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Dynamic deformations of shallow sediments in the Valley of Mexico, Part II: Single-station estimates

Instituto de Geofísica and Instituto de Ingeniería UNAM, 04510 México, D.F., México
Centro Nacional de Prevención de Disastres, Delfin Madrigal 665, 04650 México, D.F., México
Center for Earthquake Research and Information University of Memphis, Memphis, Tennessee 38152
U.S. Geological Survey Center for Earthquake Research and Information University of Memphis, Memphis, Tennessee 38152

Abstract

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, _max and u_max, at the surface. The maximum surface strain _max is related to _max by _max = _max/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 (u_max/z) computed from sensors at 0 and 30 m equals (u_max)_z=0/z, z = 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 u_max 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).

From the free-field recordings of the 19 September 1985 Michoacan earthquake, we estimate a maximum surface strain, _max, between 0.05% and 0.11%, and a lower bound for the peak vertical gradient (u_max/_z) between 0.3% and 1.3%. This implies that (1) the extensive failure of water pipe joints during the Michoacan earthquake in the valley occurred at axial strains of about 0.1%, not 0.38% as previously reported, and (2) the clays of the valley behave almost linearly even at shear strain of about 1%, in agreement with laboratory tests. The available data in the valley can be used to predict deformations during future earthquakes using self-similar earthquake scaling.

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