AbstractThe paper studies certain dynamic characteristics of soil deposits with wave velocities increasing with depth according to (1 + μz)m, wherem= 1, 2/3, 1/2, 1/4 and 0. Analytical solutions are presented for the fundamental periods, mode shapes and amplification functions due to vertically propagating shear waves and the effects of type (m) and rate (μ) of heterogeneity are systematically investigated. The analytical–numerical techniques are used to study the attenuation with depth in a deposit of the vertical and horizontal displacements due to travelling of Rayleigh waves. Differences attributed to different heterogeneities are discussed in connection with the machine isolation problem and the steady‐state vibration technique for soil exploration. Finally, the dependence on soil heterogeneity of the time–distance response curves, obtained during seismic refraction surveys, is graphically illu