Wavefield separation using the f–ξ domain for vertical seismic profiling data

Wavefield separation is an essential and critical step in data processing of vertical seismic profiles (VSPs). The τ–p transform is one of the effective approaches for separating the VSP wavefield. To further improve the efficiency of the τ–p transform, we developed an f–ξ domain τ–p transform based on the high-resolution Radon transform. The introduction of a new variable ξ removes the frequency dependence of the transform operator. As a result, the transform operator needs to be computed only once for all frequency components, which significantly improves the computational efficiency without decreasing accuracy. Furthermore, because the events of upgoing and downgoing waves are distributed in the vicinity of straight lines with different slopes through the origin in the f–ξ domain, we can easily define a filter to separate the upgoing and downgoing waves. Model tests showed that the wavefields are well separated and that the new method is a factor of ~3 faster than its counterpart in the τ–p domain. The field data example further demonstrates the effectiveness and feasibility of the approach.