Wavelet-like denoising of GNSS data through machine learning. Application to the time series of the Campi Flegrei volcanic area (Southern Italy)

The great potential of the Global Navigation Satellite System (GNSS) in monitoring ground deformation is widely recognized. As with other geophysical data, GNSS time series can be significantly noisy, hiding elusive ground deformation signals. Several denoising techniques have been proposed to improve the signal-to-noise ratio over the years. One of the most effective denoising techniques has been proved to be multi-resolution decomposition through the discrete wavelet transform. However, wavelet analysis requires long data sets to be effective, as well as long computation times, that hinder its use as a real or near real-time monitoring tool. We propose training by a Convolutional Neural Network (CNN) to perform the equivalent of wavelet analysis to overcome these limitations. Once trained, the CNN model provides answers within seconds, making it feasible as a real-time data analysis tool. Our Machine Learning algorithm is tested on daily GNSS time series collected in the Campi Flegrei caldera (Southern Italy), which is a highly volcanic risk area. Without significant gaps, the retrieved RMSE and R-2 values vary in the ranges 0.65-0.98 and 0.06-0.52 cm, respectively. These results are encouraging, as they hint at the possibility of applying this methodology in more effective real-time monitoring solutions for active volcanoes.