Reverse time shot-geophone migration

Shot-geophone migration, commonly accomplished using wavefield depth extrapolation (“survey sinking”), has a two way reverse time realization as well. The reverse time version permits imaging of overturned reflections. Shot-geophone migration differs from other prestack migrations in the definition of the prestack image volume which it creates. This difference is most clearly seen by identifying shot-geophone migration as the adjoint of an appropriate forward modeling operator. The offset vector parametrizing shot-geophone image gathers need not be horizontal, and this fact can be used to good effect in constructing prestack images of near-vertical or overturned structures. Unlike other prestack migrations, the image property of shotgeophone migration characteristic of correct velocity focussing of reflection energy at zero offset holds in strongly refracting media. INTRODUCTION The basis of migration velocity analysis is the semblance principle: prestack migrated data volumes contain flat image gathers, i.e. are at least kinematically independent of the bin or stacking parameter, when the velocity is correct (Kleyn, 1983; Yilmaz, 1987). Migration velocity analysis (as opposed to standard NMO-based velocity analysis) is most urgently needed in areas of strong lateral velocity variation, i.e. “complex” structure such as salt flanks, chalk tectonics, and overthrust geology. However strong refraction implies multiple raypaths connecting source and receiver locations with reflection points, and multiple raypaths in turn imply that the semblance principle is not valid: that is, image gathers are not in general flat, even when the migration velocity closely approximates the true propagation velocity (Stolk and Symes, 2004). The Rice Inversion Project, Department of Computational and Applied Mathematics, Rice University, Houston TX 77251-1892 USA, email [email protected] Department of Applied Mathematics, University of Twente, Drienerlolaan 5, 7522 NB Enschede, The Netherlands, email [email protected] Stanford Exploration Project, Department of Geophysics, Stanford University, Stanford CA 943052215 USA, email [email protected] The Rice Inversion Project, Department of Earth Sciences, Rice University, Houston TX 77251-1892 USA, email [email protected]