Abstract:The lithology analysis in complicated structure area requires that a migrated seismic section in the area where seismic velocity varies laterally and vertically displays clear images of steep structure and fault;but the Stolt,stretch ,f-k and cascaded f-k migrations fails to meet the above requirement because of their limitations.Thus parallel f-k migration,a new fast migration,is put forward in the paper. It ineludes the following steps:Derive steep dip-dependent image velocity from the relationship between Gazdag phase migration and Stolt migration;Apply the image velocity to a group of constant-velocity Stolt migration to produce a set of migrated data;The proper interpolation of the migrated data brings a migration result equivalent to that of Gazdag method.The method is highly parallel and it is particularly suitable to mufti-CPU parallel computer system. Interactive mode is the best option in real varied velocity section construction which is achieved by making the migrated data interpolation. It is shown that the method is applicable to the situation where velocity varys laterally and vertically ,and results in clear high-steep image,good image effect,high signal noise ratio ,less processing cost,etc.