VSP wavefield separation using the gray-scale Hough transform: synthetic data

The principal objective in Vertical Seismic Profile (VSP) processing is the separation of the downgoing and upgoing wavefields. Several methods have been suggested in this area. This paper presents a new approach based on the gray-scale Hough transform (GSHT) which is an extension of the conventional Hough transform used to detect straight lines and other curves. The technique, we suggest here, directly maps the gray-scale VSP image, including the downgoing and upgoing linear events, in image coordinate space (x,t,g) to the gray Hough parameter counting space (θ,ρ,g), where θ and ρ are the polar parameters and g is the gray-scale value. In this new space, the downgoing events appear in the negative angles θ quadrant and the upgoing in the positive quadrant, owning to their opposite apparent velocities. The inverse GSHT algorithm, we developed in this study, is performed for extracting separately these two wavefields by considering the straight lines that satisfy the corresponding filtering conditions. The experimental results on synthetic VSP datasets are convincing. The wave separation is well performed, even in the presence of loud noise levels, with signal to noise ratio improvement and amplitude preservation, in contrast to median filtering.