The effect of magnitude uncertainty on the Gutenberg–Richter b-value estimation and the magnitude–frequency distribution: 'what hump?'. Issue 2 (14th June 2022)

• Record Type: Journal Article
• Authors: Taroni, Matteo
• Is Part Of: Geophysical journal international. Volume 231:Issue 2(2022)
• Page Start: 907
• Page End: 911
• Publication Date: 2022-06-14
• Subjects: Probability distributions -- Statistical methods -- Statistical seismology; Geophysics -- Periodicals; 550
• DOI: 10.1093/gji/ggac219
• Languages: English
• ISSNs: 0956-540X

Abstract

Summary: The uncertainties on magnitudes of the earthquakes have a negligible effect on the estimation of the Gutenberg–Richter b -value if these uncertainties have a homogeneous distribution, that is, the magnitude error is the same for all the earthquakes. Here, we show that a non-uniform error distribution can have a significant impact on the b -value estimation, and it generates a hump in the magnitude–frequency distribution. Through a simulation approach, we show when the bias in the estimation is large, when it can be neglected, and how it is possible to avoid it.