Relationships between reported modified Mercalli intensity and simulated ground acceleration for historical crustal earthquakes in Mexico

Abstract A set of new empirical relationships between modified Mercalli intensity (MMI) and synthetic peak ground acceleration (PGA) is developed for shallow crustal earthquakes in central and north-west Mexico. Few strong-motion recordings of shallow crustal earthquakes in these regions have led to uncertainties in estimating seismic risk even though they comprise some of the most densely populated urban sites in the country. We present relationships in which MMI is a function of PGA and its inverse form. No relationship for this type of events has been developed, although these earthquakes represent a high-risk potential for nearby highly populated urban regions. Ground motion data from 18 moderate-to-large earthquakes (4.5 < M W < 7.5) that took place in the Basin and Range, Sierra Madre Oriental Fold-thrust belt, and Trans-Mexican Volcanic Belt provinces and the corresponding 531 MMI information reports were employed. Synthetic PGA data were generated using the finite-fault stochastic method, assuming different rupture scenarios to extend the limitations of the dataset. Linear and bilinear regression techniques were used, considering a binning averaging procedure and the whole dataset, respectively. As the first approach, a set of MMI predictive equations independent of moment magnitude ( M W ) and hypocentral distance ( R ) was derived. Despite weak dependencies of the residuals on M W and R terms, we also developed complementary predictive relationships that include these parameters as independent variables. The conversion equations between PGA and MMI, including all terms, 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 variations in input data, particularly concerning the macroseismic intensity assignments, which are inherently subjective, and the tectonic regime. The conversion relationships that we have developed can be used to generate maps of estimated shaking intensities based on ground motion observations for crustal earthquakes in Mexico.