Analysis of DAS Seismic Noise Generation and Elimination Process Based on Mean-SDE Diffusion Model

Suppressing various noises while achieving precise signal reconstruction in distributed acoustic sensing vertical seismic profiling (DAS VSP) remains a challenge. Existing denoising methods are insufficient due to factors such as the unknown noise-disturbing mechanism, low signal-to-noise ratio (SNR), and limited training data. Therefore, this study proposes the Mean-stochastic differential equation (SDE) diffusion model as an advanced solution. Built upon the standard diffusion model, which incorporates forward and backward diffusion processes, our model introduced three modifications to enhance performance: 1) improving the forward diffusion process: transforming the final state into a combination of the noisy DAS VSP and Gaussian noise. This adjustment allows precise representations of multitype noise generation and facilitates backward sampling; 2) enhancing noise prediction between successive steps in the backward process: a nonlinear activation-free network (NAFnet) with a time multilayer perception (MLP) was employed to provide accurate noise predictions at different states; and 3) addressing training instability inherent in standard diffusion: the objective function is modified to seek the optimal trajectory of the best quality of signal reconstruction rather than directly evaluating the noise prediction. The forward diffusion is a dynamic evolution of adding noise to the pure signal, while the backward processing aims to remove the noise step by step. Comprehensive experiments demonstrate the superiority of our method in diverse noise suppression, signal resolution enhancement, and amplitude preservation. Moreover, grounded in physics-based equations, our method exhibits less dependence on training data compared to conventional deep learning methods.