GNGTS 2019 - Atti del 38° Convegno Nazionale

GNGTS 2019 S essione 3.3 757 within an angle range between 0 and 45 degrees. We considered two scenarios with different S/N ratios and with Gaussian-distributed noise affecting the data. In the first and second case the noise standard deviation is equal to 0.001 and 0.07, respectively. In both cases we use 30 chains each one running for 10000 iterations. The models sampled after 3000 iterations are used to numerically compute the posterior model but for the lack of space only the maximum- a-posteriori (MAP) solution is discussed here. For a high S/N ratio both approaches provide final MAP solutions in good agreement with the reference model and where the formation boundaries can be mapped with high accuracy. Differently, as the noise increases, the standard Bayesian algorithm without lateral constraints provides an estimated model characterized by significant scattering that is produced by the noise propagation from the data to the model space. On the contrary, the implemented rjMCMC algorithm efficiently attenuates the ill-conditioning of the inversion procedure: From the one hand, the averaging of the AVA response within the same Voronoi cell significantly increases the S/N ratio of the observed data. From the other hand, the averaging of the elastic properties estimated for the CDP positions falling within the same cell, inherently introduces lateral constraints into the inversion framework. Both these characteristics of the rjMCMC algorithm ensure a more stable inversion procedure and more reliable results. Conclusions. We used a reversible jump Markov chain Monte Carlo algorithm (rjMCMC) to include data-driven lateral constraints into target-oriented AVA inversion. The aim of this method is two-fold: increase the S/N ratio of the recorded data and automatically adapt both the parameterization of the subsurface and the lateral model constraints to the lateral variability of the observed data. Synthetic inversion tests under different S/N ratios were used to validate the implemented method and to compare its predictions to those provided by a standard Bayesian inversion algorithm without lateral constraints. Our experiments showed that in case of high S/N ratios both approaches yield similar results. For low S/N ratios the standard Bayesian approach fails to reconstruct the actual subsurface structures and provides a final prediction totally covered by noise. Differently the proposed rjMCMC ensures much more stable and reliable results, in which the lateral elastic discontinuities are accurately recovered. The superior performance of the proposed rjMCMC method is guaranteed by the transdimensional inversion framework that inherently adapts the subsurface parametrization to the lateral variability of the observed data. In other terms the rjMCMC algorithm samples solutions with an appropriate level of complexity to fit the data to statistically meaningful levels. The following step of our research is to apply the implemented algorithm to field data. Fig. 3 - Comparison between the reference model and the MAP solutions provided by the rjMCMC and by the standard Bayesian approach for different S/N ratios. RI and RJ represent the relative contrasts in the Ip and Is values at the reflecting interface, respectively.