Improved Model Fitting for the Empirical Green's Function Approach Using Hierarchical Models

Abstract

AbstractStress drops calculated from source spectral studies currently show larger variability than what is implied by empirical ground motion models. One of the potential origins of the inflated variability is the simplified model‐fitting techniques used in most source spectral studies. This study examines a variety of model‐fitting methods and shows that the choice of method can explain some of the discrepancy. The preferred method is Bayesian hierarchical modeling, which can reduce bias, better quantify uncertainties, and allow additional effects to be resolved. Two case study earthquakes are examined, the 2016 MW7.1 Kumamoto, Japan earthquake and a MW5.3 aftershock of the 2016 MW7.8 Kaikōura earthquake. By using hierarchical models, the variation of the corner frequency, fc, and the falloff rate, n, across the focal sphere can be retrieved without overfitting the data. Other methods commonly used to calculate corner frequencies may give substantial biases. In particular, if fc was calculated for the Kumamoto earthquake using an ω‐square model, the obtained fc could be twice as large as a realistic value.