Smiles and frowns in migration/velocity analysis

Reliable seismic depth migrations require an accurate input velocity model. Inaccurate velocity estimates will distort point diffractors into smiles or frowns on a depth section. For both poststack and prestack migrated sec- tions, high velocities cause deep smiles while low veloci- ties cause shallow frowns on migrated gathers. However, for prestack images in the offset domain, high veloci- ties cause deep frowns while low velocities cause shallow smiles. If the velocity is correct, there will be no varia- tion in the depth migration as a function of offset and no smiles or frowns in the offset domain. We explain migra- tion responses both mathematically and graphically and thereby provide the basis for depth migration velocity analysis.