Quasi-Static Deformation of a Uniform Thermoelastic Half –Space Due to Seismic Sources and Heat Source

This paper investigates the quasi-static plane deformation of an isotropic thermoelastic half-space due to buried seismic sources and heat source. Governing equations of thermo-elasticity are solved to obtain solutions for seismic sources in a thermoelastic half-space. The general solutions are acquired with the aid of Laplace and Fourier transforms and with the use of boundary conditions. The case of dip-slip line dislocation is studied in detail along with line heat source. Analytical solutions for two limiting cases: adiabatic and isothermal, are obtained. The solutions for displacement, stresses and temperature in space-time domain are obtained by using a numerical inversion procedure. The accuracy of the proposed method is verified through a comparison of the results obtained with the existing solutions for elastic medium. In addition, numerical results for displacements, stresses and temperature function, induced by a vertical dip-slip dislocation and line heat source, are presented graphically to illustrate the effect of inclusion of thermal effect in simulation of the problem.