Two-Stage Earthquake Detection from Magnitude Statistics: Spatial Identification by Compression, Temporal Triggering by Foreshock Spike, and 26.5-Hour Advance Signal Before the 2011 Tohoku M9.0

Abstract Whether measurable statistical changes in earthquake catalogs precede large earthquakes remains one of the most debated questions in seismology. This study introduces and validates a two-stage earthquake detection framework built on the rolling standard deviation of earthquake magnitudes computed within local spatial windows. The core observation is simple: the diversity of earthquake sizes within 10–300 km of future mainshock epicenters decreases systematically by 6–22% in the 7–21 days before large earthquakes. This suppression strengthens monotonically as the measurement radius decreases toward the epicenter (− 6% at 200 km, − 11% at 50 km, − 22% at 10 km), establishing a spatial gradient confirmed across three independent catalogs in two tectonic regimes. At near-field distances (10–50 km), a two-phase temporal pattern emerges: magnitude compression at 7–21 days, followed by a sudden variance increase at 1–3 days consistent with foreshock-cascade onset. Three independently measurable quantities are combined into a unified seismic state index: Ψ(t) = C(t) × Q(t) × [1 + S(t)], where C measures magnitude variance compression, Q measures seismicity rate quiescence, and S measures magnitude skewness anomaly indicating energy accumulation. The multiplicative form requires all three simultaneously: compression alone, quiescence alone, or skewness alone does not produce a high Ψ. A complementary lock-to-load ratio R = (C × Q)/(1 + E) measures fault lock integrity relative to contained energy, analogous to the Griffith fracture criterion. These findings yield a two-stage detection framework. Stage 1 (Spatial Identification—WHERE) computes Ψ continuously across all grid cells and flags the most compressed regions, providing months to years of advance notice for region-specific preparation: infrastructure inspection, emergency plan review, and supply pre-positioning. Stage 2 (Temporal Triggering—WHEN) monitors flagged regions for a sudden variance spike—the S4→S1 foreshock flip—converting the long-term spatial flag into a short-term temporal alert. Neither stage alone is sufficient: Stage 1 without Stage 2 gives years of vague warning; Stage 2 without Stage 1 produces too many false alarms. Together, they provide both WHERE and WHEN. Using the JMA unified hypocenter catalog (2000–2023, 178,577 events, 288 isolated M ≥ 6.0 mainshocks), USGS Japan data (2000–2026, 46,515 events), and USGS Turkey data (2000–2026, 7,238 events), this study demonstrates nine principal results: (1) spatial decay from − 6% at 200 km to − 22% at 10 km across three catalogs; (2) walk-forward prospective testing with frozen 2000–2009 training achieves AUC = 0.761 on 71 mainshocks (likelihood ratio 3.5×); (3) the Ψ index achieves AUC = 1.000 (p = 0.018) across eight events, and R independently achieves AUC = 1.000 (p = 0.014); (4) year-by-year prospective scanning detects M ≥ 6.0 events in 100% of years (14/14), with 59% event detection at 116 km average distance, including the 2011 Tohoku M9.0 at 17 km from the flagged cell; (5) Stage 1 provides 10–18 years of advance flagging, while Stage 2 provides 1.7 hours to 53 days of trigger signal in 78% of events—including 26.5 hours before the Tohoku M9.0; (6) blind tests detect the 2024 Noto M7.6 (703 deaths, S4 = 95%), 2020 Elazig M6.7 (41 deaths), 2011 Van M7.1 (604 deaths), and 2023 Kahramanmaras M7.5; (7) spatial scanning identifies nucleation zones within 200 km in 50% of retrospective tests, including Tohoku at 62 km (14 months advance) and Noto at 62 km (4 years advance); (8) a two-force physical model—compression from stress homogenization versus energy accumulation from continued tectonic loading—explains the patterns, with universal S4→S1 post-event reset confirming physical reality; and (9) current assessment identifies Van (Turkey, Ψ = 0.718), Erzincan (Turkey, Ψ = 0.644, rising, 87-year seismic gap), and Akita/Iwate (Japan, Ψ = 0.591) as the highest-Ψ regions globally, with specific nucleation-zone coordinates. The method does not predict individual earthquakes. The Ψ calibration comprises only 8 events; AUC = 1.000 may not generalize. Detection rate is approximately 50–60%; critically, the Tohoku M9.1 and Kahramanmaras M7.8—the two deadliest earthquakes in the study period—were not detected by Stage 1. Timing cannot be predicted: S4 duration ranged from 10 days to over 8 years. Formal nearest-neighbor declustering was not applied. The practical value lies not in prediction but in preparation: providing a new, independent, low-cost monitoring channel—requiring nothing more than an earthquake catalog and a computer—that identifies which specific regions merit heightened attention at any given time. Reproducible code and datasets are provided.