Surface waves usually dominate the ambient noise above the microseism frequency (∼0.1 Hz). Their dispersion curves are routinely inverted for shear velocity profiles, while their amplitude is often neglected. Amplitude, however, can also carry useful information. We address the problem of predicting Rayleigh wave amplitude anomalies due to the interaction of incident Rayleigh waves with an embedded elastic inclusion (gas reservoir) between 0.5 and 5 Hz. The proposed method is designed for ambient noise applications, so we use multiple time-windows containing signals from randomly excited sources. Using the spectral-element method in the radial-vertical 2-D plane, we show that frequency-dependent spectral anomalies arise at the surface in the vicinity of the inclusion. The anomalies generated by a deep inclusion are enhanced for the overtones because of their deeper penetration. Depending on the wavefield modal content and the complexity of the background model, the anomalies can reach about 20 per cent of the initial power spectral density. For comparison, the anomalies generated by a structural anticline in a realistic sedimentary basin are one order of magnitude higher in our simulations. The Born-based finite-frequency amplitude sensitivity kernels are useful for the interpretation of the results. The anomalies are most sensitive to Vs inside the inclusion, followed by ρ, as expected for surface waves. The sensitivity is concentrated in slow shallow layers when they are present in the model.