A suite of ground motion prediction equations for cumulative absolute velocity in shallow crustal earthquakes including epistemic uncertainty

Abstract

Recent research has highlighted the usefulness of cumulative absolute velocity [Formula: see text] in several contexts, including using the [Formula: see text] at the ground surface for earthquake early warning and using the [Formula: see text] at rock reference conditions for evaluation of the liquefaction risk facing structures. However, there are relatively few ground motion prediction equations for CAV, they are based on relatively small data sets, and they give relatively similar results. This study develops nine ground motion prediction equations for [Formula: see text] based on a global database of ground motion records from shallow crustal earthquakes. Its provision of nine models enables characterization of epistemic uncertainty for ranges of earthquake characteristics that are sparsely populated in the regression database. The functional forms provide different perspectives on extrapolation to important ranges of earthquake characteristics, particularly large magnitude events and short distances. The variability and epistemic uncertainty in the models are characterized. Spatial autocorrelation of the models’ errors is investigated. The models’ predictions agree with existing broadly applicable models at small to moderate magnitudes and moderate to long distances. These models can be used to improve hazard analysis of [Formula: see text] that incorporates the influence of epistemic uncertainty.

Can geotechnical liquefaction indices serve as predictors of foundation settlement?

“…The sufficiency of predicted CAV is below 5% for most of the models considered. If a single ground motion IM were used to predict settlement, CAV at outcropping rock ( V S , 30 equal to 1100 m/s) predicted by Campbell and Bozorgnia (2010, 2019) or Bullock et al (2017, 2020) is optimum for predicting foundation settlement on a liquefiable deposit. Note that IMs on the soil surface (as opposed to the outcropping rock) were also considered in this comparison (detailed by Bullock et al, 2019b), as obtained from non-linear and equivalent-linear site response analyses.…”

“…The same GMPEs are combined with the correlation models of Baker and Jayaram (2008) to make predictions of S a , avg over the following period ranges: 0 . 2 T st − 3 T st , 0 . 2 T so − 1 . 5 T so , and 0 . 2 T so − 2 T so . Campbell and Bozorgnia (2010, 2019) and Bullock et al (2017, 2020) are used to make predictions of CAV . Kempton and Stewart (2006) and Afshari and Stewart (2016) are used to predict D 5 − 95 and D 5 − 75 .…”

“…However, for forward analysis, spatial correlation models are available for PGA (e.g. Jayaram and Baker, 2009) but not for CAV (see, for example, Bullock, 2019; Bullock et al, 2020; Foulser-Piggott and Goda, 2015, for discussion of the problems facing spatial analysis of CAV ). Until robust spatial correlation models for CAV are available, it may be preferable to develop maps of a geotechnical liquefaction index and relate that value to F site .…”

Site‐specific liquefaction fragility analysis: Cloud, stripe, and incremental approaches

“…Examples in the literature tend to use duration as the conditioned IM, 35,36 and the conditional mean spectrum as the primary IM. The target distribution is obtained from ground motion prediction equations (GMPEs) for the other IM of interest, GMPEs for those IMs used for selection and scaling, and models for the correlation among all relevant IMs 37–39 …”

“…We choose Campbell and Bozorgnia 79 because these models are based on large databases of shallow crustal ground motion records and because Campbell and Bozorgnia 38 also provides a correlation model based on the same database. Among the available, GMPEs, Campbell and Bozorgnia 38 and Bullock et al 39 . are unique among GMPEs for in terms of database size and global applicability.…”