Reply to Comment by J. Zhang and N. Makris on “Estimates of the Ground Accelerations at Point Reyes Station during the 1906 San Francisco Earthquake” by A. Anooshehpoor, T. H. Heaton, B. Shi, and J. N. Brune

Abstract

Contrary to the comments by Zhang and Makris (hereafter, ZM), our equations of motion governing the rocking response of a rectangular block subjected to a full-sine acceleration pulse are correct. Therefore, the first part of ZM's discussion, which is based primarily upon the assumption that the equations of motion in our article were incorrect, is inappropriate. In the second part of the discussion, ZM present new results for mode 2, toppling without impact. We did not consider this mode because it was not relevant to the Point Reyes train, which by eyewitness accounts, had overturned after experiencing one impact. However, as explained in this reply, toppling with no impact is never the minimum condition for overturning, and would in general involve very large horizontal accelerations, especially at frequencies where mode 2 is the only overturning mode.