Recursive f-k migration of a body of seismic data performed in N stages, including establishing from an RMS velocity VRMS a laterally-averaged interval velocity profile extending from a surface at time zero to time t; determining layer boundaries within the laterally averaged interval velocity profile, including identifying a unique set of pairs of depth and vertical travel time giving rise to a minimum sum of squares of residuals for the layers; calculating reference velocities for each layer; time-stretching the entire body of seismic data; performing, upon the data in each layer of the body of seismic data not yet fully migrated, recursive stages of f-k migration, including using as input to a current recursive migration stage that portion of the output from a previous recursive migration stage that comprises data partially migrated; and inversely time-stretching the entire body of seismic data.
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