Bayesian Modeling in Engineering Seismology: Ground-Motion Models

The ground-motion model (GMM) is a key tool of the engineering seismologist. It predicts peak seismic ground-motion parameters given primary independent variables such as earthquake magnitude, distance from the earthquake, site effects, and more. The empirical GMM is expressed as a simple mathematical equation containing regression parameters to be inferred through a calibration of the model to a given dataset. Engineering seismologists strive for improved GMM predictions through the systematic reduction of model variability by incorporating additional independent variables, preferably physics-based ones. That leads to greater confidence in probabilistic seismic hazard assessment (PSHA), which is the foundation of earthquake-resistant building design and the mitigation of seismic risk of our modern society. In this chapter, we show examples of the application of the Bayesian statistical framework in ground-motion modeling. We use a large dataset of seismic ground motions recorded on a small urban strong-motion array in Southwest Iceland to calibrate a simple GMM using the Bayesian hierarchical modeling (BHM) approach. The partitioning of the model residuals into source, path, and site terms and the BHM quantifying their posterior distributions facilitates a physics-based interpretation of residual behavior. Namely, the modeling approach quantifies the relative contribution of the terms to the total residual variability, thereby identifying the term that contributes most to the overall variability, in this case, the site term. Second, by systematically analyzing the behavior of the individual elements that constitute the site term, we show how they are the manifestation of site-specific seismic wave amplification effects due to the local geological structure. On this basis, the GMM can be improved through the incorporation of geological amplification effects into the GMM. Then, using a regional dataset of seismic motions, we show how prior distributions of GMM parameters, which otherwise would be poorly constrained by limited data, can guide the Bayesian inference such that the GMM provides physically meaningful predictions in the range of limited data. Finally, we show how the Bayesian statistical framework can be used to objectively select the most appropriate GMM for use in PSHA in Iceland.