Application of regularized discrimination analysis to regional seismic event identification

We present multivariate seismic event identification methods that can be applied to a large number of highly correlated regional discriminants. The methods employ the ridge discrimination techniques first proposed by Smidt and McDonald (1976). Ridge discrimination was developed to address the problems associated with discrimination in high-dimension, colinear settings and is readily adaptable to linear, quadratic, and outlier identification rules. Ridge discrimination is a special case of regularized discrimination analysis (RDA) developed by Friedman (1989). RDA includes linear discrimination (LDA), quadratic discrimination (QDA), and Euclidean distance-based nearest mean discrimination in its parameterization. We propose a new approach to the optimal selection of RDA parameters. We show that the techniques presented in this article can be used to transition from an outlier analysis approach to seismic identification to classical discrimination, as quality explosion calibration data are collected. We demonstrate the importance of including the correlation structure between seismic measurements in event identification. Not including this correlation structure in any identification framework can aggravate identification errors and give an erroneous impression of capability. With the techniques presented, a large number of discriminants can be used and no a priori subselection of discriminants is necessary.