Application of Regularized Discrimination Analysis to Regional Seismic Event Identification

We present a generalized multivariate seismic event identification method, Regularized Discrimination Analysis (RDA) [Friedman 1989], that can be applied to a large number of regional discriminants. RDA is readily adaptable to an outlier or classical identification approach to regional seismic identification. RDA is designed to address the problems associated with linear (LDA) and quadratic (QDA) discrimination in small-sample, high-dimensional settings. RDA includes LDA, QDA and Euclidean distance based nearest neighbor discrimination in its parameterization. RDA can be used to transition from an outlier analysis approach to seismic identification to classical discrimination as quality explosion calibration data are collected. Further, RDA provides the statistical structure to model highly correlated seismic measurements. 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 RDA, a large number of amplitudes from a Magnitude and Distance Amplitude Correction (MDAC) analysis [see Taylor et al. 1999] can be used and no a priori sub-selection of amplitudes (or discriminants) is necessary.