Moment vs local magnitude scaling of small-to-moderate earthquakes from seismic moment estimation of 10 years (2009-2018) of Italian seismicity

We computed moment (M_w) and local magnitude (M_L) of about 250,000 earthquakes occurred in Italy from 2009 to 2018 and recorded at seismic stations of the Italian National Network managed by INGV.

For moment magnitude computation, we start from raw velocity waveforms and invert the displacement spectra of more than 2,000,000 S-waves manually picked. We use the probabilistic method of Supino et al. [2019] to estimate the a-posteriori joint probability density function of the source parameters: seismic moment M₀, corner frequency f_c and high-frequency decay γ. M_w is obtained from M₀ using the Kanamori [1977] equation.

We start from the same waveforms to compute local magnitude using two designed on purpose codes, PyAmp and PyML [Di Stefano et al., 2023], and an attenuation law specific for the Italian region, Di Bona et al. [2016], obtaining M_L values characterized by quality and homogeneity.

Both magnitude catalogs can be reproduced due to the availability in open databases of all the input and output parameters used for processing.

We observe a self-similar scaling between f_c and M₀ for M_w larger than ~2.0. For smaller magnitudes, S-wave spectra show an almost constant corner frequency (~10 Hz), which does not scale with the earthquake source (seismic moment). We interpret this as the constant cut-off frequency of the anelastic attenuation, which acts as a low-pass filter and produces an apparent corner frequency. The latter is lower than expected, and corresponds to an apparent larger source duration.

Because of the conservation of total displacement integral after a low-pass filtering, signals must exhibit a maximum amplitude lower than expected to “compensate” the apparent larger source duration. M_L values are therefore expected to be underestimated while moment magnitudes, by definition, are not affected by this as they are proportional to the displacement integral.

Coherently, the comparison of our M_w and M_L estimates shows the systematic underestimation of M_L with respect to M_w for small magnitude events. The deviation from a 1:1 scaling relationship between M_L and M_w overlaps the magnitude range where the constant apparent corner frequency arises in the M₀-f_c scaling (M_L <~ 2).

Regarding the upcoming of a new generation of earthquake catalogs characterized by very low completeness magnitudes (M_C << 2), our results suggest that a robust analysis of the statistical features of these catalogs (e.g., event size distribution) should consider the use of a precise magnitude estimate such as M_w instead of M_L.