GNGTS 2013 - Atti del 32° Convegno Nazionale

the earthquake coda, which may be masked by the presence of noise, volcanic tremor, or other shocks (Del Pezzo e Petrosino, 2001; D’Amico e Maiolino, 2005). A first attempt to estimate the local magnitude M L was performed by D’Amico and Maiolino (2005), which used a dataset of earthquakes recorded at Mt. Etna during the 2002- 2003 eruption and Lahr (1999) relationship: M L = log A + a log Δ – b (2) where A is maximum half-amplitude of the horizontal component of the seismic recording measured in mm and «+ a logΔ− b » is a correction factor which describes the variation of maximum amplitude taking into account the distance from source to receivers and takes the place of the term «−logA 0 » of Richter (1935) relationship. In Eq. (2) a = 0.15, b = 0.16 (for Δ<200 km). Starting from 2005, thanks to the improvement of Mt. Etna seismic network and the installation of digital stations equipped with broad band three component sensors, the local magnitude M L estimated by using amplitude of the horizontal ground displacements of the earthquake, became a routine procedure in monitoring of seismic signals of the volcano. However, for monitoring purpose, in order to maintain a long dataset of coherent magnitude observations, M D continued till today to be evaluated as well. Data analysis and results. It is known in literature that a sort of bias is present when com- paring duration vs local magnitudes estimates (Gasperini, 2002; D’Amico and Maiolino, 2005; Castello et al. , 2007; Giampiccolo et al. 2007). Since magnitude estimation in M D and M L , although mutually related, do not produce the same results, it is mandatory to adopt an empir- ical conversion to produce a homogeneous catalogue for Mt. Etna region. The Standard Linear Regression (SLR) is the simplest and most commonly used regression procedure applied in literature (e.g. Gasperini and Ferrari, 2000; Gasperini, 2002; Bindi et al. , 2005; Braunmiller et al. , 2005). However its application without checking whether its basic requirements are sat- isfied may lead to wrong results (Castellaro et al. , 2006). In particular, the condition that the uncertainty on the independent variable is at least one order magnitude smaller than the one on the dependent variable must be met to obtain correct results. For magnitude scale conversion it is common to consider only one of the magnitudes to be in error. How- ever, in case both the magnitudes have measurement errors, due to saturation or otherwise, the use of least-squares linear regression pro- cedure may not be appropriate. As an alternative it is better to use Gen- eral Orthogonal Regression (GOR) relation (Carrol and Ruppert, 1996), which takes into account the errors on both the magnitude types (Cas- tellaro et al. 2006; Das et al. , 2011). Fig. 1 – Plot of M D vs M L values of the earthquakes occurred at Mt. Etna from 2005 to 2012. The scale colours indicate the number of earthquakes with equal M D - M L couple. The black diamonds indicate the average value of M L for each M D value. 35 GNGTS 2013 S essione 2.1