Cavity and topographic effects in tilt and strain measurement

Cavities, surface topography, and inhomogeneities in elastic constants all distort the strains and tilts produced by stresses in the earth. Hence locally observed strains and tilts deviate from those calculated on the basis of simple earth models. We investigate these deviations on the assumption that the scale of these inhomogeneities is small in comparison with that of the stress fields. The results are applicable to observations of free modes, earth tides, and regional tectonic stresses. Analytical results are given for the deformation of an ellipsoidal cavity in a homogeneous medium in which the strain is uniform at large distances from the cavity. One important result is that greatly magnified strains are expected across narrow cavities. Finite element techniques are employed to study two features of importance in actual cavities, the influence of the corner in a tunnel of square cross section and the influence of the end face in a cylindrical tunnel with plane ends. The floor of the perfectly regular square tunnel remains flat, but irregularities produce large local tilts. Longitudinal strain in the cylindrical cavity is magnified near its ends, and most of the anomalous strain is concentrated within one tunnel diameter of the end. Topographic effects are also studied by finite element techniques. These are found to be very large and to result in strain magnifications in valleys, strain diminutions in hills, and strain-induced tilts which are different for vertical and horizontal surfaces. In one case, regional compression actually results in local tension, and even a 1 in 10 (5.7°) slope produces a 36% perturbation in strain. Geological effects are investigated for a profile near Boulder, Colorado, where there is a very abrupt transition between the sedimentary rocks of the plains and the basement rocks of the Front Range of the Rocky Mountains. The surface strains perpendicular to the boundary fall from 177% to 37% of their regional values on crossing this boundary, and strain-induced tilts attain values of about 0.5 times the regional strain in its vicinity. Long-base strain meters and tiltmeters can give good results in underground sites, but short-base instruments are very susceptible to local effects arising from geometric irregularities or rock inhomogeneities. Corrections for local topography are required for most installations. This topographic effect can be exploited to measure regional strains with tiltmeters, while the geological effects provide the basis of a technique for using earth tide observations to explore geological structure.