Triply Laplacian Scale Mixture Modeling for Seismic Data Noise Suppression

TL;DR

This work tackles seismic data noise suppression in the presence of nonstationary noise and acquisition footprints. It introduces a triply Laplacian scale mixture (TLSM) prior that jointly estimates sparse tensor coefficients and their hidden variances, solved efficiently with an ADMM-based algorithm. The method demonstrates significant improvements in quantitative metrics (PSNR/SSIM) and visual quality on both synthetic and field seismic data, while maintaining computational efficiency. By unifying low-rank tensor recovery with learned sparsity priors, TLSM offers robust denoising with strong practical impact for seismic analysis and interpretation.

Abstract

Sparsity-based tensor recovery methods have shown great potential in suppressing seismic data noise. These methods exploit tensor sparsity measures capturing the low-dimensional structures inherent in seismic data tensors to remove noise by applying sparsity constraints through soft-thresholding or hard-thresholding operators. However, in these methods, considering that real seismic data are non-stationary and affected by noise, the variances of tensor coefficients are unknown and may be difficult to accurately estimate from the degraded seismic data, leading to undesirable noise suppression performance. In this paper, we propose a novel triply Laplacian scale mixture (TLSM) approach for seismic data noise suppression, which significantly improves the estimation accuracy of both the sparse tensor coefficients and hidden scalar parameters. To make the optimization problem manageable, an alternating direction method of multipliers (ADMM) algorithm is employed to solve the proposed TLSM-based seismic data noise suppression problem. Extensive experimental results on synthetic and field seismic data demonstrate that the proposed TLSM algorithm outperforms many state-of-the-art seismic data noise suppression methods in both quantitative and qualitative evaluations while providing exceptional computational efficiency.

Figures (6)

• Figure 1: Comparison of noise suppression results between the proposed TLSM approach and state-of-the-art methods on synthetic data ($F = 0.2, \sigma = 0.03$). (a) Original seismic data; (b) Noisy seismic data; (c) FR-Net qian2023unsupervised; (d) UTV-LRTA qian2023improved; (e) Proposed TLSM.
• Figure 2: Noise suppression results of seismic data (first, third, and fifth rows) and the corresponding removed noise (second, fourth, and sixth rows) using different methods on the synthetic data with size $100\times200\times400$. (a) Noisy seismic data ($F = 0.2, \sigma = 0.01$); (b) DRR chen2016simultaneous (21.15dB); (c) SGRDL chen2021statistics (35.41dB); (d) FR-Net qian2023unsupervised (39.31dB); (e) DNLR xu2023deep (27.79dB); (f) S2S-WTV xu2023s2s (35.69dB); (g) UTV-LRTA qian2023improved (39.58dB); (h) TLSM (45.22dB); (i) Original seismic data.
• Figure 3: Noise suppression results of seismic data (first, third, and fifth rows) and the corresponding removed noise (second, fourth, and sixth rows) using different methods on the Penobscot-3D dataset. (a) Noisy seismic data; (b) DRR chen2016simultaneous; (c) SGRDL chen2021statistics; (d) FR-Net qian2023unsupervised; (e) DNLR xu2023deep; (f) S2S-WTV xu2023s2s; (g) UTV-LRTA qian2023improved; (h) TLSM.
• Figure 4: Noise suppression results of seismic data (first, third, and fifth rows) and the corresponding removed noise (second, fourth, and sixth rows) using different methods on the Kerry-3D dataset. (a) Noisy seismic data; (b) DRR chen2016simultaneous; (c) SGRDL chen2021statistics; (d) FR-Net qian2023unsupervised; (e) DNLR xu2023deep; (f) S2S-WTV xu2023s2s; (g) UTV-LRTA qian2023improved; (h) TLSM.
• Figure 5: Parameter Analysis. (a) Analysis of different parameter $a$; (b) Analysis of different parameter $b$; (c) Analysis of different parameter $c$; (d) Analysis of different parameter $\tau$; (e) Analysis of different parameter $\lambda_1$; (f) Analysis of different parameter $\lambda_2$.