We have developed an analytical solution for the rocking and overturning response of a two-dimensional, symmetric rigid block subject to a full sine wave of horizontal ground acceleration. We use this solution to provide lower-bound estimates of the peak ground acceleration at Point Reyes Station, California, during the 1906 San Francisco earthquake that toppled the San Francisco-bound train. Our results, for a 3% damping ratio, indicate that for a single cycle of a sine wave the minimum toppling accelerations at 1, 1.5, and 2 Hz are 0.35g, 0.5g, and 1.05g, respectively. For more realistic accelerograms the toppling accelerations are about 1.1g (complex synthetic) and 0.76g (Lucerne record of the 1992 Landers earthquake).

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