Bayesian hierarchical model for variations in earthquake peak ground acceleration within small‐aperture arrays

Abstract

Knowledge of the characteristics of earthquake ground motion is fundamental for earthquake hazard assessments. Over small distances, relative to the source–site distance, where uniform site conditions are expected, the ground motion variability is also expected to be insignificant. However, despite being located on what has been characterized as a uniform lava‐rock site condition, considerable peak ground acceleration (PGA) variations were observed on stations of a small‐aperture array (covering approximately 1 km2) of accelerographs in Southwest Iceland during the Ölfus earthquake of magnitude 6.3 on May 29, 2008 and its sequence of aftershocks. We propose a novel Bayesian hierarchical model for the PGA variations accounting separately for earthquake event effects, station effects, and event‐station effects. An efficient posterior inference scheme based on Markov chain Monte Carlo (MCMC) simulations is proposed for the new model. The variance of the station effect is certainly different from zero according to the posterior density, indicating that individual station effects are different from one another. The Bayesian hierarchical model thus captures the observed PGA variations and quantifies to what extent the source and recording sites contribute to the overall variation in ground motions over relatively small distances on the lava‐rock site condition.

Spatial correlations of ground motion for non‐ergodic seismic hazard analysis

“…15,37,43,57 We have investigated different covariance functions, and though the exponential function led to slightly better predictive performance, the other ones had similar MSE/MSLL values. Alternatively, one can estimate the spatial correlations during the estimation of the GMM.…”

“…Alternatively, one can estimate the spatial correlations during the estimation of the GMM. 15,37,43,57 We have investigated different covariance functions, and though the exponential function led to slightly better predictive performance, the other ones had similar MSE/MSLL values. Hence, in a non-ergodic PSHA application, it should be investigated whether epistemic uncertainty in the covariance function needs to be included.…”

“…An example of a GMM with spatially correlated site terms can be found in Rahpeyma et al 37 In the following, we describe the models for calculating spatial correlations of residuals. It is reasonable to assume that these are spatially correlated as well, but our focus is mainly on spatial correlation models for sitespecific non-ergodic PSHA.…”

“…It is reasonable to assume that these are spatially correlated as well, but our focus is mainly on spatial correlation models for sitespecific non-ergodic PSHA. An example of a GMM with spatially correlated site terms can be found in Rahpeyma et al 37 In the following, we describe the models for calculating spatial correlations of residuals. Most previous studies investigating such correlations 21,34,35,[38][39][40][41] are done using geostatistical methods such as fitting a semivariogram.…”

Frequency-dependent site factors for the Icelandic strong-motion array from a Bayesian hierarchical model of the spatial distribution of spectral accelerations

“…Recently, we proposed a practical Bayesian inference scheme in order to estimate the contribution of source, path, and site effects given the spatial distribution of PGA recorded on a dense small-aperture strong-motion array (ICEARRAY I) that is located within an urban area in the town of Hveragerði in south Iceland (Rahpeyma et al, 2018). The proposed model is a Bayesian Hierarchical Model (BHM) tailored for spatial strong motion data that offers a flexible probabilistic framework for multilevel modeling of earthquake ground motion parameters, in which a collection of random variables can be decomposed into a series of conditional models.…”