The quality of the surface‐consistency assumption in short‐wavelength static correction

Abstract

Founded on the assumption of surface consistency, reflection‐based residual‐statics correct for the time distortions in seismic data arising from rapid near‐surface variations. The assumption is founded on a vertical‐path, ray‐theoretical model of wave propagation in the near surface. Since ray theory does not hold for models with rapid spatial variation, we resort to finite‐difference modeling to study the influence of wave‐theoretical aspects on the character of time distortions and the validity of the surface‐consistency assumption. For near‐surface models that are admittedly simple and idealized, we find that the character of time distortions is highly influenced by a wavefront‐healing phenomenon whose strength depends on the ratio of the size of the frequency‐dependent Fresnel zone to the wavelength of lateral variation in the model. As experienced in practice, the quality of the surface‐consistency assumption degrades with increasing ratio of spreadlength to reflector depth. The validity of the assumption is best for longer‐wavelength anomalies in a weathering layer that is relatively thin. Wavefront healing, however, limits significantly the time‐distortion problem where the weathering layer is relatively thick. Interestingly, wavefront healing also helps to reduce the size of the time‐distortion problem when the velocity in the surface layer is large relative to that in the layers beneath, such as in areas of permafrost.