Drivers to seismic hazard curve slope

The slope of a linear approximation of a probabilistic seismic hazard curve, when it is represented in the log-log scale, is a key parameter for seismic risk assessment based on closed-form solutions, and other applications. On the other hand, it is observed that different hazard models can provide, at the same site, comparable ground shaking, yet appreciably different slopes for the same exceedance return period. Moreover, the slope at a given return period can increase or decrease from low- to high-hazardous sites, depending on the models the probabilistic seismic hazard analysis (PSHA) is based on. In the study, the sensitivity of the slope to the main model components involved in PSHA was explored, that is: the earthquake rate, the magnitude and source-to-site distance distributions, and the value of the residual of ground motion models (GMM). With reference to a generic site, affected by an ideal seismic source zone, where magnitude follows the Gutenberg-Richter (G-R) relationship, it was found that the local slope of hazard curve increases with the following factors in descending order of importance: (i) increasing distance from the source; (ii) decreasing maximum magnitude and increasing $b$-value of the G-R model; (iii) increasing rate of earthquakes of interest; (iv) increasing residual of the GMM. These results help explain the systematic differences in hazard curve slopes found in three authoritative hazard models for Italy, and the related impact on simplified risk assessment.