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

Jump to navigation
Jump to search

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.