A consistent stochastic framework to quantify large-scale geological uncertainty in stochastic seismic inversion

Geostatistical seismic inversion uses stochastic sequential simulation and co-simulation as the perturbation techniques to generate and perturb elastic models. These inversion methods allow retrieve high-resolution inverse models and assess the spatial uncertainty of the inverted properties. However, they assume a given number of a priori parametrization often considered known and certain, which is exactly reproduce in the final inverted models. This is the case of the top and base of main seismic units to which regional variogram models and histrograms are assigned. Nevertheless, the amount of existing well-log data (i.e., direct measurements) of the property to be inverted if often not enough to model variograms and its histograms are biased towards the more sand-prone facies. This work shows a consistent stochastic framework that allows to quantify uncertainties on these parameters which are associated with large-scale geological features. We couple stochastic adaptive sampling (i.e., particle swarm optimization) with global stochastic inversion to infer three-dimensional acoustic impedance from existing seismic reflection data. Key uncertain geological parameters are first identified, and reliable a priori distributions inferred from geological knowledge are assigned to each parameter. The type and shape of each distribution reflects the level of knowledge about this parameter. Then, particle swarm optimization is integrated as part of an iterative geostatistical seismic inversion methodology and these parameters are optimized along with the spatial distribution of acoustic impedance. At the end of the iterative procedure, we retrieve the best-fit inverse model of acoustic impedance along with the most probable value for the location of top and base of each seismic unit, the most likely histogram and variogram model per zone. We couple stochastic adaptive sampling (i.e., particle swarm optimization) with global stochastic inversion to infer three-dimensional acoustic impedance from existing seismic reflection data. Key uncertain geological parameters are first identified, and reliable a priori distributions of potential values are assigned to each parameter. The type and shape of each distribution reflects the level of knowledge about this parameter. Then, particle swarm optimization is integrated as part of an iterative geostatistical seismic inversion methodology and these parameters are optimized along with the spatial distribution of acoustic impedance. At the end of the iterative procedure we retrieve the best-fit inverse model of acoustic impedance along with the most probable value for the location of top and base of each seismic unit, the most likely histogram and variogram model per zone.