VSP migration by single shot record inversion

Vertical seismic profile (VSP) data have been used for many years to obtain lithological information from the subsurface in the direct vicinity of the borehole, and to 'calibrate' the seismic processing of surface data (Hardage 1983; Balch & Lee 1984). A relatively unexplored aspect of VSP data is the potential to obtain structural information from the subsurface around the borehole. Structural information can be obtained both from surface data and from VSP data by seismic migration. As opposed to surface data migration, however, very few publications on VSP data migration have appeared in the seismic literature. Amongst others, we mention Gazdag & Sguazzero (1983) and Chang & McMechan (1986). Some important complications to be dealt with in VSP migration are the severe variations of the propagation velocity along the borehole, the steep propagation angles (relative to the normal to the borehole) and the sometimes significant deviations of the borehole from the vertical. In this paper we discuss an efficient, wave-equation-based VSP migration scheme which copes with all these problems. The scheme is a generalisation of pre-stack migration by single shot record inversion as proposed by Berkhout (1984).