Modified Mercalli intensity scaling of the frequency dependent duration of strong ground motion

Abstract

New empirical models of the duration of strong ground motion in terms of the Modified Mercalli intensity at the recording station are presented. Two groups of regression equations are considered: one explicitly includes the dependence of the duration on the distance to the source, and the other excludes this dependence. The Modified Mercalli intensity serves as a parameter in both types of models. The models of the first type are more descriptive, but are also more region dependent, because the regional dispersion and attenuation laws are ‘built into’ the frequency dependent regression coefficients. For a given site intensity, the duration grows when the distance from the source to the recording site increases. For a given distance from the source, the dependence of the duration on the site intensity is more complex. At low frequencies, the duration of strong motion decreases when the intensity increases, while at high frequency it grows with increasing intensity. A smooth transition from one type of dependence to another occurs at intermediate frequencies. When compared to basement rock sites, the duration of strong motion at sedimentary sites is prolonged by about 5 s at frequencies near 1 Hz. The prolongation of the duration on the soft soils can be as much as 7 s. The influence of the type of soils on the duration is stronger at higher frequencies ( f = 0.3−25 Hz), while the effect of the presence of sedimentary deposits can be observed at lower frequencies ( f = 0.15−2 Hz). The residuals of the empirical regression equations were also studied, and their distribution function is proposed.