In addition, we discuss a generalized finite-offset NMO expression that can likewise be applied to active-source diffraction data and passive seismic events.

Following the early work of de Bazelaire, we suggest a simple transformation between both domains and introduce generalized dual representations of the hyperbolic CRS, multifocusing, and the two recently introduced double-square-root expressions implicit CRS and nonhyperbolic CRS. In this work we seek to demystify the wavefront picture by demonstrating that the conventional and multi-dimensional NMO operators can conveniently be derived from the same auxiliary straight-ray geometry, either representing the optical projection or formulated in an effective replacement medium. In addition, CRS and multifocusing show distinctly different behavior in that they respond differently to both, overburden heterogeneity and curvature of the target interface, and either are or are not susceptible to moveout stretch. As a consequence, the unifying nature of multi-parameter NMO is still not well appreciated. Multi-parameter expressions such as the common reflection surface (CRS) or multifocusing are parameterized in terms of local slopes and curvatures of emerging wavefronts rather than effective velocities, which makes these approaches appear conceptually different from conventional velocity analysis.

While in the past, in the context of stacking, traveltime moveout was only formulated in individual common-midpoint (CMP) gathers, multi-parameter stacking utilizes normal moveout (NMO) approximations, which span several neighboring CMPs.

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