A procedure for developing uncertainty-consistent Vs profiles from inversion of surface wave dispersion data

Abstract

Non-invasive surface wave methods have become a popular alternative to traditional invasive forms of site-characterization for inferring a site's subsurface shear wave velocity (Vs) structure. The advantage of surface wave methods over traditional forms of site characterization is that measurements made solely at the ground surface can be used routinely and economically to infer the subsurface structure of a site to depths of engineering interest (20–50 m), and much greater depths (>1 km) in some special cases. However, the quantification and propagation of uncertainties from surface wave measurements into the Vs profiles used in subsequent engineering analyses remains challenging. While this has been the focus of much work in recent years, and while considerable progress has been made, no approach for doing so has been widely accepted, leading analysts to either address the propagation of uncertainties in their own specialized manner or, worse, to ignore these uncertainties entirely. In response, this paper presents a new, effective, and verifiable method for developing uncertainty-consistent Vs profiles from inversion of surface wave dispersion data. We begin by examining four approaches presented in the literature for developing suites of Vs profiles meant to account for uncertainty present in the measured dispersion data. These methods are shown to be deficient in three specific ways. First, all approaches are shown to be highly sensitive to their many user-defined inversion input parameters, making it difficult/impossible for them to be performed repeatedly by different analysts. Second, the suites of inverted Vs profiles, when viewed in terms of their implied theoretical dispersion curves, are shown to significantly underestimate the uncertainty present in the experimental dispersion data, though some may appear satisfactory when viewed purely qualitatively. Third, if the uncertainties in the implied theoretical dispersion curves were to be examined quantitatively, which has not been done previously, there is no obvious remedy available for the analyst to resolve any inconsistency between the measured and inverted dispersion uncertainty. Therefore, a new approach is proposed that seeks to remedy these shortcomings. First, beyond appropriate considerations that must be given to all inversions, the new approach is governed by only one user-defined input parameter, to which it is not overly sensitive. Second, the new approach is shown to produce suites of Vs profiles whose theoretical dispersion curves quantitatively reproduce the uncertainties in the experimental dispersion data. Third, the final step of the procedure requires the analyst to compare the measured and inverted dispersion uncertainties quantitatively, and should the analyst find the results of the new approach to be lacking, clear guidance is provided on the additional actions necessary to produce Vs profiles whose theoretical dispersion curves better account for the experimental uncertainty. Using two synthetic tests and a real-world example, the procedure is shown to produce suites of Vs profiles that accurately capture the site's Vs structure, while rigorously propagating the dispersion data's uncertainty through the inversion process.