Recalibration of the local magnitude scale of the Belgian seismic network: Improved models of geometrical spreading and path duration

The current local magnitude (\(\:{M}_{L}\)) scale for local and regional earthquakes recorded by the Belgian seismic network was developed in 1985 using Lg-wave amplitudes measured on paper seismograms from vertical seismographs, and has been applied to records from digital seismometers installed progressively since then. However, the seismic attenuation in this scale does not properly reflect the relative contribution of geometrical spreading and anelastic attenuation of crustal S-waves at distances \(\:<150\) km. Furthermore, the scale is not well constrained at distances \(\:<\sim20\) km, encumbering magnitude evaluation of shallow small earthquakes (e.g., induced seismicity) recorded only by nearby stations.We recalibrate the Belgian \(\:{M}_{L}\) scale based on hypocentral distance, extending the range of validity to shorter distances (\(\:>\sim6\) km), while keeping good agreement with the original scale at larger distances. The recalibrated scale features a segmented powerlaw geometrical spreading model, shows improved residuals, and yields lower magnitudes for earthquakes with \(\:{M}_{L}<\sim1.5\). We also performed a calibration using horizontal components, but residuals are significantly higher, hampering adoption. Nevertheless, these results allowed obtaining improved models of geometrical spreading and path duration for horizontal S-waves, which are important elements in many seismological applications. Finally, we also derive an empirical relation between \(\:{M}_{L}\) and moment magnitude.