Addressing surface wave inversion non-uniqueness and the implications for seismic site response analyses
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Surface ground motions predicted from a seismic site response analysis are strongly dependent on the shear wave velocity (Vs) profile used to represent the small-strain shearing stiffness of subsurface materials as a function of depth. Moreover, uncertainties are present in the input Vs profile and this uncertainty leads to uncertainty in the predicted site response. When Vs profiles are obtained from surface wave inversion, the final derived Vs profiles are non-unique, with many different interpretations of the subsurface shearing stiffness that are consistent with the measured surface wave field data. This non-uniqueness is exacerbated by the ambiguous interpretation of surface wave modes and the subjectivity of defining the inversion parameterization (trial number of layers and ranges in their respective Vs, compression wave velocities, and mass densities). Thus, it is necessary to develop strategies to systematically address these issues in order to develop Vs profiles with realistic estimates of uncertainty for use in site response analyses. First, a-priori information should be sought to aid in interpreting modes and to develop a realistic parameterization to guide the surface wave inversion. In complex geologic settings, it can be extremely challenging or even impossible to obtain geologically-realistic Vs profiles without this a-priori information. However, there are many situations when a-priori information is scarce or nonexistent. In such cases, alternative mode interpretations and/or parameterizations must be considered. Even with abundant a-prior information, the non-uniqueness issue generally cannot be eliminated and the variation in seismic site response associated with non-unique Vs profiles derived from the same surface wave dataset is of interest. At the two sites considered in this study, very different Vs profiles derived from surface wave inversion of the same dataset produced very similar site response estimates, provided that the experimental surface wave dispersion data was well-fit. Furthermore, the site response estimates associated with these Vs profiles were more accurate and less variable than those associated with Vs profiles that were developed using common strategies of accounting for Vs uncertainty. Thus, despite the non-uniqueness issue, Vs profiles derived from a rigorous surface wave inversion can yield robust site response estimates.