In homogenous half spaces

the wave-fields in the shallow depth are dominated by Rayleigh waves elicited by surface sources. When the forward Rayleigh waves encounter a shallow heterogeneity

the surface response spectrum over the heterogeneity is changed. When the length of the heterogeneity is significantly long compared to the wavelength of the forward Rayleigh waves

the effects of the stiffness contrast between the heterogeneity and the surrounding soil on the behavior of the diffracted waves are analyzed from the dispersion curves extracted from the spectrum performed on the surface response over the heterogeneity. Compared to Rayleigh waves in the half space containing the soft or hard soil layer

it can be found that the behavior of the diffracted waves is similar to that of Rayleigh waves. The spectral changes over the heterogeneity are related to the stiffness contrast. The phenomena of the spectral changes are explained using the displacement structure differences between the diffracted waves and the incident Rayleigh waves. It is shown from the results that the spectrum over the heterogeneity is obviously different from those in front of and behind the heterogeneity. In the offset-wavelength domain

compared to the spectrum in front of the heterogeneity

the spectral density decreases as a whole over a soft heterogeneity

while the spectral density increases over a hard heterogeneity. The location and the burial depth of a suspected heterogeneity can be estimated from the offsets and the wavelengths corresponding to the spectral changes

respectively. The type of the heterogeneity can be identified from the relative decrease or increase in the spectral density.