A fundamental solution for SH-waves in a class of inhomogeneous anisotropic media

In the present work we derive a fundamental solution for SH waves in a class of inhomogeneous anisotropic media. The derivation is accomplished in terms of a “transmutation” formula. The time-harmonic fundamental solution is also obtained and a non-propagating (‘evanescent’) mode is identified for sources with lower frequencies than the critical one. We show that the same transmutation formula can be used to derive the fundamental solution for inhomogeneous media with linear velocity variation as presented by Watanabe and Payton [K. Watanabe, R.G. Payton, Green’s function and its non-wave nature for SH-wave in inhomogeneous elastic solid, Int. J. Eng. Sci. 42 (2004) 2087–2106].