Expand Dimensional of Seismic Data and Random Noise Attenuation Using Low-Rank Estimation

Random noise attenuation in seismic data requires employing leading-edge methods to attain reliable denoised data. Efficient noise removal, effective signal preservation and recovery, reasonable processing time with a minimum signal distortion and seismic event deterioration are properties of a desired noise suppression algorithm. There are various noise attenuation methods available that more or less have these properties. We aim to obtain more effective denoised seismic data by assuming 3-D seismic data as a tensor in order three and increasing its dimension to 4-D seismic data by employing continuous wavelet transform (CWT). First, we map 3-D block seismic data to smaller blocks to estimate the low-rank component. The CWT of the tensor is calculated along the third dimension to extract the singular values and their related left/right vectors in the wavelet domain. Afterward, the effective low-rank component is extracted using optimized coefficients for each singular value. Thresholding is applied in the wavelet domain along the third dimension to calculate effective coefficients. Two synthetic and field data examples are considered for performance evaluation of the proposed method, and the results were compared with the competitive random noise suppression methods, such as the tensor optimum shrinkage singular value decomposition, the iterative block tensor singular value thresholding, and the block matching 4-D algorithms. Qualitative and quantitative comparison of the proposed method with other methods indicates that the proposed method efficiently eliminates random noise from seismic data.