GNGTS 2022 - Atti del 40° Convegno Nazionale

522 GNGTS 2022 Sessione 3.3 DIX INVERSION THROUGH MACHINE LEARNING M. Tavoletti 1,2 , F. Bleibinhaus 2 , F. Grigoli 1 , E. Stucchi 1 1 University of Pisa, Earth Sciences Department, Pisa, Italy 2 Montanuniversität Leoben, Department of Applied Geosciences and Geophysics, Leoben, Austria Introduction. Over the past years, machine learning algorithms have been increasingly popular in geophysics (Yu and Ma, 2021) as an alternative to standard approaches. Along this path, this work investigates the applicability of fully connected artificial neural networks (FC-ANNs; LeCun et al. , 2015) to solve the Dix inversion (Dix, 1955) which is known to be an ill-conditioned inverse problem. The Dix inversion is linear when considering the square of the interval velocity to be the unknown, however regularized inversion techniques are needed to tackle the ill-conditioning of this inverse problem (Koren and Ravve, 2006). In this work we propose the use of FC-ANNs to retrieve interval velocity profiles from the root-mean-square (rms) ones while tackling the ill conditioning of the Dix Inversion. Solving an inverse problem with machine learning corresponds to approximating the mapping done by the inverse operator given the so-called training dataset, which consists of a set of observed data (input) and the set of the correspondent model parameters (output). In the Dix inversion perspective, the input data is represented by rms velocity profiles while the correspondent blocky interval velocity profiles are the output data. One of the issues in the practical application of ANNs to approximate inverse operators, is the availability of large enough training dataset (real data). In this study we train FC-ANNs with synthetic data and then test it with a real marine seismic dataset (Line 12 of the Viking-Graben 2D marine dataset). The method. We started generating a synthetic labelled dataset composed by 10,000 regularly sampled blocky interval velocity profiles and the corresponding rms velocity profiles. Each velocity profile was represented in the time-domain and was composed by 1,001 samples with a sampling rate of 0.001 s. We then split the synthetic dataset in subsets of 9,000, 750, and 250 examples for the training, validation, and test datasets, respectively. In this study, we used the 3 FC-ANNs represented in Fig. 1. The training dataset was exploited to update the internal parameters of the FC-ANNs minimizing the L2-norm loss function for a fixed number of epochs equal to 5,000. The validation dataset was used only to evaluate the evolution of the training phase and not to update the internal parameters of the networks. After the training phase, we used the test dataset to evaluate if the updated network parameters approximated a proper mapping between a rms velocity profile and the correspondent interval velocity profile. Fig. 1 - Simplified sketch of the 3 fully connected artificial neural networks (FC-ANNs) used in this work. In red the input layer, in yellow the hidden layer(s), and in green the output layer; each layer is composed by 1001 units. For simplicity, the bias terms are omitted. The FC-ANN with 1 hidden layer (a) exploits the tanh activation function. The FC-ANN with 2 hidden layers (b) exploits the ReLU and the tanh for the 1 st and 2 nd layer, respectively. The FC-ANN with 3 hidden layers (c) exploits the ReLU for the 1 st and 2 nd layer and the tanh for the 3 rd layer.