Partitioning Ground Motion Uncertainty When Conditioned on Station Data

Abstract

Rapid estimation of earthquake ground shaking and proper accounting of associated uncertainties in such estimates when conditioned on strong-motion station data or macroseismic intensity observations are crucial for downstream applications such as ground failure and loss estimation. The U.S. Geological Survey ShakeMap system is called upon to fulfill this objective in light of increased near-real-time access to strong-motion records from around the world. Although the station data provide a direct constraint on shaking estimates at specific locations, these data also heavily influence the uncertainty quantification at other locations. This investigation demonstrates methods to partition the within- (phi) and between-event (tau) uncertainty estimates under the observational constraints, especially when between-event uncertainties are heteroscedastic. The procedure allows the end users of ShakeMap to create separate between- and within-event realizations of ground-motion fields for downstream loss modeling applications in a manner that preserves the structure of the underlying random spatial processes.

ProbShakemap v1.0: a Python toolbox propagating source uncertainty to ground motion prediction for urgent computing applications

“…2) inter-event variability: GMM variability within the frame of multivariate normal distribution (Worden et al, 2018;Engler et al, 2022). In ProbShakeMap, the GMMs uncertainty is modelled as in ShakeMap.…”

“…At its core, ShakeMap software is a seismologically-based data interpolator that relies on parametric ground motion data, GMMs and local site amplifications. Maps of ShakeMap uncertainties are calculated based on the spatial variability of peak ground motions (which is assumed to be zero at the recording stations and increases with distance) and on the total variability of the implemented GMMs (Worden et al, 2018;Engler et al, 2022). These maps are generated for a single earthquake source, with initial parameter estimates typically available within 30 minutes of the earthquake's origin time.…”

Post‐earthquake estimates of different ground motion intensity measures for the 2012 Emilia earthquake

“…This is neglected in the present paper because, as discussed in Section 3, the attenuation models used have very small between‐event uncertainties. An improvement on this conditioning has recently been proposed by Engler et al 25 …”

“…This is neglected in the present paper because, as discussed in Section 3, the attenuation models used have very small between-event uncertainties. An improvement on this conditioning has recently been proposed by Engler et al 25 It should be noticed that, according to the approach adopted, the conditional IM distribution at the location of one of the GMRSs has a mean value corresponding the recorded IM value and zero variance. Therefore, the present model does not consider any measurement error in GMRSs.…”

Instantaneous Physics‐Based Ground Motion Maps Using Reduced‐Order Modeling

“…However, the generally sparse spatial coverage of observations leads to significant uncertainties in the shaking distributions (Wald et al., 2008). To fill in the gaps, recent approaches include spatial and spectral interpolation (Worden et al., 2018), Gaussian process regression (Tamhidi et al., 2021), and conditional simulation (Bailey et al., 2022; Engler et al., 2022), but rapidly estimating the full distribution of shaking intensity remains a challenge. Most EEW systems and large‐scale seismic hazard studies (e.g., Kohler et al., 2017; Meletti et al., 2021; Petersen et al., 2020; Stirling et al., 2012) instead use empirical ground motion models (GMMs) which give instantaneous ground motion estimates for given source, path, and site parameters.…”