Thermoelastic stresses and the energy of earthquakes

Abstract

The nonuniform distribution of temperature and the heterogeneity of physical properties produce thermoelastic stresses in the earth's mantle. The variation of the earth's temperature with time due to radioactive heat generation results in the accumulation of such stresses. A horizontal temperature gradient is shown to exist and to reach a value of the order of 2 deg/km for the transitional zone between the oceanic and continental crust in the subjacent mantle of the Kuril Islands. The distributions of the radial and tangential stresses as well as the variation of stress differences with depth are calculated for a variable thermal expansion coefficient from the equilibrium equation of the thermoelastic displacements for a sphere. The largest stresses in the upper mantle are tangential. They are tensions in the upper 50 km, and are compressions below 50 km. The radial stresses are much weaker; they are compressions in the upper layers and tensions in the lower layers. The stress differences are shown to reach the strength limit for rocks (109 dynes/cm2). The maximum value of stress difference in the earth can amount to 10 to 30×1010 dynes/cm2. Near the surface the accumulation rate of stress difference appears to be 20 dynes/cm2 year. The calculated thermoelastic energy at different depths is comparable to the rate of the seismic energy release determined by Gutenberg within the accuracy of such determinations. At a depth of over 100 km its increase appears to be greater than that of the seismic energy by one to two orders of magnitude. There remains the possibility that an allowance for relaxation processes will reduce the calculated accumulation of thermoelastic energy.