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Distributed acoustic sensing (DAS) technology demonstrates significant potential for high-resolution seismic exploration due to its dense spatial sampling and cost-effectiveness. Nevertheless, downhole DAS data often suffer from the low signal-to-noise ratio, plagued by strong background noise, which degrades imaging. To mitigate this, we propose a deep learning framework using an attentive neural network tailored for downhole DAS noise suppression. During the inference, a transfer learning strategy, guided by some conventional filtering methods, fine-tunes the well-trained model using several field sections. Tests on synthetic data and field downhole DAS data indicate effective noise attenuation and signal preservation.