A nonstationary description of depth migration

Robert James Ferguson, Gary F. Margrave

Application of nonstationary filters in a depth-stepping manner allows an estimate of the angle-dependent reflectivity for a heterogeneous subsurface. For simplicity, a 2D geometry is adopted and scalar wave propagation is assumed. Migration of a single source gather proceeds by nonstationary combination filtering, followed by an offset dependent time shift and spreading correction. Source gather migration generalizes, for a seismic line, to nonstationary combination filtering of source gathers, followed by nonstationary convolution filtering of geophone gathers. Zero offset migration, when derived as a special case of source migration, uses a single nonstationary extrapolator that is a symmetric of combination and convolution filters.