We consider a large data set of waveforms (5053 recordings for the horizontal components and 9933 for the vertical) to calibrate a local magnitude scale valid for northeastern Italy in the hypocentral distance range of 10–250 km. The data refer to 1096 events occurring in the period January 1995 to December 2002 in the area between 44.4° and 47.6° N and 10.1° and 15.7° E.
For each available signal, we simulate the corresponding Wood-Anderson seismogram. Using the geometrical mean of the two horizontal peaks, we simultaneously estimate the distance attenuation, the station correction terms, and the magnitude of the events. Estimations are obtained with the standard parametric approach accounting for the geometrical spreading and the anelastic attenuation, and by using two different methods of nonparametric regression, based on a stepwise-linear approximation and on kernel functions, respectively. The nonparametric solutions agree and show stronger attenuation in the first 70 km than what was found in central California. Furthermore, a noticeable discontinuity occurs around 100 km, because later phase arrivals. Such discontinuity is not fitted well by the parametric curve.
We investigate the effect of magnitude-dependent attenuation on magnitude estimation. We also account for the bias induced by data truncation (i.e., data loss due to the limited dynamics of the instruments). The analysis shows that at short distances the standard, magnitude-independent attenuation model underestimates high magnitudes (e.g., by 0.49 units at 10 km for magnitude 5.5) and overestimates low magnitudes (e.g., by 0.17 units at 10 km for magnitude 1.5, 0.34 units if we extrapolate the relation down to magnitude 0.5).
Finally, various factors suggest one should adopt the solution proposed in the literature to redefine the ML scale such that ML 3 corresponds to 10 mm of motion on a Wood-Anderson instrument at 17 km hypocentral distance.