Statistical Discriminants from Two-Dimensional Grids of Regional P/S Spectral Ratios
Steven R. Taylor · Bulletin of the Seismological Society of America · 2011
Abstract This paper describes a statistical methodology for earthquake/explosion discrimination using two-dimensional (2D) grids (frequency of S against frequency of P ) of regional P / S ratios. A method similar to that of scan statistics is developed by applying a counting rule on an N -length bitmap image of the 2D plots. An average density of bits is computed for explosions in the training set; it is assumed that each bitmap cell represents an independent sample taken from a Bernoulli process. A hypothesis test H 0 : explosion is designed, and a p value (a statistical measure) indicating the degree of membership of a new event to the explosion population is computed. A statistical method is presented that allows construction of p values under the null hypothesis that the event in question is an explosion. The field of view is the lower-right triangular corner plot for P / S ratios closely related to the high-frequency P to low-frequency S discriminant. The plot is converted to a bit map, and bits are summed and treated as a Bernoulli random variable. Using a set of calibration data, the background density of bits for explosions can be estimated and used to compute p values for new events. Importantly, the p values from the 2D P / S ratios can be naturally combined with other p values from other discriminants constructed under the same hypothesis to form a multivariate discriminant as in Anderson et al. (2007).