Heterogeneity and anomalous critical indices in the aftershocks distribution of L Aquila earthquake

The data analysis of aftershock events of L Aquila earthquake in Apennines following the main 6.3 Mw event of April 6, 2009 has been carried out by standard statistical geophysical tools. The results show the heterogeneity of seismic activity in five different geographical sub-regions indicated by anomalous critical indices of power law distributions: the exponents of the Omori law, the b values of Gutenberg-Richter magnitude-frequency distribution, and the distribution of waiting times. The heterogeneous distribution of dynamic stress and a different morphology in the five sub-regions has been found and two anomalous sub-regions have been identified.

💡 Research Summary

The paper presents a detailed statistical analysis of aftershocks generated by the Mw 6.3 L’Aquila earthquake that struck the Apennines on April 6, 2009. The authors collected seismic records from the Italian Seismic Bulletin (INGV) and the public ISIDE database covering the period from January 1, 2008 to April 24, 2009, focusing on the 18‑day window immediately following the main shock. Geographic coordinates of each event were transformed from latitude–longitude to Cartesian (kilometer) space using an average Earth radius of 6371 km. In addition, an ENVISAT interferogram was processed to locate the events on a satellite‑derived deformation map, revealing that the main shock epicenter lies slightly off the centre of the nine concentric fringes (CCFI) that mark the region of maximum ground displacement (≈25 cm).

Based on the spatial clustering of aftershocks, the authors divided the study area into five distinct sub‑regions, labelled (1+2), 3, 4, 5, and (6a+6b). The boundaries of each polygon are listed in Table 1 and are visualised in Figure 1 with different colours and symbols. This subdivision allows the authors to treat each zone as a quasi‑homogeneous ensemble for statistical testing.

Three classic seismic scaling laws were examined in each sub‑region:

1. Gutenberg‑Richter magnitude–frequency relation – The authors fitted log₁₀ N = A − b m for magnitudes above a completeness threshold m₀ = 1.4, using several upper‑magnitude cut‑offs (3 < m_c < 4.5) to assess the stability of the b‑value. The results show that zones (1+2) and 4 have relatively high b‑values (≈1.0), whereas zones 3, 5, and (6a+6b) display lower b‑values (≈0.7–0.9). The variation suggests differing stress regimes or fault heterogeneity across the area.

2. Omori aftershock decay law – The temporal decay of aftershocks was modelled as n(t) ∝ t^{−α}. Zones 3, 5, and (6a+6b) yielded α values between 0.5 and 0.9, consistent with the canonical Omori exponent (≈1). In contrast, zones (1+2) and 4 deviate markedly: their cumulative aftershock counts increase almost linearly with time, implying an α close to 0 (or a logarithmic behaviour with α≈1 but with a different functional form). This anomalous decay indicates a persistent release of stress rather than the rapid relaxation typical of most aftershock sequences.

3. Waiting‑time (inter‑event time) distribution – The probability density P(T) of the time interval T between successive events was examined. Zone 3 exhibits a two‑regime power‑law: a steeper slope (γ≈1.2) for short T and a shallower slope (γ≈0.8) for long T, reflecting a crossover from correlated to nearly uncorrelated seismicity. Zone (1+2) shows a single power‑law with γ≈1.3 and lacks the crossover, reinforcing the notion of a distinct, possibly more homogeneous stress field.

Radial distribution functions were computed using the CCFI as the origin for two time windows (April 6–12 and April 6–24). The curves are virtually unchanged, indicating that the spatial spread of aftershocks does not evolve dramatically over the examined period. However, when the main‑shock epicenter is used as the centre, the radial distribution changes markedly with time, underscoring the asymmetry of the main rupture relative to the deformation pattern captured by the interferogram.

The authors argue that the observed heterogeneity—particularly the anomalous α and b values in sub‑regions (1+2) and 4—cannot be captured by a single, globally averaged power‑law model. Instead, they attribute these deviations to a multiscale heterogeneous distribution of dynamic stress, variations in fault morphology, and differing lithological structures across the Apennine segment. The study highlights that seismic hazard assessments must account for spatially variable statistical parameters rather than relying on uniform regional averages.

In summary, the paper demonstrates that aftershock sequences in the L’Aquila region are not monolithic; they consist of sub‑domains with distinct statistical signatures. This nuanced view advances our understanding of how complex fault networks and stress heterogeneity shape seismicity, and it provides a methodological framework for more refined, region‑specific earthquake forecasting.