Signal stationarity testing and detecting of its abrupt change

Abstract

Automatic testing of stationarity and detecting of its abrupt change are of primary importance in numerous applications ranging from exploratory data analysis to diagnosis or surveillance. In which case, we are interested in points where the signal stationarity is violated. We consider the problem of how to detect these change-points, which we identify by finding sharp changes in the signal characteristics. Several different methods are considered. Here we suggest a method for detecting and picking these abrupt changes automatically. We divide a record into intervals of equal lengths and check the "local stationarity" between two consecutive intervals by using cross correlation. Because of its ability to accentuate abrupt changes in the signal frequency, it can be effectively employed to detect weak signals in a stationary noise background. In this paper we demonstrate the technique on the problem of detecting and picking P-arrival phase seismic. The intervals have approximately the same characteristics when these include only background noise. But, the similarity breaks abruptly when a seismic signal arrives. This break of similarity makes us possible to detect P-wave arrival. Because the method can detect changes both in frequency and amplitude we can use it on a basic problem in seismic data analysis, which is recognition of weak signals in the presence of ambient noise.