GNGTS 2019 - Atti del 38° Convegno Nazionale

GNGTS 2019 S essione 3.3 755 inversion starts from a model drawn from the prior distribution; the model parameters include the number of Voronoi cells, the position of their nuclei, and the elastic properties associated to each polygon. All this a-priori information is uniformly distributed over a given parameter range, whereas the likelihood function is based on the L2 norm difference between observed and predicted AVA responses under the assumption of Gaussian distributed noise. To all the N CDP positions falling within the same cell are assigned the same elastic property values that are computed as the average of their RI and RJ values. Similarly, the average AVA response of the N CDPs constitute the observed data for the considered cell. Then the algorithm evolves by sampling the model space, that is by sampling the RI and RJ values, the number of cells, and the positions of their nuclei. The sampling is driven by the acceptance probability given in Eq. 2, in which models with better fit with the observed data and with a parsimonious parameterization (lower number of cells) are more likely to be accepted. During the iterations the algorithm tends to gather within the same Voronoi cell adjacent CDPs with similar AVA responses to which are assigned the elastic properties that produces a good fit with the observed data. At each iteration, the algorithm applies a perturbation to the current model chosen with equal probability from the following list: 1. Birth move : Create a new polygon within the Voronoi tessellation and assign the elastic properties to the newly created polygon by drawing a random realization from the prior RI and RJ distribution. Note that only the neighboring cells of the new-born cell have their geometry changed during this step. 2. Death move : Delete one polygon from the Voronoi tessellation and rearrange the shape of the remaining polygons based on the positions of their nuclei. 3. Elastic move : Randomly choose one Voronoi cell and perturb the RI and RJ values for all the CDP positions enclosed in the selected cell. This perturbation follows a Gaussian proposal centered on the current RI and RJ values. 4. Cellmove :RandomlychooseoneVoronoi cell andchange thepositionof the corresponding center without modifying the associated RI and RJ values. This perturbation will produce a slightly rearrangement of the Voronoi tessellation over the considered 2D horizon. To increase the computational efficiency of the algorithm we employ a parallel tempering strategy in which multiple and interactive chains are simultaneously run at different temperature levels. High-temperature chains ensure a wide exploration of the model space, whereas low- Fig. 1 - Schematic representation of the rjMCMC inversion.