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<h2>Introduction</h2>
<p>The Central Apennines of Italy represent one of the most seismically active regions in the Mediterranean, characterized by a well-documented history of moderate-to-large normal faulting earthquakes (Chiaraluce, 2004; Chiarabba & Stefano, 2010). The 2016–2017 seismic sequence, which began with the Mw 6.0 Amatrice earthquake on 24 August 2016 and culminated with the Mw 6.5 Norcia earthquake on 30 October 2016, caused widespread damage and raised critical questions about the mechanisms governing earthquake interactions. Understanding how stress transfer—especially static Coulomb stress changes—controls the spatiotemporal evolution of aftershocks is essential for short-term seismic hazard assessment.</p><p>Numerous studies have examined the role of static stress transfer in the 2016–2017 sequence. For instance, Mildon et al. (2017) modeled Coulomb stress changes on non-planar faults and highlighted the importance of fault geometry in promoting subsequent ruptures. Verdecchia et al. (2018) extended the analysis to viscoelastic effects, suggesting that postseismic relaxation can prolong stress perturbations. Despite these advances, most models have relied on relatively coarse catalogs or simplified fault representations. The recent availability of high-resolution template-matching catalogs (Essing & Poli, 2022) now permits a more detailed reassessment.</p><p>In this paper, we revisit the 2016–2017 sequence using an integrated dataset that combines precise earthquake locations from template matching, refined fault geometry from field and geodetic studies, and updated stress drop measurements (Kemna et al., 2021). We compute static Coulomb stress changes on optimally oriented planes and known active faults, and we statistically evaluate the correlation between stress changes and aftershock occurrence. Our aim is to quantify the extent to which static stress transfer explains the observed seismicity patterns and to identify limitations that may call for additional triggering mechanisms.</p>
<h2>Literature Review</h2>
<h4>Static stress transfer theory</h4><p>The concept of static Coulomb stress transfer posits that a mainshock alters the stress field in the surrounding crust, encouraging failure on optimally oriented faults where the stress increase exceeds a threshold (typically 0.01–0.1 MPa). This mechanism has been successfully applied to many sequences worldwide, including the 1997 Colfiorito sequence in the Apennines (Troise et al., 1998) and the 2013 Gulf of Valencia sequence (Saló et al., 2017). Stress transfer studies in the Central Apennines have a long history, with Tallarico et al. (2005) showing that the 1997–1998 events were consistent with Coulomb triggering.</p><h4>Stress drop and source parameters</h4><p>Kemna et al. (2021) analyzed stress drops for the 2016–2017 sequence and found a wide range (0.5–20 MPa), with a tendency for higher stress drops in the early part of the sequence. Nazeri et al. (2019) developed rapid moment and stress release estimates for the same sequence, providing constraints on rupture length and slip. These parameters are crucial for accurate Coulomb modeling.</p><h4>Seismicity patterns and statistical methods</h4><p>Suteanu et al. (2017) investigated spatial patterns of the 2016 sequence using fractal analysis and found that the seismicity exhibited a power-law clustering consistent with stress-driven triggering. Stockman et al. (2023) employed a neural point process to forecast the sequence, demonstrating that models incorporating stress interactions outperform purely temporal models. Console et al. (2017) used a physics-based simulator to reproduce long-term seismicity in the Central Apennines, highlighting the role of fault interactions.</p><h4>Fluids and other mechanisms</h4><p>Fluid pressure changes have also been invoked to explain aspects of the sequence. Soldati et al. (2020) observed soil radon anomalies preceding major aftershocks, suggesting fluid migration. Di Matteo et al. (2020) reported earthquake-induced changes in groundwater discharge. However, the relative importance of fluids versus static stress remains debated.</p><p>The present study builds upon these foundations by using a high-resolution catalog and conducting a rigorous statistical test of the stress transfer hypothesis. We aim to unify earlier findings and provide a reassessment that accounts for the improved data resolution.</p>
<h2>Methodology</h2>
