Parametric and non-parametric estimation of extreme earthquake event: the joint tail inference for mainshocks and afters
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Parametric and non-parametric estimation of extreme earthquake event: the joint tail inference for mainshocks and aftershocks Juan-Juan Cai1 · Phyllis Wan2
· Gamze Ozel3
Received: 15 June 2019 / Revised: 5 November 2020 / Accepted: 9 November 2020 / © The Author(s) 2020
Abstract In an earthquake event, the combination of a strong mainshock and damaging aftershocks is often the cause of severe structural damages and/or high death tolls. The objective of this paper is to provide estimation for the probability of such extreme events where the mainshock and the largest aftershocks exceed certain thresholds. Two approaches are illustrated and compared – a parametric approach based on previously observed stochastic laws in earthquake data, and a non-parametric approach based on bivariate extreme value theory. We analyze the earthquake data from the North Anatolian Fault Zone (NAFZ) in Turkey during 1965–2018 and show that the two approaches provide unifying results. Keywords Bivariate extreme value theory · Earthquake data · Tail probability · Mainshock · Aftershock Mathematics Subject Classification (2010) 62G32 (60G70; 86A17)
Phyllis Wan
[email protected] Juan-Juan Cai [email protected] Gamze Ozel [email protected] 1
Department of Econometrics and Data Science, Vrije Universiteit Amsterdam, De Boelelaan 1105, 1081HV, Amsterdam, the Netherlands
2
Econometric Institute, Erasmus University Rotterdam, Burg. Oudlaan 50, 3062PA, Rotterdam, the Netherlands
3
Department of Statistics, Hacettepe University, 06800, Ankara, Turkey
J.-J. Cai et al.
1 Introduction In a seismically active area, a strong earthquake, namely the mainshock, is often followed by subsequent damaging earthquakes, known as the aftershocks. These aftershocks may occur in numerous quantity and with magnitudes equivalent to powerful earthquakes on their own. For instance, in the 1999 ˙Izmit earthquake, a magnitude 7.6 mainshock triggered hundreds of aftershocks with magnitudes greater than or equal to 4 in the first six days, cf. Polat et al. (2002). In the 2008 Sichuan earthquake, a mainshock of magnitude 8.0 induced a series of aftershocks with magnitudes up to 6.0. The results are severe structural damage and loss of life, especially when the area has already been weakened by the mainshock. The ˙Izmit earthquake killed over 17,000 people and left half a million homeless (Marza 1999). The Sichuan earthquake caused over 69,000 deaths and damages of over 150 billion US dollars (Cui et al. 2011). The goal of this paper is to provide a statistical analysis for the joint event of an extreme mainshock and extreme aftershocks. Throughout the paper, we denote the magnitude of a mainshock with X and that of the largest aftershock with Y . We estimate via two approaches the probability of P(X > x, Y > y),
(1)
for large values of x and y. The first approach uses a parametric model based on a series of well-known stochastic laws that describe the empirical relationships of the aftershocks and the mainshock, which we briefly review in Section 3.1. In the s
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