Modelling and Optimization Techniques for Acoustic Full Waveform Inversion in Seismic Exploration

Full Waveform Inversion has become an important research field in the context of seismic exploration, due to the possibility to estimate a high-resolution model of the subsurface in terms of acoustic and elastic parameters. To this aim, issues such as an efficient implementation of wave equation solution for the forward problem, and optimization algorithms, both local and global, for this high non-linear inverse problem must be tackled. In this thesis, in the framework of 2D acoustic approximation, I implemented an efficient numerical solution of the wave equation based on a local order of approximation of the spatial derivatives to reduce the computational time and the approximation error. Moreover, for what concerns the inversion, I studied two different global optimization algorithms (Simulated Annealing and Genetic Algorithms) on analytic functions that represent different possible scenarios of the misfit function to estimate an initial model for local optimization algorithm in the basin of attraction of the global minimum. Due to the high number of unknowns in seismic exploration context, of the order of some thousands or more, different strategies based on the adjoint method must be used to compute the gradient of the misfit function. By this procedure, only three wave equation solutions are required to compute the gradient instead of a number of solutions proportional to the unknown parameters. The FWI approach developed in this thesis has been applied first on a synthetic inverse problem on the Marmousi model to validate the whole procedure, then on two real seismic datasets. The first is a land profile with two expanding spread experiments and is characterized by a low S/N ratio. In this case, the main variations of the estimated P-wave velocity model well correspond to the shallow events observed on the post-stack depth migrated section. The second is a marine profile extracted from a 3D volume where the local optimization, based on the adjoint method, allows to estimate a high-resolution velocity model whose reliability has been checked by the alignment of the CIGs computed by pre-stack depth migration.