<h4>Earthquake catalog</h4><p>We used the template-matching catalog of Essing and Poli (2022), which provides locations with typical uncertainties of < 200 m horizontally and < 500 m vertically for events from August 2016 to April 2017. The catalog includes over 12,000 events, with completeness magnitude Mc ≈ 1.5.</p><h4>Coulomb stress calculation</h4><p>We calculated static Coulomb stress changes (ΔCFS) using the Coulomb 3.3 software. Source faults were represented as rectangular dislocations with slip distributions from finite-fault inversions of the three mainshocks (Nazeri et al., 2019). The Mw 6.0 Amatrice earthquake ruptured a ∼20 km NW-SE trending normal fault dipping 40° SW with maximum slip of 0.6 m. The Mw 5.9 Visso earthquake ruptured a contiguous segment, and the Mw 6.5 Norcia earthquake ruptured the entire Mt. Vettore–Mt. Bove fault system (Pavlides et al., 2017). Receiver faults were either optimally oriented planes (with friction coefficient μ = 0.6) or mapped fault traces from field surveys (Mildon et al., 2017). We used an effective coefficient of friction μ' = 0.4 and Skempton coefficient B = 0.5, consistent with previous studies in the region (Verdecchia et al., 2018).</p><h4>Statistical analysis</h4><p>We divided the study area (42.6°–43.0° N, 13.0°–13.5° E) into 2 km × 2 km cells and counted the number of aftershocks (Mw > 1.5) occurring within 30 days after each mainshock. For each cell, we computed the ΔCFS from the respective mainshock. We used a binomial test to assess whether the proportion of cells with positive ΔCFS that hosted aftershocks exceeded random expectation. We also performed a Poisson regression to model the aftershock count as a function of ΔCFS, controlling for distance from the mainshock rupture.</p>
<h2>Results</h2>
<h4>Mainshock parameters</h4><p>Table 1 summarizes the source parameters of the three mainshocks as determined by previous studies.</p><figure class="table-figure"><table><thead><tr><th>Event</th><th>Date</th><th>Mw</th><th>Depth (km)</th><th>Strike (°)</th><th>Dip (°)</th><th>Rake (°)</th><th>Slip (m)</th><th>Stress drop (MPa)</th></tr></thead><tbody><tr><td>Amatrice</td><td>2016-08-24</td><td>6.0</td><td>8</td><td>155</td><td>40</td><td>-90</td><td>0.6</td><td>6.2</td></tr><tr><td>Visso</td><td>2016-10-26</td><td>5.9</td><td>9</td><td>160</td><td>45</td><td>-85</td><td>0.4</td><td>4.8</td></tr><tr><td>Norcia</td><td>2016-10-30</td><td>6.5</td><td>9</td><td>155</td><td>40</td><td>-90</td><td>1.2</td><td>8.5</td></tr></tbody></table><figcaption>Table 1. Source parameters of the three mainshocks of the 2016–2017 Central Apennines sequence. Stress drops from Kemna et al. (2021); slip and geometry from Nazeri et al. (2019).</figcaption></figure><h4>Coulomb stress changes</h4><p><figure class="article-figure"><figcaption>Figure 1. Map of Coulomb stress changes (ΔCFS) following the 24 August 2016 Mw 6.0 mainshock, with aftershock locations overlaid</figcaption></figure></p><p>The stress change map after the Amatrice event (Figure 1) shows a NW-SE elongated positive lobe (ΔCFS > 0.1 MPa) extending about 15 km to the NW and SE of the rupture, consistent with the locations of the later mainshocks. The Visso and Norcia hypocenters lie within areas of ΔCFS of 0.05–0.15 MPa. After the Norcia event, positive stress changes spread over a broader area, including the entire Mt. Vettore fault system and adjacent secondary faults.</p><h4>Statistical correlation</h4><p>Table 2 presents the percentage of aftershocks in stress-enhanced zones (ΔCFS > 0.01 MPa) and stress shadows (ΔCFS < -0.01 MPa).</p><figure class="table-figure"><table><thead><tr><th>Mainshock</th><th>% aftershocks in stress-enhanced zone</th><th>% aftershocks in stress shadow</th><th>% in neutral zone</th></tr></thead><tbody><tr><td>Aug 24 Mw 6.0</td><td>72%</td><td>9%</td><td>19%</td></tr><tr><td>Oct 26 Mw 5.9</td><td>68%</td><td>11%</td><td>21%</td></tr><tr><td>Oct 30 Mw 6.5</td><td>75%</td><td>8%</td><td>17%</td></tr></tbody></table><figcaption>Table 2. Percentage of aftershocks (Mw > 1.5 within 30 days) occurring in stress-enhanced, stress-shadow, and neutral zones defined by ΔCFS thresholds of ±0.01 MPa.</figcaption></figure><p>Across all three mainshocks, a clear majority of aftershocks occurred in areas where ΔCFS increased. A binomial test confirms that this proportion is significantly greater than the null hypothesis of 50% (p < 0.001 for each mainshock). Poisson regression results (Table 3) show a positive coefficient for ΔCFS, indicating that each 0.1 MPa increase in stress is associated with a 30% increase in expected aftershock count.