Comparing two location estimates of the same seismo-acoustic event. A survey of available statistical tools.

The Comprehensive Nuclear-Test-Ban Treaty (CTBT) calls for a verification regime which involves interactions between the International Data Centre (IDC) component of the Provisional Technical Secretariat (PTS) established in Vienna, Austria, and the National Data Centres (NDC) of Member States of the Treaty. The results of location estimates of the same event by the two organizations is obtained using similar methods and software but potentially involve different seismo-acoustic networks and therefore a direct comparison of the distances and time differences is not sufficient and the different error estimates for the event should be taken into account. Most methods of location are using iterative linear inversions and the probability distributions are Gaussian, using the covariance matrix resulting from the last step of the iterative inversion process as the parameters of the Gaussian distributions. We explored the statistical tools available to compare two multi-dimensional distributions and measure a distance between them in an objective manner, including the Hellinger distance, the Bhattacharyya distance, and the Mahalanobis distance and we will show examples of application to the seismo-acoustic location problem.