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Inter occurrence time statistics of successive large earthquakes: analyses of the global CMT dataset

Bantidi Thystere Matondo

Acta Geophysica

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2022

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Vol. 70, no 6

2603--2619

EN

The purpose of this study is to discuss the statistical distributions of the inter-occurrence times of successive large earthquakes. We examine the Global Centroid Moment Tensor Catalog from 1976 to 2021 to analyze shallow earthquakes with a moment magnitude, Mw ≥ 7.0. After removing the aftershocks that occur in and around the faults of the mainshock within a given time–space window, we select the main events and search for successive ones in the space–time window to group them in clusters. We use four renewal models (Brownian passage time, gamma, lognormal, and Weibull) to fit the data. We estimate the models’ parameters using the maximum likelihood estimation method. Then, we perform two goodness-of-fit tests: the Akaike information criterion and the Kolmogorov–Smirnov test to evaluate the suitability of the model distributions to the observed data. The results reveal that the lognormal distribution provides the best fit to the observed data in at least 50% of the regions under consideration. An intermediate fit comes from the Weibull distribution, whereas the Brownian passage time and gamma distributions exhibit a poor fit. Then, we estimated the conditional probability of the occurrence of successive large earthquakes for the 10-year period between 2022 and 2032. Estimates range from 16 to 96%. To evaluate the usefulness of the interevent time-dependent earthquake modeling, we compared the results with the time-independent Poisson distribution. The results show that the renewal model, associated with a time-dependent earthquake hazard, is significantly better than a time-independent Poisson model.

2

Alternatywne metodyki obliczania niepewności pomiaru

Fotowicz P.

Pomiary Automatyka Kontrola

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2010

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R. 56, nr 11

1305-1307

PL

Przedstawiono dwie alternatywne metodyki obliczania niepewności pomiaru stosowane współcześnie w metrologii. Pierwsza z nich opiera się na zaleceniach Przewodnika i zawartym tam prawie propagacji niepewności. Druga opiera się na prawdopodobieństwie warunkowym wynikającym z zastosowania twierdzenia Bayesa. Obie metodyki prowadzą do różnych wyników, bowiem wykorzystują inne podstawy obliczeniowe. Pierwsza opiera się na splocie rozkładów wielkości wejściowych, a druga na ich iloczynie. Pierwsza chętnie stosowana jest przy ocenie wyników określonego pomiaru, a druga przy opracowaniu wyników porównań.

EN

The alternative methodologies for calculating the measurement uncertainty used in modern metrology are presented. The first method is based on recommendation of the Guide and the law of uncertainty propagation. The second method is based on conditional probability and application of the Bayes theorem. Those methodologies leads to different results because of using different basis of calculations. The calculation of the first method is connected with convolution of input quantity distributions but the calculation of the second method is connected with multiplication of input quantity distributions. The coverage interval calculated with the GUM method is larger than the coverage interval calculated with the Bayesian method. In the first method the estimate of the measurand is an arithmetic average of observations, but in the second method the estimate is a weighted average, modified by the standard uncertainty attributed to the specified result of observation. The Bayesian method is willingly utilized at inter-laboratory comparisons, but the GUM method is commonly used in evaluation of any other result of measurement.

3

Alternatywne metodyki obliczania niepewności pomiaru

Fotowicz Paweł

Metrologia : biuletyn informacyjny Głównego Urzędu Miar

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2010

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nr 3

13--16

PL

Przedstawiono dwie alternatywne metodyki obliczania niepewności pomiaru stosowane współcześnie w metrologii. Pierwsza z nich opiera się na zaleceniach Przewodnika i zawartym tam prawie propagacji niepewności. Druga opiera się na prawdopodobieństwie warunkowym wynikającym z zastosowania twierdzenia Bayesa. Obie metodyki prowadzą do różnych wyników, bowiem wykorzystują inne podstawy obliczeniowe. Pierwsza opiera się na splocie rozkładów wielkości wejściowych, a druga na ich iloczynie. Pierwsza chętnie stosowana jest przy ocenie wyników określonego pomiaru, a druga przy opracowaniu wyników porównań.

EN

The alternative methodologies for calculating measurement uncertainty used in modern metrology are presented. The first method is based on recommendation of the Guide and the law of uncertainty propagation. The second method is based on conditional probability and application of the Bayes theorem. Those methodologies lead to different results because of using different basis of calculations. The calculation of the first method is connected with convolution of input quantity distributions but the calculation of the second method is connected with multiplication of input quantity distributions. The coverage interval calculated with the GUM method is larger than the coverage interval calculated with the Bayesian method. In the first method the estimate of the measurand is an arithmetic average of observations, but in the second method the estimate is a weighted average, modified by the standard uncertainty attributed to the specified result of observation. The Bayesian method is willingly utilized at inter-laboratory comparisons, but the GUM method is commonly used in evaluation of any other result of measurement.

4

Analiza produkcji energii elektrycznej przy pomocy modeli probabilistycznych

Miłkowski M.

Rynek Energii

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2007

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nr 3

20-25

PL

Omówiono probabilistyczne podejście do oceny wysokości zysków przy produkcji energii elektrycznej w sys-temach zasilania ze źródłami energii odnawialnej i źródłami konwencjonalnymi. Na podstawie danych statystycznych określono rozkłady prawdopodobieństw bezwzględnych i względnych dotyczących produkcji energii elektrycznej omawianego systemu. Powiązanie tych rozkładów z cenami i kosztami związanymi z działalnością elektrowni pozwala oszacować przestrzeń zależności zysku od losowych wartości produkcji. Przedstawiono modelowanie i analizę omawianego zagadnienia przy pomocy sieci bayesowskich.

EN

The paper presents probability approach to validation of the net income of power supply system based on renewable and conventional utility. Database set determine prior and posterior probability distribution energy output of system utilities. Combine prices of power production and given them probability distributions lead to create space of likelihood events of net income depends of power production. Bayesian network are present as a tool for modeling and analysis of presented issue.

5

Transformed conditional probabilities in the analysis of stochastic sequences

Kudzys A.

Journal of Polish Safety and Reliability Association

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2007

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Vol. 2

243--250

EN

The need to use unsophisticated probability-based approaches and models in the structural safety analysis of the structures subjected to annual extreme service, snow and wind actions is discussed. Statistical parameters of single and coincident two extreme variable actions and their effects are analysed. Monotone and decreasing random sequences of safety margins of not deteriorating and deteriorating members are treated, respectively, as ordinary and generalized geometric distributions representing highly-correlated series systems. An analytical analysis of the failure or survival probabilities of members and their systems is based on the concepts of transformed conditional probabilities of safety margin sequences whose statistically dependent cuts coincide with extreme loading situations of structures. The probability-based design of members exposed to coincident extreme actions is illustrated by a numerical example.