Scaling Analysis of Seismic Ground Motion Signals

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 far from thermodynamic equilibrium. However, whether comparable signatures, such as scale invariance and anomalous diffusion, can be detected directly within individual ground motion recordings remains an open question. This work investigates whether acceleration, velocity, and displacement signals recorded during the 2009 Mw 6.1 L'Aquila earthquake display statistical properties consistent with non-equilibrium complex systems, and whether different seismic phases carry distinct, reproducible statistical signatures. P- and S-wave onset times are estimated using AR-AIC, with adaptive search windows centred on theoretical arrivals from the CRUST1.0 velocity model. Coda onset is determined using three complementary criteria combined into a median ensemble, enabling the segmentation of each recording into up to five temporal windows. Displacement moment scaling is analysed for each window and signal type, within the framework of strong anomalous diffusion, yielding the scaling exponents ζ(q). Robustness is systematically assessed against the choice of coda onset method, the empirical thresholds defining coda onset and end, the sub-interval of τ used in the moment scaling fit, and the filter band applied to the ground motion signals. Evidence for anomalous diffusion is nuanced: both its sign and magnitude depend on the seismic phase, with only a subset of configurations remaining stable across all segmentation schemes tested. These results indicate that anomalous scaling signatures, when present, are not universal, and that systematic robustness analyses are essential to distinguish genuine physical effects from segmentation artefacts.