@article{god14,
author = {Godano C, and Lippiello E, and de Arcangelis L,},
pages = {1765-1771},
title = {Variability of the b value in the Gutenberg-Richter distribution},
volume = {199},
note = {Articolo in rivista},
issn = {0956-540X},
journal = {GEOPHYSICAL JOURNAL INTERNATIONAL},
doi = {10.1093/gji/ggu359},
year = {2014},
wosId = {WOS:000345509800033},
scopusId = {2-s2.0-84924561552},
abstract = {The b value of the Gutenberg - Richter distribution is estimated as a function of a threshold magnitude m_th
and it is found to depend on
m_th for magnitudes larger than the completeness magnitude m_c. We identify a magnitude interval [m_c;m_m]
where b is a decreasing
function of m_th
followed by a regime of increasing b for large magnitudes. This is a
common feature of experimental catalogues for different geographic areas. The increase at large m_th
is explained in terms of an upper magnitude cut-off in experimental catalogues due to finite size effects. We develop a rigorous mathematical framework to relate the decrease of
b in the intermediate regime to the functional form of the distribution of the b
values. We propose two hypotheses: The first is that the spatial and temporal vari-
ability of b leads to a b
distribution peaked around its average value. The second is that mainshocks and aftershocks are distributed according to the Gutenberg-Richter law with different b
values, leading to a bimodal distribution of b. Simulated Epidemic Type Aftershock Sequences (ETAS) catalogues, generated according to this hypothesis, exhibit the same magnitude distribution of experimental ones. In alternative we cannot exclude
the b dependence on m caused by magnitudes not homogeneously evaluated in a seismic catalogue. In the latter scenario our results provide the correction terms to the estimated magnitudes.}
}