Earthquakes exhibit well-documented statistical regularities at the catalogue level, such as the Gutenberg-Richter magnitude-frequency relation and the Omori-Utsu aftershock decay, often interpreted as signatures of seismicity as a driven, dissipative system operating far from thermodynamic equilibrium. However, whether comparable signatures such as heavy-tailed distributions, scale invariance, and anomalous diffusion, can be detected directly within individual seismic ground motion recordings, rather than only in catalogue-level statistics, remains an open question. This thesis investigates whether acceleration, velocity, and displacement signals recorded during two seismic events: the 2009 Mw 6.1 L'Aquila earthquake and the 2024 Mw 3.8 Maritime Alps (Queyras) earthquake, display statistical properties compatible with non-equilibrium complex systems, and whether different seismic phases carry distinct and reproducible statistical signatures.