The turn of the millennium has seen the long expected affordability of 3D prestack depth migration based on wave-equation, or better said, band-limited algorithms. The success of wave-equation PreSDM (prestack depth migration) comes from the fulfillment of two, and only two, promises: correct handling of geometrical spreading and correct handling of multipathing, in complex media. Even then, the migration velocity model needs to be accurate enough to ensure the full effectiveness of this expectedly correct handling of wave propagation. How to get a complex though correct velocity model is still an open issue and is beyond our scope. There are nevertheless capabilities of Kirchhoff migration that wave-equation PreSDM cannot emulate yet, though progress is being made. On the imaging side, Kirchhoff has the well-known capability of imaging steep dips. Kirchhoff migration can also handle velocity models with various types of anisotropy. On the amplitude side, Kirchhoff migration offers better handling of irregular acquisition, better amplitude control through the theory of Beylkin, and better understanding of all illumination and regularization issues. This understanding is needed because the regularization of illumination is the key to a reduction of classic migration artifacts, to an improvement of the image quality, and to the reliability of the migration amplitudes for AVA and 4D processing.

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