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Probabilistic Tsunami Hazard Assessment from Incomplete and Uncertain Historical Catalogues with Application to Tsunamigenic Regions in the Pacific Ocean

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Abstract

The paper presents a new method for empirical assessment of tsunami recurrence parameters, namely the mean tsunami activity rate \(\lambda_{\text{T}}\), the Soloviev–Imamura frequency–magnitude power law \(b_{\text{T}}\)-value, and the coastline-characteristic, maximum possible tsunami intensity \(i_{ \text{max} }\). The three coastline-characteristic recurrence parameters are estimated locally by maximum likelihood techniques using only tsunami event catalogues. The method provides for incompleteness of the tsunami catalogue, uncertainty in the tsunami intensity determination, and uncertainty associated with the parameters in the applied tsunami occurrence models. Aleatory and epistemic uncertainty is introduced in the tsunami models by means of the use of mixture distributions. Both the mean tsunami activity rate \(\lambda_{\text{T}}\) of the Poisson occurrence model, and the \(b_{\text{T}}\)-value of the Soloviev–Imamura frequency–intensity power law are random variables. The proposed procedure was applied to estimate the probabilities of exceedance and return periods for tsunamis in the tsunamigenic regions of Japan, Kuril–Kamchatka, and South America.

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Fig. 1

Modified after Kijko and Sellevoll (1992)

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Acknowledgements

The authors wish to thank V. K. Gusiakov of the Novosibirsk Tsunami Laboratory of the Institute of Computational Mathematics and Mathematical Geophysics (NTL/ICMMG) SDRAS, Novosibirsk, Russia, for the tsunami catalogue used in this paper, I. Fabris-Rotelli and P.J van Staden from the Department of Statistics at the University of Pretoria for their valuable contributions when preparing the manuscript as well as the two anonymous reviewers and Editor in chief for their insightful and helpful feedback. This work is based on research supported wholly or in part by the National Research Foundation of South Africa (Grant Numbers 76906 and 94808).

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  1. University of Pretoria Natural Hazard Centre, Department of Geology, University of Pretoria, Private Bag X20, Hatfield, Pretoria, 0028, South Africa

    Ansie Smit & Andrzej Kijko

  2. Department of Statistics, University of Pretoria, Private Bag X20, Hatfield, Pretoria, 0028, South Africa

    Ansie Smit & Alfred Stein

  3. Faculty of Geo-information Science and Earth Observation (ITC), University of Twente, Enschede, The Netherlands

    Alfred Stein

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Smit, A., Kijko, A. & Stein, A. Probabilistic Tsunami Hazard Assessment from Incomplete and Uncertain Historical Catalogues with Application to Tsunamigenic Regions in the Pacific Ocean. Pure Appl. Geophys. 174, 3065–3081 (2017). https://doi.org/10.1007/s00024-017-1564-4

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