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Abstract
Many natural hazards exhibit inverse powerlaw scaling of frequency and event size, or an exponential scaling of event magnitude (m) on a logarithmic scale, e.g. the GutenbergRichter law for earthquakes, with probability density function p(m) ∼ 10−bm. We derive an analytic expression for the bias that arises in the maximum likelihood estimate of b as a function of the dynamic range r. The theory predicts the observed evolution of the modal value of mean magnitude in multiple random samples of synthetic catalogues at different r, including the bias to high b at low r and the observed trend to an asymptotic limit with no bias. The situation is more complicated for a single sample in real catalogues due to their heterogeneity, magnitude uncertainty and the true bvalue being unknown. The results explain why the likelihood of large events and the associated hazard is often underestimated in small catalogues with low dynamic range, for example in some studies of volcanic and induced seismicity.
Original language  English 

Pages (fromto)  2080–2086 
Journal  Geophysical Journal International 
Volume  232 
Issue number  3 
Early online date  3 Nov 2022 
DOIs  
Publication status  Epub ahead of print  3 Nov 2022 
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Dive into the research topics of 'Accuracy and precision of frequencysize distribution scaling parameters as a function of dynamic range of observations: example of the GutenbergRichter law bvalue for earthquakes'. Together they form a unique fingerprint.Projects
 1 Finished

NERC DTP: U.K. Natural Environment Research Council (Grant NE/L002558/1) University of Edinburgh's E3 Doctoral Training Partnership
Hajduk, G.
1/10/14 → 31/03/18
Project: Other (NonFunded/Miscellaneous)