Because the conversion between different types of magnitudes is frequently an essential component to seismotectonic and seismic hazard studies, it is important to understand the advantages and limitations of different conversion methods that have been proposed in the literature. In fact, there is an aspect of the conversion that is the matter of current debate, which can be summarized as follows. Given two sets of different types of magnitudes, the conversion generally takes the form of a linear relation between the two magnitudes. As both magnitudes are affected by errors, this relation is obtained using regression techniques that take into...

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