Epistemic uncertainty in the location and magnitude of earthquakes in Italy from Macroseismic data

Three independent techniques (Bakun and Wentworth, 1997; Boxer from Gasperini et al., 1999; and Macroseismic Estimation of Earthquake Parameters [MEEP; see Data and Resources section, deliverable D3] from R.M.W. Musson and M.J. Jimenez) have been proposed for estimating an earthquake location and magnitude from intensity data alone. The locations and magnitudes obtained for a given set of intensity data are almost always different, and no one technique is consistently best at matching instrumental locations and magnitudes of recent well-recorded earthquakes in Italy. Rather than attempting to select one of the three solutions as best, we use all three techniques to estimate the location and the magnitude and the epistemic uncertainties among them. The estimates are calculated using bootstrap resampled data sets with Monte Carlo sampling of a decision tree. The decision-tree branch weights are based on goodness-of-fit measures of location and magnitude for recent earthquakes. The location estimates are based on the spatial distribution of locations calculated from the bootstrap resampled data. The preferred source location is the locus of the maximum bootstrap location spatial density. The location uncertainty is obtained from contours of the bootstrap spatial density: 68% of the bootstrap locations are within the 68% confidence region, and so on. For large earthquakes, our preferred location is not associated with the epicenter but with a location on the extended rupture surface. For small earthquakes, the epicenters are generally consistent with the location uncertainties inferred from the intensity data if an epicenter inaccuracy of 2-3 km is allowed. The preferred magnitude is the median of the distribution of bootstrap magnitudes. As with location uncertainties, the uncertainties in magnitude are obtained from the distribution of bootstrap magnitudes: the bounds of the 68% uncertainty range enclose 68% of the bootstrap magnitudes, and so on. The instrumental magnitudes for large and small earthquakes are generally consistent with the confidence intervals inferred from the distribution of bootstrap resampled magnitudes.