A Mathematical Statistics Formulation of the Teleseismic Explosion Identification Problem with Multiple Discriminants

Seismic monitoring for underground nuclear explosions answers three questions for all global seismic activity: Where is the seismic event located? What is the event source type (event identification)? If the event is an explosion, what is the yield? The answers to these questions involve processing seismometer waveforms with propagation paths predominately in the mantle. Four discriminants commonly used to identify teleseismic events are depth from travel time, presence of long-period surface energy (mb versus Ms), depth from reflective phases, and polarity of first motion. The seismic theory for these discriminants is well established in the literature (see for example Pomeroy et al. [1982] and Blandford [1982]). However the physical basis of each has not been formally integrated into probability models to account for statistical error and provide discriminant calculations generally appropriate for multi-dimensional event identification. This paper develops a mathematical statistics formulation of these discriminants and offers a novel approach to multi-dimensional discrimination that is readily extensible to other discriminants. For each discriminant a probability model is formulated under a general null hypothesis of H0: Explosion Characteristics. The veracity of the hypothesized model is measured with a p-value calculation (see Stuart et al. [1994] and Freedman et al. [1991]) that is filtered to be approximately normally distributed and is in the range [0, 1]. A value near zero rejects H0, and a moderate to large value indicates consistency with H0. The hypothesis test formulation ensures that seismic phenomenology is tied to the interpretation of the p-value. These p-values are then embedded into a multi-discriminant algorithm that is developed from regularized discrimination methods proposed by Smidt and McDonald (1976), DiPillo (1976) and Friedman (1989). Performance of the methods is demonstrated with 102 teleseismic events with magnitudes (mb) ranging from prepared in collaboration with Quantum Technology Sciences, Inc.. Presented at 29th Monitoring Research Review: Ground-Based Nuclear Explosion Monitoring Technologies, Denver, CO 25-27 Sep 2007, sponsored by the National Nuclear Security Administration (NNSA) and the Air Force Research Laboratory (AFRL). Published in proceedings of the same p526-530. The original document contains color images.