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.

Understanding the dynamics of microearthquakes is a timely challenge with the potential to address current paradoxes in earthquake mechanics, and to better understand earthquake ruptures induced by fluid injection. We perform fully 3D dynamic rupture simulations caused by fluid injection on a target fault for FEAR experiments generating Mw ≤ 1 earthquakes. We investigate the dynamics of rupture propagation with spatially variable stress drop caused by pore pressure changes and assuming different constitutive parameters. We show that the spontaneous arrest of propagating ruptures is possible by assuming a high fault strength parameter S, that is, a high ratio between strength excess and dynamic stress drop. In faults with high S values (low rupturing potential), even minor variations in Dc (from 0.45 to 0.6 mm) have a substantial effect on the rupture propagation and the ultimate earthquake size. Our results show that modest spatial variations of dynamic stress drop determine the rupture mode, distinguishing self-arresting from run-away ruptures. Our results suggest that several characteristics inferred for accelerating dynamic ruptures differ from those observed during rupture deceleration of a self-arresting earthquake. During deceleration, a decrease of peak slip velocity is associated with a nearly constant cohesive zone size. Moreover, the residual slip velocity value (asymptotic value for a crack-like rupture) decreases to nearly zero. This means that an initially crack-like rupture becomes a pulse-like rupture during spontaneous arrest. In summary, our findings highlight the complex dynamics of small earthquakes, which are partially contrasting with established crack-like models of earthquake rupture.

Moment tensor inversions of broadband velocity data are usually managed by adopting Green’s functions for 1D layered seismic wavespeed models. This assumption can impact on source parameter estimates in regions with complex 3D heterogeneous structures and rock properties discontinuities. In this work, we present a new Centroid Moment Tensor (CMT) Catalog for the Amatrice–Visso–Norcia (AVN) seismic sequence based on a recently generated 3D wavespeed model for the Italian lithosphere. Forward synthetic seismograms and Fréchet derivatives for CMT–3D inversions of 159 earthquakes with Mw ≥ 3.0 are simulated using a spectral–element method (SEM) code. By comparing the retrieved solutions with those from Time Domain Moment Tensor (TDMT) catalog, obtained with a 1D wavespeed model calibrated for Central Apennines (Italy), we observe a remarkable degree of consistency in terms of source geometry, kinematics, and magnitude. Significant differences are found in centroid depths, which are more accurately estimated using the 3D model. Finally, we present a newly designed parameter, τ, to better quantify and compare a–posteriori the reliability of the obtained MT solutions. This parameter measures the goodness of fit between observed and synthetic seismograms accounting for differences in amplitude and arrival time, percentage of fitted seconds, together with the usual L2–norm estimate. These CMT–3D solutions represent the first Italian CMT catalog based on a full–waveform 3D wavespeed model and provide robust source parameters with potential implications for the structures activated during the sequence. The developed approach can be readily applied to more complex Italian regions where a 1D wavespeed model is underperforming.