The effect of observation errors on parameter estimates applied to seismic hazard and insurance risk modelling

Abstract

The research attempts to resolve which method of estimation is the most consistent for the parameters of the earthquake model, and how these different methods of estimation, as well as other changes, in the earthquake model parameters affect the damage estimates for a specific area. The research also investigates different methods of parameter estimation in the context of the log-linear relationship characterised by the Gutenberg-Richter relation. Traditional methods are compared to those methods that take uncertainty in the underlying data into account. Alternative methods based on Bayesian statistics are investigated briefly. The efficiency of the feasible methods is investigated by comparing the results for a large number of synthetic earthquake catalogues for which the parameters are known and errors have been incorporated into each observation. In the second part of the study, the effects of changes in key parameters of the earthquake model on damage estimates are investigated. This includes an investigation of the different methods of estimation and their effect on the damage estimates. It is found that parameter estimates are affected by observation errors. If errors are not included in the method of estimation, the estimate is subject to bias. The nature of the errors determines the level of bias. It is concluded that uncertainty in the data used in earthquake parameter estimates is largely a function of the quality of the data that is available. The inaccuracy of parameter estimates depends on the nature of the errors that are present in the data. In turn, the nature of the errors in an earthquake catalogue depends on the method of compilation of the catalogue and can vary from being negligible, for single source catalogues for an area with a sophisticated seismograph network, to fairly impactful, for historical earthquake catalogues that predate seismograph networks. Probabilistic seismic risk assessment is used as a catastrophe modelling tool to circumvent the problem of scarce loss data in areas of low seismicity and is applied in this study for the greater Cape Town region in South Africa. The results of the risk assessment demonstrate that seemingly small changes in underlying earthquake parameters as a result of the incorporation of errors can lead to significant changes in loss estimates for buildings in an area of low seismicity.