“…Therefore, they cannot actually describe the real and complicated behaviour of viscoelastic materials. These considerations directed the authors to study the near-surface wave dispersion and attenuation of a viscoelastic covered half-space utilising a more realistic mathematical model (Akbarov and Negin 2017b) by using Rabotnov (1980) fractionalexponential operators which are used in the papers by Akbarov (2014Akbarov ( , 2015, Akbarov and Kepceler (2015), Akbarov et al (2016a, b) and Kocal and Akbarov (2017) in the first place. This study, in that sense, is actually an extension of the authors' previous studies (Negin et al 2014;Negin 2015; Akbarov and Negin 2017a) on dispersion of the generalised Rayleigh waves in an initially stressed elastic covered half-space to the viscoelastic case, where the constitutive relations of the materials of the covering layer and the half-space are described through the fractional-exponential operator by Rabotnov (1980).…”