Estimating Unbiased Statistics for Fundamental Site Frequency Using Spatially Distributed HVSR Measurements and Voronoi Tessellation
Publication: Journal of Geotechnical and Geoenvironmental Engineering
Volume 147, Issue 8
Abstract
A site’s fundamental resonance frequency (), or its reciprocal, the fundamental period (), 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 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 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 across an area of interest. To address this problem, we propose the use of Voronoi tessellations to obtain an unbiased, statistical representation of or 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 values at each HVSR location are reported deterministically (i.e., as single values without variance) or statistically (i.e., as 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 . The third application compared the relative degree of spatial variability in at two downhole array sites to assess the applicability of performing one-dimensional (1D) ground response analyses.
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Data Availability Statements
Many of the HVSR data sets used in the sections “Application 1: Correcting for Preferential Spatial Sampling” and “Application 2: Seismic Site Classification using Spatial Statistics of ” have been archived and made publicly available on DesignSafe-CI (Cox and Vantassel 2018). The open-source Python package for HVSR processing, hvsrpy, is publicly available online (Vantassel 2020). Other data or codes that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
The HVSR data from CentrePort, Wellington, New Zealand were collected with funding from the US National Science Foundation (NSF) Grant CMMI-1724915 and the New Zealand Earthquake Commission (EQC) under the Capability Building Fund at the University of Auckland, through the Natural Hazards Research Platform (NHRP) Grant “Kaikoura Earthquake response–geotechnical characterization of CentrePort reclamations” through MBIE, and QuakeCoRE through Technology Platform 2. However, any opinions, findings, conclusions, or recommendations expressed in this paper are those of the authors and do not necessarily reflect the views of either NSF or EQC. The authors acknowledge Dr. Liam Wotherspoon from the University of Auckland for his help in collecting and interpreting the data from CentrePort, and Tiffany Krall from CentrePort Ltd. for assisting with the dynamic site characterization efforts. Note that 81 of the 114 time records from CentrePort data are available for open-access download through DesignSafe-CI under the title “PRJ-2075: Dynamic Characterization of Wellington, New Zealand” (Cox and Vantassel 2018). The HVSR data from DPDA and TIDA were collected with funding from Pacific Gas and Electric (PG&E). However, any opinions, findings, conclusions, or recommendations expressed in this paper are those of the authors and do not necessarily reflect the views of PG&E. The authors thank Dr. Albert Kottke, Dr. David Teague, Dr. Krishna Kumar, and Michael Yust for their help in collecting HVSR data at TIDA. The authors wrote this paper jointly. Tianjian Cheng was primarily responsible for all HVSR data processing and the concept of using Voronoi tessellations for declustering. Mohamad M. Hallal contributed significantly to the geostatistical portions of the work and data processing for the TIDA and DPDA sites. Joseph P. Vantassel organized the data acquisition at TIDA and DPDA and incorporated the statistical concepts presented into a new release of the open-source Python package hvsrpy (Vantassel 2020). Brady R. Cox was primarily responsible for identifying the need for a statistical approach to account for spatial variability in HVSR values.
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Journal of Geotechnical and Geoenvironmental Engineering
Volume 147 • Issue 8 • August 2021
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© 2021 American Society of Civil Engineers.
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Received: Jun 17, 2020
Accepted: Mar 5, 2021
Published online: Jun 1, 2021
Published in print: Aug 1, 2021
Discussion open until: Nov 1, 2021
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