Time‐varying time‐shift correction by quasi‐elastic deformation of seismic traces [Link]

Residual static correction is based on a model of time shifts (delays) that depend solely on source and receiver locations at the surface. This assumption is valid if all raypaths are vertical in the near‐surface layering. We consider a more general model of the time‐varying time shifts that remain after hyperbolic NMO correction (of non‐hyperbolic trajectories) and static correction. We assume that the wavelet distortion caused by the time‐varying shifts is smooth. We have developed an algorithm for its correction (phase correction), based on minimization of the target functional with a penalty term similar to the quasi‐elastic energy of the time‐axis deformation. The use of a mechanical analogy for optimization is well known (e.g. simulated annealing). We propose here a stable numerical method that deals with a pair of seismic traces. It may be applied to phase correction of CMP (or CDP) gathers and stacked sections. Synthetic and field examples confirm that our method appreciably increases the signal‐to‐noise ratio, and improves the coherence and resolution.