  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.
