Abstract. The subject of the article is the theoretical development of the probabilistic model for a Poisson-type tsunami sequence that is consistent with data on the manifestations of historical events, in order to obtain estimates of the accuracy of the tsunami activity parameters. An example of a tsunami recurrence function, which is the most important quantitative characteristic of tsunami activity for the Port of Malokurilskoye, one of the places in the South Kuril Islands region with the most reliable tsunami height dataset, was created on the basis of a theoretical essay. An explanation for the weak statistical stability of all large values of the tsunami heights, especially for the largest one in the series of observations, was given based on the probability density functions of the ranked tsunami heights. In particular, it means, for example, that the maximum tsunami height recorded at a certain location during a 30-year observation period should be correlated with a wide range of possible recurrence periods of about 10 to 100 years. Synthetic catalogs of the tsunami heights, built for the Port of Malokurilskoye, showed that the tsunami height datasets with a duration of at least 250 or 500 years without gaps are needed to obtain the tsunami activity parameters with an acceptable accuracy of 10 or 5 %. The most important results are the analytical equations for the variances of estimates of the tsunami activity parameters, which characterize the accuracy of these estimates, depending on a priori unknown values of the tsunami activity parameters and the amount of data used.

For citation: Kaistrenko V.M. The problem of the accuracy of the tsunami activity parameters. Geosistemy perehodnykh zon = Geosystems of Transition Zones, 2023, vol. 7, no. 2, 9 p. (In Engl.).
https://doi.org/10.30730/gtrz.2023.7.2.149-159, http://journal.imgg.ru/web/full/f-e2023-2-3.pdf

1. Levin B.W., Nosov M.A. 2016. Physics of Tsunamis. Springer, 310 p.

2. Kaistrenko V., Sedaeva V. 2001. 1952 North Kuril Tsunami: New data from archives. In: G.T. Hebenstreit (ed). Tsunami research at the end of a critical decade. Dordrecht: Kluwer Acad. Publ., 91–102. (Advances in Natural and Technological Hazards Research; 18). https://doi.org/10.1007/978-94-017-3618-3_8

3. MacInnes B., Pinegina T., Bourgeois J., Razjigaeva N., Kaistrenko V., Kravchunovskaya E. 2009. Field survey and geological effects of the 15 November 2006 Kuril tsunami in the middle Kuril Islands. Pure and Applied Geophysics, 166(1-2): 9–36. https://doi.org/10.1007/s00024-008-0428-3

4. Kaistrenko V., Razjigaeva N., Kharlamov A., Shishkin A. 2013. Manifestation of the 2011 Great Tohoku Tsunami on the coast of the Kuril Islands: A tsunami with ice. Pure and Applied Geophysics, 170: 1103–1114. https://doi.org/10.1007/s00024-012-0546-9

5. Gonzalez F.I., Geist E.L., Jaffe B.E., Kanoglu U., Mofjeld H., Synolakis C.E., Titov V.V., Arcas D., Bellomo D., et al. 2009. Probabilistic tsunami hazard assessment at Seaside, Oregon, for near- and far-field seismic sources. J. of Geophysical Research, 114: C11023. https://doi.org/10.1029/2008JC005132

6. Gusiakov V.K., Chubarov L.B., Beizel S.A. 2015. Assessment of tsunami hazard due to regional and remote sources: The coast of the Sea of Okhotsk. J. of Volcanology and Seismology, 9(4): 276–288. https://doi.org/10.1134/S0742046315040041

7. Kulikov E., Rabinovich A., Thomson R. 2005. Estimation of tsunami risk for the coasts of Peru and Northern Chile. Natural Hazards, 35: 185–209. doi:10.1007/s11069-004-4809-3

8. Leonard L., Rogers G., Mazzotti S. 2014. Tsunami hazard assessment of Canada. Natural Hazards, 70(1): 237–274. https://doi.org/10.1007/s11069-013-0809-5

