The relation between the VSP-CDP transformation and VSP migration

Abstract

Mapping offset VSP data from the depth-time domain in which it is acquired to the offset-depth domain in which structural interpretation is most easily performed can be done by VSP-CDP transformation or wave-equation migration. The transformation is the most widely accepted method because it is based on a model of the structure that may incorporate information from other sources; for example, well logs and surface seismic data, The transformation is also useful because it requires relatively little computation and, therefore, can be performed iteratively to obtain a good match between data and model. An assumption underlying the transform method is that the signal arriving at a given time on a given trace is from a unique reflection point. When reflections from more than one point arrive at the same time, the transformation cannot map both of them to their correct locations. VSP migration based on the wave equation does not have this limitation, but it cannot be applied until a velocity model has been defined; and it works best when the range of dips allowed in the migrated image is restricted. Because of these complementary capabilities, VSP-CDP transformation and VSP migration are applied most usefully when the transformation is used to produce a refined velocity and dip model, and migration is performed afterward using that model. The transformed and migrated images are quite similar when migration is performed with the local dip of the image tightly limited of the dip of the transform-derived model; but migration also correctly images simultaneous, cross-dipping events when the dip limits of the migrated image allow dips not mapped by the transformation.