We develop simple relations to estimate dynamic displacement gradients (and hence the strains and rotations) during earthquakes in the lake-bed zone of the Valley of Mexico, where the presence of low-velocity, high-water content clays in the uppermost layers cause dramatic amplification of seismic waves and large strains. The study uses results from a companion article (Bodin et al., 1997) in which the data from an array at Roma, a lake-bed site, were analyzed to obtain displacement gradients. In this article, we find that the deformations at other lake-bed sites may differ from those at Roma by a factor of 2 to 3. More accurate estimates of the dominant components of the deformation at an individual instrumented lake-bed site may be obtained from the maximum horizontal velocity and displacement, νmax and umax, at the surface. The maximum surface strain ɛmax is related to νmax by ɛmax = νmax/C, with C ∼ 0.6 km/sec. From the analysis of data from sites equipped with surface and borehole sensors, we find that the vertical gradient of peak horizontal displacement (Δumax/Δz) computed from sensors at 0 and 30 m equals (umax)z=0/Δz, Δz = 30 m, within a factor of 1.5. This is the largest gradient component, and the latter simple relation permits its estimation from surface records alone. The observed profiles of umax versus depth suggest a larger gradient in some depth range of 10 to 20 m, in agreement with synthetic calculations presented in Bodin et al. (1997).
