Goos–Hänchen induced normal moveout correction for wide-angle reflections

The Goos–Hänchen (GH) lateral shift has been theoretically simulated and observed in lab. GH lateral shift introduces additional traveltime and distance when the incidence angles are larger than the critical angle. For seismic wave, this GH shift is caused by the total reflection of an incident beam of P-wave from low to high impedance medium at near and post-critical angles. Because of its large influences on traveltime and lateral shift displacement, the GH shift should be corrected in normal moveout (NMO) correction for wide-angle reflections in seismic data processing. In this paper, we derive the partial derivatives of reflection coefficients (PP- and PSV-wave) with respect to circular frequency using the Zoeppritz equations. Then, the delay time and NMO correction term with the behavior of GH lateral shift is derived. The characteristics of delay time and GH induced time differences are analyzed. The results show that this GH shift could be either positive or negative and the delay on time has large influences on seismic reflections when the incidence angles are larger than the critical angles. The efficiency of GH induced NMO correction is tested using synthetic seismic data. The GH induced NMO correction should be done for wide-angle reflections during the progress of seismic data processing.