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Time derivative of earthquake acceleration

Mai Tong, Guo-Quan Wang and George C. Lee

Multidisciplinary Center for Earthquake Engineering Research, University at Buffalo, Buffalo, NY 14261-0025 USA

Abstract: Unlike acceleration, velocity, and displacement, the time derivative of acceleration (TDoA) of ground motion has not been extensively studied. In this paper, the basic characteristics of TDoA are evaluated based on records from the 1999 Chi-Chi, earthquake (Mw 7.6) and one of its aftershocks (Mw 6.2). It is found that the maximum TDoA at a free-field station was over 31,200 cm/s3 (31.8 g/s); and the duration of "strong" TDoA, between the first and the last time points exceeding 2,000 cm/s3 (2 g/s), was almost one minute near the epicenter area. Since ground TDoA sensors are not commonly available, the time series are calculated by direct numerical differentiation of acceleration time series. Relative error analysis shows that the error is non-transitive and total error is within 4%. The density function of TDoA amplitude, frequency content and spatial distribution of peak ground jerk (PGJ) are evaluated. The study also includes examination of some TDoA responses from a seven-story building and comparison of ground TDoA with the limit TDoA used in the transportation industry for ride comfort. Some potential impacts of TDoA on humans have also been reviewed.

Keywords: time derivation of acceleration; peak ground jerk; acceleration time series; earthquake ground motion; earthquake effect on human activities