GNGTS 2016 - Atti del 35° Convegno Nazionale

516 GNGTS 2016 S essione 3.1 here, which involves genetic algorithms (GAs) and a Markov Chain Monte Carlo resampler, provides also the uncertainties associated with the maximum a posteriori model, that is, it returns Posterior Probability Distributions (PPD) of the model parameters. These PPDs in turns can be propagated via Local FWI (LFWI) to obtain high-resolution estimates of the PPDs. To make the GAs inversion computationally feasible, we apply a two-grid approach that uses a coarse grid with a variable grid spacing in the optimization phase and a fine regular grid in the forward modelling phase. To obtain unbiased estimates of the GA PPD we importance sample the GA-model ensemble by means of a Gibbs sampler (GS). We validate the reliability of the GA FWI+GS approach by checking the uncertainty propagation from the starting models to the final LFWI models. This procedure has been tested on a variation of the 2D acoustic inclusion model of Mora (1989). It results that the multimodal and wide marginal PPDs derived from the global optimization (GA FWI+GS) become unimodal and narrower after local FWI and, in the most illuminated part of the subsurface, contain the true model parameters. This indicates that the set of models derived from the GA+GS PPD produces an ensemble of starting models that enable local FWI to converge toward the same model-space region. The practical use of this method is presently limited to 2D and acoustic inversions due to the intensive computational cost of this procedure. Acknowledgements. We wish to thank ENI for the continued support in this research. References Aleardi, M., Mazzotti, A.; 2016; 1D elastic full-waveform inversion and uncertainty estimation by means of a hybrid genetic algorithm-Gibbs sampler approach, Geophysical Prospecting. doi:10.1111/1365-2478.12397. Fernández-Martínez, J.L., Fernández Muñiz, Z., Tompkins, M.J.; 2012; On the Topography of the Cost Functional in Linear and Nonlinear Inverse Problems, Geophysics, 77 (1), W1-W15. ���� ���������������������� doi: 10.1190/geo2011-0341.1 Holland, J. H.; 1975; Adaptation in natural and artificial systems. Ann Arbor, MI: University of Michigan Press. Mora, P.; 1989; Inversion=migration+tomography, Geophysics, 54 (12), pp. 1575–1586. ���� ����������������� doi: 10.1190/1.1442625 Sajeva, A., Aleardi, M., Stucchi, E., Bienati, N., Mazzotti, A. [2016] Estimation of acoustic macro-models using a genetic full-waveform inversion: Applications to the Marmousi model. Geophysics, 81 (4): pp. R173-184. ����doi: 10.1190/geo2015-0198.1 Sambridge, M.; 1999; Geophysical Inversion with a Neighbourhood Algorithm--II. Appraising the Ensemble. Geophysical Journal International, 138 (3), pp. 727–746. doi: 10.1046/j.1365-246x.1999.00900.x Schlierkamp-Voosen, D., M���������� ��� ����� ���������� ������ ��� ��� ������� ������� ���������� ������������ ühlenbein, H.; 1993; Predictive models for the breeder genetic algorithm. Evolutionary Computation 1 (1), 25-49. doi:10.1162/evco.1993.1.1.25 Tognarelli, A., Stucchi, E., Bienati, N., Sajeva, A., Aleardi, M. and Mazzotti, A.; 2015; Two-grid Stochastic Full Waveform Inversion of 2D Marine Seismic Data. In 77th EAGE Conference and Exhibition, doi: 10.3997/2214- 4609.201413197. Fig. 3 – The cloud of model parameters organized as vertical slices for three offsets from the far left to the center of the model; from left to right: at offsets 0 m, 2000 m, and 4500 m. Note that the cloud of final models (cyan beam) gets thinner moving toward the center.