Random noise attenuation using local signal-and-noise orthogonalization

Abstract

We propose a novel approach to attenuate random noise based on local signaland-noise orthogonalization. In this approach, we first remove noise using one of the conventional denoising operators, and then apply a weighting operator to the initially denoised section in order to predict the signal-leakage energy and retrieve it from the initial noise section. The weighting operator is obtained by solving a least-squares minimization problem via shaping regularization with a smoothness constraint. Next, the initially denoised section and the retrieved signal are combined to form the final denoised section. The proposed denoising approach corresponds to orthogonalizing the initially denoised signal and noise in a local manner. We evaluate denoising performance by using local similarity. In order to test the orthogonalization property of the estimated signal and noise, we calculate the local similarity map between the denoised signal section and removed noise section. Low values of local similarity indicate a good orthogonalization and thus a good denoising performance. Synthetic and field data examples demonstrate the effectiveness of the proposed approach in applications to noise attenuation for both conventional and simultaneous-source seismic data.

Least-squares reverse time migration with and without source wavelet estimation

“…Since seismic data are usually contaminated with noises, an average reference trace is better than a single one because averaging can improve the signal-to-noise ratio (SNR). The definition and physical interpretation of SNR could be referred to Chen (2015); Chen and Fomel (2015), and Chen et al (2016). However, it should be noted that a normal-move-out (NMO) correction for the first arrivals should be conducted to make sure of an in-phase stack.…”

An open-source Matlab code package for improved rank-reduction 3D seismic data denoising and reconstruction

“…snrcyk.m This code is used to numerically measure the signal-to-noise ratio (SNR) of the reconstructed and denoised data based on the criteria introduced in Chen and Fomel (2015).…”

Elastic wave‐vector decomposition in heterogeneous anisotropic media

“…">3.We then implement equation with modified coefficients according to equation applying the low‐rank approximation as formulated in equation . 4.As the last step, we compensate for the lost in amplitude information from the previous smoothing step using local signal–noise orthogonalisation (Chen and Fomel ) as described by …”

“…We subsequently propose a constructive method for locating singularities that can be used for defining a smoothing filter (weighting function) to mitigate the artefacts caused by discontinuities of polarisation vectors. We recover from amplitude loss caused by the smoothing filter via the process of local signal–noise orthogonalisation (Chen and Fomel ). We test the proposed method with a set of synthetic examples of increasing complexity.…”