Erratic and random noise attenuation using adaptive local orthogonalization

Abstract

The local orthogonalization (LO) approach has been broadly applied to attenuate random noise and deal with the signal-leakage problem induced using the traditional denoising schemes. First, this approach removes noise and applies the LO weight (LOW) operator to the originally estimated signal. Then, the signal leakage is predicted and subsequently recovered from the original noise component. Finally, the original denoised component and the recovered signal are mixed to output the denoised seismic signal. However, this approach has limits when the seismic data include random and erratic noise. We find that this shortcoming is mainly caused by the weakness of the traditional denoising operators (e.g., curvelet and f- x deconvolution methods), which are insufficient to adapt themselves to the originally denoised signal and noise sections for the LOW process. Therefore, we aim to attenuate random and erratic noise using an adaptive LO method. By mixing the hard thresholding (HT) operator and the exponential moving-average (EMA) filter, we have developed a novel operator, which we call the HTEMA operator. Then, by introducing this novel operator into the curvelet method framework, we adapt the initially denoised signal and noise sections for the LOW process. The proposed operator is applied to the frequency domain curvelet coefficients provided by the inverse transform. Then, we use the LOW operator to compensate for the damage of useful signals. The proposed approach is not limited to the curvelet method but can be applied to other traditional denoising methods. We estimate the noise attenuation performance by the visual inspections, local similarity maps, and the signal-to-noise ratio. Synthetic and field data examples indicate the effectiveness of the proposed method in applications to erratic and random noise attenuation compared with the curvelet, f- x deconvolution, and the LO methods.