GNGTS 2024 - Atti del 42° Convegno Nazionale

Session 3.3 GNGTS 2024 Methods We performed our training in DCT-domain as a strategy to reduce the memory storage of the dataset, to enable a fexible matching relaton between input and output second dimensions using a versatle number of coefcients, thereby facilitatng the applicaton of a reasonable number of geophones, and to reduce the number of model and data parameters during the learning process, leading to accelerate the training. The DCT is a linear orthogonal transformaton that decomposes a signal into a combinaton of cosine functons oscillatng at varying frequencies (Ahmed et al., 1974). To construct the Vs model dataset, we carefully selected a set of "base models" representng prevalent geological environments, including features like landslide, sinkholes, stratfcaton, layer displacements, and landflls. Subsequently, we generated multvariate normal random models by utlizing the mean values of these base models and fve distnct covariance matrices. To compute the seismograms, we utlized SOFI2D algorithm, an elastc forward solver proposed by Bohlen (2002). We kept fxed the hyperparameters of the forward computaton guaranteeing that the CFL conditons were satsfed, and for all the computatons we employed a Ricker wavelet of 15 Hz. In this way we generated 9500 Vs-model and data as the training dataset, with an additonal of 500 for validaton. Figure 1a depicts a schematc representaton of the neural network, showcasing the transformaton of both input seismograms and the output velocity model into the DCT domain. The architecture comprises an encoding-decoding stage, employing max-pooling and transposed convoluton, respectvely. The number of channels progressively increases from 64 to 1024, with each stage duplicatng its number untl reaching a latent space, before decoding the informaton into the truncated DCT model dimension. Figure 1b displays the training and validaton monitoring curves. Validaton is conducted on 500 seismograms and velocity models pairs that were not utlized during the training process. The Mean Square Error (MSE) Loss functon is utlized for monitoring the training (blue curve), alongside the L2-norm of the predicted data computed from the proposed model, serving as the validaton metric (orange curve). Note that with an increase in the number of epochs, both the MSE and L2-norm decrease, indicatng successful learning improvement by the network. However, afer 1300 epochs (black-dashed curve), the loss functon reached convergence, and the L2-norm becomes unstable, suggestng a potental occurrence of overftng during training.