The effect of magnitude uncertainty on the Gutenberg–Richter b-value estimation and the magnitude–frequency distribution: ‘what hump?’

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.

This article has been accepted for publication in Geophysical Journal International ©:The Author(s) 2022. Published by Oxford University Press on behalf of the Royal Astronomical Society. All rights reserved. Uploaded in accordance with the publisher's self-archiving policy.