Noise Analysis of InSAR SBAS-derived Deformation Time Series: Tests on Simulated Data

Earth deformation rates are usually derived by fitting a linear function to the InSAR-retrieved time series. This implicitly assumes that only white (Gaussian) noise is present in these time series, and will be incorrect if temporally-correlated (i.e., coloured) noise is present. Accurate estimates of functional model parameters (e.g., displacement velocity) and their errors require the use of a correct noise model. The objective of this study is to analyse the content of the noise in deformation time series by applying Maximum Likelihood Estimation (MLE) method. The MLE is applied in this study because of its advantages over the spectral analysis method. This is carried out by generating simulated interferograms, then applying the Small Baseline Subset (SBAS) method to derive deformation time series for pixels, then analyse noise content for these time series. We found that the combination of white noise plus flicker noise is the model that best describes the noise characteristics of the data in this study. It is also shown that, though the interferograms are individually simulated, the temporally-correlated noise is present. A long time series is generally required for a correct result of noise analysis. The simulated data comprise a network of 2,510 interferograms covering a 10-year time period. Each interferogram contains an assumed deformation signal degraded by simulated noise sources: digital elevation model error, atmospheric artefacts, orbital error, and temporal decorrelation. The 'true' (simulated) deformation signal is computed from a linear trend (bounded within the range -40 to +40 mm/yr) plus an annual function with amplitude limited between 10-20 mm. The SBAS technique is applied to derive deformation time series for the whole simulated imagery of 500x500 pixels. The deformation time series of 25 regularly-distributed pixels are extracted and analysed for their noise content in the public-domain Create and Analyze Time Series (CATS) package. The amplitude of white and coloured noise together with the spectral indices of these 25 pixels are then derived. The results show that the spectral indices vary between -0.2±0.2 and -1.5±0.4 with a mean value of -0.8±0.1 that is closer to flicker noise spectral index (κ=-1) than that of random walk (κ=-2).