In the free state, the phase velocity of the planar Rayleigh waves in layered media is related to the frequency and the material properties of media. Rayleigh waves activated by the surface sources propagate with cylindrical wave-fronts. The phase velocity is related to the travelling distance as well as the frequency. Thus, without taking the spatial behavior into consideration, the theory of the planar Rayleigh waves in layered media can not be appropriately applied to analyzing the propagation behavior of the activated Rayleigh waves. Based on the displacement of Rayleigh waves obtained by the thin layer method for the disk-like vertical surface sources, the phase velocities of the activated Rayleigh waves are derived. The difference between the activated and the normal Rayleigh waves is compared. The spatial behavior of activated modes is analyzed and its mechanism is investigated. The results show that the effect of sources on the spatial behavior of activated modes is confined within the wave field about one wavelength from the sources. The nearer the wave field is, the slower the phase velocity of vertical vibration is. In the wave field with multiple activated modes, the spatial behavior of apparent phase velocity is obvious due to the constructive and destructive interferences of these modes. The study results can provide some guidelines for developing new inverse mathematical models and algorithms which could include both the frequency behavior and the spatial behavior.