Summary 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 the unknown noise-disturbing mechanism, low 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 two 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 multi-type noise generation and facilitates backward sampling. 2. Addressing training instability 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. In the SDE diffusion, the denoising process is continuous and interpretable. 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 dependency on training data compared to conventional deep learning methods.

Noise Generation and Attenuation in DAS-VSP Using the Diffusion Model

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