Multidimensional wavelet analysis of geophysical monitoring time series

A method for the analysis of low-frequency geophysical monitoring time series based on the concept of the wavelet-aggregated signal previously introduced by the author is proposed. The goal of this study is the recognition of the time intervals during which the intensity of small-scale variations synchronously occurring in all time series increases. A similar problem was previously studied by the author when searching for fast spectral variations (disarrangement) in the high-frequency component of a given signal simultaneously present in all time series analyzed. This common signal was previously extracted from the aggregated signal constructed on the basis of the classic Fourier transform of the initial time series, and the time moments of the disarrangement discovered in low-frequency monitoring problems were called "slow events" by analogy with slow earthquakes. Such anomalies can indicate motions on block boundaries and fracture of the crustal material and are relevant to the search for critical geophysical phenomena. Based on the joint processing of variations in the groundwater level measured in four aquifers in the Moscow region during the period from 1993 through 1997, this paper addresses the application of orthogonal wavelets as compared with the ordinary Fourier basis.