Sparse Time–Frequency Analysis of Seismic Data: Sparse Representation to Unrolled Optimization

Time-frequency analysis (TFA) is widely used to describe local time-frequency (TF) features of seismic data. Among the commonly used TFA tools, sparse TFA (STFA) is an excellent one, which can obtain a TF spectrum with good readability. However, many STFA algorithms suffer from expensive calculation time and unavoidable prior knowledge, such as the iterative shrinkage-thresholding algorithm (ISTA) and the sparse reconstruction by separable approximation (SpaRSA). Inspired by the unrolled algorithm and its successful applications in signal processing, we propose a deep learning-based ISTA unrolled algorithm, which is named the sparse time-frequency analysis network (STFANet). The STFANet contains two parts, i.e., the sparse time-frequency spectrum generator and the reconstruction module. The former learns how to transform a one-dimensional (1D) seismic signal from a large amount of unlabelled data into a two-dimensional (2D) sparse time-frequency spectrum, which is implemented based on the proposed unrolled iterative dynamic shrinkage-thresholding (UIDST) algorithm. Note that the UIDST algorithm is carried out by using a simplified deep learning network. The latter serves as a physical constraint of model training to ensure that our generator obtains an accurate TF spectrum, which is actually an inverse time-frequency transform. In this study, the traditional inverse short-time Fourier transform (STFT) is utilized in the reconstruction module. To test the effectiveness of the proposed model, we apply it to 3D post-stack field data. The results show that, compared with the traditional TFA tools, the STFANet can availably compute time-frequency spectrum with better readability, which benefits seismic attenuation delineation.