Antileakage least-squares spectral analysis for seismic data regularization and random noise attenuation

Abstract

Spatial transformation of an irregularly sampled data series to a regularly sampled data series is a challenging problem in many areas such as seismology. The discrete Fourier analysis is limited to regularly sampled data series. On the other hand, the least-squares spectral analysis (LSSA) can analyze an irregularly sampled data series. Although the LSSA method takes into account the correlation among the sinusoidal basis functions of irregularly spaced series, it still suffers from the problem of spectral leakage: Energy leaks from one spectral peak into another. We have developed an iterative method called antileakage LSSA to attenuate the spectral leakage and consequently regularize irregular data series. In this method, we first search for a spectral peak with the highest energy, and then we remove (suppress) it from the original data series. In the next step, we search for a new peak with the highest energy in the residual data series and remove the new and the old components simultaneously from the original data series using a least-squares method. We repeat this procedure until all significant spectral peaks are estimated and removed simultaneously from the original data series. In addition, we address another problem, which is random noise attenuation in the data series, by applying a certain confidence level for significant peaks in the spectrum. We determine the robustness of our method on irregularly sampled synthetic and real data sets, and we compare the results with the antileakage Fourier transform and arbitrary sampled Fourier transform.

Application of spectral analysis and wavelet transforms to full-scale dynamic drainages at minesites

“…8) on these databases will use alternative wavelet techniques for confirmation and refinement of these initial interpretations. These techniques will include least-squares wavelet analyses that can accommodate unevenly spaced data [20][21][22][23].…”

“…• application of other wavelets, such as the Mexican Hat which can better characterize the infrequent discontinuities, • least-squares wavelet analysis which accommodates unevenly spaced data [20][21][22][23], • finely scaled discrete wavelets,…”

Unsupervised deep learning with higher-order total-variation regularization for multidimensional seismic data reconstruction

“…Interpolation and regularization of the subsampled wavefield is an important and necessary processing step since coarse and irregular sampling of the seismic wavefield affects migration quality and analysis of amplitude variations with offset and azimuth (Trad, 2009). Several techniques have been developed for tackling the interpolation problem, such as frequency-space domain methods (Spitz, 1991;Porsani, 1999;Crawley, 2000;Naghizadeh and Sacchi, 2007), minimum weighted norm interpolation (MWNI) (Liu and Sacchi, 2004), projection onto convex sets (POCS) (Abma and Kabir, 2006), shaping regularization (Fomel, 2007), rank reduction based (Trickett et al, 2010(Trickett et al, , 2013, spectral analysis (Ghaderpour et al, 2018;Ghaderpour, 2019), common reflection surface (CRS) attribute-based (Hoecht et al, 2009;Xie and Gajewski, 2016;Zhao et al, 2020), Fourier based (Xu et al, 2005;Zwartjes and Sacchi, 2007;Schonewille et al, 2009;Naghizadeh and Sacchi, 2010b), Radon based (Ibrahim et al, 3 2015), Curvelet (Naghizadeh and Sacchi, 2010a;Herrmann and Hennenfent, 2008), Seislet (Gan et al, 2015) and Focal transform (Kutscha et al, 2010). Amongst the popular techniques for multidimensional interpolation, such as 5D interpolation, are (Trad, 2014): MWNI, POCS, Anti-Leakage Fourier Transform (ALFT) (Xu et al, 2005), and rank reduction of Hankel tensors (Trickett et al, 2013).…”

Seismic Data Denoising Based on Sparse and Low-Rank Regularization

“…Denoising methods based on the gradient sparsity of a signal, such as total variation (TV) [8] and total generalized variation [9], have also been hot topics in recent years. In addition, nonlocal means [10], dictionary learning methods [11] and antileakage least-squares spectral analysis [12,13] have also attracted wide attention.…”