Duration of the 2011 Tohoku earthquake ground motions

We compared several different duration measures for the 2011 M9.0 Tohoku earthquake sequence, because empirical duration models are of great interest for purposes of correlation with structural damage, and the Tohoku mainshock was remarkable for its long duration. Among the three considered definitions, RMS duration (McCann and Shah, Bull Seism Soc Am 69: 1253–1265, 1979) is best able to predict the duration within which pulses or groups of pulses of energy arrive; it is particularly suitable for the Tohoku mainshock, for which source complexity caused time-series with multiple-phase arrivals. Two other considered definitions, both of which tend to underestimate the observed duration, are: (i) duration defined by random vibration theory (RVT); and (ii) the significant duration as defined by the interval between 5 and 75 % or 95 % of the integral of the square of the ground acceleration (known as “Arias intensity” (Arias 1970)) or velocity (known as “energy integral” (Anderson 2004)). In the Tohoku mainshock, significant amplitudes precede the 5 % of the Arias intensity marker; we need to use 0.3 % of the maximum of the accumulated energy as the lower bound marker to appropriately estimate the duration using the significant duration definition. The RVT duration (used in stochastic simulations) can be estimated easily from the 5–75 % of the Arias intensity (significant duration) definition as the two measures give very similar durations. Overall, the significant duration of ground motions observed during the 2011 M9.0 Tohoku earthquake increases with distance as 0.19Rcd for the horizontal components or 0.33Rcd for the vertical component, where Rcd is the closest distance to the fault plane. By comparison, the duration of four aftershocks (M4.5–7.7) increases with distance as ~0.10Rhypo where Rhypo is the hypocentral distance. For the mainshock, the distance-dependent slope term is greater, presumably due to the large fault plane size.