Defects and waves in anisotropic and layered media: Stroh formalism in terms of the Cartesian system of vector functions

When waves propagate through anisotropic elastic media, P- and SV-type waves (Rayleigh waves) are generally coupled with SH-type waves (Love waves). In contrast, in isotropic elastic media, SH/Love waves are decoupled and separate from other body/surface waves. However, the conditions under which these waves in anisotropic media may be decoupled remain unclear. In this paper, we introduce a Cartesian vector function system, named as the Cartesian LMN vector system, and derive solutions using this system within the Stroh formalism. This approach inherently accounts for both coupling and decoupling cases. Various source functions based on the Cartesian LMN vector system are derived. The Cartesian LMN system further enables a straightforward reduction to two-dimensional wave problems, including simplified source functions for line forces and lattice dislocations.