Bootstrap determination of the reliability of b-values: an assessment of statistical estimators with synthetic magnitude series | INSTITUT DE PHYSIQUE DU GLOBE DE PARIS

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  Bootstrap determination of the reliability of b-values: an assessment of statistical estimators with synthetic magnitude series

Type de publication:

Journal Article

Source:

Natural Hazards, Volume 65, Ticket 1, p.443-459 (2013)

ISBN:

0921-030X

URL:

http://link.springer.com/article/10.1007%2Fs11069-012-0376-1

Mots-clés:

Dynamique des fluides géologiques ; Power law ; Bootstrap ; b-values ; Earthquake series, UMR 7154

Résumé:

We consider some practical issues of the determination of the b-value of sequences of magnitudes with the bootstrap method for short series of length L and various quantization levels \Updeltam of the magnitude. Preliminary Monte Carlo tests performed with \Updeltam=0 demonstrate the superiority of the maximum likelihood estimator b MLE, and the inconsistency of the, yet often used, b LR estimator defined as the least-squares slope of the experimental Gutenberg–Richter curve. The Monte Carlo tests are also applied to an estimator, b KS, which minimizes the Kolmogorov–Smirnov distance between the cumulative distribution of magnitudes and a power-law model. Monte Carlo tests of discrete versions of the b MLE and b KS estimators are done for \Updeltam={0.1,0.2,0.3} and used as reference to evaluate the performance of the bootstrap determination of b. We show that all estimators provide b estimates within 10 % error for L ≥ 100 and if a large number, n = 2 × 105, of bootstrapped sample series is used. A resolution test done with \Updeltam=0.1 reveals that a clear distinction between b = 0.8, 1.0, and 1.2 is obtained if L ≥ 200.

Notes:

Times Cited: 0