Gaussian beam migration of multi-valued zero-offset data

We develop a method for migration of zero-offset data based on the Gaussian beam approach and explore it for exploding reflector data in situations where input data are multi-valued because of caustics of different geometrical structure and physical nature. To this end we consider the following two 2D models. The first one can be referred to as "exploding sine" in inhomogeneous media with constant vertical gradient of the velocity where caustics appear due to curvature of the reflector. The second one contains a low-velocity lens immersed in a constant velocity layer. This lens gives rise to caustics and therefore multi-valued data on the seismic line. The results of imaging of the reflectors occurs to be different in those cases. For the first model the migration image of the reflector is sharp for a wide range of parameters of the medium and geometrical characteristics of the reflector. For the second model we observe dimming and even distorting phenomena on the migration image of the reflector underneath the lens.