Calibration of Imperfect Geophysical Models by Multiple Satellite Interferograms with Measurement Bias

Abstract

Model calibration consists of using experimental or field data to estimate the unknown parameters of a mathematical model. The presence of model discrepancy and measurement bias in the data complicates this task. Satellite interferograms, for instance, are widely used for calibrating geophysical models in geological hazard quantification. In this work, we used satellite interferograms to relate ground deformation observations to the properties of the magma chamber at K i¯lauea Volcano in Hawai‘i. We derived closed-form marginal likelihoods and implemented posterior sampling procedures that simultaneously estimate the model discrepancy of physical models, and the measurement bias from the atmospheric error in satellite interferograms. We found that model calibration by aggregating multiple interferograms and downsampling the pixels in the interferograms can reduce the computation complexity compared to calibration approaches based on multiple data sets. The conditions that lead to no loss of information from data aggregation and downsampling are studied. Simulation illustrates that both discrepancy and measurement bias can be estimated, and real applications demonstrate that modeling both effects helps obtain a reliable estimation of a physical model’s unobserved parameters and enhance its predictive accuracy. We implement the computational tools in the RobustCalibration package available on CRAN.

KEYWORD:

• Bayesian inference
• Data aggregation
• Identifiability
• Prediction
• Prior
• Radar interferogram

Acknowledgments

The authors thank the editor, AE, Chuck Wicks, and two referees for their comments that substantially improved the article. Any use of trade, firm, or product names is for descriptive purposes only and does not imply endorsement by the U.S. Government.

Additional information

Funding

This research is supported by the National Science Foundation under Award No. DMS-2053423.