Conversion relationships between Modified Mercalli Intensity and Peak Ground Acceleration for historical shallow crustal earthquakes in Mexico

Abstract. New empirical relationships between modified Mercalli intensity (MMI) and synthetic peak ground acceleration (PGA) are developed for shallow crustal earthquakes in Mexico. Ground motion data from 18 moderate-to-large earthquakes (4.5 < M_W < 7.5) and the corresponding 531 MMI information reports were employed. Synthetic PGA data were generated using the finite-fault stochastic method considering different rupture scenarios in order to extend the limitations of the dataset. Linear and bilinear regression techniques were used considering a binning averaging procedure and the whole dataset. On one hand, a set of MMI predictive equations independent of moment magnitude (M_W) and hypocentral distance (R) were derived. Despite weak dependencies of the residuals on M_W and R terms, on the other hand, we also developed refined predictive relationships that include these parameters as independent variables. The refined PGA to MMI conversion equations show slightly less variability than simple linear equations in predicting intensity values. The proposed predictive equations are consistent with similar relationships in other regions of the world. The discrepancies among the different relationships may reflect the differences in input data, particularly related to the macroseismic intensity assignments, which are inherently subjective, and the tectonic regime. The proposed relationships can be used for improved hazard assessments in Mexico.