Equilibrium position of a phase boundary under horizontally varying surface loads

Abstract

Summary A two-dimensional and a three-dimensional cylindrically symmetric model are used to determine the change in equilibrium position of a phase boundary when horizontally varying loads are applied at the Earth's surface. Under the assumption that the phase boundary motion is relatively small, the problem is reduced to a linear integral equation that is solved by integral transform techniques. The results of the study show that: (1) the effects of the elastic deformations caused by the phase boundary motion are negligible as long as the surface load contains only large wavelengths (compared to the depth of the phase boundary); (2) the conclusions reached with one-dimensional models on the amplitude of the phase boundary motion are valid in the regions where the load does not vary rapidly over distances of the order of the phase boundary depth; (3) these models confirm the conclusions of one-dimensional models on the importance of phase changes in the lithosphere for explaining the subsidence of geosynclines and basins under the load of accumulating sediments when the scale of these features is larger than 200–300 km.