Coupling geological and seismic interpretation uncertainty into geostatistical seismic inversion

Petro-elastic models retrieved from seismic inversion allow inferring the spatial distribution of the subsurface properties of interest, for example, acoustic impedance and porosity, to allow better reservoir characterization and field management (Bosch et al. 2010). Geostatistical seismic inversion methodologies allows retrieving considerable different petro-elastic inverse models that generate synthetic seismic with a good match against the recorded one. However, these models are plagued with different levels of uncertainty due to the intrinsic nature of seismic inversion problems: ill-posed, nonlinear and with non-unique solutions (Tarantola 2005). There is a potential in simultaneously assessing uncertainty and integrating data with different resolution (i.e., well-log and seismic reflection data) through iterative geostatistical seismic inversion methodologies (e.g. Bortoli et al, 1993, Soares et al. 2007, Nunes et al. 2012, Azevedo et al. 2015), which has rapidly increased its importance for seismic reservoir characterization studies. This family of inversion methodologies are based on stochastic sequential simulation as a model perturbation technique and a genetic algorithm, driven by the local mismatch between real and synthetic seismic traces, as the global optimizer of the iterative procedure. There are advantages and pitfalls in the use of stochastic sequential simulation for the model perturbation. On one hand it allows assessing spatial variability of the inverted properties, on the other hand it assumes no uncertainty in the reproduction of a given spatial continuity pattern, imposed for example by a variogram model, and the probability distribution of the elastic properties of interest in all the models generated during the iterative procedure. This work introduces a statistical framework that couples stochastic adaptive sampling and Bayesian inference to assess uncertainty associated with the large scale geological parameters such as: regional variogram models ranges, regional probability distribution for the elastic property of interest and the structural and stratigraphic interpretation. The proposed methodology was tested and implemented in a real case study from an onshore Middle East field. The results show how the synthetic seismic reflection data matches the recorded one with respect to uncertainty in the large-scale geological parameters.