A review and new insights on the estimation of the b-valueand its uncertainty
By Warner Marzocchi, Laura Sandri. 2003
263 citations recorded by the source corpus.
The estimation of the b-value of the Gutenberg-Richter Law and its uncertainty is crucial in seismic hazard studies, as well as in verifying theoretical assertions, such as, for example, the universality of the Gutenberg-Richter Law. In spite of the importance of this issue, many scientific papers still adopt formulas that lead to different estimations. The aim of this paper is to review the main concepts relative to the estimation of the b-value and its uncertainty, and to provide some new analytical and numerical insights on the biases introduced by the unavoidable use of binned magnitudes, and by the measurement errors on the magnitude. It is remarked that, although corrections for binned magnitudes were suggested in the past, they are still very often neglected in the estimation of the b-value, implicitly by assuming that the magnitude is a continuous random variable. In particular, we show that: i) the assumption of continuous magnitude can lead to strong bias in the b-value estimation, and to a significant underestimation of its uncertainty, also for binning of ?M = 0.1; ii) a simple correction applied to the continuous formula causes a drastic reduction of both biases; iii) very simple formulas, until now mostly ignored, provide estimations without significant biases; iv) the effect on the bias due to the measurement errors is negligible compared to the use of binned magnitudes.
Subfields: Geophysics
View Paper: https://www.semanticscholar.org/paper/4627e62bde5d56f641cebd3ecefe7ee18e6cb4fc
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In Geophysics
Citations in the corpus
- A robust method to estimate the b-value of the magnitude–frequency distribution of earthquakes (2015, background): “But it shows significant bias under relatively common conditions and some author [23] even suggested not using it.”
- Data‐driven spatial b value estimation with applications to California seismicity: To b or not to b (2015, methodology): “Wewant to point out that we use this formula rather than the commonly used corrections [Utsu, 1966; Bender, 1983] because it gives more accurate and stable results under varying sample sizes [Marzocchi and Sandri, 2003].”