Efficient Nonlocal Tensor Function Representation for 3D Seismic Random Noise Attenuation

High-dimensional 3D seismic data is inevitably contaminated by random noise due to environmental interference and acquisition system limitations. While many deep learning methods have been proposed for random noise attenuation, they often suffer from various limitations. For instance, some convolutional neural network (CNN)-based methods tend to be computationally inefficient when processing 3D seismic volumes, while implicit neural representation (INR)-based methods frequently fail to recover complex structural details owing to the spectral bias. To address these challenges, this study introduces an efficient nonlocal tensor function representation (NLTFR) for unsupervised 3D seismic denoising. Specifically, we cluster similar cubes within 3D seismic data into nonlocal similar groups. To efficiently and effectively exploit the nonlocal self-similarity inherent in seismic data, we employ tensor function factorization parameterized by INRs to model these clustered nonlocal similar groups. Furthermore, we propose a partially shared transfer learning strategy for NLTFR to accelerate model convergence when applied to large-scale seismic datasets. Multiple-frequency sinusoidal functions are incorporated into the INRs to mitigate spectral bias, thereby enhancing the model’s representation ability. Additionally, a weighted total variation and a second-order 3D total variation are introduced to improve denoising performance and robustness of the NLTFR model. Comprehensive experiments conducted on synthetic and field 3D seismic datasets demonstrate that the proposed NLTFR achieves a superior balance between efficiency and effectiveness compared with conventional deep learning methods. Overall, our method attains an average performance gain of 1.5dB while significantly reducing execution time relative to traditional deep learning methods for 3D seismic volumes, underscoring its practical efficiency.