Behnam Jafarpour, Texas A&M University

IAMCS Workshop in Large-Scale Inverse Problems and Uncertainty Quantification

February 24-25, 2011

Stephen W. Hawking Auditorium

George P. and Cynthia Woods Mitchell Institute for Fundamental Physics and Astronomy

Texas A&M University

College Station, Texas

Model Error Identification Using Sparsity-Based Inversion Techniques for Subsurface Characterization

Insufficient data and imperfect modeling assumptions are two main contributors to uncertainty in subsurface characterization and predictive flow and transport modeling. Failure to account for these sources of uncertainty can lead to biased inverse modeling solutions and inaccurate predictions. Data scarcity necessitates the incorporation of direct or indirect prior information for well-posed inverse problem formulation and stable solution algorithms. Traditionally, in constraining predictive models, structural prior assumptions (e.g., a covariance model) are treated with certainty. However, prior continuity models are typically derived from incomplete information and can be subject to significant uncertainty that, if ignored, can lead to biased solutions with little predictive power. I will discuss a new algorithm for incorporation of prior information while protecting against errors in it. To do this, the prior information is included in the model calibration process by assuming a wide range of variability (uncertainty) in it. Incorporating a wide range of prior structural variability implies that a significant portion of the prior features has negligible contribution to reconstruction of the final solution. I will present a sparse model representation and inversion approach that provides an effective framework for posing and solving the resulting inverse problem.