GNGTS 2022 - Atti del 40° Convegno Nazionale

GNGTS 2022 Sessione 3.3 483 The standard deviation map suggests small deviations in the shallow parts of the model, where we have good data coverage and good illumination. These small deviations indicate that the predicted velocity values are well constrained in these areas and the inversion results have less uncertainties. On the other hand, the deeper parts and the edges of the model have higher variations (0.3 km / s and above) due to poor data coverage and poor illumination, and so the inverted velocity values are less constrained and have a wider range of values, suggesting larger uncertainties. The highest variations correspond, as expected, to the low velocity anomaly in the bottom right corner of the model (around 1.2 km / s ). Conclusions. In this work we have presented a GB-MCMC sampling method based on the Bayesian inference framework to solve the ill-posed inverse problem in high dimensions. We have shown that, with the help of the local gradient and Hessian information, a proposal distribution which is a good approximation of the posterior distribution, is easy to construct and samples can be drawn efficiently from the proposal. We have shown the results of the GB- MCMC FWI applied to a synthetic model and, unlike the traditional local optimization-based FWI methods, we have obtained statistical assessments by which the uncertainties related to the inversion can be estimated. The following steps of our research are to use more chains and to mix the information brought from each chain, using the so-called Differential Evolution Markov Chain (DEMC), in order to increase the efficiency and the rate of convergence, and to apply the implemented algorithm to field data. REFERENCES Aleardi M.; 2021: A gradient-based Markov chain Monte Carlo algorithm for elastic pre-stack inversion with data and model space reduction . Geophysical Prospecting 69(3), doi:10.1111/1365-2478.13081. Hastings W. K.; 1970: Monte Carlo sampling methods using Markov chains and their applications . Biometrika, 57, 97–109. Louboutin M., Lange M., Luporini F., Kukreja N., Witte, P.A., Herrmann F.J., Velesko P., Gorman G.J.; 2019: Devito (v3.1.0): an embedded domain specific language for finite differences and geophysical exploration. Geoscientific Model Development 12, 1165–1187. Mosegaard K. and Tarantola A.; 2002: Probabilistic approach to inverse problems . International Geophysics Series, 81, 237–268. Virieux J. and Operto S.; 2009: An overview of full-waveform inversion in exploration geophysics . Geophysics, 74, no. 6, WCC1–WCC26, doi:10.1190/1.3238367.