We have developed a new iterative geostatistical seismic amplitude variation with angle (AVA) inversion algorithm that inverts prestack seismic data, sorted by angle gathers, directly for high-resolution density, P-wave velocity, S-wave velocity, and facies models. This novel iterative geostatistical inverse procedure is based on two key main principles: the use of stochastic sequential simulation and cosimulation as the perturbation technique of the model parameter space and a global optimizer based on a crossover genetic algorithm to converge the simulated earth models toward an objective function, in this case, the mismatch between the recorded and synthetic prestack seismic data. As a geostatistical approach, all the elastic models simulated during the iterative procedure honors the well-log data at its own locations, the marginal prior distributions of P-wave velocity and S-wave velocity, and density estimated from the available well-log data, and the corresponding joint distributions between density versus P-wave velocity and P-wave versus S-wave velocity. We successfully tested and implemented this new algorithm on a synthetic prestack data set that mimicked the main properties of a real reservoir, and on a real seismic data set acquired over a deepwater turbidite oil reservoir. In both cases, the results showed a good convergence between the recorded and synthetic seismic. The synthetic example showed high-resolution inverted petroelastic models that reproduced the true petroelastic models. The inverted petroelastic models retrieved from the real case study found high resolution and do agree with previous seismic reservoir characterization studies.

Due to the nature of seismic inversion problems, there are multiple possible solutions that can equally fit the observed seismic data while diverging from the real subsurface model. Consequently, it is important to assess how inverse-impedance models are converging toward the real subsurface model. For this purpose, we evaluated a new methodology to combine the multidimensional scaling (MDS) technique with an iterative geostatistical elastic seismic inversion algorithm. The geostatistical inversion algorithm inverted partial angle stacks directly for acoustic and elastic impedance (AI and EI) models. It was based on a genetic algorithm in which the model perturbation at each iteration was performed recurring to stochastic sequential simulation. To assess the reliability and convergence of the inverted models at each step, the simulated models can be projected in a metric space computed by MDS. This projection allowed distinguishing similar from variable models and assessing the convergence of inverted models toward the real impedance ones. The geostatistical inversion results of a synthetic data set, in which the real AI and EI models are known, were plotted in this metric space along with the known impedance models. We applied the same principle to a real data set using a cross-validation technique. These examples revealed that the MDS is a valuable tool to evaluate the convergence of the inverse methodology and the impedance model variability among each iteration of the inversion process. Particularly for the geostatistical inversion algorithm we evaluated, it retrieves reliable impedance models while still producing a set of simulated models with considerable variability.