Reduced seismic activity after mega-earthquakes

Earthquakes are destructive spatiotemporal phenomena governed by empirical laws such as the Gutenberg-Richter law governing magnitude-frequency statistics and the Omori-Utsu law describing aftershock decay. Prior work has shown clustering, long-range correlations, and memory in interevent times and distances, and has explored models such as ETAS to account for spatiotemporal clustering. Remote (dynamic) triggering has been observed after some large events, though evidence is mixed, and detection capabilities can be reduced immediately after large mainshocks. From a physical perspective, global occurrence rates beyond the aftershock zone could decrease following large earthquakes due to energy and stress release, analogous to suppressed short waiting times after large avalanches in self-organized critical systems. The objective of this study is to quantify how earthquake rates vary with distance and time after mega-earthquakes (m ≥ 7.5), test statistically whether post-mainshock activity is reduced or enhanced beyond aftershock zones, identify a characteristic distance scale for aftershocks, and assess whether the global ETAS model reproduces the observed behaviors.

The literature establishes key seismicity regularities: Gutenberg-Richter magnitude-frequency scaling (b ≈ 1) and Omori-Utsu aftershock decay. Numerous studies report clustering and memory in earthquake occurrence, including correlated interevent intervals and long-range correlations detected by DFA. Research on foreshocks suggests an increase in seismicity rates prior to some mainshocks (inverse Omori), though this is less robust than the Omori-Utsu law. Spatially, static Coulomb stress changes explain nearby aftershocks, while dynamic stress may trigger remote events thousands of kilometers away; however, evidence for remote triggering is mixed across studies. Reduced detection capability immediately after large earthquakes has also been documented. Global ETAS models have been used to capture spatiotemporal clustering and aftershock sequences but do not include mechanisms for suppressing seismicity following large events. These prior findings motivate investigating both enhanced and potentially reduced remote activity after mega-earthquakes and evaluating whether standard models capture such effects.

Data: The USGS global earthquake catalog from May 1979 to May 2023 was analyzed for events with magnitude ≥5.1 (Mw, Mb, Ms), depth 0–700 km. The catalog includes 57,085 earthquakes, with 193 events of magnitude ≥7.5 and 37 events ≥8.0. Completeness was assessed via Gutenberg-Richter scaling and is supported for thresholds 5.0–5.1; the main analysis uses 5.1, with sensitivity checks at 5.0 and 5.2.

Significance testing framework: For each mega-earthquake, the count of subsequent events n(T, R) is computed in a post-event window of duration T days and at distances greater than R km from the mainshock epicenter, excluding the immediate aftershock zone within R. To test whether observed counts differ from typical local rates, a null hypothesis assumes independence of the count n(T, R) and the mainshock time. Surrogate data are generated by fixing the mainshock location but selecting 10^4 random start times uniformly over the catalog period to compute surrogate counts n′(T, R). The empirical PDF of n′(T, R) defines lower (10%) and upper (90%) quantiles. An observed count below the 10% quantile indicates significantly reduced activity; above the 90% quantile indicates significantly increased activity. Ratios r of significant events are computed as Ns/N over all mega-earthquakes, with uncertainty from the floor/ceiling discretization of non-integer quantiles (averaging both choices and using their difference as an error bar). Analyses explored R from 10 to 8000 km and T from 3 to 60 days. Robustness checks used 5%/95% quantiles and alternative metrics (median, mean, multiples of mean), and different magnitude thresholds (5.0, 5.2).

Illustrative case: For the 2017 Chiapas M8.2 earthquake, counts of M≥5.1 events during T=5 days and at distances >500 km yielded an observed count below the 10% surrogate quantile, indicating reduced remote activity.

Model comparison: A global space-time ETAS model was calibrated via an EM-type algorithm using standard components: background rate μ(x,y)=μ0 u(x,y); magnitude productivity k(M)=A exp(α(M−M0)); temporal triggering g(Δt)=(1+cΔt)^{−p}; and spatial kernel f(Δx,Δy,M)=1/(π ζ^2 [1+ (Δx^2+Δy^2)/ζ^2]) with ζ= D exp[γm (M−M0)]. Background events follow a Poisson process with spatial density u(x,y); aftershocks are simulated via thinning. Multiple independent synthetic catalogs were generated (50 realizations) matching the observational magnitude threshold and time span. Ratios of significant events in the simulations were computed identically to the real-catalog analysis, and the fraction of ETAS realizations exceeding the real-data ratios was mapped over (R,T) to assess agreement.

Parameter values estimated for the ETAS model are summarized in Table 2 of the paper; details on catalog preparation, estimation procedures, and simulation are provided in the Methods and cited references.

