An extension to the procedure for developing uncertainty-consistent shear wave velocity profiles from inversion of experimental surface wave dispersion data

Abstract

Measurements of shear wave velocity (Vs) with uncertainty are critical for site-specific probabilistic seismic hazard studies. However, rigorously quantifying the uncertainty in Vs over large enough areas and great enough depths remains challenging. In 2021, Vantassel and Cox (i.e., VC21) proposed a procedure for developing suites of Vs profiles from surface wave testing whose uncertainty were consistent with the experimental dispersion data's uncertainty. The VC21 procedure was a significant step forward, however, it requires a full dispersion data matrix to compute inter-wavelength phase velocity correlations. While applicable to many practical cases, VC21 could not be applied to the case where multiple surface wave arrays of different sizes were deployed at a site as a means of developing broadband dispersion data and deeper Vs profiles. In response, this work extends the VC21 procedure using two possible approaches for estimating a full dispersion data matrix. Approach 1 uses a selection of theoretical dispersion curves from an initial, traditional surface wave inversion. Approach 2 estimates the full data matrix by combining pieces of the data matrix obtained from the experimental dispersion measurements. Both approaches are evaluated using two synthetic datasets; one relatively-simple, three-layered model and one more-complex, five-layered model. Approach 1 and Approach 2 were able to reasonably estimate the true correlation matrix and recover uncertainty-consistent Vs profiles similar to the true distribution of Vs. While the uncertainty of the recovered Vs profiles were higher than is often assumed, the engineering proxies computed from those Vs profiles, namely the time averaged shear wave velocity in upper 30 m and the fundamental site period, showed substantially less uncertainty indicating the Vs profiles, while uncertain, are effective at capturing a site's engineering behavior. Both approaches were applied to real data from the Garner Valley Downhole Array (GVDA) site and found to yield better estimates of small-strain site amplification than achieved previously.