Abstract
Abstract. Interpretation of land subsidence time-series to understand the evolution of the phenomenon and the existing relationships between triggers and measured displacements is a great challenge. Continuous wavelet transform (CWT) is a powerful signal processing method mainly suitable for the analysis of individual nonstationary time-series. CWT expands time-series into the time-frequency space allowing identification of localized nonstationary periodicities. Complementarily, Cross Wavelet Transform (XWT) and Wavelet Coherence (WTC) methods allow the comparison of two time-series that may be expected to be related in order to identify regions in the time-frequency domain that exhibit large common cross-power and wavelet coherence, respectively, and therefore are evocative of causality. In this work we use CWT, XWT and WTC to analyze piezometric and InSAR (interferometric synthetic aperture radar) time-series from the Tertiary aquifer of Madrid (Spain) to illustrate their capabilities for interpreting land subsidence and piezometric time-series information.
Highlights
The study of the existing relationships between ground displacements associated with land subsidence caused by aquifer-system compaction and the principal driving factor, groundwater levels, is a key aspect to understand the mechanisms driving this type of land subsidence
When two time series are analysed the Cross Wavelet Transform (XWT) and Wavelet Transform Coherence (WTC) techniques permit the identification of the common cross-wavelet power and wavelet co
The wavelet powers computed from the Continuous Wavelet Transform (CWT) clearly show the linear variability of the period with time
Summary
The study of the existing relationships between ground displacements associated with land subsidence caused by aquifer-system compaction and the principal driving factor, groundwater levels, is a key aspect to understand the mechanisms driving this type of land subsidence These relationships are usually studied using the analysis of time series of displacements and water levels. Quantitative analysis typically entails evaluating correlations in the frequency domain, assuming that the underlying processes are stationary, i.e. the mean, variance and autocorrelation structure do not change over time (Grinsted et al, 2004) In these cases, the analysis of the Fourier-transformed time series allows the identification of the dominant frequencies for a specified frequency bandwidth, which tends to ignore localized temporal information. When two time series are analysed (e.g. ground displacements and groundwater levels) the Cross Wavelet Transform (XWT) and Wavelet Transform Coherence (WTC) techniques permit the identification of the common cross-wavelet power and wavelet co-
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