Inversion of Single-Station S-Wave HVSR for Shallow Velocity Structure: Utility and Limitations

It is well known that unlithified, near-surface sediments modify seismic waves. Quantifying the response of these sediments to incident waves is needed for predicting the effects of strong earthquake shaking, which requires determination of the S-wave velocity (Vs) structure. The importance of accounting for site response increases when the impedance contrast between the sediment overburden and underlying bedrock is strong, which can trap seismic waves, yielding amplification in excess of that due to the sediment-bedrock impedance contrast alone (e.g., as quantified by the quarter-wavelength approximation).

Although it has been shown that the horizontal-to-vertical spectral ratio (HVSR) of ambient noise does not reliably measure site resonance above the fundamental frequency, weak-motion S-wave HVSR can estimate the empirical site transfer functions (TF) for sites with strong soil-bedrock impedance contrasts up to a site-dependent maximum frequency, f_max. Amplification of vertical motions from incident P- or SV-waves reduces the spectral ratio with respect to TF for frequencies greater than f_max. Therefore, S-wave HVSR, for frequencies up to f_max, can be inverted for Vs structure. At both deep-soil vertical seismic arrays in the northern Mississippi Embayment—USA, VSAP (100 m) and CUSSO (585 m)—f_max is approximately the fifth natural frequency of vertically propagating SH-waves.

We modified the OpenHVSR Monte Carlo inversion algorithm by forward-modeling the site response using Thompson-Haskell propagator matrices for incident SH-waves to obtain the best-fitting family of soil models that fit mean S-wave HVSR curves. We incorporated attenuation using the Kelvin-Voigt viscoelastic model and retained the algorithm's inclusion of optional model constraints such as depth to bedrock and frequency-independent Qs (derived from Vs). Using the observations at the VSAP and CUSSO sites and an additional, nearby USGS station on thinner sediments (30 m), where the velocity structures are known, we demonstrated the utility and limitations of this approach. For example, because of the frequency limitations of this single-station technique, shallow layers may not be resolved in thick-sediment settings.