Simplified Green's function for surface waves in quasi-incompressible elastic plates with application to elastography

Surface wave elastography is a growing method to estimate the elasticity in soft solids. It is particularly useful in the case of agrifoods like meat, cheese, or fruits because it does not require major infrastructure or large equipment and could be developed in portable devices. However, estimating the shear elastic properties from surface wave measurements is not straightforward. The shear wavelength in those materials is cm sized for the excitation frequencies usually employed in elastography (similar to 10(2) Hz), and the size of samples is comparable to it. Thus, the surface wave speed is frequency dependent with no direct relation to the shear wave speed. In this work we propose a simplified Green's function for soft solid elastic plates which allows to retrieve the shear elasticity from near field measurements. The model is compared with experimental results obtained in agar-gelatin phantoms and food samples (cheese and bovine liver). The results show a good overall agreement although improvements can be achieved by incorporating diffraction and viscosity to the model.