On the Influence of Relief on Thermoelastic Deformations and Tilt in the Upper Layer of the Earth’s Crust

Abstract—A two-dimensional thermoelasticity problem for a half-plane with a periodic relief is considered: on the relief line, the temperature changes with time according to a harmonic law with a period of 1 year. The results obtained by the authors earlier for the temperature field were used. A perturbation theory has been constructed that allows one to obtain almost exact values of stresses and deformations in a wide class of cases. Formulas for longitudinal deformation and tilt in first-order perturbation theory are written out. It is shown that they can be interpreted as asymptotics that are valid at a sufficiently large depth.