Seismic waves contain information about the earthquake source, the geologic structure they traverse, and many forms of noise. Separating the noise from the earthquake is a difficult task because optimal parameters for filtering noise typically vary with time and, if chosen inappropriately, may strongly alter the original seismic waveform. Diffusion models based on Deep Learning (DL) have demonstrated remarkable capabilities in restoring images and audio signals. However, those models assume a Gaussian distribution of noise, which is not the case for typical seismic noise. Motivated by the effectiveness of "cold" diffusion models in speech enhancement, medical anomaly detection, and image restoration, we present a cold variant for seismic data restoration. We describe the first Cold Diffusion Model for Seismic Denoising (CDiffSD), including key design aspects, model architecture, and noise handling. Using metrics to quantify the performance of CDiffSD models compared to previous works, we demonstrate that it provides a new standard in performance. CDiffSD significantly improved the Signal to Noise Ratio (SNR) by about 18% compared to previous models. It also enhanced Cross-correlation by 6%, showing a better match between denoised and original signals. Moreover, testing revealed a 50% increase in the recall of P-wave picks for seismic picking. Our work show that CDiffSD outperforms existing benchmarks, further underscoring its effectiveness in seismic data denoising and analysis. Additionally, the versatility of this model suggests its potential applicability across a range of tasks and domains, such as GNSS, Lab Acoustic Emission, and DAS data, offering promising avenues for further utilization.