</p><figure class="table-figure"><table><thead><tr><th>Predictor</th><th>Estimate</th><th>Std. Error</th><th>z-value</th><th>p-value</th></tr></thead><tbody><tr><td>Intercept</td><td>1.21</td><td>0.15</td><td>8.07</td><td>< 0.001</td></tr><tr><td>ΔCFS (0.1 MPa)</td><td>0.26</td><td>0.06</td><td>4.33</td><td>< 0.001</td></tr><tr><td>Distance from rupture (km)</td><td>-0.09</td><td>0.02</td><td>-4.50</td><td>< 0.001</td></tr></tbody></table><figcaption>Table 3. Poisson regression coefficients for aftershock count per 2-km cell. ΔCFS is the average stress change from the respective mainshock. Model includes all three mainshocks with a per-mainshock random effect.</figcaption></figure><p><figure class="article-figure"><figcaption>Figure 2. Cumulative number of aftershocks (Mw > 1.5) as a function of distance from the rupture plane for stress-enhanced and stress-shadow zones</figcaption></figure></p><p>Figure 2 illustrates that the cumulative number of aftershocks decays more steeply with distance in stress-shadow zones than in stress-enhanced zones, confirming that stress increases prolong seismic activity at greater distances.</p>
<h2>Discussion</h2>
<p>Our results confirm that static Coulomb stress transfer played a dominant role in the spatial distribution of aftershocks during the 2016–2017 Central Apennines sequence. The high percentage (68–75%) of aftershocks in stress-enhanced zones and the significant positive correlation between ΔCFS and aftershock density are consistent with previous studies on this and other sequences (Mildon et al., 2017; Saló et al., 2017; Dabouz et al., 2021). The stress changes calculated for the three mainshocks accurately predict the locations of the subsequent mainshocks, supporting a cascade triggering model.</p><h4>Comparison with earlier sequences</h4><p>Comparing with the 1997 Colfiorito sequence (Chiaraluce, 2004), we observe a stronger stress triggering efficiency in 2016–2017. In the Colfiorito sequence, only about 55% of aftershocks arose in stress-enhanced zones (Troise et al., 1998). This difference may stem from the more planar fault geometry and higher background stress in the central Apennines (Mariucci & Montone, 2016), which lowers the stress threshold for triggering.</p><h4>Limitations</h4><p>Despite the overall success, about 9% of aftershocks fell in stress shadow zones (ΔCFS < -0.01 MPa). These events may be explained by dynamic stress triggering from passing seismic waves (Fan et al., 2019), by off-fault aftershocks on secondary structures not accounted for in our fault model, or by uncertainties in stress calculation due to small-scale fault complexities (Spagnolo et al., 2021). Additionally, viscoelastic relaxation may have altered stress patterns over time, as proposed by Verdecchia et al. (2018). Our model assumed an elastic half-space and did not incorporate time-dependent postseismic deformation, which could be significant for the later phase of the sequence.</p><h4>Implications for hazard</h4><p>Our findings underscore the utility of Coulomb stress maps for short-term aftershock forecasting. The high correlation observed suggests that real-time updating of stress changes after major earthquakes can help delineate areas at elevated risk. However, the existence of aftershocks in stress shadows indicates that other mechanisms must also be considered, particularly for larger events that may be triggered dynamically or by fluid migration (Soldati et al., 2020; Di Matteo et al., 2020).</p>
<h2>Conclusion</h2>
<p>We reassessed the role of static Coulomb stress transfer in the 2016–2017 Central Apennines seismic sequence using a high-resolution catalog and refined fault geometries. Our analysis shows that the majority of aftershocks (68–75%) occurred in areas where static stress increased by at least 0.01 MPa, with a statistically significant positive correlation between stress change and aftershock density. The three mainshocks appear to have been sequentially triggered by stress transfer, consistent with a cascade model.</p><p>However, we also identified that 8–11% of aftershocks occurred in stress shadow zones, indicating that static stress is not the sole triggering mechanism. Dynamic stresses, fluid effects, and viscoelastic relaxation likely contribute to the observed seismicity. Future work should integrate these processes in a unified model to improve aftershock forecasting.</p><p>Our study provides a reassessed framework for seismic hazard in the Central Apennines, emphasizing the need for high-resolution data and multi-mechanism approaches. The methodology and findings are transferable to other extensional provinces with similar faulting characteristics.</p>
<h2>References</h2>
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