Shallow-seismic Rayleigh and Love waves are attractive for geotechnical site investigations. They exhibit a high signal to noise ratio in field data recordings and have a high sensitivity to the S-wave velocity, an important lithological and geotechnical parameter to characterize the very shallow subsurface. In this work we compare the performance on field data of individual full waveform inversion (FWI) of Rayleigh or Love waves and explore the benefits of a simultaneous joint-inversion of both types of surfaces waves. For this purpose we utilized field data, which is recorded on a test side where a shallow small-scale low-velocity anomaly (trench) is embedded in a depth dependent background model. The assumed shallow S-wave low-velocity anomaly could be reconstructed successfully by both the individual waveform inversion of Rayleigh and Love wave FWI as well as by the simultaneous joint-inversion of both wave types. The individual Love wave FWI was able to reveal the contour of the trench sharper than individual Rayleigh wave FWI. The simultaneous combination of both wave types by the joint inversion further improves the image of the anomaly.