Ground motion spatial correlation fitting methods and estimation uncertainty

Abstract

Ground shaking intensity varies spatially in earthquakes, and many studies have estimated correlations of intensity from past earthquake data. This paper presents a framework for quantifying uncertainty in the estimation of correlations and true variability in correlations from earthquake to earthquake. A procedure for evaluating estimation uncertainty is proposed and used to evaluate several methods that have been used in past studies to estimate correlations. The results indicate that a weighted least squares algorithm is most effective in estimating spatial correlation models and that earthquakes with at least 100 recordings are needed to produce informative earthquake-specific estimates of spatial correlations. The proposed procedure is also used to distinguish between estimation uncertainty and the true variability in model parameters that exist in a given data set. The estimation uncertainty is seen to vary between well-recorded and poorly recorded earthquakes, whereas the true variability is more stable.

Spatial correlation of broadband ground motions from physics‐based numerical simulations

“…These analyses point out that an average receiver spacing lower than 5.5 km approximately ( N = 100) is needed to have accurate estimates with a stable mean and variance. It is worth noting as this result is in agreement with the research study of Baker and Chen 41 who, analyzing the NGA West‐2 dataset, 24 concluded that at least 100 stations are needed to limit estimation uncertainty and that for earthquakes with fewer stations, earthquake‐specific estimation of spatial correlations should be performed with caution.…”

Spatial correlation in ground motion prediction errors in Central and Eastern North America

“…However, a sensitivity study using weighted least squares for representative events (Mineral and Sparks) and using the R software's gstat package weighting method (Gra¨ler et al, 2016) resulted in generally similar percent difference changes as compared to the ordinary least squares approach. Application of the model by Baker and Chen (2020), which was developed for shallow crustal regions, resulted in a substantially larger change for the Sparks event but a percent difference change of 26% for the Mineral event.…”

“…Where possible and justified, given the limitations of our dataset, we have similarly sought to explore the sensitivity of CENA correlation models to modeling assumptions. Several authors have investigated the specific method in which to fit a model to their data (Baker and Chen, 2020;Esposito and Iervolino, 2011;Jayaram and Baker, 2009). We have selected the method of least squares as discussed in the section ''Comparison with previous studies,'' but have not pursued the use of any other method because we do not judge the current data availability warrants this level of precision.…”

“…However, we also present limited results for other spectral frequencies in the section ''Spectral period dependence.'' Correlation in Vs30 (Du and Wang, 2013;Jayaram and Baker, 2009;Sokolov et al, 2010) and path effects (Baker and Chen, 2020;Kuehn and Abrahamson, 2020;Park et al, 2007) are known to influence spatial correlation models. We assessed potential bias from these properties in the section ''Identification of data bias.''…”

Spatial correlation of broadband earthquake ground motion in Norcia (Central Italy) from physics-based simulations

“…(3) the earthquake magnitude (Mw); (4) the vibration period; (5) local site-effects; and (6) ground motion prediction models. In this regard, a valuable contribution can be also found in Baker and Chen (2020), who recently propose an alternative approach to assess the uncertainty in spatial correlation models in terms of both true and estimation variability. These authors suggest that differences in terms of true variability in correlation among well-recorded and poorly-recorded events are negligible.…”