Gravity waves in Mexico City?—I. Gravity perturbed waves in an elastic solid

Abstract

Abstract Local site effects caused unprecedented damage at Mexico City during the 19 September 1985, Michoacan, earthquake. Notwithstanding significant efforts, observed long duration strong ground motion in the lake zone has not yet received a truly satisfactory explanation. Following the suggestions of Gilbert (1967) and Lomnitz (1988, 1989), we explore in this paper the possibility of explaining this long duration in terms of gravity perturbed waves in an elastic solid. After a brief review of Gilbert9s model and of its limitations, we use a linearization of the free surface boundary condition for nonnegligeable vertical displacements to introduce gravity in our equations. We consider modifications due to gravity in Rayleigh9s function and in free surface reflection coefficients, and we find that Rayleigh9s pole is significantly affected by gravity for very high Poisson9s ratios. Finally, we present results for the problem of ground-motion simulation on the surface of an irregular, thin layer of very soft clay. Our results show that gravity may affect Rayleigh9s wave velocity by a factor larger than 2 only in the case of an extremely soft surface layer (Poisson9s ratio larger than 0.499999), but that the transition between Rayleigh waves in solids and gravity waves in fluids suggested by Lomnitz (1991) does not exist. Regarding Mexico City, we show that gravity perturbations in an elastic solid do not affect either the character of surface motion or amplitudes or duration of ground motion, and thus do not provide an explanation for the long duration of strong motion in Mexico City.