Filtering coherent noise during prestack depth migration

We can often suppress short-period multiples by predictive deconvolution. We can often suppress coherent noise with significantly different moveout by time-invariant dip filtering on common-shot, common-receiver or NMO-corrected common-midpoint gathers. Unfortunately, even time variant dip filtering on NMO-corrected data breaks down in the presence of strong lateral velocity variation where the underlying NMO correction breaks down. Underattenuated multiples, converted waves, and diffracted head waves can significantly impede and/or degrade prestack migration-driven velocity analysis and amplitude variation with offset analysis as well as the quality of the final stacked image. Generalization of time-variant dip filtering based on conventional NMO corrections of common-midpoint gathers also breaks down for less conventional data processing situations where we wish to enhance data having nonhyperbolic moveout, such as converted wave energy or long-offset P-wave reflections in structurally deformed anisotropic media. We present a methodology that defines a depth-variant velocity filter based on an approximation to the true velocity/depth structure of the earth developed by the interpreter/processor during the normal course of their prestack imaging work how Velocity filtering in the depth domain requires the design and calibration of two new least-squares transforms: a constrained least-squares common offset Kirchhoff depth migration transform and a transform in residual migration-velocity moveout space. Each of these new least-squares transforms can be considered to be generalizations of the well-known discrete Radon transform commonly used in the oil and gas exploration industry.