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1 Swiss Seismological
Service
Institute of Geophysics
ETH-Hönggerberg
CH-8093
Zürich, Switzerland
A simple theoretical analysis shows that both local magnitude
ML and seismic moment M0 or equivalently
moment magnitude Mw are, in principle, measures of basic
properties of the earthquake source: ML is proportional to
the maximum of the moment-rate function, whereas M0 is
proportional to its integral. Thus, in theory, this implies that
ML 
(2/3) log M0 and
ML = Mw over the entire range for
which ML can be determined. In practice, observed
differences between ML and Mw are
telling us something either about the physics of the earthquake source or about
inadequacies in our wave-propagation model and in our ways of measuring
ML. If influences of propagation and instrument response
were properly corrected for and if effects of radiation pattern and rupture
directivity were averaged out, then systematic deviations of
ML relative to Mw could be interpreted
in terms of changes in stress drop or rupture velocity. However, model
calculations show that, because of the way attenuation along the path is usually
corrected for, we have to expect that, in most cases, ML for
small events (Mw < 2) is systematically underestimated by
as much as a whole unit. Moreover, for small events with few recordings,
single-station scatter due to radiation pattern and directivity can be
responsible for random errors that are also on the order of a whole unit. Thus
systematic and random errors in the determination of ML for
small earthquakes are likely to be much greater than the variability of
ML with respect to Mw, which could be
expected from variations in source properties. The extrapolation of constant
offset corrections between regional ML scales and
Mw to smaller events, for which independent determinations
of M0 are usually lacking, is not advisable: in most cases
the large random errors and systematic underestimation of ML
can contribute a significant bias to magnitude recurrence relations.
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