• DCT
• FWI
• neural networks

Full waveform inversion (FWI) aims to use the full information content of the seismic waveforms to reconstruct high-resolution images of the subsurface. Usually, the FWI is solved through a deterministic approach in which an optimization algorithm is used to minimize a data misfit function. This method face challenges, especially related to the need of a good initial model, cycle-skipping issues, and interparameter crosstalk. Additionally, the deterministic strategy lacks the ability to estimate model uncertainties accurately, which is crucial for a comprehensive interpretation of the results. To address these limitations, a probabilistic approach could be adopted and in this context a Monte Carlo algorithm might be used to numerically sample the posterior probability density (PPD) function, which fully expresses the model uncertainties. However, this numerical sampling needs high computational costs related to the large numbers of forward modelling evaluations. In this thesis, I propose to accelerate both deterministic and probabilistic FWI for near surface investigations, utilizing neural network data-driven starting models. We limited to elastic synthetic examples to assess the feasibility of the proposed method, and we use a finite-difference (FD) forward modelling code to generate the seismic data from the subsurface elastic models. For what concerns the probabilistic inversion we use a gradient-based MCMC algorithm.

First, to determine the optimal hyparameters settings for the finite-difference code, we conducted a 1D benchmark test in which the FD results are compared with the analytical solution as provided by the reflectivity method. The aim of this procedure is to identify the appropriate number of points per wavelength to be used in the generation of the training set for the network, thus, to find the optimal compromise between the accuracy of the simulated seismic gathers and the related computational cost.

After this preliminary study I introduce the Elastic Model Proposal Fully-Connected-Network (eMP-FCN) as a supervised data-driven model prediction deep-learning approach. The eMP-FCN combines Neural Networks together with Discrete Cosine Transform (DCT) compression techniques to learn the non-linear mapping from the data to the model space in the DCT-domain. To the best of my knowledge, this work represents the first approach to employing surface-waves data-driven training for predicting near-surface shear-wave velocity models. I trained the FCN using image- to-image relationships in the DCT-domain, thus reducing training costs and facilitating feature size relations. Training in DCT-domain also allowed us to relate data and models with different size-dimensions, this is extremely useful to address common scenarios in near-surface with limited number of channels. The Vs-model training dataset is created encompassing random realizations representing near-surface common geology scenarios like landslide features, sinkholes, stratification, layer displacements, and landfills.

The results of my work, showcase the efficacy of integrating FCN-generated starting models within a probabilistic framework, resulting in a substantial reduction in the computational time needed to reach the burn-in period (i.e. the number of iterations after which the sampling of the PPD starts). Furthermore, I found that employing the FCN-predicted Vs models as a starting point for the deterministic approach not only diminishes computational expenses but also mitigates the convergence toward suboptimal (local) solutions. Finally, in situations where the calculated data from the proposed eMP-FCN model exhibits an exceptionally close match to the observed data, the predicted model itself could potentially function as a suitable "general solution", obviating the need for an inversion procedure.