Stacking of seismic data is conventionally done in the time-offset domain. This has the disadvantage that geometric spreading must be removed before true-amplitude processing can be attempted. This inconvenience arises since wave motion in the time-offset domain is determined by spherical waves. Plane waves in layered media, on the other hand, are not subject to geometric spreading. Hence, processing of both isotropic and anisotropic data in such media benefits from first applying a plane-wave decomposition such as a proper τ-p transform. The resulting τ-p gathers can be flattened and stacked over slowness. Subsequent time differentiation is needed to counter the loss of high frequencies during stacking. This approach has the advantage that the geometric spreading is removed without prior knowledge of the actual (an)isotropic velocity field and without any need to pick traveltimes or moveout velocities. Subsequent moveout corrections naturally require knowledge of the velocity field.

The proposed methodology is exact for 3D data volumes and arbitrary anisotropy in laterally homogeneous media or for 2D acquisition lines over 1D, isotropic media or over 1D, transversely isotropic media with vertical axis of symmetry (VTI). It relies on the same principles as more conventional geometric spreading corrections and time-offset stacking. In many respects, it is even more flexible. For instance, geometric spreading has been correctly removed for all present wave modes and types simultaneously (primary, multiple, pure-mode, and converted waves), and nonhyperbolic moveout resulting from isotropic layering is also taken into account. In addition, head waves may now contribute constructively to the stacked section. Moreover, both multiple elimination and predictive deconvolution are straightforward and known to yield very good results in the τ-p domain. The resulting stacked section can then be used for any poststack processing such as time migration.

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