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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

Seismological Laboratory 174
Mackay School of Mines
University of Reno
Reno, Nevada 89557-0141
(A. A., B. S., J. N. B.)

California Institute of Technology
Dept. of Civil Engineering, MS 104-44
Pasadena, California 91125
(T. H. H)

The first 20% of the full text of this article appears below.

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.

As ZM correctly point out, the sign of the second term on the right-hand side of equation (3) in our article must be negative. However, this error (not present in our first paper on rocking motion, Shi et al., 1996) was not reflected in the linearized equations (5) and (7). In Figures 4 and 5, we have plotted the "inertial acceleration" of the center of mass whereas the term "ground acceleration" is used in both the legends and the figure captions. ZM are also correct that the value of in the captions of Figures 6 and 8 should have been 0.9 instead of 0.95.

In describing rocking motion of a two-dimensional rigid block one in general needs to use two separate equations of motion, one about each of the two rocking points. Equations (5) and (7) in our article describe the rocking motion about O₁ and O₂, subject to the . . . [Full Text of this Article]

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