GRAVITY-WAVES IN MEXICO-CITY .1. GRAVITY PERTURBED WAVES IN AN ELASTIC SOLID

Local site effects caused unprecedented damage at Mexico City during t he 19 September 1985, Michoacan, earthquake. Notwithstanding significa nt efforts, observed long duration strong ground motion in the lake zo ne has not yet received a truly satisfactory explanation. Following th e suggestions of Gilbert (1967) and Lomnitz (1988, 1989), we explore i n this paper the possibility of explaining this long duration in terms of gravity perturbed waves in an elastic solid. After a brief review of Gilbert's model and of its limitations, we use a linearization of t he free surface boundary condition for nonnegligeable vertical displac ements to introduce gravity in our equations. We consider modification s due to gravity in Rayleigh's function and in free surface reflection coefficients, and we find that Rayleigh's pole is significantly affec ted by gravity for very high Poisson's ratios. Finally, we present res ults 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 Rayleigh's wave velocity by a factor larger than 2 only in the case of an extremely soft surface layer (Poisson's ratio larger t han 0.499999), but that the transition between Rayleigh waves in solid s and gravity waves in fluids suggested by Lomnitz (1991) does not exi st. Regarding Mexico City, we show that gravity perturbations in an el astic solid do not affect either the character of surface motion or am plitudes or duration of ground motion, and thus do not provide an expl anation for the long duration of strong motion in Mexico City.