Statistical modelling of felt intensity data for three New Zealand earthquakes

Abstract

The aims of this study are to develop objective statistical methods for fitting attenuation curves and smooth isoseismals of simple form to felt intensity data. The main analyses were carried out with data from three major New Zealand earthquakes: Buller (1929), Inangahua (1968) and Edgecumbe (1987). Both non-parametric and parametric approaches were used, making use of subroutines available within the statistical language S-PLUS.

The non-parametric methods produced useful results for the attenuation curves, less so for the smoothed isoseismals. A simple elliptical model, representing expected intensity as a function of distance and angle relative to the centre of shaking, was then fitted to the felt intensity data using two approaches. It was fitted first directly by minimising the sum of squares between observed and expected intensities, and secondly indirectly by using the expected intensity to generate a family of probability distributions for the observed intensity, and fitting these probabilities by maximum likelihood.

Even with such simplified forms, the three events gave rise to significantly different parametric values. However, the attenuation curves (corrected for different relative attenuations along the major and minor arcs of the ellipse) were very similar to those estimated non-parametrically, and close also to a common power law decay with distances (geometric spreading), with index somewhat below 2. All three fits also suggested an elliptical pattern of isoseismals, with the major axis oriented approximately NNE/SSW. However, the ellipticity term was clearly statistically significant only for the Inangahua earthquake.

Preliminary comparisons of the histograms of observed and expected numbers of felt intensities of different values within a given isoseismal band suggested that more consistent isoseismal patterns could be obtained by correcting the biases due to under-reporting of small intensities and absence of reports from regions with low population densities.