This paper completes a previous study of the role of gravity during the 19 September 1985, Michoacán earthquake, at Mexico City. It is assumed, as suggested by Lomnitz (1989, 1990), that nonlinear mechanisms could bring the rheology of the Mexico City soft clay layer nearer to a fluid than to a solid. In order to test whether gravity waves in a viscous fluid could provide an explanation of exceedingly long duration observed at Mexico City, we have studied the motion on the surface of an irregular viscous fluid layer overlaying an elastic half-space. Our formulation takes into account vertical displacement at the free surface of the fluid layer, but requires a linearization of the corresponding boundary condition. A decomposition of diffracted fields in terms of plane waves allows the use of Aki-Larner's method. Excitation is given by vertically incident SV waves. We present results both for nonviscous and viscous fluids and show that an adequate free boundary condition is essential for this problem. Lacking data, we have performed several simulations for values of viscosity going from 300 to 30,000 Pa.s. In the case of a nonviscous fluid, gravity surface waves are generated efficiently by diffraction of elastic waves on the irregular interface, but attenuate rapidly when including viscosity and are not significant for viscosities above 3000 Pa.s. The results presented in our companion paper and here, allow us to conclude that gravity is not a likely explanation to the long duration of ground motion observed at Mexico City. In a more general context, our model may be useful to study the interaction of seismic waves with water reservoirs, such as dams.