Seismic migration in stratified media

A point diffractor is located in a medium where the velocity of sound propagation is linear in the vertical direction. The analysis is based upon the exploding reflector concept of D. Leowenthal et al. (1976), in which reflectors are replaced by seismic sources which explode at time t=0. The point diffractor is activated at time t=0, and the zero-offset time section is migrated with a constant velocity. Kinematic migration is a simple method to track waves through a medium of known velocity. There are two distinct parts of seismic migration: extrapolation and imaging. Extrapolation presupposes that the velocity changes are known, but to obtain an image of the subsurface, an imaging principle must be applied. An unknown velocity gradient and the depth of a point diffractor can be determined by relaxing the imaging condition to allow for an extra time-shift. The extra time-shift must be determined by focusing of the migrated output. The rays and the caustic enveloped by the family of rays stay fixed in space; hence, the present method yields unique results