A scaling law, S ∝ Lα, governs the relationship between the area S enclosed by a human mobility loop and its trajectory length L. Previous studies have established that for short-range movements (L < 5 km), the scaling exponent is typically α ∼ 2.0, indicative of two-dimensional efficient exploratory behavior that efficiently covers the surrounding area. For long-range movements (L ≥ 5 km), it is typically α ∼ 1.5–1.6, corresponding to one-dimensional destination-oriented behavior characterized by a nearly straight-line trajectory toward the destination. In this study, we analyze highresolution (1-min interval) GPS data from Agoop, comprising approximately 20,000 daily records, to examine human mobility traces in Ishikawa Prefecture before and after the Noto Peninsula Earthquake on 1 January 2024. We focus on the changes in the scaling exponent α. This major earthquake provides a valuable “natural experiment” to investigate collective human behavior under established social norms. Our analysis revealed a highly anomalous phenomenon immediately following the earthquake. Contrary to normal conditions, the long-range scaling exponent, αLong, surged to α ∼ 1.8 across the entire prefecture, a value comparable to the short-range exponent, αShort. This phenomenon was observed even in areas with relatively minor physical damage and returned to its baseline value by the next day. This anomalous change in the scaling exponent strongly suggests that the shift in mobility patterns was not a direct result of the earthquake’s physical damage. Rather, it indicates that individuals who were outdoors temporarily altered their movement from one-dimensional, destination-oriented travel to two-dimensional, exploratory behavior while evacuating to safer locations, such as higher ground, in response to tsunami alerts. This study is the first to demonstrate that the mobility scaling exponent can function as a real-time quantitative indicator for characterizing collective psychological states, such as widespread precautionary evacuation, even in the absence of direct physical damage.
- Open Access
- Article
Anomalous Surge in the Mobility Scaling Exponent Reveals Unique Collective Behavior during the 2024 Noto Peninsula Earthquake
- Atushi Ishikawa 1,*,†,
- Shouji Fujimoto 1,†,
- Takayuki Mizuno 2,†
Author Information
Received: 29 Sep 2025 | Revised: 12 Dec 2025 | Accepted: 13 Jan 2026 | Published: 27 Jan 2026
Abstract
Keywords
sociophysics | computational social science | human mobility | scaling law | big data | disaster science | mobility during disasters | evacuation behavior
References
- 1.
Noulas, A.; Scellato, S.; Lambiotte, R.; et al. A Tale of Many Cities: Universal Patterns in Human Urban Mobility. PLoS ONE 2012, 7, e37027.
- 2.
Zhao, K.; Boguna, M.; Vespignani, A. Explaining the Power-law Distribution of Human Mobility Through Transportation Modality Decomposition. Sci. Rep. 2014, 4, 7452.
- 3.
Yan, X.-Y.; Wang, W.-X.; Di, Z.; et al. Universal model of individual and population mobility. Nat. Commun. 2017, 8, 1639.
- 4.
Schlapfer, M.; Dong, L.; O’Keeffe, K.; et al. The universal visitation law of human mobility. Nature 2021, 593, 522–527.
- 5.
Zhao, K.; Vespignani, A.; Wang, W.-X. Explaining the power-law distribution of human mobility. Sci. Rep. 2015, 5, 9136.
- 6.
Brockmann, D.; Hufnagel, L.; Geisel, T. The Scaling Laws of Human Travel. Nature 2006, 439, 462–465.
- 7.
Gonz´alez, M.C.; Hidalgo, C.A.; Barab´asi, A.L. Understanding Individual Human Mobility Patterns. Nature 2008, 453, 779–782.
- 8.
Song, C.; Koren, T.; Wang, P.; et al. Modelling the Scaling Properties of Human Mobility. Nat. Phys. 2010, 6, 818–823.
- 9.
Ishikawa, A.; Fujimoto, S.; Mizuno, T.; et al. Statistical Law between Areas and Perimeters Created by a Moving Trajectory. Electronics 2024, 13, 4018. https://doi.org/10.3390/electronics13204018.
- 10.
Wang, Q.; Taylor, J.E. Patterns and limitations of urban human mobility resilience under the influence of multiple types of natural disaster. PLoS ONE 2016, 11, e0147299.
- 11.
Rezaei, B.A.; Sarshar, N.; Roychowdhury, V.P.; et al. Disaster management in power-law networks: recovery from and protection against intentional attacks. Phys. A 2007, 381, 497–514.
- 12.
Jiang, Y.; Li, Z.; Cutter, S.L. Social distance integrated gravity model for evacuation destination choice. Int. J. Digit. Earth 2021, 14, 1004–1018.
- 13.
Haraguchi, M.; Nishino, A.; Kodaka, A.; et al. Human mobility data and analysis for urban resilience: A systematic review. Environ. Plan. B 2022, 49, 1507–1535.
- 14.
Ahmouda, A.; Hochmair, H.H.; Cvetojevic, S. Using twitter to analyze the effect of hurricanes on human mobility patterns. Urban Sci. 2019, 3, 87.
- 15.
Yabe, Y.; Sekimoto, Y.; Ukkusuri, S.V. Human-mobility-based evacuation behaviors during sequential earthquakes. Nat. Commun. 2022, 13, 3753.
- 16.
Agoop Corp. Survey Report: Analysis of Human Flow for Hatsumode 2022—A Comparison of Human Flow at 10 Shrines and Temples Nationwide with the Previous Year and Pre-COVID-19. 2022. Available online: https://www.agoop.co.jp/news/press-release/20220107/ (accessed on 26 September 2025).
- 17.
Agoop Corp. Official Website. 2025. Available online: https://www.agoop.co.jp/ (accessed on 19 September 2025).
- 18.
Survey Research Center, Kanazawa University. Survey on Evacuation Behavior and Disaster Preparedness in Suzu City during the 2024 Noto Peninsula Earthquake. 2024. Available online: https://www.city.suzu.lg.jp/ (accessed on 23 January 2026).
- 19.
Toyama Prefecture. Survey Report on Residents’ Evacuation Behavior and Perceptions After the 2024 Noto Peninsula Earthquake. 2024. Available online: https://www.pref.toyama.jp/ (accessed on 23 January 2026).
- 20.
Numazawa, T.; Kure, S. Tsunami behavior and evacuation in the coastal region of Toyama Prefecture during the 2024 Noto Peninsula earthquake. Coast. Eng. J. 2025, in press.
- 21.
Makinoshima, F.; Yotsui, S.; Sato, S.; et al. Massive geolocation data reveal evacuation behaviour during the 2024 Noto Peninsula earthquake and tsunami. arXiv 2024, arXiv:2412.05795.
- 22.
Ishibashi, K. Survey on tsunami evacuation during the 2024 Noto Peninsula Earthquake. J. Nat. Disaster Sci. 2025, in press.
- 23.
Yuhi, M.; Umeda, S.; Arita, M.; et al. Post-Event Survey of the 2024 Noto Peninsula Earthquake Tsunami in Japan. Coast. Eng. J. 2024, 66, 405–418: https://doi.org/10.1080/21664250.2024.2368955.
- 24.
Research Group on the 2024 Noto Peninsula Earthquake. Field Report of the 2024 Noto Peninsula Earthquake—Current situations of evacuation centers and lifeline recovery. Preprints 2024, 2024010001.
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