Estimating Unbiased Statistics for Fundamental Site Frequency Using Spatially Distributed HVSR Measurements and Voronoi Tessellation

Abstract

A site’s fundamental resonance frequency (f0), or its reciprocal, the fundamental period (T0), is a critical parameter in seismic studies due to its proven ability to aid in predicting local site effects (i.e., frequency-dependent amplification of seismic waves). The horizontal-to-vertical spectral ratio (HVSR) method is a popular nonintrusive technique that can be used to estimate f0 in a time-efficient and cost-effective manner. Although it is becoming more and more common to perform several HVSR measurements to investigate spatial variability in f0 across a site, the measurements often are irregularly spaced due to access and/or budget restrictions. This has the potential of introducing significant bias when attempting to estimate a single, representative f0 across an area of interest. To address this problem, we propose the use of Voronoi tessellations to obtain an unbiased, statistical representation of f0 or T0 from spatially distributed HVSR measurements. After area boundaries are set, Voronoi tessellation yields unique spatial estimates in a relatively simple and fast manner, which makes it appealing for standardization. To accommodate the current state of practice in HVSR processing, two distinct statistical approaches were presented. The choice of which approach to use is governed by whether the f0 values at each HVSR location are reported deterministically (i.e., as single f0 values without variance) or statistically (i.e., as f0 values with associated variance). Three example applications were presented to illustrate potential uses. The first application demonstrated the effectiveness of the adopted approach in correcting for bias introduced by irregular spatial sampling. The second application illustrated how better-informed seismic site classifications can be made using a statistical representation of T0. The third application compared the relative degree of spatial variability in f0 at two downhole array sites to assess the applicability of performing one-dimensional (1D) ground response analyses.