Ground roll attenuation in the radial trace domain

The radial trace transform was introduced by the Stanford Exploration Project many years ago (Ottolini, 1979 and Claerbout, 1983), primarily for use in migration and imaging applications. It has been shown subsequently, because of its particular geometry, to be very useful for wavefield separation (Claerbout, 1983) and coherent noise attenuation (Henley, 1999). The radial trace transform, unlike such transforms as the F-K transform, is a mapping transform which takes each point of the X-T plane into a point of the R-T plane, and vice versa for the inverse.
R-T coherent noise techniques rely on the fact that separation of linear noise from reflections can be achieved in the radial trace domain by aligning the transform coordinate trajectories with the linear noise wavefronts in the X-T domain. This causes linear noises which spread across all the traces of an X-T gather to be isolated into small groups of radial traces. In addition, the apparent frequencies of these events are shifted from the seismic band to much lower frequencies (Henley, 1999) by the geometric distortion of the transform.
The Radial Trace Transform (RTT), is a simple coordinate transform of normal (t , x) domain seismic gathers; x=vt. The radial coordinate is termed “v” because the RTT sorts the data by apparent velocity. Neglecting dispersion effects, ground roll maps to zero temporal frequency in the RT domain. A linear noise distributed across many traces of an X-T gather maps into relatively few radial traces; and the apparent frequencies of these noise traces shift from the seismic band to sub-seismic frequencies (Henley, 1999). Both these effects of the R-T transform can be used to attenuate the noise relative to reflection signal in the R-T domain. The most straightforward way to attenuate coherent noise in the R-T domain is to apply a high-pass (low-cut) filter to the radial traces, which directly suppresses coherent noises mapped by the R-T transform to sub-seismic frequencies.
Filtering seismic data in the radial trace (R-T) domain is an effective technique for attenuating coherent noise on ensembles of seismic traces. In some applications R-T filtering can be more effective than more established methods like F-K filtering. One of the important advantages of the radial transform with respect to F-K transform is the ability to transform non-uniformly sampled data, such as a shot gather with irregular source-receiver offset values.