Comment 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

The above-titled article presented response-time histories and spectra for the minimum acceleration amplitude of a full sine pulse that is needed to overturn a rigid, rectangular, free-standing block. The construction of the overturning spectra is achieved with the analytical solution of the linearized equations of motion of a rocking block which is pieced together at the instant when the rotation reverses and at the instant when the block enters the free-vibration regime. While some segments of the methodology presented are correct the article contains several logical, algebraic, and typographical errors which are reflected in nearly every result presented. This discussion addresses systematically these errors and oversights. The same notation used in the original article is adopted herein. The noun article refers to the article under discussion by Anooshehpoor et al.; the noun comment refers to this discussion. With reference to its Figure 3, the article investigates the rocking response of a rigid block subjected to a horizontal backwards displacement (motion from the right to the left of the page) with acceleration history \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \[\ a(t)=\left\{\begin{array}{cc}-\mathrm{A}\mathrm{sin}({\omega}t+{\psi})&-{\psi}{/}{\omega}{\leq}t{\leq}(2{\pi}-{\psi}){/}{\omega}\\0o Spanos and Koh, 1984; Hogan, 1989; Makris and Roussos, 1998, among others). The sign of the last term that contains the horizontal ground acceleration is negative. Unfortunately, equation (3) of the article which corresponds to equation …