GNGTS 2013 - Atti del 32° Convegno Nazionale

In Eq. (3) M X * is the abscissa of the point on the GOR line which is the orthogonal projection of the given point ( M Xobs M Yobs ) and a and b represent the slope and the intercept of the line, respectively. To develop and validate the GOR relation between M D and M L a Monte Carlo test was performed. Seismic dataset was randomly split into two subsets of 1861 and 1500 earthquakes. The two dataset were randomly generated 1000 times and for each run the relationships were calculated The first subset was used to calculate the coefficients a and b of the GOR. The final values of coefficients a and b were obtained as mean of the coefficients distribution, while the related uncertainties were obtained as standard deviation of coefficients distributions. The GOR relationship (Fig. 3) obtained is: M L = 1.237 (± 0.009)* M D -0.483 (± 0.016) (4) with a correlation coefficient R = 0.90; rms and standard deviation of the residuals between observed and calculated M L are respectively 0.266 and 0.172. The regression relation derived in this study reduces the previous bias between M D and M L for Mt. Etna earthquakes and will be used to develop a homogeneous magni- tude catalogue for the earthquake recorded since 1988, by calibrating the M D observations collected in the area with the more recent and reliable M L values. References Azzaro R.; 2004: Seismicity and active tectonics in the Etna region: constraints for a seismotectonic model . In:Bonaccorso A., Calvari S., Coltelli M., Del Negro C. and Falsaperla S. (eds), Mt. Etna: volcano laboratory, American Geophysical Union, Washington (USA), pp. 205-220. Bindi D., Spallarossa C., Eva C. and Cattaneo M.; 2005: Local and duration magnitude in northwestern Italy and seismic moment versus magnitude relationships , Bull. Seism. Soc. Am., 95 , 2, 592-604. Caltabiano T., Condarelli D., Gresta S., Patanè D. and Patanè D. 1986: Analisi preliminare dei dati della stazione sismica di Serra Pizzuta Calvarina , CNR IIV Open File Rep. 10/86. Cardaci C. and Privitera E.; 1996: Applicazione di metodi per la stima della magnitudo ai terremoti locali registrati dalla rete sismica permanente dell’Etna , CNR IIV Open File Rep. 3/96. Carroll R..J. and Ruppert D.; 1996: The use and misuse of orthogonal regression in linear errors-in-variables models , American Statistician, 50 , 1-6. Castellaro S., Mulargia F. and Kagan Y.Y.; 2006: Regression problems for magnitudes , Geophys. J. Int. 165, 913–930. Castellaro, S. and Bormann, P.; 2007: Performance of Different Regression Procedures on the Magnitude Conversion Problem , Bull. Seism. Soc. Am., 97 , 1167-1175 Castello B., Olivieri M. and Selvaggi G.; 2007: Local and duration magnitude determination for the Italian Earthquake Catalog, 1981–2002 , Bull. Seism. Soc. Am., 97 , 128–139. D’Amico S. and Maiolino V.; 2005: Local magnitude estimate at Mt. Etna , Ann. Geophys., 48 , 2, 215-229. Fig. 3 – Plot of regression relation for M L and M D obtained by using GOR (red line). Colour scale bar indicates the number of earthquakes. 37 GNGTS 2013 S essione 2.1