Effect of topography on thermoelastic deformations of the Earth’s core: Corrections of the temperature field

Schmidt Institute of Physics of the Earth, Russian Academy of Sciences

**Journal:**Seismic instruments

**Tome:**58

**Number:**4

**Year:**2022

**Pages:**62-80

**UDK:**550.34.01

**DOI:**10.21455/si2022.4-4

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Tsurkis I.Ya. Effect of topography on thermoelastic deformations of the Earth’s core: Corrections of the temperature field
// . 2022. Т. 58. № 4. С. 62-80. DOI: 10.21455/si2022.4-4

@article{TsurkisEffect2022,
author = "Tsurkis, I. Ya.",
title = "Effect of topography on thermoelastic deformations of the Earth’s core: Corrections of the temperature field
",
journal = "Seismic instruments",
year = 2022,
volume = "58",
number = "4",
pages = "62-80",
doi = "10.21455/si2022.4-4",
language = "English"
}

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**Keywords:**boundary line, radius of curvature, expected error, local depth, heated layer

**Аnnotation:**This work presents a preparatory stage for solving thermoelasticity problem for a halfspace with relief. The ef-fect of the relief on diurnal and season variations of the temperature in upper layer of the Earth crust induced by variations of the temperature in atmosphere is studied. The case of weak two-dimensional relief is discussed. In this paper we say that relief is weak if: 1) angle of inclination of the element of relief to the horizon is small; 2) thickness d of the heated layer is small comparably with the radius of curvature of the line of relief. For the diurnal mode we have d15 cm, for the season one d3 m. The heat equation with boundary condition of the first kind is considered, the approximate analytical solution is obtained. The comparison with numerical solution which one can consider as exact solution is fulfilled. The approximate formula gives satisfactory result if: 1) angle of inclination of the element of relief to the horizon does not exceed 0.2 rad; 2) curvature of the line of relief does not exceed 2.410–2 m–1 for the diurnal mode and 1.210–3 m–1 for the season one. In this case relative discrepancy between numerical solution and approximate analytical one is less then 4 %, if the depth 20d. Variations of temperature at depth 20d, already practically absent – amplitude does not exceed ~10–9–10–8 C. So, underline layers do not effect essentially on displacements and tilts of the elements located near the surface.