Processing of anisotropic data in the tau-p domain: I.
Geometric spreading and moveout corrections
Mirko van der Baan
School of Earth Sciences,
University of Leeds, Leeds LS2 9JT, UK.
earmarvb@earth.leeds.ac.uk
ABSTRACT
Stacking of seismic data is conventionally done in the time-offset domain. This has the disadvantage that geometrical 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 geometrical spreading. Hence, processing of both isotropic and anisotropic data in such media benefits from first applying a plane-wave decomposition such as a proper tau-p
transform.
The resulting tau-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 geometrical 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 do require knowledge of the velocity field.
The proposed methodology is exact for 3-D data volumes and arbitrary anisotropy in laterally homogeneous media or for 2-D acquisition lines over 1-D, isotropic or VTI media. It relies on the same principles as more conventional geometrical-spreading corrections and time-offset stacking. In many respects, it is even more flexible. For instance, geometrical spreading has been correctly removed for all present wave modes and types simultaneously (primary, multiple, pure-mode and converted waves), and non-hyperbolic moveout due to 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 tau-p domain. The resulting stacked section can then be used for any post-stack processing such as time migration.