Surrogate model based iterative ensemble smoother for subsurface flow data assimilation

Subsurface geological formation properties often involve some degree of uncertainty. Thus, for most conditions, uncertainty quantification and data assimilation are necessary for predicting subsurface flow. The surrogate model based method is one common type of uncertainty quantification method, in which a surrogate model is constructed for approximating the relationship between model output and model input. Based on the prediction ability, the constructed surrogate model can be utilized for performing data assimilation. In this work, we develop an algorithm for implementing an iterative ensemble smoother (ES) using the surrogate model. We first derive an iterative ES scheme using a regular routine. In order to utilize surrogate models, we then borrow the idea of Chen and Oliver (2013) to modify the Hessian, and further develop an independent parameter based iterative ES formula. Finally, we establish the algorithm for the implementation of iterative ES using surrogate models. Two surrogate models, the PCE surrogate and the interpolation surrogate, are introduced for illustration. The performances of the proposed algorithm are tested by synthetic cases. The results show that satisfactory data assimilation results can be obtained by using surrogate models that have sufficient accuracy.