GNGTS 2013 - Atti del 32° Convegno Nazionale

an acoustic approximation. This low frequency range combined with a finite difference seismic propagator allowed us to use a very wide grid (where the distance between each node is 288 m in every spatial direction) without dealing with numerical dispersion during the forward model computations. The consequent low number of model parameters (16 cells along the x direction and 4 in the z direction) allowed us to use a global optimization method. We simulated a 3D seismic propagation on a 2D model with in-line extension of 4600 m, and a maximum depth of roughly 800 m (see Fig. 3a). Regarding the seismic acquisition parameters, we used 15 shot points and 60 geophones, a source interval of 288 m and a receiver distance equal to 72 m. For the inversions, we considered the admissible range for each model parameter to be 400 m/s wide and set around the true value. In the NA inversion, the user defined parameters were set to ns =128 and nr =32 for 320 iterations. This parameters were chosen following the rule of thumb given by Sambridge (1999a) that links the free-parameters to the dimension of the model space. With the GA we chose the following control parameters: 300 individuals for the population of each generation and maximum number of 30 generations; a selection rate of 0.8 (which means that for each generation we replaced the 80% of models, while the remaining best 20% survived unchanged); we used a mutation rate of 10%, and a selection pressure of 2 over a linear ranking. We divided the population in 20 subpopulations, that migrated every 15 generations into each other. Figs. 3b and 3c show the differences between the true and the inverted model for both the GA and NA optimization, respectively. Note a better convergence of GA with respect to NA. Fig. 3 – The true acoustic model (a); difference between the true model and the final computed model for NA (b) and for GA (c) inversions, respectively. The evolution of the misfit with respect to the iterations in the NA inversion (d), and with respect to the generations in the GA inversion (e). In (d) the current minimum misfit per iteration and the global current minimum misfit per iteration are shown. In (e) each colored line represents the misfit evolution of a different subpopulation. 64 GNGTS 2013 S essione 3.1