Duration of strong ground motion in terms of earthquake magnitude, epicentral distance, site conditions and site geometry

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Abstract
The physical bases and empirical equations for modelling the duration of strong earthquake ground motion in terms of the earthquake magnitude, the epicentral distance and the geological and local soil site conditions are investigated. At 12 narrow frequency bands, the duration of a function of motion f(t), where f(t) is acceleration, velocity or displacement, is defined as the sum of time intervals during which the integral S f2 (τ) dτ gains a significant portion of its final value. All the records are band‐pass filtered through 12 narrow filters and the duration of strong ground motion is studied separately in these frequency bands. It is shown that the duration of strong motion can be modelled as a sum of the source duration, the prolongation due to propagation effects and the prolongation due to the presence of the sediments and local soils. It is shown how the influence of the magnitude on the duration of strong ground motion becomes progressively stronger, in going from low to moderate frequencies, and that the duration is longer for ‘soft’ than for ‘hard’ propagation paths, at low and at moderate frequencies. At high frequencies, the nature of the broadening of the strong motion portion of the record with increasing distance is different, and is most likely related to the diffraction and scattering of the short waves by the velocity inhomogeneities along the wave path. It is also shown that the geological and local soil conditions should both be included in the model. The duration can be prolonged by 3–5 sec at a site on a deep sedimentary layer at frequencies near 0.5 Hz, and by as much as 5–6 sec by the presence of soft soil underneath the station, at a frequency of about 1 Hz. An empirical equation for a probabilistic estimate of the discrepancies of the predictions by our models relative to the observed data (distribution function of the residuals) is presented.

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