Uncertainty quantification in electrical resistivity tomography inversion: Hybridizing block-wise bootstrapping with geostatistics

Electrical resistivity tomography inversion often encounters uncertainty stemming from two primary sources: epistemic uncertainty, arising from imperfect underlying physics and improper initial approximation of model parameters, and aleatory variability in observations due to measurement errors. Despite the widespread application of electrical resistivity tomography in imaging, the resistivity distribution of subsurface structures for various hydro-geophysical and engineering purposes, the assessment of uncertainty is seldom addressed within the inverted resistivity tomograms. To explore the combined impact of epistemic and aleatory uncertainty on resistivity models, we initially perturb the observed data using non-parametric block-wise bootstrap resampling with an optimal choice of the block size, generating different realizations of the field data. Subsequently, a geostatistical method is applied to stochastically generate a set of initial models for each bootstrapped data set from the previous step. Finally, we employ a globally convergent homotopic continuation method on each bootstrapped data set and initial model realization to explore the posterior resistivity models. Uncertainty information about the inversion results is provided through posterior statistical analysis. Our algorithm’s simplicity enables easy integration with existing gradient-based inversion methods, requiring only minor modifications. We demonstrate the versatility of our approach through its application to various synthetic and real electrical resistivity tomography experiments. The results reveal that this approach for quantifying uncertainty is straightforward to implement and computationally efficient.

Mots clés

electrical resistivity tomography; inverse theory; numerical modelling; hydrogeophysics