Translations:Mathematical foundation of 3-D migration/4/en

This equation describes propagation of a 3-D compressional zero-offset wavefield P(x, y, z, t) in a medium with constant material density and compressional wave velocity v(x, y, z), where x is the horizontal spatial axis in the inline direction, y is the horizontal spatial axis in the crossline direction, z is the depth axis (positive downward), and t is time. Given the upcoming seismic wavefield P(x, y, z = 0, t), which is recorded at the surface, we want to determine reflectivity P(x, y, z, t = 0). This requires extrapolating the surface wavefield to depth z, then collecting it at t = 0.