The knowledge of systematic traveltime differences in seismic recordings is essential for many important applications in exploration. Based on the assumption of locally coherent wavefields, I discuss the important concept of traveltime moveout and revisit the notion of virtual seismic sources, which, being central ingredients of the famous normal incidence point (NIP) and normal wave experiments, make use of reciprocity and raypath symmetries to replace the generally complex two-way ray geometry of a reflection by analogous simplified one-way propagating wavefronts. Using this concept of virtual seismic sources, I re-derive the well-known traveltime moveout expressions of the hyperbolic common reflection surface (CRS), multifocusing and the recently introduced implicit CRS operator, solely based on the simple geometry of straight rays and circular wavefronts. In the cause of these derivations I find, that the double-square-root moveouts of multifocusing and the implicit CRS reduce to the same expressions Höcht found for the zero-offset section and the common-reflection-point (CRP) gather. In these domains, the traveltime moveout is fully governed either by the normal or by the NIP wavefront, which indicates a high potential for unification of these approaches.
Continuing this path of unification, I catch up ideas of de Bazelaire formulated in the late eighties and suggest two conceptually different mechanisms to justify the assumption of straight rays and circular wavefronts for generally heterogeneous media. While one of these mechanisms constitutes in a shift in velocity to account for overburden heterogeneity, in the second approach a constant shift of the reference time leads to the same adaption of the moveout, indicating a fundamental duality of higher-order expressions in heterogeneous media. Based on this dual formulation, I suggest generalized expressions for the classical common midpoint (CMP) hyperbola, the hyperbolic CRS moveout, multifocusing and the implicit CRS operator, for which the joint application of both mechanisms suggests exciting applications, like diffraction separation, multiple discrimination or the inversion of the excitation time of a passive seismic source, whose applicability is confirmed in synthetic and field data examples. Utilizing the formal coincidence of the fictitious NIP and the physically real passive seismic one-way experiment, subsequent inversion of the passive seismic wavefront measurements via NIP tomography resulted in a reasonable estimate of the true velocity gradient. In this framework, the often misinterpreted role of multifocusing gets a unique explanation.
Complementing the moveout duality for heterogeneous media, I study the higher orders of these operators under controlled conditions and conclude that the fundamental notion of coupling is essential to explain the observed systematic differences. In that frame I find that the decreased performance of hyperbolic CRS for diffractions can be quantitatively explained by a lack of the necessary influence of the normal wave radius on the higher offset orders and consequently, a coupling strength, which is decreased by up to a factor of three, compared to the accurate diffraction reference. For diffractions, the study of the higher orders reveals that, while the midpoint half-offset coordinates obey the strongest possible coupling, the respective source receiver moveout contributions are completely decoupled for any reference offset. Following from this higher-order analysis, I, again, propose versatile applications, like finite-offset extrapolation, diffraction operator decomposition and partial CRS migration and demigration and proof their applicability for synthetic and field data examples.