GNGTS 2018 - 37° Convegno Nazionale

GNGTS 2018 S essione 3.3 737 for different subsets of the DWT coefficients. The choice of the coefficient subsets is made by the Monte Carlo technique, which operates by selecting, in each wavelet scale s , N random subsets of k coefficients from the whole set consisting of 2 s DWT coefficients. For each set of coefficients, the impedance tensor is then estimated through a least square procedure. Finally, the obtained impedance vectors are normalized using a logistic transformation that scales all possible values between 0 and 1, and then, each normalized impedance tensor is transformed into a vector of eight elements used as input vector for the SOM clustering. Once the clustering procedure is over, for each cluster, the apparent resistivity and phase are evaluated in each wavelet scale by using all the wavelets coefficients that have generated the impedance tensor estimates falling in the cluster.As an example, Fig. 1 shows the results for the apparent resistivity and phase clusters by using clean data (Fig. 1a) and noisy data (Fig. 1b) obtained after the addition of a Gaussian noise to one-fifth of a synthetic MT time series. As it can be seen, in absence of noise, all the apparent resistivities and phases clusters lie on the synthetic curve, while, in presence of noise, the clusters are scattered around the synthetic noise-free curve, thus highlighting that the clustering procedure is sensitive to the presence of noise. Specifically, the SOM procedure is able to assign noisy and clean estimates to different clusters. MT data denoising through a selection criterion. The scattering of the apparent resistivity and phase values in presence of noise (see Fig. 1b) raises the problem of identifying the most reliable apparent resistivity and phase curve, especially when there is no additional information about it, which is the most common case in MT prospecting. This means that a selection criterion able to recognize, for each frequency, the most reliable resistivity and phase values is needed. The MT impedances, or equivalently the apparent resistivity and phase curves, exhibit smooth trends according to the diffusive nature of the MT field (Weidelt, 1972). Thus, basing on the idea to maximize the smoothness of apparent resistivity and phase curves, the proposed selection criterion chooses among all the resistivities (or phases) provided by the SOM clustering for each frequency, the one that minimizes the difference with the apparent Fig. 2 - Apparent resistivity and phase curves for the xy (a) and yx (b) components of the impedance tensor. These curves have been obtained by applying the SOM filter procedure on a MT signal affected by a Gaussian white random noise, with a SNR of 0.83 (83%), that has been added to one-fifth of the entire MT time series of the electric component. As it can be seen, in both images, most of the resistivities and phases lie on the synthetic noise-free curve.