Subsurface, thermoelastic line source excitation of a transversely isotropic half space

Abstract

In this work, mathematical descriptions of material displacements in the wavefield surrounding a subsurface, thermoelastic line source in a transversely isotropic half space are given. These are derived from continuum representations that yield wave equations describing material motion that are solved using transform techniques. These solutions provide insight into the overall character of these sources in anisotropic materials and can also be used to model more generalized source distributions that might occur in a range of physical systems. Analytical, closed form solutions for epicentral displacements are derived and are graphically represented for particular source locations below the surface of a titanium half space. These results illustrate general aspects of the wavefield including the nature of various component modes of the displacement waveform. Wavefront characteristics associated with these modes are considered along with the nature of direct shear wave emission by this type of source. Mathematical results for displacements are used to illustrate how the surface-borne thermoelastic line source can be represented as a surface, shear stress dipole and are also used to represent more complicated subsurface source distributions that might occur in physical systems.