Model selection and uncertainty in earthquake hazard analysis

According to a recent UN report, seismic risk from large earthquakes continues to increase globally in line with infrastructure and population increase in developing nations. This implies the vulnerability is not decreasing relative to increased exposure. Specific examples include recent devastating earthquakes in Haiti and Sumatra in areas of known seismic hazard, but clearly this is part of a much wider problem. Seismologists and engineers can play a key role in public engagement, in communicating known best practice to local planners and practitioners on appropriate mitigation strategies, and in fundamental research to quantify seismic hazard in a probabilistic way. All probabilistic hazard forecasts are subject to epistemic (systematic) and aleatory (statistical) uncertainty. To date it has been assumed that the major uncertainties in probabilistic seismic hazard analysis are due to uncertainties in ground motion attenuation. As new strong ground motion data become available, and site response is better characterized locally in advance of major earthquakes, this uncertainty will reduce. Here we address uncertainties arising from the first two steps in seismic hazard analysis by quantifying the effect of sampling bias and statistical error in earthquake recurrence rates from finite records of seismic sources. We find even simple parameters such as mean event rate converge to a central limit much more slowly than would be expected for a Gaussian process. The residuals in the frequency-magnitude distribution instead follow a Poisson distribution to a good approximation at all magnitudes. Finite temporal sampling of this slowly-converging system has resulted in a best-fitting distribution for the global earthquake population that can be changed from a tapered G-R law to a pure G-R law by a single large event and its aftershocks. In regional studies of subduction zones it is currently not possible to reject the G-R hypothesis in favour of the characteristic earthquake model within the Poisson error, even when visually a few extreme events appear as significant outliers on a log frequency-magnitude plot. The epistemic and aleatory uncertainties described here must be taken into account in assessing the skill of time-dependent hazard models relative to the uncertainties in time-independent models. in preparedness and in planning for disaster risk reduction in developing nations. A recent UN report concluded that earthquake risk is increasing globally more or less in direct proportion to exposure in terms of growth of the population and the built environment, and that the main barriers to reducing economic and human losses in natural hazard preparedness in general are a combination of ‘poverty and a lack of good governance’ (UN International Strategy for Disaster Reduction Secretariat, 2009). These two can combine to devastating effect, particularly in the development of ‘informal’ settlements not subject to any building control, and where shelter against more frequent hazards such as hurricanes may be seen as more of a priority. The statistics also highlight the extent to which textbook best practice from the seismological and engineering communities (e.g. Reiter, 1991) are often not yet penetrating