Bayesian Modelling in Engineering Seismology: Spatial Earthquake Magnitude Model

The specification of the spatial characterisation of earthquake sources in a seismic region and their seismic activity are two of the three key elements of probabilistic seismic hazard assessment, the third one being ground motion modelling. The seismic activity rate is specified by a magnitude–frequency relationship that is usually modelled using an exponential distribution for the earthquake magnitudes. We propose a Bayesian latent Gaussian model for the earthquake magnitudes that assumes a generalised Pareto distribution with a spatially varying scale parameter as an alternative to the exponential distribution with a constant scale parameter. We apply it to estimate the spatial variations of earthquake magnitudes across Southwest Iceland including the South Iceland transform zone, which is the region with the highest earthquake hazard and seismic risk in Iceland. We show that the generalised Pareto distribution, with a spatially varying scale parameter, provides a substantially better fit to the earthquake magnitudes than the exponential distribution with a constant scale parameter. An analysis based on the proposed spatial model reveals that the scale parameter takes different values depending on the location along the seismic region. The spatial distribution of seismicity in the region and its tectonic characteristics indicate that the scale parameter can be correlated with physical parameters that characterise seismicity. The results indicate that modelling earthquake magnitudes with the generalised Pareto distribution with a spatially varying scale parameter can be useful in hazard assessment.