Efficient traveltime calculations for Kirchhoff migration

Abstract

Acoustic Kirchhoff migration is performed for each point (x, z) in an output depth section by an integrating or weigthed summing procedure. Each trace of the input time section contained in an aperture about x contributes to the sum, and the contribution from a trace at x + Δx consists of the element whose time is equal to the total time required for a seismic wave to travel from the source to the point (x, z) to (x+Δx,0). That is, Kirchhoff migration sees every subsurface location as a possible point scatterer and explicitly reverses the operation of scattering the diffracted seismic energy from such an obstacle onto an array of receivers as a function of time. Continuous reflectors are considered ensembles of point scatterers, and they are imaged by summing over traces for each point on the reflector. If the array of [Formula: see text] output depth points for a two‐dimensional (2-D) poststack migration contains [Formula: see text] points, and on the average [Formula: see text] points are included in each summation aperture, Kirchhoff summation requires [Formula: see text] add‐multiply operations.