Recalibration of the intensity prediction equation in Italy using the Macroseismic Dataset DBMI15 V2.0

We re-compute the coefficients of the intensity prediction equation (IPE) in Italy using the data of the DBMI15 V2.0 intensity database and the instrumental and combined (instrumental plus macroseismic) magnitudes reported by the CPTI15 V2.0 catalog. We follow the same procedure described in a previous article, consisting of a first step in which the attenuation of intensity I with respect to the distance D from macroseismic hypocenter is referred to the expected intensity at the epicenter I_Eand a second step in which I_Eis related to the instrumental magnitude M_i, the combined magnitude M_c, the epicentral intensity I₀ and the maximum intensity I_max, using error-in-variable (EIV) regression methods. 

The main methodological difference with respect to the original article concerns the estimation of the uncertainty of I_Eto be used for EIV regressions, which is empirically derived from the standard deviation of regression between I_E and M_iand also used for the regressions of I_Ewith M_c, I₀ and I_max. 

In summary, the new IPE determined from DBMI15 V2.0 is

                                        𝐼=𝐼_𝐸−0.0081(𝐷−ℎ)−1.072[ln(𝐷)−ln(ℎ)]

 where 𝐷=√(𝑅²+ℎ²), h=4.49 km and I_Ecan be calculated from the intensity data distribution of the earthquake. If the intensity data distribution is not available, I_Ecan be calculated from the following relationships

                                        𝐼_𝐸=−2.578+1.867𝑀_𝑤

                                                      I_E=I₀