The Modified Mercalli intensity and the geometry of the sedimentary basin as scaling parameters of the frequency dependent duration of strong ground motion

Abstract

Several new empirical equations of the frequency dependent duration of strong earthquake ground motion are presented. The duration is considered as being composed of two parts: (1) the duration of stong motion as it is observed at recording stations located on basement rocks, and (2) the prolongation of this duration for stations located on sediments. The first part, called the ‘basic duration’, is modelled in terms of the Modified Mercalli intensity and (in some cases) the hypocentral distance. The depth of the sediments under the station, the distance from the station to the rocks surrounding it, and the angular measure of the size of those rocks (as seen from the station) are chosen as the parameters for modelling the prolongation of the duration. The new empirical equations are compared (a) with each other, (b) with our previous models which used similar ‘prolongation’ terms, but the ‘basic duration’ was expressed in terms of the magnitude of the earthquake and the source-to-station distance, and (c) with models with ‘intensity-type’ ‘basic duration’, but with a simplified ‘prolongation’ term (the geological conditions at the stations are modeled by lumping all the sites into three groups: basement rock, sediments and intermediate geology). This collection of models is found to have good internal consistency. The choice of the proper model depends on the availability of the earthquake and site parameters. The residuals of the empirical regression equations are found to have similar distribution functions for all the models. An explicit functional form for such distributions is proposed, and the frequency dependent coefficients are found for all the models of duration. This allows one to predict (for each set of earthquake and site parameters) the probability of exceedance of any given level of duration of strong ground motion at a given frequency.