Application of the Radon-FCL approach to seismic random noise suppression and signal preservation

The fractal conservation law (FCL) is a linear partial differential equation that is modified by an anti-diffusive term of lower order. The analysis indicated that this algorithm could eliminate high frequencies and preserve or amplify low/medium-frequencies. Thus, this method is quite suitable for the simultaneous noise suppression and enhancement or preservation of seismic signals. However, the conventional FCL filters seismic data only along the time direction, thereby ignoring the spatial coherence between neighbouring traces, which leads to the loss of directional information. Therefore, we consider the development of the conventional FCL into the time-space domain and propose a Radon-FCL approach. We applied a Radon transform to implement the FCL method in this article; performing FCL filtering in the Radon domain achieves a higher level of noise attenuation. Using this method, seismic reflection events can be recovered with the sacrifice of fewer frequency components while effectively attenuating more random noise than conventional FCL filtering. Experiments using both synthetic and common shot point data demonstrate the advantages of the Radon-FCL approach versus the conventional FCL method with regard to both random noise attenuation and seismic signal preservation.