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.

Seismic urgent computing enables early assessment of an earthquake's impact by delivering rapid simulation-based ground-shaking forecasts. This information can be used by local authorities and disaster risk managers to inform decisions for rescue and mitigation activities in the affected areas. Uncertainty quantification for urgent computing applications stands as one of the most challenging tasks. Present-day practice accounts for the uncertainty stemming from Ground Motion Models (GMMs), but neglects the uncertainty originating from the source model, which, in the first minutes after an earthquake, is only known approximately. In principle, earthquake source uncertainty can be propagated to ground motion predictions with physics-based simulations of an ensemble of earthquake scenarios capturing source variability. However, full ensemble simulation is unfeasible under emergency conditions with strict time constraints. Here we present ProbShakemap, a Python toolbox that generates multi-scenario ensembles and delivers ensemble-based forecasts for urgent source uncertainty quantification. The toolbox implements GMMs to efficiently propagate source uncertainty from the ensemble of scenarios to ground motion predictions at a set of Points of Interest (POIs), while also accounting for model uncertainty (by accommodating multiple GMMs, if available) along with their intrinsic uncertainty. ProbShakemap incorporates functionalities from two open-source toolboxes routinely implemented in seismic hazard and risk analyses: the USGS ShakeMap software and the OpenQuake-engine. ShakeMap modules are implemented to automatically select the set and weights of GMMs available for the region struck by the earthquake, whereas the OpenQuake-engine libraries are used to compute ground shaking over a set of points by randomly sampling the available GMMs. ProbShakemap provides the user with a set of tools to explore, at each POI, the predictive distribution of ground-motion values encompassing source uncertainty, model uncertainty and the inherent GMMs variability. Our proposed method is quantitatively tested against the 30 October 2016 Mw 6.5 Norcia, and the 6 February 2023 Mw 7.8 Pazarcik earthquakes. We also illustrate the differences between ProbShakemap and ShakeMap output.