Improved CENA Regression Relationships between Modified Mercalli Intensities and Ground-Motion Parameters

Comparisons between peak ground motions (PGMs) and intensities are mainly based on the regression of felt intensity with peak ground acceleration (PGA), peak ground velocity (PGV), response spectral values, and occasionally with maximum displacement. Using the Next Generation Attenuation-East database, we update and extend the relations of Dangkua and Cramer (2011). We start by developing magnitude and distance-independent linear regression relationships between modified Mercalli intensity (MMI) in the range of I <= MMI <= VII and the ground-motion parameters (GMPs) of PGA, PGV, and 21 pseudospectral accelerations for central and eastern North America (CENA). We correct for recently acknowledged differences between community Internet intensities (CIIs) and MMI (Hough, 2013, 2014; Boyd and Cramer, 2014; Tosi et al., 2015). We then perform residual analysis to evaluate whether there are any discrepancies and dependency, first with magnitude and then distance. For the magnitude-dependent analysis, we use a bilinear fit. This bilinear magnitude dependence is especially important for longer periods. The residuals show homoskedasticity with zero mean and are serially correlated. We correct for the serial correlation using the Cochrane-Orcutt procedure. Our new ground-motion intensity correlation equations for CENA have the form log(10)(Y) = c(1) + c(2) x 1 + c(3) x min{M-w; M-t} + c(4) x log(10) (Dist), in which log(10) (Y) is the GMP, Mw is the moment magnitude, Mt is the magnitude of the bend in the bilinear magnitude dependence, log(10)(Dist) is the distance term, I is the intensity of interest (MMI or CII), and c(1), c(2), c(3), and c(4) are the coefficients of regression. The equation is invertible for obtaining both CII and MMI from the PGM of interest and vice versa.