Abstract
The objective of most formulations of inverse modeling in the Earth Sciences is to estimate the model parameters given the observation data. In this paper, an additional element to these formulations is considered, namely, the prediction for which the models are built. An example of such modeling is the prediction of solute transport using geological models of the subsurface constrained to existing geophysical, flow dynamic and solute observations. The paper then illustrates and addresses a fundamental question relating data, model and prediction: does model inversion reduce uncertainty in prediction variables given the observed data? To investigate this question, a diagnostic tool is proposed to assess whether matching the observed data significantly reduces uncertainty in the prediction variables. In addition, for some cases, a quick estimate of uncertainty can be obtained without applying inverse modeling. It relies on a dimensionality reduction method using non-linear principal component analysis (NLPCA) calibrated from evaluating the prediction and data response variables on a few prior Earth models. The proposed diagnostic tool is applied on a simple example of tracer flow and, for the cases investigated, the NLPCA provided an accurate diagnostic and a satisfactory pre-estimation of uncertainty in the prediction variables.
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Acknowledgments
The authors would like to acknowledge the Swiss National Science Foundation for financial support under the contract CRSI22 122249/1: Integrated methods for stochastic ensemble aquifer modeling (ENSEMBLE) project.
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Scheidt, C., Renard, P. & Caers, J. Prediction-Focused Subsurface Modeling: Investigating the Need for Accuracy in Flow-Based Inverse Modeling. Math Geosci 47, 173–191 (2015). https://doi.org/10.1007/s11004-014-9521-6
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DOI: https://doi.org/10.1007/s11004-014-9521-6