The Goos-Hänchen shift of wide-angle seismic reflection wave

The partial derivative equations of Zoeppritz equations are established and the derivatives of each matrix entry with respect to wave vectors are derived in this paper. By solving the partial derivative equations we obtained the partial derivatives of seismic wave reflection coefficients with respect to wave vectors, and computed the Goos-Hänchen shift for reflected P- and VS-waves. By plotting the curves of Goos-Hänchen shift, we gained some new insight into the lateral shift of seismic reflection wave. The lateral shifts are very large for glancing wave or the wave of the incidence angle near the critical angle, meaning that the seismic wave propagates a long distance along the reflection interface before returning to the first medium. For the reflection waves of incidence angles away from the critical angle, the lateral shift is in the same order of magnitude as the wavelength. The lateral shift varies significantly with different reflection interfaces. For example, the reflected P-wave has a negative shift at the reflection interface between mudstone and sandstone. The reflected VS-wave has a large lateral shift at or near the critical angle. The lateral shift of the reflected VS-wave tends to be zero when the incidence angle approaches 90°. These observations suggest that Goos-Hänchen effect has a great influence on the reflection wave of wide-angles. The correction for the error caused by Goos-Hänchen effect, therefore, should be made before seismic data processing, such as the depth migration and the normal-moveout correction. With the theoretical foundation established in this paper, we can further study the correction of Goos-Hänchen effect for the reflection wave of large incidence angle.