Detectability Limits of Seismic Rate Changes: Statistical Constraints from Synthetic and Global Earthquake Catalogs

Temporal variations in earthquake occurrence rates are widely investigated as indicators of stress evolution, fault-zone processes, or preparatory phases preceding large earthquakes. However, the statistical observability of such rate changes is fundamentally constrained by finite event counts, seismicity clustering, catalog heterogeneity, and analysis design choices. Here, we reformulate the problem of seismic rate variability as an explicit detectability question: given a baseline rate, observation window, significance level, and target power, what is the minimum fractional rate change that can be statistically resolved? We derive exact detectability thresholds for count-based hypothesis tests under both Poisson and overdispersed Negative Binomial (NB) models, explicitly accounting for window length, overdispersion, and multiple testing. Synthetic experiments demonstrate that overdispersion alone, even in stationary processes, substantially inflates detectability thresholds relative to Poisson expectations, whereas sliding-window analyses further degrade statistical power through multiplicity effects. Applying this framework to the global U.S. Geological Survey earthquake catalog (Mw ≥ 5.5, 1973–2025), we show that empirically inferred NB thresholds remain significantly higher than Poisson-based predictions across sub-annual to multiyear timescales. Observed rolling-window rate fluctuations frequently exceed Poisson thresholds but almost never surpass NB thresholds, indicating that most apparent global rate anomalies are statistically indistinguishable from intrinsic catalog variability. Additional analyses show that these conclusions are robust to the choice of statistical power and are not primarily driven by the aggregation of heterogeneous tectonic settings. Our results demonstrate that null detections of seismic rate changes are often the expected outcome of fundamental statistical constraints rather than evidence against underlying physical processes. The proposed detectability framework provides a quantitative benchmark for interpreting reported rate anomalies, reassessing claims of seismic quiescence or activation, and designing statistically defensible analyses of earthquake-rate variability.