Body waves in a weakly anisotropic medium—I. Plane waves

A systematic perturbation approach to elastic-wave processes in a weakly anisotropic medium is discussed. As a simple practical example, the propagation of plane waves in a homogeneous medium is considered in detail. The limitations of perturbation theory are described. The second-order corrections for velocity and polarization are found in the case of general weak anisotropy. The particular case of transverse isotropy is considered.