Preserved‐traveltime smoothing

Abstract

ABSTRACTMost ray‐based migration and tomography methods require a certain degree of smoothness of the depth velocity model. Since smoothing changes the velocity model, it is generally impossible to preserve the traveltime between all pairs of points in the model. Using conventional smoothing, the traveltime errors are particularly large at discontinuities in the velocity model. These errors are offset‐dependent and they cause errors in both the depth and residual moveout (RMO) of depth migrated images. Here we propose a new method, Preserved‐Traveltime Smoothing (PTS) with an objective of preserving traveltimes (and hence depths) at these discontinuities. This is accomplished by smoothing of velocity moments for anisotropic models using a specific cross‐correlation filter with the desired smoothness properties. The method is valid for isotropic, transversely isotropic with vertical symmetry axis (VTI) and structural transverse isotropic (STI) models. The variations of the model parameters perpendicular to the symmetry axis of the anisotropy are assumed to be small.