A semi-empirical approach to prediction of long-period ground motions from great earthquakes

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Abstract
Predictability of long-period (1 sec or longer) ground motions generated by long strike-slip earthquakes such as the 1906 San Francisco and the 1857 Fort Tejon earthquakes, is investigated. Most large earthquakes are complex multiple events at this period range, and the resulting ground motion may be synthesized by convolving the ground motions of the individual event with the source function that describes the space-time history of the multiple shock sequence. Since it is not possible to predict deterministically the complexity of the rupture propagation, a semi-empirical approach was taken. For the ground motion from the individual events, the displacement records observed for the 1968 Borrego Mountain, California, earthquake were used after correcting for the distance and the radiation pattern. These records which were used as an empirical Green's function for the individual events were superposed, with some randomness, to produce ground motions resulting from a large earthquake. The models were constrained by gross seismological data at three periods. At 1 sec they are constrained by the observed upper bound of the local magnitude (ML = 714⁠), and, at about 10 sec, by the upper bound of the seismic moment of the individual event of multiple shocks (5 × 1026 dyne-cm). At very long periods, the models have the correct total seismic moment. The results obtained for a model of the 1857 earthquake indicate that: (1) the velocity response spectra of ground motions in the near-field are nearly flat at about 50 cm/sec over the period range from 1 to 10 sec under normal conditions; (2) under certain circumstances they can be as large as 150 cm/sec; (3) the maximum duration of the ground motion is 6 min. These results are considered reasonable because they satisfy all the seismological constraints currently available over a wide period range.