Abstract: | An explicit asymptotic model for transient Love waves is derived from the exact equations of anti-plane elasticity. The perturbation
procedure relies upon the slow decay of low-frequency Love waves to approximate the displacement field in the substrate by
a power series in the depth coordinate. When appropriate decay conditions are imposed on the series, one obtains a model equation
governing the displacement at the interface between the coating and the substrate. Unusually, the model equation contains
a term with a pseudo-differential operator. This result is confirmed and interpreted by analysing the exact solution obtained
by integral transforms. The performance of the derived model is illustrated by numerical examples |