Possible resonance effect in the distribution of earthquake damage in Mexico City

Abstract

The destruction caused by the earthquake of 19 September 1985 in Mexico City shows three remarkable features1. First, a (concentration of damage in the former lake bed; second, a peculiar distribution of high- and low-damage areas alternating within a few city blocks, and third, a selectivity for buildings between five and fifteen storeys high. While the last point is understood by civil engineers2 and the first confirms the relevance of the soft ground, the second feature is the most puzzling. To a physicist such a pattern evokes the idea of a standing wave, with low- and high-damage areas corresponding to nodes and antinodes. This suggests a resonance phenomenon of the waterlogged ground moving collectively. From the Navier equations of classical elasticity, it is known3 that a transfer of the incoming seismic-wave energy to longitudinal waves takes place if a sharp change from hard to soft ground exists. Solving then the two-dimensional Poisson equation for the longitudinal waves within the ancient lake boundaries, we show that for the observed seismic wave period of 2 s, a standing-wave solution exists which explains qualitatively the damage distribution pattern.