• There is a statistically significant excess of mega-earthquakes (m ≥ 7.5) followed by reduced remote seismic activity compared to expectation under the null hypothesis. For T=5 days and R=500 km, the ratio of reduced-activity cases is r = 0.194 with uncertainty 0.176–0.212, exceeding the 0.1 expected under the 10% quantile threshold. The ratio of increased-activity cases is r = 0.078 with uncertainty 0.077–0.079, below 0.1.
• Example: The 2017 Chiapas M8.2 event showed an observed remote count (T=5 days, R>500 km, M≥5.1) below the 10% surrogate quantile, indicating reduced activity.
• Distance-time dependence: Near the epicenter (R ≤ 250–300 km), increased activity dominates (ratios above the 90% quantile >0.1) consistent with aftershocks that decay with distance and time. Beyond ~500 km, the fraction of reduced-activity cases stabilizes near ~0.15 (for T≈3–60 days), indicating reduced post-mainshock activity at remote distances. Across (R,T), the below-10% ratio crosses 0.1 at ~100 km, while the above-90% ratio crosses 0.1 at ~1000 km, implying an aftershock-affected extent of roughly 100–1000 km.
• Magnitude dependence: For most magnitudes ≥7.5, reduced activity is more prevalent than increased activity. For the strongest events (m ≥ 8.0), both significantly reduced and significantly increased remote activity are observed more often than expected (examples include Sumatra-Andaman 2004 with increased activity and Illapel 2015 with reduced activity), though small sample size increases uncertainty (37 events ≥8.0).
• Robustness: Findings persist when using stricter quantiles (5%/95%), alternative central-tendency thresholds (median, mean, multiples of mean), and different magnitude thresholds (5.0, 5.2).
• ETAS comparison: The global ETAS model reproduces near-field aftershock clustering reasonably but fails to reproduce the observed long-distance reduction in post-mainshock seismicity; for distances beyond several hundred kilometers, ETAS ratios do not show the elevated frequency of reduced-activity cases seen in real data. At short distances, ETAS tends to underestimate the real aftershock enhancement, but this does not explain the remote suppression discrepancy.

The statistical analyses demonstrate that after mega-earthquakes, remote regions (hundreds to thousands of kilometers away) experience reduced seismic activity more frequently than expected from typical rates at those locations and times. This contrasts with the well-known near-field aftershock enhancement and reveals a dual response: enhancement within an aftershock-affected zone (≈100–1000 km) and suppression beyond it. The phenomenon is robust across multiple thresholds and analysis choices. The strongest events (m ≥ 8.0) can produce either suppressed or enhanced global activity, suggesting that very large stress perturbations may sometimes promote dynamic triggering at great distances but also can lead to a quiescent period elsewhere.

The ETAS model, which encapsulates spatiotemporal clustering and long-range triggering via its spatial kernel, lacks a mechanism for reducing background activity post-mainshock and therefore fails to reproduce the observed remote suppression. This indicates a missing physical ingredient in current statistical models, potentially linked to global stress redistribution and energy release after massive ruptures. The inferred aftershock extent (≈100–1000 km) emerges from contrasting crossing distances of reduced vs. increased-activity ratios and is broadly consistent with decay of stress and aftershock productivity with distance. These findings suggest that incorporating transient reductions in background rates or explicit stress-redistribution mechanisms into forecasting models could improve realism.

This study introduces a statistical framework to quantify post-mainshock seismicity changes as functions of distance and time and applies it to a complete global catalog (1979–2023). It finds that mega-earthquakes (m ≥ 7.5) are followed by significantly more instances of reduced remote activity than expected, while near-field increases reflect aftershocks. The transition distances imply an aftershock extent of approximately 100–1000 km. The strongest events (m ≥ 8.0) can be followed by either reduced or increased remote activity. Comparison with a calibrated global ETAS model shows that standard formulations do not capture the remote suppression, indicating a missing mechanism—possibly transient global stress/energy relaxation.

Future research should: (i) enlarge samples as more mega-events accrue, especially for m ≥ 8.0; (ii) investigate physical mechanisms and fault-network pathways for stress redistribution that could generate remote suppression; (iii) develop and test ETAS extensions allowing time-varying background rates or stress-coupled suppression effects; and (iv) assess operational forecasting gains from incorporating remote quiescence following mega-events.

• Sample size: Only 193 mega-earthquakes (m ≥ 7.5) and 37 with m ≥ 8.0 were available; the small number of the strongest events increases uncertainty in magnitude-stratified analyses.
• Statistical discretization: For short time windows leading to small counts, using floor/ceiling of non-integer quantiles introduces uncertainty in significance classification.
• Detection effects: Although the analysis excludes near-field regions and uses higher magnitude thresholds to mitigate completeness issues, transient detection limitations immediately after large events may still affect counts.
• Model comparison: ETAS parameterization and global assumptions may influence discrepancies; however, the key finding of remote suppression appears robust to modeling choices.
• Generalizability: The inferred aftershock extent (100–1000 km) is based on global statistics and may vary regionally with tectonic settings.