Migration and migration inversion are the seismic processing methods for structural determination and subsequent amplitude analysis, respectively. To date, the most well-founded and physically interpretable migration method is based on predicting a coincident source and receiver experiment at depth at time equals zero. We have extended that migration method for heterogeneous media and to accommodate two-way propagation in a local sense at every point from the source to the target reflector and back from the reflector to the receiver and in a global sense, separately for each of the two legs from the source to the reflector and from the reflector to the receiver. That provides the first migration method that avoids high-frequency assumptions in the imaging principle and how it is implemented, and hence, it is equally effective at all frequencies at the target or reservoir. This advance for two-way wave propagation migration then provides a tool to quantitatively, unambiguously, and definitively define the role of primaries and multiples in migration. Our conclusion was that with data consisting of primaries and multiples, for an accurate discontinuous velocity model, only primaries contribute to migration with the same image and inversion results independent of whether multiples are kept or removed. However, for a smooth and continuous velocity model (i.e., generally assumed in practice), every multiple will result in a false, misleading, and potentially injurious subsurface image and hence must be removed before migration. In practice, we migrate with a smooth velocity model, and hence multiples must be removed. When the collection of primaries is incomplete, a multiple can be used to provide an approximate image of an unrecorded primary. However, it is always the migration of primaries that provides subsurface structure and amplitude information.

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