The vertical (black) and horizontal (red) compliance at a solid medium surface due to acoustic-wave incidence under different incident angles (θ in Fig. A1). We convert each incident angle to the corresponding horizontal apparent velocity (c, top x-axis). The solid curves are from our theory, eqs (5) and (6), at a frequency of 1 Hz. The dashed curves between 10° and 25° are from Sorrells’s theory (Sorrells 1971). The circles are from the P–Sv-wave reflection and transmission on the air–solid interface (R/T, Appendix  A); we stop plotting circles when the incident angle exceeds the critical angle. The elastic properties of this solid medium are following: α = 5400 m s⁻¹, β = 3120 m s⁻¹ and ρ = 2600 kg m⁻³. V_R denotes Rayleigh-wave phase velocity, which is 2868 m s⁻¹ in this medium. The acoustic-wave velocity (V_a) is 340 m s⁻¹, typical for Earth atmosphere.