GNGTS 2019 - Atti del 38° Convegno Nazionale

754 GNGTS 2019 S essione 3.3 (AVA) inversion. In our case target-oriented means that only the AVA responses of the target layer are inverted, and these AVA responses are extracted for each considered CDP position. The results are 2D maps representing the lateral variability of the elastic contrasts along the considered reflecting interface. The AVA inversion is a severely ill-conditioned problem highly affected by noise contamination in which it is crucial adopting a reliable regularization strategy to retrieve reliable and stable results. In a transdimensional inversion the number of model parameters (that codes the optimal subsurface model parameterization) is considered unknown and is estimated using a probabilistic sampling. In our case the inverted 2D horizon is divided into Voronoi cells, whose number and shape are automatically determined by the rjMCMC sampling. The algorithm autonomously partitions the considered 2D horizon on the basis of the spatial variability of data, producing subsurface 2D models discretized in Voronoi polygons each one enclosing CDP positions with similar AVA responses. This also means that the CDPs falling within the same cell also share similar elastic properties and for this reason the same elastic property values are assigned to these CDPs. These values are computed by averaging the model properties pertaining to the CDPs falling within each cell. Similarly, the observed data for each polygon is computed by averaging the AVA responses of the CDPs falling within each Voronoi cell. From the one hand, this strategy constitutes a data-driven approach to include lateral constraints into the AVA inversion because these constraints are automatically inferred from the lateral variability of the data and not arbitrarily infused into the inversion framework. From the other hand, the averaging of the AVA responses pertaining to CDPs falling within the same cell inherently increases the signal-to-noise (S/N) ratio of the observed data. These two aspects revealed to be of crucial importance for stabilizing the inversion even in case of severely noise-contaminated data. For the lack of field data, we test the implemented rjMCMC algorithm performing synthetic inversions with different S/N ratios. The proposed method is benchmarked against a more standard Bayesian AVA inversion without lateral constraints. The method. In case of parameterizations with different number of unknowns n , the Bayes theorem can be written as (Bodin and Sambridge 2009): (1) where d is the observed data vector, and m is the model parameter vector. The left-hand side term of equation 1 is the target PPD that could be numerically estimated from the ensemble of models sampled by the MCMC algorithm. In a transdimensional rjMCMC, the Metropolis- Hasting rule that determines the acceptance probability α (that is the probability to move from a model m with dimension n to a model m΄ with dimension n΄ at a given step of the chain) becomes: (2) where J is the Jacobian of the transformation from m to m΄ and is needed to account for the scale changes when the transformation involves a jump between models with different dimensions; q () is the proposal distribution that defines the new model m΄ as a random deviate from a probability distribution q ( m΄|m ) conditioned only on the current model m . As the forward modelling we use the Ursenbach and Stewart equations (Ursenbach and Stewart, 2008) that constitutes an approximation of the exact Zoeppritz equations, parameterized in terms of relative contrasts in P-impedance and S-impedance ( RI and RJ , respectively) at the reflecting interface. We discretize the investigated 2D horizon using the Voronoi polygons defined over equally spaced grid points representing the CDP positions. A discrete set of points, the center of the Voronoi cells, partitions the considered 2D horizon and each cell encloses the CDP gathers with the smallest distance from the center of the associated Voronoi polygons. The