Denoising of pre‐stack seismic data using subspace estimation methods

Abstract

Denoising is one of the core steps in seismic data processing flow. The seismic gather consists of multiple traces captured at different receivers. A set of receivers observe waves which are reflected from the same reflection point. Those traces need to be grouped together as they contain the same information about the earth subsurface layers. This is done by finding a common mid-point (CMP) between the source and geophones. The time delay between CMP gathered traces are corrected by the normal move out correction method but the individual traces are corrupted by noise. In this paper we, propose a method for denoising individual traces. The set of traces can be modelled as belonging to a low-dimensional subspace of an ambient signal space. This allows for construction of sparse representations of each trace in terms of other traces in the CMP gather. The resulting sparse representations are subsequently utilised to construct approximations of individual traces and thus, noise is suppressed. We constructed, the approximations using orthogonal matching pursuit. We applied proposed method to synthetic and field seismic data, the proposed technique performs better on established benchmarks while capturing the true locations of weak reflections and effectively attenuating the random noise. Nomenclature M number of traces N length of each trace Y seismic trace matrix A noise-free trace matrix G Gaussian noise matrix E impulse noise matrix w source wavelet L length of source wavelet W wavelet dictionary D number of shifted wavelets (atoms) in the wavelet dictionary R reflection matrix K number of non-zero rows in reflection matrix n time index, n ∈ [N] i trace index in the CMP gather, i ∈ [M]

Low‐rank and sparse reconstruction for fast diffusion nuclear magnetic resonance spectroscopy

“…The authors introduce a constraint on the low rank of DOSY data to effectively handle the exponential dimension: where λ 1 and λ 2 are regularisation parameters, and ‖⋅‖ * represents the nuclear norm of a matrix [14–19]. P is an operator that converts a vector h into a matrix so that the low rank of spectral plane can be constrained.…”

“…where λ 1 and λ 2 are regularisation parameters, and ‖⋅‖ * represents the nuclear norm of a matrix [14][15][16][17][18][19]. P is an operator that converts a vector h into a matrix so that the low rank of spectral plane can be constrained.…”

Peak Colocalized Orthogonal Matching Pursuit for Seismic Trace Decomposition

“…Sparse decomposition, which assumes that signals can be sparsely represented in one certain domain, plays an important role in seismic signal processing, including timefrequency analysis [1]- [3], noise attenuation [4]- [8], seismic inversion [9], deconvolution [10], data compression [11], etc. Matching pursuit is one representative sparse method [12].…”