Model Selection and Calibration with Sparse Representations

Abstract:

Data limitations and geologic heterogeneity lead to significant uncertainty in describing subsurface models and the underlying flow and transport phenomena. While prior geologic models can provide important input to constrain the spatial variability in subsurface models, in many cases several plausible, but distinct, geologic scenarios may present equally likely descriptions of the available static data. We present an effective model calibration framework for discriminating against several candidate geologic scenarios using nonlinear dynamic data. Our formulation exploits sparse representations for flexible and robust low-rank description of geologic continuity to capture field-scale reservoir connectivity under alternative geologic scenarios. This sparse formulation offers a model selection regularization that is invoked during model calibration to discriminate against proposed geologic scenarios. We demonstrate the advantages of the proposed methods using several examples and case studies.