Velocity-independent $\tau$ -$p$ moveout in a horizontally-layered VTI medium

Conclusions

Local slopes of seismic events carry complete information about the structure of the subsurface. We have developed a velocity-independent $\tau$ -$p$  imaging approach to perform moveout correction in 2D layered VTI media. We process Radon-transformed data because $\tau$ -$p$  is the natural domain for anisotropic parameter estimation in vertically-variable media. Effective VTI parameters turn into data attributes through the use of slopes and are directly mappable to the zero-slope traveltime. Interval parameters turn into data attributes as well. We have developed the analytical theory for the slope-based Dix inversion in $\tau$ -$p$  , as well as two alternative sets of equations that can be regarded as an extension of Claerbout's method for straightedge determination of interval velocity. Both sets of equations exploit the intrinsic layer stripping power of the $\tau$ -$p$   domain to estimate interval parameters directly without involving effective parameters.

The equations we have introduced to retrieve both effective and interval parameters in VTI media require directly or indirectly an estimation of the local data curvature. On the other hand, Fowler's equations do not require an explicit use of the curvature. Therefore, we propose bypassing the curvature estimation by exploiting a curvature-independent estimation of the zero-slope time $\tau _{0}$ field that, together with the slopes, provides the input to Fowler's method. The zero-slope time can be found efficiently by employing the predictive painting algorithm. A reference trace at the zero-slope time $\tau _{0}$ is spread along the local data slope to predict the $\tau _0$ field along reflection curves in the $\tau$ -$p$ CMP gather. This estimation appears robust and efficient enough to enable automated, slope-based, dense estimation of interval parameters.

Velocity-independent $\tau$ -$p$ moveout in a horizontally-layered VTI medium