تضعیف نوفه‌های تصادفی در داده‌های لرزه‌ای بازتابی به روش بازنمایی تنک داده لرزه‌ای با استفاده از یادگیری لغت‌نامه

Random noise remains a persistent challenge in reflection seismic data processing, significantly degrading the signal-to-noise ratio (SNR) and compromising the accuracy of subsequent processing stages such as migration, inversion, and geological interpretation. Conventional noise attenuation techniques, including f–x predictive filtering, Radon transforms, wavelet-based methods, and singular spectrum analysis, rely heavily on predefined mathematical assumptions or fixed transform domains. While effective in structurally simple settings, these model-driven approaches often suffer from parameter sensitivity, inadequate adaptability to non-stationary signals, and substantial signal leakage, particularly in complex subsurface environments or low-SNR conditions. Conversely, emerging deep learning frameworks offer strong adaptability but demand extensive labeled datasets, lack physical interpretability, and carry a high risk of overfitting or unintended signal suppression. To bridge this gap, dictionary learning has emerged as a robust hybrid paradigm that learns optimal basis functions directly from the data, enabling efficient sparse representation of coherent seismic events while inherently suppressing incoherent random noise.

This study presents a comprehensive implementation and evaluation of a two-dimensional (2D) dictionary learning framework specifically tailored for random noise attenuation in 2D reflection seismic data. Unlike traditional one-dimensional (1D) dictionary learning approaches that vectorize image patches—thereby destroying intrinsic spatial neighborhood relationships and introducing artificial high-frequency artifacts at block boundaries—the proposed method operates natively on 2D data blocks. By employing a separable dictionary structure constructed via the Kronecker product of horizontal and vertical atom matrices, the algorithm preserves the geometric continuity of seismic reflectors, including discontinuities such as faults, pinch-outs, and curved events. The workflow comprises three core stages: (1) extraction of overlapping 2D patches from the noisy section, (2) dictionary training using the K-SVD algorithm to iteratively update atom matrices based on sparse coding residuals, and (3) sparse representation of each patch via the 2D Orthogonal Matching Pursuit (2D-OMP) algorithm under a strict sparsity constraint. Since random noise lacks repetitive structural patterns, it requires a dense combination of atoms for accurate representation; consequently, enforcing sparsity inherently filters out the noise while reconstructing the coherent signal components. The final denoised section is reconstructed by averaging the overlapping processed patches.

The performance of the proposed 2D framework was rigorously evaluated using both synthetic and field seismic datasets, with quantitative comparisons against time-frequency peak filtering (TFPF), f–x singular spectrum analysis (FX-SSA), and classical 1D dictionary learning. Evaluation metrics included output SNR, reconstruction error (RE), local correlation coefficients to quantify signal leakage, and amplitude spectrum preservation. On a synthetic section contaminated with −4 dB random noise, the 2D approach achieved an output SNR of 11.81 dB and an RE of 0.1096, substantially outperforming the 1D variant (10.20 dB SNR, 0.1895 RE), FX-SSA (6.12 dB, 0.153), and TFPF (3.73 dB, 0.394). Notably, the 2D method demonstrated superior preservation of dipping events and fault discontinuities, with negligible signal leakage in the residual sections. A systematic parameter sensitivity analysis identified optimal configurations for patch size (22×22), dictionary dimensions (44×44), sparsity level (4–8), iteration count (50), and training patch sampling (5,000). The 2D framework exhibited greater robustness to larger window sizes and higher noise levels compared to the 1D approach, where vectorization-induced dimensionality explosion rapidly degrades reconstruction quality. Furthermore, the algorithm maintains stable denoising performance across a wide input SNR range (−8 to +8 dB), with the structural preservation advantage of the 2D formulation becoming increasingly pronounced under severe noise contamination.

Application to a real 44-trace field record corroborates the synthetic findings. The 2D dictionary learning method effectively attenuated random background noise while preserving high-frequency reflector details, lateral amplitude variations, and steeply dipping events. Local correlation analysis confirmed minimal signal loss, whereas conventional filters and 1D dictionary learning exhibited notable leakage. Spectral analysis further demonstrated that the proposed approach maintains the original frequency bandwidth without introducing artificial harmonic distortions or phase shifts.

In conclusion, two-dimensional dictionary learning provides a highly effective, interpretable, and parameter-stable solution for seismic random noise attenuation. By operating natively on spatial patches and leveraging separable dictionary structures, it overcomes the geometric degradation inherent in 1D vectorization, yielding superior noise suppression and signal preservation. This methodology holds significant promise for integration into standard seismic processing workflows, particularly in exploration scenarios characterized by complex geology, low SNR, and critical discontinuity mapping. Future developments will focus on computational acceleration through adaptive patch sampling and extension to 3D tensor dictionary learning for multidimensional seismic volumes.