Evaluating the Fit of Alternative Hypocenters to Arrival Times

Statistical methods for comparing travel time residuals are reviewed and the importance of using a statistic that is both robust and a measure of dispersion is demonstrated. Results from relocations based on travel times from the Jeffreys-Bullen (JB) tables and from a tomographic (3D) model are compared using the variance of the Winsorized samples, which is a robust measure of dispersion. The improvement of the residuals is significant at a high level of confidence globally and in many individual regions. The same events are relocated with travel times of the modern one-dimensional model ak135. The incremental improvements from JB to ak135 residuals and from ak135 to 3D residuals are each very small. Each of the small incremental improvements is statistically significant when all earthquakes from around the world are taken as a single sample, but regional samples of even hundreds of earthquakes rarely show that either of the incremental improvements is significant.