9. Salah P., Sasaki J., Soltanpour, M. 2021. Comprehensive probabilistic tsunami hazard assessment in the Makran subduction zone. Pure and Applied Geophysics, 178: 5085–5107. https://doi.org/10.1007/s00024-021-02725-y

10. Shevchenko G.V., Loskutov A.V., Kaistrenko V.M. 2018. A new map of tsunami hazard for the South Kuril Islands. Geosystems of Transition Zones, 2(3): 225–238. (In Russ., abstr. in Engl.). doi:10.30730/2541-8912.2018.2.3.225-238

11. Kagan Y.Y. 2010. Earthquake size distribution: Power-law with exponent β≡1/2? Tectonophysics, 490 (1–2): 103–114. https://doi.org/10.1016/j.tecto.2010.04.034

12. Grezio A., Babeyko A., Baptista M.A., Behrens J., Costa A., Davies G., Geist E.L., Glimsdal S., Gonzalez F.I., et al. 2017. Probabilistic tsunami hazard analysis: multiple sources and global applications. Reviews of Geophysics, 55: 1158–1198. https://doi.org/10.1002/2017RG000579

13. Basili R., Brizuela B., Herrero A., Iqbal S., Lorito S., Maesano F.E., Murphy S., Perfetti P., Romano F., et al. 2021. The making of the NEAM tsunami hazard model 2018 (NEAMTHM18). Frontiers in Earth Science, 8: 616594. https://doi.org/10.3389/feart.2020.616594

14. Behrens J., Lovholt F., Jalayer F., Lorito S., Salgado-Galvez M.A., Sorensen M., Abadie S., Aguirre-Ayerbe I., Aniel-Quiroga I., et al. 2021. Probabilistic tsunami hazard and risk analysis: A review of research gaps. Frontiers in Earth Science, 9: 628772. https://doi.org/10.3389/feart.2021.628772

15. Kaistrenko V. 2011. Tsunami recurrence versus tsunami height distribution along the coast. Pure and Applied Geophysics, 168: 2065–2069. https://doi.org/10.1007/s00024-011-0288-0

16. Kaistrenko V. 2014. Tsunami recurrence function: structure, methods of creation, and application for tsunami hazard estimates. Pure and Applied Geophysics, 171: 3527–3538. https://doi.org/10.1007/s00024-014-0791-1

17. Kaistrenko V. 2023. Tsunami recurrence and hazard evaluation for the South Kuril Islands. Pure and Applied Geophysics. (In Print). https://doi.org/10.1007/s00024-022-03163-0

18. Dawson A.G., Stewart I. 2007. Tsunami deposits in the geological record. Sedimentary Geology, 200: 166–183. https://doi.org/10.1016/j.sedgeo.2007.01.002

19. Pinegina T.K., Razjigayeva N.G. 2013. Paleotsunami studies on the Far East coast of Russia. In: Lobkovsky L.I. (ed.) World Ocean. Vol. 1. Geology and tectonics of the ocean. Catastrophic phenomena in the ocean. Moscow: Scientific World, p. 488–498. (In Russ.).

20. Ayvasyan S.A., Enyukov I.S., Meshalkin L.D. 1983. Applied statistics: Basics of modeling and primary data processing. Moscow: Finansy i statistika, 471 p. (In Russ.).

21. Himmelblau D.M. 1970. Process analysis by statistical methods. New York: John Wiley and Sons, 463 p.

22. Cramer H. 2016. Mathematical methods of statistics. Princeton Univers. Press, 575 p.

23. Geist E.L., Parsons T. Distribution of tsunami interevent times. 2008. Geophysical Research Letters, 35(2): 18 p. https://doi.org/10.1029/2007GL032690

24. Historical Tsunami Database for the Pacific (HTDB/PAC). URL: http://tsun.sscc.ru/On_line_Cat.htm (accessed 15.12.2022).

25. Tsunami Data and Information. https://doi.org/10.7289/V5PN93H7