Random noise attenuation of 2D seismic data based on sparse low-rank estimation of the seismic signal

Abstract Attenuation of noise in seismic data is a crucial and difficult task in analyzing seismic data. We propose a new noise suppression algorithm in which the noise can be suppressed; meanwhile, the seismic signal is preserved. In the proposed algorithm, first we analyze each seismic trace using a linear time–frequency method, i.e., the short-time Fourier transform, then we estimate the sparse low-rank matrix from the obtained noisy matrix. To this aim, an objective function comprising of a data-faithfulness term and two parameterized non-convex penalty functions is proposed. Finally, the denoised signal is synthesized using the obtained semi-low-rank matrix. We assess the proposed technique considering a synthetic seismic trace and seismic section. We have also assessed the proposed technique using pre-stack real data collected from a hydrocarbon field located in the southwest area of Iran. The performance of the proposed method is evaluated and compared with other state-of-the-art techniques such as the synchrosqueezed wavelet transform and low-rank signal matrix approximation by Semi-Soft GoDec (WSST-GoDec) algorithm, classical f − x singular spectrum analysis ( f − x SSA) and the sparse signal estimation and extraction low-rank component by optimum singular value estimation (SLR-OptShrink). The results indicate the advantage of the proposed method over the selected methods.