First, we need to generate a multiple model with correct kinematics and amplitudes. This can be quite a computation burden. Nonetheless, multiple attenuation is a prerequisite to any imaging step. Thus, instead of trashing these multiples, we might simply use them for migration. As an intermediate solution, I propose to use both primaries and multiples in the up-going wavefield. This is a cheap alternative to the full multiple attenuation that yields an interpretable image of the subsurface.
Second, the final image after migration of multiples is more noisy than the migration of primaries. In the synthetic data example I proposed using the water-bottom reflection for the source function. In practice the amount of muting depends on the subsurface, i.e., the main ``generators'' of multiples.
Last, we might not be able to simply add the different images in order to increase the signal-noise ratio. When primaries are migrated, we use a synthetic source that is not the true seismic source. When multiples are migrated, the source is perfectly taking into account because we use the recorded wavefield as a source. Hence a direct addition of the migration results of primaries and multiples must be done with care.
As a final comment, the North Sea example perfectly illustrated the need for a targeted preprocessing of the data. In this case I should have corrected for cable feathering before multiple migration. Similar preprocessing steps are needed for the surface-related multiple attenuation technique ().