Data Assimilation in Spatio-Temporal Models with Non-Gaussian Initial States-The Selection Ensemble Kalman Model

Featured Application Porosity/permeability inversion in petroleum engineering; Log-conductivity inversion with heads and tracer data in hydrogeology; Source contribution identification in air pollution monitoring. Assimilation of spatio-temporal data poses a challenge when allowing non-Gaussian features in the prior distribution. It becomes even more complex with nonlinear forward and likelihood models. The ensemble Kalman model and its many variants have proven resilient when handling nonlinearity. However, owing to the linearized updates, conserving the non-Gaussian features in the posterior distribution remains an issue. When the prior model is chosen in the class of selection-Gaussian distributions, the selection Ensemble Kalman model provides an approach that conserves non-Gaussianity in the posterior distribution. The synthetic case study features the prediction of a parameter field and the inversion of an initial state for the diffusion equation. By using the selection Kalman model, it is possible to represent multimodality in the posterior model while offering a 20 to 30% reduction in root mean square error relative to the traditional ensemble Kalman model.