Multimodal interpretation of surface wave data

Surface Wave Methods become quite popular tools for geotechnical characterization since they supply the stiffness profile of the sites with a cost effective testing procedure. Several acquisition and processing approaches have been developed to infer the Rayleigh wave dispersion curve which is then inverted (Nazarian and Stokoe, 1984; Park et al., 1999). Independently by the chosen procedure, the inversion is mainly carried out assuming that the experimental dispersion curve is actually the first Rayleigh mode. It is a rather diffuse commonplace among geophysicists that, for normally dispersive site, the first mode is in fact prevailing and that only for inversely dispersive site the role of higher Rayleigh modes has to be taken into account (Tokimatsu et al., 1992). By using a multi-modal modelling it can be easily shown that higher Rayleigh modes contribute to the effective dispersion curve not only for inversely dispersive stratigraphies but also in presence of quite high velocity contrasts. Beside this, since one of the main advantages of surface wave methods is to be effective even in case of velocity inversion, when for instance seismic refraction fails, it is quite important to overcome the limitation due to the influence of higher modes, considering them in the interpretation process. Furthermore it can be also shown that the analysis of higher modes can help to obtain much reliable information also in cases of normally dispersive sites (Foti et al., 2002). As far as concern the dispersion curve interpretation some further considerations are deserved. The simplest approach is to transform the dispersion curve from the phase velocity vs. frequency into the phase velocity vs. wavelength domain and to attribute the velocity values (multiplied by a factor of 1.1) to a depth approximately equal to one-third or half the wavelength. This approach, quite popular in the professional practice of surface wave testing is usually considered an approximated approach but can be easily demonstrated that it is in fact erroneous because the energy distribution with depth can strongly vary depending on stiffness contrasts among layers. A more rigorous approach, which is also widely diffuse, is to invert the experimental dispersion curve considering it as the first Rayleigh wave mode. This procedure can be effective and supplies reliable results only in those cases in which one can be sure that the first mode is prevailing within the considered frequency range. Otherwise it can lead to some degree of error in the estimation of the stiffness profile. The experience carried out at more than 50 different sites, where surface wave test results could be compared with other reference data, has shown that, in the majority of the encountered cases, to perform a reliable interpretation the influence of higher Rayleigh modes could not be neglected. Multi-modal interpretation involves the possibility of recognising experimentally the modal curves but this is usually impossible by using traditional acquisition and processing approach. Another possibility is to invert the experimental dispersion curve but, since it depends also on the acquisition layout, it has to be considered as an apparent curve (Foti et al., 2000). Furthermore its pattern can change dramatically also for quite small changes of the model parameters. For this reason is not easy to use the apparent dispersion curve in an iterative inversion process and trial and error inversion (Tarantola, 1987) can be preferred.