The establishment of standardized tsunami magnitude scales is a challenging issue. Five main types of scales have been proposed since the 1940s but no comparative studies have been carried out so far. Based on data of local and remote tsunamis reaching Japan from the historical times up to 2011 we established for the first-time empirical relationships between the Imamura-Iida (m), Soloviev (S), Hatori (m′), Abe (Mt) and Murty-Loomis (ML) scales, as well as among these magnitudes and the moment magnitude, Mw, of the parent earthquakes. Mt and ML do not represent real tsunami magnitude scales but alternative earthquake magnitude estimates since both calibrates for Mw. The best correlation was found for the pair Mw/Mt. However, no good correlation was found for the pairs Mw/ML and Mt/ML. This is due to difficulties in calculating accurately ML from the potential energy at the source which is the physical basis of ML. Between the various pairs composed by m, S, m′ and Mw (or Mt), the magnitude m′, ranging from − 1 to 4, showed the best correlation performance very likely since it calibrates wave height, h, for epicentral distance, Δ. On the contrary, m and S do not calibrate h for Δ. Utilizing the seismological tradition, we developed tsunami frequency-magnitude distributions (FMDs) based on the Gutenberg-Richter law established for earthquakes. Tsunami hazard descriptors in Japan have been calculated from empirical relationships and FMDs. For example, the mean repeat time of m′ ≥ 3.0 (heavily damaging wave) is about 38 yrs, while the maximum m′ expected in 10 and 100 years is ~ 2.4 and ~ 3.4, respectively. Earthquakes of Mw (or Mt) ≥ 8.2, regardless local or remote, that generate tsunamis reaching Japan repeat about every 21 years with corresponding m′ of ~ 2.4. We tested successfully the applicability of the relations developed with data of recent tsunamis generated by the 1 Jan. 2024 Noto Peninsula, Japan, earthquake (Mw = 7.5; we found m′ = 0.18, Mt = 7.48) and the 30 Oct. 2020 Samos, east Aegean Sea, Greece, earthquake (Mw = 7.0; we found m′ = 0, Mt ~ 6.9). Systematic magnitude calculation of past tsunamis will allow the development of regional FMDs and tsunami hazard descriptors in tsunami prone regions of the world with possible contribution in the long-term tsunami risk mitigation planning. However, the scales m, S, m′ are characterized by coarse resolution and do not allow for accurate hazard assessments.

Empirical Relationships Between Earthquake and Tsunami Magnitudes in Japan as Tsunami Hazard Descriptors

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2025年9月23日

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Ioanna Triantafyllou,
Fumihiko Imamura,
Anawat Suppasri

摘要

The establishment of standardized tsunami magnitude scales is a challenging issue. Five main types of scales have been proposed since the 1940s but no comparative studies have been carried out so far. Based on data of local and remote tsunamis reaching Japan from the historical times up to 2011 we established for the first-time empirical relationships between the Imamura-Iida (m), Soloviev (S), Hatori (m′), Abe (M_t) and Murty-Loomis (ML) scales, as well as among these magnitudes and the moment magnitude, M_w, of the parent earthquakes. M_t and ML do not represent real tsunami magnitude scales but alternative earthquake magnitude estimates since both calibrates for M_w. The best correlation was found for the pair M_w/M_t. However, no good correlation was found for the pairs M_w/ML and M_t/ML. This is due to difficulties in calculating accurately ML from the potential energy at the source which is the physical basis of ML. Between the various pairs composed by m, S, m′ and M_w (or M_t), the magnitude m′, ranging from − 1 to 4, showed the best correlation performance very likely since it calibrates wave height, h, for epicentral distance, Δ. On the contrary, m and S do not calibrate h for Δ. Utilizing the seismological tradition, we developed tsunami frequency-magnitude distributions (FMDs) based on the Gutenberg-Richter law established for earthquakes. Tsunami hazard descriptors in Japan have been calculated from empirical relationships and FMDs. For example, the mean repeat time of m′ ≥ 3.0 (heavily damaging wave) is about 38 yrs, while the maximum m′ expected in 10 and 100 years is ~ 2.4 and ~ 3.4, respectively. Earthquakes of M_w (or M_t) ≥ 8.2, regardless local or remote, that generate tsunamis reaching Japan repeat about every 21 years with corresponding m′ of ~ 2.4. We tested successfully the applicability of the relations developed with data of recent tsunamis generated by the 1 Jan. 2024 Noto Peninsula, Japan, earthquake (M_w = 7.5; we found m′ = 0.18, M_t = 7.48) and the 30 Oct. 2020 Samos, east Aegean Sea, Greece, earthquake (M_w = 7.0; we found m′ = 0, M_t ~ 6.9). Systematic magnitude calculation of past tsunamis will allow the development of regional FMDs and tsunami hazard descriptors in tsunami prone regions of the world with possible contribution in the long-term tsunami risk mitigation planning. However, the scales m, S, m′ are characterized by coarse resolution and do not allow for accurate hazard assessments.