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![]() | Random noise attenuation using local signal-and-noise orthogonalization | ![]() |
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Suppose that the seismic data
is composed of signal
and noise
, a successful random noise attenuation will give accurate signal and noise estimation:
and
, where
and
are the estimated signal and noise. However, the ideal situation may not occur in practice for two main possible reasons: incorrect parameter selection or inadequacy of denoising assumptions. When those assumptions are not met, the conventional denoising approaches may not achieve the optimal performance. For most noise attenuation approaches, the noise section will contain a certain amount of useful signal, which can be called signal-leakage energy. Sometimes, the leakage energy is negligible, whereas in other cases, this loss of energy may result in a decrease in resolution.
Local seismic attributes measure seismic signal characteristics neither instantaneously, at each signal point, nor globally, across a data window, but locally in the neighborhood of each point (Fomel, 2007a). One of the most useful local attributes is local similarity, which has found numerous successful applications in different areas of seismic data processing: multicomponent image registration (Fomel et al., 2005; Fomel, 2007a), time-lapse registration (Fomel and Jin, 2009; Zhang et al., 2013), time-frequency analysis (Liu et al., 2011b), structure-enhancing filtering (Liu et al., 2010), phase estimation (Fomel and van der Baan, 2014), etc. By using a weighted stacking of seismic data according to local similarity to the reference trace, a seismic image with an increased signal-to-noise ratio can be obtained (Liu et al., 2011a,2009). In this paper, we introduce a new local seismic attribute: local orthogonalization weight (LOW) in order to perform local orthogonalization. LOW appeared previously in the definition of local similarity and can be obtained by solving a minimization problem using shaping regularization with a smoothness constraint.
In order to compensate for the loss of useful signal in traditional noise attenuation approaches, because of incorrect parameter selection or inadequacy of denoising assumptions, we employ a weighting operator on the initially denoised section for the retrieval of useful signal from the initial noise section. The new denoising process corresponds to local orthogonalization of signal and noise based on the assumption that final estimated signal and noise should be orthogonal to each other in the time-space domain. The orthogonality assumption is similar as assuming that the signal and noise do not correlate with each other. Thus, the orthogonality assumption is assumed to be valid for all kinds of noise that do not correlate with the useful signal, e.g., random noise. The proposed local-orthogonalization approach can be considered as a specific case of previously proposed nonstationary matching filtering (Fomel, 2009) for one-point filter length. The proposed approach is not very sensitive to the parameter selection, and thus is robust in practice. We use two synthetic examples and three field data examples to demonstrate successful performance of the proposed approach in applications to both conventional and simultaneous-source seismic data.
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![]() | Random noise attenuation using local signal-and-noise orthogonalization | ![]() |
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