What question did this study set out to answer?

To examine how periodic relief affects thermoelastic deformations and slopes in the upper layer of the Earth's crust.

February 22, 2026

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

Key Points

To examine how periodic relief affects thermoelastic deformations and slopes in the upper layer of the Earth's crust.
Explored a two-dimensional thermoelasticity problem for a half-plane with periodic relief.
Applied harmonic temperature changes with a period of 1 year along the relief line.
Utilized perturbation theory to derive exact values of stresses and deformations.
Formulated equations for longitudinal deformation and slope using first-order perturbation theory.
Shown that results are valid at significant depths within the crust.

Abstract

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

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