 3‐D depth migration

Abstract

We introduce an efficient one-pass 3-D depth migration algorithm as an alternative to the spli t t ing approach (Claerbout, 1985). This algorithm extends the k separation approach (Black and Leong, 1987) with a time-dependent modifying operation we call dilation. Dilation in conjunction with parallel operations of downward continuation on the k slices yields a depth migration Y algorithm with better efficiency and accuracy characteristics than the splitting approach. k -dilation migration c o n s i s t s o f a Y single pass over the 3-D data volume with each k slice downward continued independently. Y Any downward-continuation algorithm based upon the 3-D wave equation may be used. Before the 3-D data volume is decomposed, the lateral velocity variations are accomodated with dilation. Dilation is a time-dependent modifying operation which transforms a time and spatially-variant velocity field into a time-variant velocity field only. The reverse operation is conducted after the migration and inverse k transformation. Analytic, model Y and field data studies indicate that migration us ing k separation in conjunction with Y dilation is a viable means of performing depth migration.