Duration of strong earthquake ground motion: physical basis and empirical equations, 1993

In this work, the physical bases and empirical equations for modeling the duration of strong earthquake ground motion in terms of earthquake magnitude, epicentral distance and the geological and local soil site conditions are investigated.; At 12 narrow frequency bands, the duration of strong motion in function f(t), where f(t) is acceleration, velocity or displacement, is defined as the sum of time intervals during which the integral graph of the function f²(τ)dτ between τ=0 and τ=t gains a significant portion of its final value. It is confirmed that the duration of strong ground motion can be represented as a sum of the source duration, the prolongation due to propagation effects and the prolongation due to presence of sediments and local soils. It is shown that the influence of the magnitude on the duration of strong ground motion becomes progressively stronger, when moving from low to moderate frequencies. The estimate of the characteristic size of the source, obtained using our definition and our models of strong motion duration, is shown to agree with the estimates of other authors. It is shown that in terms of the epicentral distance, the duration is longer for "soft" than for "hard" propagation paths, at low and at moderate frequencies. It is shown that the geological and local soil conditions (when available) should both be included in the model. The duration can be prolonged by 3.5 sec at a site located on 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 frequency of about 1 Hz.; In addition to the "traditional" scaling parameters (magnitude, epicentral distance and geological and local soil site conditions), three other parameters, which describe the geometry of the sedimentary basins surrounding the recording stations, are considered. Those parameters are: the depth, h, and the width, R, of the sedimentary basin, where the recording site is located, and the angle φ, subtended at the station by the rocks, located at the edges of the valley and capable of reflecting the seismic waves towards the station. Those parameters describe the geology under and around the station in greater detail, than the qualitative classification "sediments-rock." The prolongation of duration on sediments can then be approximated by a sum of a coupled quadratic function of h and R and a linear function of the angle φ. The maximum prolongation occurs at moderate depths (2÷3 cm) and widths (30÷50 km) of the sediments. The additional duration can be as much as 6÷7 sec at frequencies near 1 Hz. Studies of the length and of the number of strong motion intervals, contributing to the overall duration of strong motion, show that this additional duration occurs due to multiple reflection of waves from the bottom and from the edges of the sedimentary valleys.; As a result of this study, several regression models of the frequency dependent duration of strong ground motion are proposed. An algorithm for choosing the proper model depending on the availability of the site and propagation path parameters, is provided. 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.