Deformation due to surface temperature variation on a spherically layered, transversely isotropic and self-gravitating Earth

Abstract

SUMMARY We present a theory of modern, thermally induced deformation in a realistic Earth. The heat conduction equation is coupled with standard elastic deformation theory to construct a boundary-value problem comprised of eighth-order differential equations. The accurate and stable dual variable and position propagating matrix technique is introduced to solve the boundary-value problem. The thermal load Love numbers are defined to describe the displacements and potential changes driven by thermally induced deformation. The proposed analytical method is validated by comparing the present results with exact solutions for a homogeneous sphere, which are also derived in this paper. The analytical method is then applied to a realistic Earth model to evaluate the effects of layering and self-gravitation of the Earth on displacement and changes of potential. Furthermore, the frequency dependence in the thermal load is illustrated by invoking different thermal periodicities in the computation. Thermal anisotropy is also considered by comparing the results obtained using isotropic and transversely isotropic Earth models. Results show that, when simulating thermally induced deformation, invoking a homogeneous spherical Earth leads to results that substantially differ from those obtained using a more realistic Earth model.