This section details how multiples are generated by convolution of shot gathers. For a 1-D earth, the convolution can be done directly in the f-k domain. For a 2-D earth, the convolution becomes nonstationary. In addition, one convolution of the shot gathers tends to overpredict high-order multiples.
If p(g|s) represents a single frequency component of the primary reflected wavefield recorded at g after an impulsive shot at s, then the first-order surface-related multiple, m(g|s), can be computed with a Kirchhoff-style integral over the reflection surface: