Jonathan K. MacCarthy

Combined Rayleigh‐ and Love‐Wave Magnitudes for Seismic Event Discrimination and Screening Analysis

Abstract Love waves have the potential to aid in discrimination for anomalous explosion events. We develop a calibrated mathematical formulation for an explosion discriminant that combines Rayleigh‐ and Love‐wave magnitude values and employs an error model that correctly partitions variances among events and stations separately. The discriminant is calibrated using a global data set of 124 earthquakes and 26 nuclear explosions and applied to the May 2009 Democratic Republic of North Korea (DPRK) announced nuclear test, as well as the calibration data set. All 26 explosions were correctly identified; only 6 earthquakes were incorrectly identified as explosions. Compared to an analogous treatment using only Rayleigh data, the combined discriminant improves the DPRK event p ‐value only nominally but reduces the number of false positives in the calibration data set by 70%, with no additional false negatives. While not dramatically improving the discrimination power for anomalous events, such as the 2009 DPRK test, the combined discriminant proposed here offers improved screening capabilities for typical events. Online Material: Earthquake and explosion calibration data set.

Speeding up dynamic time warping distance for sparse time series data

Dynamic time warping (DTW) distance has been effectively used in mining time series data in a multitude of domains. However, in its original formulation DTW is extremely inefficient in comparing long sparse time series, containing mostly zeros and some unevenly spaced nonzero observations. Original DTW distance does not take advantage of this sparsity, leading to redundant calculations and a prohibitively large computational cost for long time series. We derive a new time warping similarity measure (AWarp) for sparse time series that works on the run-length encoded representation of sparse time series. The complexity of AWarp is quadratic on the number of observations as opposed to the range of time of the time series. Therefore, AWarp can be several orders of magnitude faster than DTW on sparse time series. AWarp is exact for binary-valued time series and a close approximation of the original DTW distance for any-valued series. We discuss useful variants of AWarp: bounded (both upper and lower), constrained, and multidimensional. We show applications of AWarp to three data mining tasks including clustering, classification, and outlier detection, which are otherwise not feasible using classic DTW, while producing equivalent results. Potential areas of application include bot detection, human activity classification, search trend analysis, seismic analysis, and unusual review pattern mining.