Data-Driven Confidence Intervals for Parametric Magnetotelluric Impedance Tensor Estimates

Uncertainties for conventional nonparametric magnetotelluric (MT) impedance tensor estimates are typically quantified by analytic and asymptotic confidence bounds. Here, we consider MT impedance tensor confidence bounds for parametric estimates to both facilitate their interpretation and comparison to conventional nonparametric estimates. In addition to the standard asymptotic confidence bounds from system identification, we propose several resampling methods based on three strategies: subsampling (SB), moving block bootstrap (BS), and model-based resampling (MR). We applied these data-driven approaches to an MT dataset exhibiting strong interference to demonstrate resampling-based methods for accurate and reliable confidence bound determination, especially when the data is limited or exhibits poor data quality. This study also investigates various practical considerations, providing a viable and comprehensive approach for both parametric MT impedance tensor estimation and associated uncertainty determination.