Geometrical fundamentals of seismic imaging: realization of contact mappings

In this paper, a general formulation of the seismic imaging process on the base of ray theory is proposed. Media and wavefields are considered within geometrical seismics: a medium consists of reflectors and refractors, a useful component of the wave field coinciding with basic terms of a ray series. As connections of reflectors and seismic traveltime surfaces belong to a class of contact mappings, the problem of migration is posed as realization of a given contact mapping in a class of wavefield transforms (including the class of pseudodifferential operators.