In the short-note I wrote in the previous SEP report Berlioux (1993b), I presented a new method to perform depth migration in 3-D, starting from time-migrated maps. Since time migration does not always produce properly migrated images or maps in areas where velocity variations are present Hatton et al. (1981), the method I proposed consists of two parts: first undo the time migration by a principle of de-migration, and then perform the depth migration.
In my previous work these two parts were based on a ray-tracing algorithm, and the de-migration process corresponded to the inverse operation of Kirchhoff time migration. De-migration and time migration have to remain associated as inverse processes. I now investigate the method introduced in 1991 by V.J. Khare to perform time migration in order to produce a de-migration scheme corresponding to this process.
In this paper, I explain briefly how V.J. Khare derived the 2-D Eikonal equation for time migration and what modifications have to be introduced to handle the 3-D case, and I make a proposal to use this equation for the de-migration process.