Abstract
This article revisits the evaluation by a perturbation theory of the modification of the Rayleigh wave velocity under a static loading varying with depth. Two derivations, that have been exposed in the past and presented as comparable, are questioned. A new derivation of the perturbation formula is given by adapting Auld's approach. Validation with exact calculations is provided. The examples cover depth-varying static stress as well as depth varying third order elastic properties.