GNGTS 2022 - Atti del 40° Convegno Nazionale

GNGTS 2022 Sessione 3.3 523 Synthetic inversion tests. Initially, we trained and tested the above-mentioned architectures (Fig. 1) on synthetic noise-free data. The forward Dix operator was used to calculate the rms velocity profile corresponding to the predicted interval velocity profiles (Fig. 2). Overall, increasing the depth of the FC-ANNs improved the performance on predicting interval velocity profiles. We expressed the accuracy in terms of the rmse between desired and predicted interval velocity profiles and between desired and predicted rms velocity profiles. Despite the good performance, considering noise-free data the (finite precision) analytic Dix inversion resulted in higher accuracy than the FC-ANNs (Fig. 2). However, the application to noisy data allowed us to evaluate the capability of the FC-ANNs to tackle the ill-conditioning of the Dix inversion. In particular, the training, validation, and test rms velocity profiles were contaminated with noise vectors drawn from a gaussian distribution with mean equal to 0 km/s and standard deviation equal to 0.05 km/s. Fig. 2 - Inversion results on synthetic data from different methods: analytic solution (a), 1 hidden layer FC-ANN (b), 2 hidden layers FC-ANN (c), and the 3 hidden layers FC-ANN (d). The predicted and desired interval velocity profiles are the blue and black lines, respectively. The re-calculated and desired rms velocity profiles are the red and green lines, respectively. The rmse for the interval and rms velocity profiles are listed in the title of the figures. The results showed that the deepest architecture performed better than the shallower ones, although the differences in performance were less evident than in the noise free test. To test the robustness of the FC-ANNs with respect to the statistics governing the noise contaminating the training dataset, we contaminated the test dataset with noise realizations generated under different statistical assumptions (standard deviation equal to 0.1 km/s) and normalized to the energy of the previous noise realizations. The deepest architecture (3 hidden layers) performed better than the shallower ones in predicting the interval velocity profiles. However, the differences in performance were again less evident than in the noise free test. Contrary to the results obtained on noise free data, FC-ANNs trained on noise contaminated inputs led to better performances than the analytic solution that in turn led to un-physical results.