Interval Estimation of Seismic Hazard Parameters

Abstract

Abstract-The paper considers Poisson temporal occurrence of earthquakes and presents a way to integrate uncertainties of the estimates of mean activity rate and magnitude cumulative distribution function in the interval estimation of the most widely used seismic hazard functions, such as the exceedance probability and the mean return period. The proposed algorithm can be used either when the Gutenberg-Richter model of magnitude distribution is accepted or when the nonparametric estimation is in use. When the Gutenberg-Richter model of magnitude distribution is used the interval estimation of its parameters is based on the asymptotic normality of the maximum likelihood estimator. When the nonparametric kernel estimation of magnitude distribution is used, we propose the iterated bias corrected and accelerated method for interval estimation based on the smoothed bootstrap and secondorder bootstrap samples. The changes resulted from the integrated approach in the interval estimation of the seismic hazard functions with respect to the approach, which neglects the uncertainty of the mean activity rate estimates have been studied using Monte Carlo simulations and two real dataset examples. The results indicate that the uncertainty of mean activity rate affects significantly the interval estimates of hazard functions only when the product of activity rate and the time period, for which the hazard is estimated, is no more than 5.0. When this product becomes greater than 5.0, the impact of the uncertainty of cumulative distribution function of magnitude dominates the impact of the uncertainty of mean activity rate in the aggregated uncertainty of the hazard functions. Following, the interval estimates with and without inclusion of the uncertainty of mean activity rate converge. The presented algorithm is generic and can be applied also to capture the propagation of uncertainty of estimates, which are parameters of a multiparameter function, onto this function.Key words: Aggregated uncertainty in the activity rate and magnitude, magnitude cumulative distribution function, interval estimation of seismic hazard functions, resampling methods, bootstrap, jackknife.

EPOS Thematic Core Service Anthropogenic Hazards in the operational phase

“…Therefore, the magnitude distribution is modelled by a non-parametric kernel estimator [e.g., Lasocki and Orlecka-Sikora, 2008;Lasocki, 2021 and the references therein]. At the end of the analysis, the user receives the point and interval estimates of the exceedance probability [Orlecka-Sikora and Lasocki, 2017]. In addition to this core block, TTASHA also comprises two complementary blocks of applications.…”

Seismic hazard estimation using databases with bimodal frequency–magnitude behaviour

“…A non-parametric approach to estimating seismic hazard does not require the assumption of an underlying distribution model (such as the Gutenberg-Richter distribution). This approach for estimating seismic hazard is referred to as a data-driven or model-free technique and has been described by Kijko et al (2001), Lasocki (2001), Lasocki and Orlecka-Sikora (2006), and Orlecka-Sikora and Lasocki (2017).…”