Seismic denoising using the redundant lifting scheme

Separating linear coherent noise, such as ground roll from reflections, remains a key challenge in seismic processing. By adapting the redundant lifting scheme (RLS), a wavelet transform method, to seismic data, we have determined how the wavelet domain can be used to suppress coherent and random noise. The RLS operates on a trace-by-trace basis decomposing each time series into wavelet-coefficient (WC) time series and consequently a single gather (in a shot, receiver, or common depth point domain) into a series of WC subgathers (SGs). The decomposition changes the relative magnitude of WCs of various events (reflection, head wave, ground roll, etc.) from one SG to another without affecting their moveout. In SG(s) in which the WCs of undesired events were significantly stronger than the desired events, the WCs can be surgically muted. Selective muting in carefully chosen SGs attenuates undesired events while having minimal effects on frequency spectra of the desired events. In addition, random noise can be suppressed in the individual SGs by designing a local thresholding mechanism (we have used modified Otsu thresholding) in combination with adaptive Wiener filtering. We have developed this approach of suppressing coherent and random noise in a step-by-step manner first using a synthetic shot gather, followed by demonstration on two real gathers. Our RLS-based denoising method has minimal effects on the lower end of signal frequency spectra, and it could be a valuable tool in a processor’s toolbox when data preconditioning for advanced processing such as waveform inversion, which benefits from low frequencies, is desired.