Are different M = a + bI0 relationships due to a statistical bias?

Abstract

Relationships between magnitude and macroseismic intensity are widely used, even though intensity is a non-metric observable. Several proposed relationships for the Italian and surrounding regions show a significant correlation of the parameters of the widely used functional form M = a + bI0 This could suggest either the common dependence on a third variable or that the different proposed relationships are due to a pivotal phenomenon around average values, mainly driven by data sampling and uncertainties. Synthetic simulations lend support to the last hypothesis.