Evidence of the dominance of higher-mode surface waves in the lake-bed zone of the Valley of Mexico

Abstract

We compare ground motions recorded at the surface and in boreholes at five different locations of the lake-bed zone of the Valley of Mexico with theoretical dispersion curves and eigenfunctions calculated for the first two modes of Rayleigh and Love waves. We find that (1) the maximum in the horizontal-to-vertical displacement ratio, which occurs at the dominant frequency of the site (0.4 Hz), corresponds to the higher mode rather than to the fundamental mode of the Rayleigh waves, (2) borehole records at depths from 0 to 100 m show that the normalized vertical displacement does not decrease rapidly below the superficial clay layer, as should be the case for the fundamental mode, but remains ≈0.8, and (3) the measured phase velocity at a period of about 2.5 s (2.0±0.5 km s-1) is too fast for the fundamental mode predicted for the known crustal velocity structure. These observations lead us to conclude that the wavefield in the lake-bed zone in Mexico City is dominated by higher-mode surface waves. This provides a plausible explanation for the long duration of the coda in the lake-bed zone. Although shear wave Q is very small (10-20) in the clay layer, the higher modes of surface waves do not propagate in the superficial clay layer but in the underlying structure where Q-values are likely to be relatively high. Thus, while the clay layer plays the passive role of amplifying the ground motion, its contribution in damping out the motion is insignificant. The results have two important practical implications. (1) The strain estimate from recorded ground velocity differs significantly for the fundamental mode as compared to the higher-mode surface waves. (2) If the ground motion is dominated by the fundamental mode, then knowledge of the superficial layer and the velocity contrast with the underlying structure is sufficient for understanding and modelling of the ground motion. If, however, the higher-mode surface waves dominate, then a detailed knowledge of the deeper structure is required.