The effect of a vertical temperature gradient in the lithosphere on seismic and tectonic waves

A linear analysis of the stability of the lithosphere considered as a viscoelastic layer with an equilibrium vertical gradient of temperature is carried out. The problem is solved with a complete system of linearized equations of a continuous medium represented in the dimensionless form and containing a set of dimensionless parameters that determine thermomechanical properties of the lithosphere. As a result of the stability analysis, decrements are found that give the time dependence of perturbations and correspond to high-frequency seismic waves and low-frequency tectonic waves. The frequency and velocity of seismic waves are determined by the elasticity and inertial properties of the lithosphere, and their attenuation, by viscous properties of the lithosphere. The temperature gradient existing in the lithosphere influences seismic waves very weakly. On the contrary, the pattern of tectonic waves is controlled by the temperature gradient and viscous properties, while the effect of elastic and inertial properties on these waves is negligibly small. The stability of a viscoelastic lithosphere is examined using such rheological models as the Maxwell, standard linear, and Andrade media (the frequency of tectonic waves is zero in the Maxwell medium).