The meaning of surface wave dispersion curves in weakly laterally varying structures

The analysis of surface wave dispersion is efficiently applied to estimate 1D subsurface velocity profiles. The same approach is even applied at sites that present weak lateral variations under the assumption that the estimated dispersion curve is representative of the average properties beneath the receiver spread. We verify this assumption by discussing the meaning of the dispersion curve in weakly laterally varying structures using the path-average approximation (PAVA). Using PAVA we compute synthetic data for different lateral variations and we extract dispersion curves using the f-k wavefield transform. If the phase slowness is linearly varying along the propagation path and the wavenumber resolution of the measuring array does not allow for separating the different wavenumbers of the propagating surface waves, the estimated dispersion curve provides the average slowness. On the contrary, if the phase slowness is not linearly varying or if the wavenumber resolution of the measuring array is enough to discriminate the wavenumbers, the retrieved dispersion curve does not represent any specific velocity of the subsurface. To mitigate this problem windowing can be successfully adopted to make the retrieved dispersion curve representative of the local property of a subsoil column that coincides with the window maximum.