New reversible relationships between ground motion parameters and macroseismic intensity for Italy and their application in ShakeMap

Abstract

SUMMARY We derived new, reversible relationships between macroseismic intensity (I), expressed in either the European Macroseismic (EMS-98) or the Mercalli–Cancani–Sieberg (MCS) scales and peak ground acceleration (PGA), peak ground velocity (PGV) and the spectral acceleration (SA) at 0.3, 1.0 and 3.0 s [SA(0.3), SA(1.0) and SA(3.0)] for Italy. We adopted the orthogonal distance regression technique to fit a quadratic function. This research aims to improve ground motion and intensity estimates for earthquake hazard applications, and for the calculation of shakemaps in Italy. To this end, the recently published INGe data set was used (https://doi.org/10.13127/inge.2). The new relations are: $$\begin{equation*} I = 3.01 \pm 0.12 + 0.86 \pm 0.04 \log ^2 \mathrm{ PGA},~\sigma = 0.30,~~\sigma _{\mathrm{ PGA}} = 0.25,~~\sigma _{I} = 0.16 \end{equation*}$$$$\begin{equation*} I = 4.31 \pm 0.15 + 1.99 \pm 0.18 \log \mathrm{ PGV} + 0.58 \pm 0.18 \log ^2 \mathrm{ PGV},~\sigma = 0.34,~~\sigma _{\mathrm{ PGV}} \\ = 0.31,~~\sigma _{I} = 0.15 \end{equation*}$$$$\begin{equation*} I = 2.77 \pm 0.15 + 0.68 \pm 0.03 \log ^2 \mathrm{ SA}(0.3),~\sigma = 0.31,~~\sigma _{\mathrm{ SA}(0.3)} = 0.28,~~\sigma _{I} = 0.14 \end{equation*}$$$$\begin{equation*} I = 3.00 \pm 0.28 + 0.91 \pm 0.55 \log \mathrm{ SA}(1.0) + 0.51 \pm 0.20 \log ^2 \mathrm{ SA}(1.0),~\sigma = 0.40,~~\sigma _{\mathrm{ SA}(1.0)} \\ = 0.38,~~\sigma _{I} = 0.14 \end{equation*}$$$$\begin{equation*} I = 4.04 \pm 0.20 + 1.63 \pm 0.19 \log \mathrm{ SA}(3.0) + 0.66 \pm 0.20 \log ^2 \mathrm{ SA}(3.0),~\sigma = 0.38,~~\sigma _{\mathrm{ SA}(3.0)} \\ = 0.35,~~\sigma _{I} = 0.14 \end{equation*}$$where PGA and SAs are expressed in cm s−2 and PGV is expressed in cm s−1. Tests performed to assess the robustness and the accuracy of the results demonstrate that adoption of quadratic relationships for this regression problem is a suitable choice within the range of values of the available data set. Comparison with similar published regressions for Italy evidences that the proposed relations provide statistically significant improved fits to the data. The new relations are also tested by inserting them in the ShakeMap system of the Italian configuration evidencing a significant improvement when compared to those implemented.